Daily Papers

Accurate representation of multimodal knowledge is crucial for event forecasting in real-world scenarios. However, existing studies have largely focused on static settings, overlooking the dynamic acquisition and fusion of multimodal knowledge. 1) At the knowledge acquisition level, how to learn time-sensitive information of different modalities, especially the dynamic structural modality. Existing dynamic learning methods are often limited to shallow structures across heterogeneous spaces or simple unispaces, making it difficult to capture deep relation-aware geometric features. 2) At the knowledge fusion level, how to learn evolving multimodal fusion features. Existing knowledge fusion methods based on static coattention struggle to capture the varying historical contributions of different modalities to future events. To this end, we propose DyMRL, a Dynamic Multispace Representation Learning approach to efficiently acquire and fuse multimodal temporal knowledge. 1) For the former issue, DyMRL integrates time-specific structural features from Euclidean, hyperbolic, and complex spaces into a relational message-passing framework to learn deep representations, reflecting human intelligences in associative thinking, high-order abstracting, and logical reasoning. Pretrained models endow DyMRL with time-sensitive visual and linguistic intelligences. 2) For the latter concern, DyMRL incorporates advanced dual fusion-evolution attention mechanisms that assign dynamic learning emphases equally to different modalities at different timestamps in a symmetric manner. To evaluate DyMRL's event forecasting performance through leveraging its learned multimodal temporal knowledge in history, we construct four multimodal temporal knowledge graph benchmarks. Extensive experiments demonstrate that DyMRL outperforms state-of-the-art dynamic unimodal and static multimodal baseline methods.

Understanding how two hands interact with each other is a key component of accurate 3D interacting hand mesh recovery. However, recent Transformer-based methods struggle to learn the interaction between two hands as they directly utilize two hand features as input tokens, which results in distant token problem. The distant token problem represents that input tokens are in heterogeneous spaces, leading Transformer to fail in capturing correlation between input tokens. Previous Transformer-based methods suffer from the problem especially when poses of two hands are very different as they project features from a backbone to separate left and right hand-dedicated features. We present EANet, extract-and-adaptation network, with EABlock, the main component of our network. Rather than directly utilizing two hand features as input tokens, our EABlock utilizes two complementary types of novel tokens, SimToken and JoinToken, as input tokens. Our two novel tokens are from a combination of separated two hand features; hence, it is much more robust to the distant token problem. Using the two type of tokens, our EABlock effectively extracts interaction feature and adapts it to each hand. The proposed EANet achieves the state-of-the-art performance on 3D interacting hands benchmarks. The codes are available at https://github.com/jkpark0825/EANet.

IoT botnet detection has advanced, yet most published systems are validated on a single dataset and rarely generalise across environments. Heterogeneous feature spaces make multi-dataset training practically impossible without discarding semantic interpretability or introducing data integrity violations. No prior work has addressed both problems with a formally specified, reproducible methodology. This paper does. We introduce BRIDGE (Benchmark Reference for IoT Domain Generalisation Evaluation), the first formally specified heterogeneous multi-dataset benchmark for IoT intrusion detection, unifying CICIDS-2017, CIC-IoT-2023, Bot-IoT, Edge-IIoTset, and N-BaIoT through a 46-feature semantic canonical vocabulary grounded in CICFlowMeter nomenclature, with genuine-equivalence-only feature mapping, explicit zero-filling, and per-dataset coverage from 15% to 93%. A leave-one-dataset-out (LODO) protocol makes the generalisation gap precisely measurable: all five evaluated architectures achieve mean LODO F1 between 0.39 and 0.47, and we establish the first community generalisation baseline at mean LODO F1 = 0.5577, a result that shifts the agenda from single-benchmark optimisation toward cross-environment generalisation. We propose TCH-Net, a multi-branch network fusing a three-path Temporal branch (residual convolutional-BiGRU, stride-downsampled BiGRU, pre-LayerNorm Transformer), a provenance-conditioned Contextual branch, and a Statistical branch via Cross-Branch Gated Attention Fusion (CB-GAF) with learnable sigmoid gates for dynamic feature-wise mixing. Across five random seeds, TCH-Net achieves F1 = 0.8296 +/- 0.0028, AUC = 0.9380 +/- 0.0025, and MCC = 0.6972 +/- 0.0056, outperforming all twelve baselines (p < 0.05, Wilcoxon) and recording the highest LODO F1 overall. BRIDGE and the full pipeline are at https://github.com/Ammar-ss/TCH-Net.

K-Nearest Neighbors (KNN) is one of the most used ML classifiers. However, if we observe closely, standard distance-weighted KNN and relative variants assume all 'k' neighbors are equally reliable. In heterogeneous feature space, this becomes a limitation that hinders reliability in predicting true levels of the observation. We propose DW-KNN (Double Weighted KNN), a transparent and robust variant that integrates exponential distance with neighbor validity. This enables instance-level interpretability, suppresses noisy or mislabeled samples, and reduces hyperparameter sensitivity. Comprehensive evaluation on 9 data-sets helps to demonstrate that DW-KNN achieves 0.8988 accuracy on average. It ranks 2nd among six methods and within 0.2% of the best-performing Ensemble KNN. It also exhibits the lowest cross-validation variance (0.0156), indicating reliable prediction stability. Statistical significance test confirmed (p < 0.001) improvement over compactness weighted KNN (+4.09\%) and Kernel weighted KNN (+1.13\%). The method provides a simple yet effective alternative to complex adaptive schemes, particularly valuable for high-stakes applications requiring explainable predictions.

The paradigm of agentic AI is shifting from engineered complex workflows to post-training native models. However, existing agents are typically confined to static, predefined action spaces--such as exclusively using APIs, GUI events, or robotic commands. This rigidity limits their adaptability in dynamic environments where the optimal granularity of interaction varies contextually. To bridge this gap, we propose CrossAgent, a unified agentic model that masters heterogeneous action spaces and autonomously selects the most effective interface for each step of a trajectory. We introduce a comprehensive training pipeline that integrates cold-start supervised fine-tuning with a Multi-Turn Group Relative Policy Optimization (GRPO) algorithm. This approach enables the agent to learn adaptive action switching--balancing high-level efficiency with low-level precision--without human-specified rules. Extensive experiments on over 800 tasks in the open-world Minecraft environment demonstrate that CrossAgent achieves state-of-the-art performance. By dynamically leveraging the strengths of diverse action spaces, our model significantly outperforms fixed-action baselines, exhibiting superior generalization and efficiency in long-horizon reasoning. All code and models are available at https://github.com/CraftJarvis/OpenHA

Building autonomous agents that perceive and operate graphical user interfaces (GUIs) like humans has long been a vision in the field of artificial intelligence. Central to these agents is the capability for GUI interaction, which involves GUI understanding and planning capabilities. Existing methods have tried developing GUI agents based on the multi-modal comprehension ability of vision-language models (VLMs). However, the limited scenario, insufficient size, and heterogeneous action spaces hinder the progress of building generalist GUI agents. To resolve these issues, this paper proposes UIPro, a novel generalist GUI agent trained with extensive multi-platform and multi-task GUI interaction data, coupled with a unified action space. We first curate a comprehensive dataset encompassing 20.6 million GUI understanding tasks to pre-train UIPro, granting it a strong GUI grounding capability, which is key to downstream GUI agent tasks. Subsequently, we establish a unified action space to harmonize heterogeneous GUI agent task datasets and produce a merged dataset to foster the action prediction ability of UIPro via continued fine-tuning. Experimental results demonstrate UIPro's superior performance across multiple GUI task benchmarks on various platforms, highlighting the effectiveness of our approach.

While recent vision-language-action models trained on diverse robot datasets exhibit promising generalization capabilities with limited in-domain data, their reliance on compact action heads to predict discretized or continuous actions constrains adaptability to heterogeneous action spaces. We present Dita, a scalable framework that leverages Transformer architectures to directly denoise continuous action sequences through a unified multimodal diffusion process. Departing from prior methods that condition denoising on fused embeddings via shallow networks, Dita employs in-context conditioning -- enabling fine-grained alignment between denoised actions and raw visual tokens from historical observations. This design explicitly models action deltas and environmental nuances. By scaling the diffusion action denoiser alongside the Transformer's scalability, Dita effectively integrates cross-embodiment datasets across diverse camera perspectives, observation scenes, tasks, and action spaces. Such synergy enhances robustness against various variances and facilitates the successful execution of long-horizon tasks. Evaluations across extensive benchmarks demonstrate state-of-the-art or comparative performance in simulation. Notably, Dita achieves robust real-world adaptation to environmental variances and complex long-horizon tasks through 10-shot finetuning, using only third-person camera inputs. The architecture establishes a versatile, lightweight and open-source baseline for generalist robot policy learning. Project Page: https://robodita.github.io.

Recent advances in Graph Neural Networks (GNNs) have revolutionized graph-structured data modeling, yet traditional GNNs struggle with complex heterogeneous structures prevalent in real-world scenarios. Despite progress in handling heterogeneous interactions, two fundamental challenges persist: noisy data significantly compromising embedding quality and learning performance, and existing methods' inability to capture intricate semantic transitions among heterogeneous relations, which impacts downstream predictions. To address these fundamental issues, we present the Heterogeneous Graph Diffusion Model (DiffGraph), a pioneering framework that introduces an innovative cross-view denoising strategy. This advanced approach transforms auxiliary heterogeneous data into target semantic spaces, enabling precise distillation of task-relevant information. At its core, DiffGraph features a sophisticated latent heterogeneous graph diffusion mechanism, implementing a novel forward and backward diffusion process for superior noise management. This methodology achieves simultaneous heterogeneous graph denoising and cross-type transition, while significantly simplifying graph generation through its latent-space diffusion capabilities. Through rigorous experimental validation on both public and industrial datasets, we demonstrate that DiffGraph consistently surpasses existing methods in link prediction and node classification tasks, establishing new benchmarks for robustness and efficiency in heterogeneous graph processing. The model implementation is publicly available at: https://github.com/HKUDS/DiffGraph.

In the latest advancements in multimodal learning, effectively addressing the spatial and semantic losses of visual data after encoding remains a critical challenge. This is because the performance of large multimodal models is positively correlated with the coupling between visual encoders and large language models. Existing approaches often face issues such as vector gaps or semantic disparities, resulting in information loss during the propagation process. To address these issues, we propose MAGE (Multimodal Alignment and Generation Enhancement), a novel framework that bridges the semantic spaces of vision and text through an innovative alignment mechanism. By introducing the Intelligent Alignment Network (IAN), MAGE achieves dimensional and semantic alignment. To reduce the gap between synonymous heterogeneous data, we employ a training strategy that combines cross-entropy and mean squared error, significantly enhancing the alignment effect. Moreover, to enhance MAGE's "Any-to-Any" capability, we developed a fine-tuning dataset for multimodal tool-calling instructions to expand the model's output capability boundaries. Finally, our proposed multimodal large model architecture, MAGE, achieved significantly better performance compared to similar works across various evaluation benchmarks, including MME, MMBench, and SEED. Complete code and appendix are available at: https://github.com/GTCOM-NLP/MAGE.

Multi-agent collaboration enhances the perception capabilities of individual agents through information sharing. However, in real-world applications, differences in sensors and models across heterogeneous agents inevitably lead to domain gaps during collaboration. Existing approaches based on adaptation and reconstruction fail to support pragmatic heterogeneous collaboration due to two key limitations: (1) Intrusive retraining of the encoder or core modules disrupts the established semantic consistency among agents; and (2) accommodating new agents incurs high computational costs, limiting scalability. To address these challenges, we present a novel Generative Communication mechanism (GenComm) that facilitates seamless perception across heterogeneous multi-agent systems through feature generation, without altering the original network, and employs lightweight numerical alignment of spatial information to efficiently integrate new agents at minimal cost. Specifically, a tailored Deformable Message Extractor is designed to extract spatial message for each collaborator, which is then transmitted in place of intermediate features. The Spatial-Aware Feature Generator, utilizing a conditional diffusion model, generates features aligned with the ego agent's semantic space while preserving the spatial information of the collaborators. These generated features are further refined by a Channel Enhancer before fusion. Experiments conducted on the OPV2V-H, DAIR-V2X and V2X-Real datasets demonstrate that GenComm outperforms existing state-of-the-art methods, achieving an 81% reduction in both computational cost and parameter count when incorporating new agents. Our code is available at https://github.com/jeffreychou777/GenComm.

LLM serving systems process heterogeneous query workloads where different categories exhibit different characteristics. Code queries cluster densely in embedding space while conversational queries distribute sparsely. Content staleness varies from minutes (stock data) to months (code patterns). Query repetition patterns range from power-law (code) to uniform (conversation), producing long tail cache hit rate distributions: high-repetition categories achieve 40-60% hit rates while low-repetition or volatile categories achieve 5-15% hit rates. Vector databases must exclude the long tail because remote search costs (30ms) require 15--20% hit rates to break even, leaving 20-30% of production traffic uncached. Uniform cache policies compound this problem: fixed thresholds cause false positives in dense spaces and miss valid paraphrases in sparse spaces; fixed TTLs waste memory or serve stale data. This paper presents category-aware semantic caching where similarity thresholds, TTLs, and quotas vary by query category. We present a hybrid architecture separating in-memory HNSW search from external document storage, reducing miss cost from 30ms to 2ms. This reduction makes low-hit-rate categories economically viable (break-even at 3-5% versus 15-20%), enabling cache coverage across the entire workload distribution. Adaptive load-based policies extend this framework to respond to downstream model load, dynamically adjusting thresholds and TTLs to reduce traffic to overloaded models by 9-17% in theoretical projections.

To improve generalization and resilience in human-robot collaboration (HRC), robots must handle the combinatorial diversity of human behaviors and contexts, motivating multi-agent reinforcement learning (MARL). However, inherent heterogeneity between robots and humans creates a rationality gap (RG) in the learning process-a variational mismatch between decentralized best-response dynamics and centralized cooperative ascent. The resulting learning problem is a general-sum differentiable game, so independent policy-gradient updates can oscillate or diverge without added structure. We propose heterogeneous-agent Lyapunov policy optimization (HALyPO), which establishes formal stability directly in the policy-parameter space by enforcing a per-step Lyapunov decrease condition on a parameter-space disagreement metric. Unlike Lyapunov-based safe RL, which targets state/trajectory constraints in constrained Markov decision processes, HALyPO uses Lyapunov certification to stabilize decentralized policy learning. HALyPO rectifies decentralized gradients via optimal quadratic projections, ensuring monotonic contraction of RG and enabling effective exploration of open-ended interaction spaces. Extensive simulations and real-world humanoid-robot experiments show that this certified stability improves generalization and robustness in collaborative corner cases.

Previous works on Treatment Effect Estimation (TEE) are not in widespread use because they are predominantly theoretical, where strong parametric assumptions are made but untractable for practical application. Recent work uses multilayer perceptron (MLP) for modeling casual relationships, however, MLPs lag far behind recent advances in ML methodology, which limits their applicability and generalizability. To extend beyond the single domain formulation and towards more realistic learning scenarios, we explore model design spaces beyond MLPs, i.e., transformer backbones, which provide flexibility where attention layers govern interactions among treatments and covariates to exploit structural similarities of potential outcomes for confounding control. Through careful model design, Transformers as Treatment Effect Estimators (TransTEE) is proposed. We show empirically that TransTEE can: (1) serve as a general purpose treatment effect estimator that significantly outperforms competitive baselines in a variety of challenging TEE problems (e.g., discrete, continuous, structured, or dosage-associated treatments) and is applicable to both when covariates are tabular and when they consist of structural data (e.g., texts, graphs); (2) yield multiple advantages: compatibility with propensity score modeling, parameter efficiency, robustness to continuous treatment value distribution shifts, explainable in covariate adjustment, and real-world utility in auditing pre-trained language models

Temporal knowledge graphs represent temporal facts (s,p,o,tau) relating a subject s and an object o via a relation label p at time tau, where tau could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

Federated reinforcement learning (FRL) has emerged as a promising paradigm for reducing the sample complexity of reinforcement learning tasks by exploiting information from different agents. However, when each agent interacts with a potentially different environment, little to nothing is known theoretically about the non-asymptotic performance of FRL algorithms. The lack of such results can be attributed to various technical challenges and their intricate interplay: Markovian sampling, linear function approximation, multiple local updates to save communication, heterogeneity in the reward functions and transition kernels of the agents' MDPs, and continuous state-action spaces. Moreover, in the on-policy setting, the behavior policies vary with time, further complicating the analysis. In response, we introduce FedSARSA, a novel federated on-policy reinforcement learning scheme, equipped with linear function approximation, to address these challenges and provide a comprehensive finite-time error analysis. Notably, we establish that FedSARSA converges to a policy that is near-optimal for all agents, with the extent of near-optimality proportional to the level of heterogeneity. Furthermore, we prove that FedSARSA leverages agent collaboration to enable linear speedups as the number of agents increases, which holds for both fixed and adaptive step-size configurations.

The emergence of Large Language Models (LLMs) has illuminated the potential for a general-purpose user simulator. However, existing benchmarks remain constrained to isolated scenarios, narrow action spaces, or synthetic data, failing to capture the holistic nature of authentic human behavior. To bridge this gap, we introduce OmniBehavior, the first user simulation benchmark constructed entirely from real-world data, integrating long-horizon, cross-scenario, and heterogeneous behavioral patterns into a unified framework. Based on this benchmark, we first provide empirical evidence that previous datasets with isolated scenarios suffer from tunnel vision, whereas real-world decision-making relies on long-term, cross-scenario causal chains. Extensive evaluations of state-of-the-art LLMs reveal that current models struggle to accurately simulate these complex behaviors, with performance plateauing even as context windows expand. Crucially, a systematic comparison between simulated and authentic behaviors uncovers a fundamental structural bias: LLMs tend to converge toward a positive average person, exhibiting hyper-activity, persona homogenization, and a Utopian bias. This results in the loss of individual differences and long-tail behaviors, highlighting critical directions for future high-fidelity simulation research.

In heterogeneous multi-task decision-making, tasks not only exhibit diverse observation and action spaces but also vary substantially in their underlying complexities. While conventional multi-task world models like UniZero excel in single-task settings, we find that when handling a broad and diverse suite of tasks, gradient conflicts and the loss of model plasticity often constrain their sample efficiency. In this work, we address these challenges from two complementary perspectives: the single learning iteration and the overall learning process. First, to mitigate the gradient conflicts, we systematically investigate key architectural designs for extending UniZero. Our investigation identifies a Mixture-of-Experts (MoE) architecture as the most effective approach. We demonstrate, both theoretically and empirically, that this architecture alleviates gradient conflicts by routing task-specific representations to specialized sub-networks. This finding leads to our proposed model, ScaleZero. Second, to dynamically allocate model capacity throughout the learning process, we introduce an online Dynamic Parameter Scaling (DPS) strategy. This strategy progressively integrates LoRA adapters in response to task-specific progress, enabling adaptive knowledge retention and parameter expansion. Evaluations on a diverse set of standard benchmarks (Atari, DMC, Jericho) demonstrate that ScaleZero, utilizing solely online reinforcement learning with one model, performs on par with specialized single-task agents. With the DPS strategy, it remains competitive while using just 71.5% of the environment interactions. These findings underscore the potential of ScaleZero for effective multi-task planning. Our code is available at magenta{https://github.com/opendilab/LightZero}.

Learning a universal policy across different robot morphologies can significantly improve learning efficiency and generalization in continuous control. However, it poses a challenging multi-task reinforcement learning problem, as the optimal policy may be quite different across robots and critically depend on the morphology. Existing methods utilize graph neural networks or transformers to handle heterogeneous state and action spaces across different morphologies, but pay little attention to the dependency of a robot's control policy on its morphology context. In this paper, we propose a hierarchical architecture to better model this dependency via contextual modulation, which includes two key submodules: (1) Instead of enforcing hard parameter sharing across robots, we use hypernetworks to generate morphology-dependent control parameters; (2) We propose a morphology-dependent attention mechanism to modulate the interactions between different limbs in a robot. Experimental results show that our method not only improves learning performance on a diverse set of training robots, but also generalizes better to unseen morphologies in a zero-shot fashion.

Multi-Agent Reinforcement Learning (MARL) algorithms are widely adopted in tackling complex tasks that require collaboration and competition among agents in dynamic Multi-Agent Systems (MAS). However, learning such tasks from scratch is arduous and may not always be feasible, particularly for MASs with a large number of interactive agents due to the extensive sample complexity. Therefore, reusing knowledge gained from past experiences or other agents could efficiently accelerate the learning process and upscale MARL algorithms. In this study, we introduce a novel framework that enables transfer learning for MARL through unifying various state spaces into fixed-size inputs that allow one unified deep-learning policy viable in different scenarios within a MAS. We evaluated our approach in a range of scenarios within the StarCraft Multi-Agent Challenge (SMAC) environment, and the findings show significant enhancements in multi-agent learning performance using maneuvering skills learned from other scenarios compared to agents learning from scratch. Furthermore, we adopted Curriculum Transfer Learning (CTL), enabling our deep learning policy to progressively acquire knowledge and skills across pre-designed homogeneous learning scenarios organized by difficulty levels. This process promotes inter- and intra-agent knowledge transfer, leading to high multi-agent learning performance in more complicated heterogeneous scenarios.

Offline reinforcement learning (ORL) holds great promise for robot learning due to its ability to learn from arbitrary pre-generated experience. However, current ORL benchmarks are almost entirely in simulation and utilize contrived datasets like replay buffers of online RL agents or sub-optimal trajectories, and thus hold limited relevance for real-world robotics. In this work (Real-ORL), we posit that data collected from safe operations of closely related tasks are more practical data sources for real-world robot learning. Under these settings, we perform an extensive (6500+ trajectories collected over 800+ robot hours and 270+ human labor hour) empirical study evaluating generalization and transfer capabilities of representative ORL methods on four real-world tabletop manipulation tasks. Our study finds that ORL and imitation learning prefer different action spaces, and that ORL algorithms can generalize from leveraging offline heterogeneous data sources and outperform imitation learning. We release our dataset and implementations at URL: https://sites.google.com/view/real-orl

Learning provides a powerful tool for vision-based navigation, but the capabilities of learning-based policies are constrained by limited training data. If we could combine data from all available sources, including multiple kinds of robots, we could train more powerful navigation models. In this paper, we study how a general goal-conditioned model for vision-based navigation can be trained on data obtained from many distinct but structurally similar robots, and enable broad generalization across environments and embodiments. We analyze the necessary design decisions for effective data sharing across robots, including the use of temporal context and standardized action spaces, and demonstrate that an omnipolicy trained from heterogeneous datasets outperforms policies trained on any single dataset. We curate 60 hours of navigation trajectories from 6 distinct robots, and deploy the trained GNM on a range of new robots, including an underactuated quadrotor. We find that training on diverse data leads to robustness against degradation in sensing and actuation. Using a pre-trained navigation model with broad generalization capabilities can bootstrap applications on novel robots going forward, and we hope that the GNM represents a step in that direction. For more information on the datasets, code, and videos, please check out our project page https://sites.google.com/view/drive-any-robot.

Neural architecture search (NAS) automates the design process of high-performing architectures, but remains bottlenecked by expensive performance evaluation. Most existing studies that achieve faster evaluation are mostly tied to cell-based search spaces and graph encodings tailored to those individual search spaces, limiting their flexibility and scalability when applied to more expressive search spaces. In this work, we aim to close the gap of individual search space restrictions and search space dependent network representations. We present ONNX-Bench, a benchmark consisting of a collection of neural networks in a unified format based on ONNX files. ONNX-Bench includes all open-source NAS-bench-based neural networks, resulting in a total size of more than 600k {architecture, accuracy} pairs. This benchmark allows creating a shared neural network representation, ONNX-Net, able to represent any neural architecture using natural language descriptions acting as an input to a performance predictor. This text-based encoding can accommodate arbitrary layer types, operation parameters, and heterogeneous topologies, enabling a single surrogate to generalise across all neural architectures rather than being confined to cell-based search spaces. Experiments show strong zero-shot performance across disparate search spaces using only a small amount of pretraining samples, enabling the unprecedented ability to evaluate any neural network architecture instantly.

While Vision-Language-Action (VLA) models show strong promise for generalist robot control, it remains unclear whether -- and under what conditions -- the standard "scale data" recipe translates to robotics, where training data is inherently heterogeneous across embodiments, sensors, and action spaces. We present a systematic, controlled study of VLA scaling that revisits core training choices for pretraining across diverse robots. Using a representative VLA framework that combines a vision-language backbone with flow-matching, we ablate key design decisions under matched conditions and evaluate in extensive simulation and real-robot experiments. To improve the reliability of real-world results, we introduce a Grouped Blind Ensemble protocol that blinds operators to model identity and separates policy execution from outcome judgment, reducing experimenter bias. Our analysis targets three dimensions of VLA scaling. (1) Physical alignment: we show that a unified end-effector (EEF)-relative action representation is critical for robust cross-embodiment transfer. (2) Embodiment mixture: we find that naively pooling heterogeneous robot datasets often induces negative transfer rather than gains, underscoring the fragility of indiscriminate data scaling. (3) Training regularization: we observe that intuitive strategies, such as sensory dropout and multi-stage fine-tuning, do not consistently improve performance at scale. Together, this study challenge some common assumptions about embodied scaling and provide practical guidance for training large-scale VLA policies from diverse robotic data. Project website: https://research.beingbeyond.com/rethink_vla

Recent advances in agentic Large Language Models (LLMs) have positioned them as generalist planners capable of reasoning and acting across diverse tasks. However, existing agent benchmarks largely focus on symbolic or weakly grounded environments, leaving their performance in physics-constrained real-world domains underexplored. We introduce AstroReason-Bench, a comprehensive benchmark for evaluating agentic planning in Space Planning Problems (SPP), a family of high-stakes problems with heterogeneous objectives, strict physical constraints, and long-horizon decision-making. AstroReason-Bench integrates multiple scheduling regimes, including ground station communication and agile Earth observation, and provides a unified agent-oriented interaction protocol. Evaluating on a range of state-of-the-art open- and closed-source agentic LLM systems, we find that current agents substantially underperform specialized solvers, highlighting key limitations of generalist planning under realistic constraints. AstroReason-Bench offers a challenging and diagnostic testbed for future agentic research.

Test-time policy adaptation for multi-turn interactions (T2PAM) is essential for aligning Large Language Models (LLMs) with dynamic user needs during inference time. However, existing paradigms commonly treat test-time adaptation as a single-axis problem, either purely refining instructions (Prompt Engineering) or only adjusting weights (Test-Time Training), ignoring that interaction failures stem from a coupled mix of ambiguity and incapacity. We argue that these two optimization paths are not merely additive but synergistic: semantic clarity acts as a pre-conditioner for effective parameter updates. To this end, we propose ROSA2, a framework that reformulates interaction as a joint optimization problem over the heterogeneous space of Words and Weights. By mathematically decomposing the error signal, ROSA2 utilizes textual gradients to rectify intent ambiguity and parameter updates to bridge capability gaps. Theoretically, we prove that this co-adaptation strictly reduces the required parameter shift for convergence. Empirically, ROSA2 outperforms state-of-the-art baselines by 30% on MATH while reducing interaction turns by 40%, demonstrating that refining the context unlocks the true potential of parameter updates.

We present a model that can perform multiple vision tasks and can be adapted to other downstream tasks efficiently. Despite considerable progress in multi-task learning, most efforts focus on learning from multi-label data: a single image set with multiple task labels. Such multi-label data sets are rare, small, and expensive. We say heterogeneous to refer to image sets with different task labels, or to combinations of single-task datasets. Few have explored training on such heterogeneous datasets. General-purpose vision models are still dominated by single-task pretraining, and it remains unclear how to scale up multi-task models by leveraging mainstream vision datasets designed for different purposes. The challenges lie in managing large intrinsic differences among vision tasks, including data distribution, architectures, task-specific modules, dataset scales, and sampling strategies. To address these challenges, we propose to modify and scale up mixture-of-experts (MoE) vision transformers, so that they can simultaneously learn classification, detection, and segmentation on diverse mainstream vision datasets including ImageNet, COCO, and ADE20K. Our approach achieves comparable results to single-task state-of-the-art models and demonstrates strong generalization on downstream tasks. Due to its emergent modularity, this general-purpose model decomposes into high-performing components, efficiently adapting to downstream tasks. We can fine-tune it with fewer training parameters, fewer model parameters, and less computation. Additionally, its modularity allows for easy expansion in continual-learning-without-forgetting scenarios. Finally, these functions can be controlled and combined to meet various demands of downstream tasks.

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

Mixture-of-Expert (MoE) models have obtained state-of-the-art performance in Neural Machine Translation (NMT) tasks. Existing works in MoE mostly consider a homogeneous design where the same number of experts of the same size are placed uniformly throughout the network. Furthermore, existing MoE works do not consider computational constraints (e.g., FLOPs, latency) to guide their design. To this end, we develop AutoMoE -- a framework for designing heterogeneous MoE's under computational constraints. AutoMoE leverages Neural Architecture Search (NAS) to obtain efficient sparse MoE sub-transformers with 4x inference speedup (CPU) and FLOPs reduction over manually designed Transformers, with parity in BLEU score over dense Transformer and within 1 BLEU point of MoE SwitchTransformer, on aggregate over benchmark datasets for NMT. Heterogeneous search space with dense and sparsely activated Transformer modules (e.g., how many experts? where to place them? what should be their sizes?) allows for adaptive compute -- where different amounts of computations are used for different tokens in the input. Adaptivity comes naturally from routing decisions which send tokens to experts of different sizes. AutoMoE code, data, and trained models are available at https://aka.ms/AutoMoE.

Evaluation plays a crucial role in the advancement of information retrieval (IR) models. However, current benchmarks, which are based on predefined domains and human-labeled data, face limitations in addressing evaluation needs for emerging domains both cost-effectively and efficiently. To address this challenge, we propose the Automated Heterogeneous Information Retrieval Benchmark (AIR-Bench). AIR-Bench is distinguished by three key features: 1) Automated. The testing data in AIR-Bench is automatically generated by large language models (LLMs) without human intervention. 2) Heterogeneous. The testing data in AIR-Bench is generated with respect to diverse tasks, domains and languages. 3) Dynamic. The domains and languages covered by AIR-Bench are constantly augmented to provide an increasingly comprehensive evaluation benchmark for community developers. We develop a reliable and robust data generation pipeline to automatically create diverse and high-quality evaluation datasets based on real-world corpora. Our findings demonstrate that the generated testing data in AIR-Bench aligns well with human-labeled testing data, making AIR-Bench a dependable benchmark for evaluating IR models. The resources in AIR-Bench are publicly available at https://github.com/AIR-Bench/AIR-Bench.

LLM-based multi-agent systems (MAS) have emerged as a promising approach to tackle complex tasks that are difficult for individual LLMs. A natural strategy is to scale performance by increasing the number of agents; however, we find that such scaling exhibits strong diminishing returns in homogeneous settings, while introducing heterogeneity (e.g., different models, prompts, or tools) continues to yield substantial gains. This raises a fundamental question: what limits scaling, and why does diversity help? We present an information-theoretic framework showing that MAS performance is bounded by the intrinsic task uncertainty, not by agent count. We derive architecture-agnostic bounds demonstrating that improvements depend on how many effective channels the system accesses. Homogeneous agents saturate early because their outputs are strongly correlated, whereas heterogeneous agents contribute complementary evidence. We further introduce K^*, an effective channel count that quantifies the number of effective channels without ground-truth labels. Empirically, we show that heterogeneous configurations consistently outperform homogeneous scaling: 2 diverse agents can match or exceed the performance of 16 homogeneous agents. Our results provide principled guidelines for building efficient and robust MAS through diversity-aware design. Code and Dataset are available at the link: https://github.com/SafeRL-Lab/Agent-Scaling.

The labor market is a complex ecosystem comprising diverse, interconnected entities, such as industries, occupations, skills, and firms. Due to the lack of a systematic method to map these heterogeneous entities together, each entity has been analyzed in isolation or only through pairwise relationships, inhibiting comprehensive understanding of the whole ecosystem. Here, we introduce Labor Space, a vector-space embedding of heterogeneous labor market entities, derived through applying a large language model with fine-tuning. Labor Space exposes the complex relational fabric of various labor market constituents, facilitating coherent integrative analysis of industries, occupations, skills, and firms, while retaining type-specific clustering. We demonstrate its unprecedented analytical capacities, including positioning heterogeneous entities on an economic axes, such as `Manufacturing--Healthcare'. Furthermore, by allowing vector arithmetic of these entities, Labor Space enables the exploration of complex inter-unit relations, and subsequently the estimation of the ramifications of economic shocks on individual units and their ripple effect across the labor market. We posit that Labor Space provides policymakers and business leaders with a comprehensive unifying framework for labor market analysis and simulation, fostering more nuanced and effective strategic decision-making.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

The pre-trained model (PTM) is revolutionizing Artificial Intelligence (AI) technology. However, the hardware requirement of PTM training is prohibitively high, making it a game for a small proportion of people. Therefore, we proposed PatrickStar system to lower the hardware requirements of PTMs and make them accessible to everyone. PatrickStar uses the CPU-GPU heterogeneous memory space to store the model data. Different from existing works, we organize the model data in memory chunks and dynamically distribute them in the heterogeneous memory. Guided by the runtime memory statistics collected in a warm-up iteration, chunks are orchestrated efficiently in heterogeneous memory and generate lower CPU-GPU data transmission volume and higher bandwidth utilization. Symbiosis with the Zero Redundancy Optimizer, PatrickStar scales to multiple GPUs on multiple nodes. % using data parallelism. The system can train tasks on bigger models and larger batch sizes, which cannot be accomplished by existing works. Experimental results show that PatrickStar extends model scales 2.27 and 2.5 times of DeepSpeed, and consistently exhibits significantly higher execution speed. PatricStar also successfully runs the 175B GPT3 training task on a 32 GPU cluster. Our code is publicly available at https://github.com/Tencent/PatrickStar.

To effectively optimize and personalize treatments, it is necessary to investigate the heterogeneity of treatment effects. With the wide range of users being treated over many online controlled experiments, the typical approach of manually investigating each dimension of heterogeneity becomes overly cumbersome and prone to subjective human biases. We need an efficient way to search through thousands of experiments with hundreds of target covariates and hundreds of breakdown dimensions. In this paper, we propose a systematic paradigm for detecting, surfacing and characterizing heterogeneous treatment effects. First, we detect if treatment effect variation is present in an experiment, prior to specifying any breakdowns. Second, we surface the most relevant dimensions for heterogeneity. Finally, we characterize the heterogeneity beyond just the conditional average treatment effects (CATE) by studying the conditional distributions of the estimated individual treatment effects. We show the effectiveness of our methods using simulated data and empirical studies.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Mixture of Experts (MoE) offers remarkable performance and computational efficiency by selectively activating subsets of model parameters. Traditionally, MoE models use homogeneous experts, each with identical capacity. However, varying complexity in input data necessitates experts with diverse capabilities, while homogeneous MoE hinders effective expert specialization and efficient parameter utilization. In this study, we propose a novel Heterogeneous Mixture of Experts (HMoE), where experts differ in size and thus possess diverse capacities. This heterogeneity allows for more specialized experts to handle varying token complexities more effectively. To address the imbalance in expert activation, we propose a novel training objective that encourages the frequent activation of smaller experts, enhancing computational efficiency and parameter utilization. Extensive experiments demonstrate that HMoE achieves lower loss with fewer activated parameters and outperforms conventional homogeneous MoE models on various pre-training evaluation benchmarks. Codes will be released upon acceptance.

We introduce DRBench, a benchmark for evaluating AI agents on complex, open-ended deep research tasks in enterprise settings. Unlike prior benchmarks that focus on simple questions or web-only queries, DRBench evaluates agents on multi-step queries (for example, ``What changes should we make to our product roadmap to ensure compliance with this standard?") that require identifying supporting facts from both the public web and private company knowledge base. Each task is grounded in realistic user personas and enterprise context, spanning a heterogeneous search space that includes productivity software, cloud file systems, emails, chat conversations, and the open web. Tasks are generated through a carefully designed synthesis pipeline with human-in-the-loop verification, and agents are evaluated on their ability to recall relevant insights, maintain factual accuracy, and produce coherent, well-structured reports. We release 15 deep research tasks across 10 domains, such as Sales, Cybersecurity, and Compliance. We demonstrate the effectiveness of DRBench by evaluating diverse DR agents across open- and closed-source models (such as GPT, Llama, and Qwen) and DR strategies, highlighting their strengths, weaknesses, and the critical path for advancing enterprise deep research. Code is available at https://github.com/ServiceNow/drbench.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

Harnesses are now central to coding-agent performance, mediating how models interact with tools and execution environments. Yet harness engineering remains a manual craft, because automating it faces a heterogeneous action space across editable components, voluminous trajectories that bury actionable signal, and edits whose effect is hard to attribute. We introduce Agentic Harness Engineering (AHE), a closed loop that addresses these challenges through three matched observability pillars: (1) component observability gives every editable harness component a file-level representation so the action space is explicit and revertible; (2) experience observability distills millions of raw trajectory tokens into a layered, drill-down evidence corpus that an evolving agent can actually consume; and (3) decision observability pairs every edit with a self-declared prediction, later verified against the next round's task-level outcomes. Together, these pillars turn every edit into a falsifiable contract, so harness evolution proceeds autonomously without collapsing into trial-and-error. Empirically, ten AHE iterations lift pass@1 on Terminal-Bench 2 from 69.7% to 77.0%, surpassing the human-designed harness Codex-CLI (71.9%) and the self-evolving baselines ACE and TF-GRPO. The frozen harness transfers without re-evolution: on SWE-bench-verified it tops aggregate success at 12% fewer tokens than the seed, and on Terminal-Bench 2 it yields +5.1 to +10.1pp cross-family gains across three alternate model families, indicating the evolved components encode general engineering experience rather than benchmark-specific tuning. Ablations localize the gain to tools, middleware, and long-term memory rather than the system prompt, suggesting factual harness structure transfers while prose-level strategy does not.

Long-horizon language-model agents are dominated, in lines of code and in operational complexity, not by their underlying model but by the harness that wraps it: context compaction, tool caching, semantic memory, trajectory reuse, speculative tool prediction, and the glue that binds the model to a sandboxed execution environment. We argue that harness design is a first-class machine-learning problem and that automated configuration search dominates manual stacking once the flag space exceeds a handful of bits. We defend this claim in two steps. First, we formalize automated harness optimization as constrained noisy Bayesian optimization over a mixed-variable, cost-heterogeneous configuration space with cold-start-corrected rewards and a posterior chance-constrained safety check, and give a reference solver, HARBOR (Harness Axis-aligned Regularized Bayesian Optimization Routine), built from a block-additive SAAS surrogate, multi-fidelity cost-aware acquisition, and TuRBO trust regions. Second, we instantiate the problem in a flag-gated harness over a production coding agent and report a controlled four-round manual-tuning case study against a fixed task suite and an end-to-end HARBOR run. The formulation itself is task-class agnostic: the configuration space, reward correction, acquisition, and safety check apply to any agent harness with a bounded flag space and a reproducible task suite.

Large transformer models display promising performance on a wide range of natural language processing (NLP) tasks. Although the AI community has expanded the model scale to the trillion parameter level, the practical deployment of 10-100 billion parameter models is still uncertain due to the latency, throughput, and memory constraints. In this paper, we proposed EnergonAI to solve the challenges of the efficient deployment of 10-100 billion parameter transformer models on single- or multi-GPU systems. EnergonAI adopts a hierarchy-controller system architecture to coordinate multiple devices and efficiently support different parallel patterns. It delegates the execution of sub-models to multiple workers in the single-controller style and applies tensor parallelism and pipeline parallelism among the workers in a multi-controller style. Upon the novel architecture, we propose three techniques, i.e. non-blocking pipeline parallelism, distributed redundant computation elimination, and peer memory pooling. EnergonAI enables the users to program complex parallel code the same as a serial one. Compared with the FasterTransformer, we have proven that EnergonAI has superior performance on latency and throughput. In our experiments, EnergonAI can achieve 37% latency reduction in tensor parallelism, 10% scalability improvement in pipeline parallelism, and it improves the model scale inferred on a single GPU by using a larger heterogeneous memory space at cost of limited performance reduction.

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Mediated by today's visual displays, information space allows users to discover, access and interact with a wide range of digital and physical information. The information presented in this space may be digital, physical or a blend of both, and appear across different dimensions - such as texts, images, 3D content and physical objects embedded within real-world environment. Navigating within the information space often involves interacting with mixed-dimensional entities, visually represented in both 2D and 3D. At times, interactions also involve transitioning among entities represented in different dimensions. We introduce the concept of mixed-dimensional information space, encompassing entities represented in both 2D and 3D. Interactions within the mixed-dimensional information space should be seamless and efficient: users should be able to focus on their primary tasks without being distracted by interactions with or transitions between entities. While incorporating 3D representations into the mixed-dimensional information space offers intuitive and immersive ways to interact with complex information, it is important to address potential seams and inefficiencies that arise while interacting with both 2D and 3D entities. This dissertation introduces new interactive techniques and systems to realize seamless and efficient interactions within the mixed-dimensional information space. This dissertation introduces three interactive systems: MemoVis which aims to use emergent generative AI to help users create reference images for 3D design feedback; PaperToPlace which demonstrates how paper-based instruction documents can be transformed and spatialized into a context-aware MR experience; and VRContour which explores how contour delineation workflow can be brought into VR.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

The heterogeneous network is a robust data abstraction that can model entities of different types interacting in various ways. Such heterogeneity brings rich semantic information but presents nontrivial challenges in aggregating the heterogeneous relationships between objects - especially those of higher-order indirect relations. Recent graph neural network approaches for representation learning on heterogeneous networks typically employ the attention mechanism, which is often only optimized for predictions based on direct links. Furthermore, even though most deep learning methods can aggregate higher-order information by building deeper models, such a scheme can diminish the degree of interpretability. To overcome these challenges, we explore an architecture - Layer-stacked ATTention Embedding (LATTE) - that automatically decomposes higher-order meta relations at each layer to extract the relevant heterogeneous neighborhood structures for each node. Additionally, by successively stacking layer representations, the learned node embedding offers a more interpretable aggregation scheme for nodes of different types at different neighborhood ranges. We conducted experiments on several benchmark heterogeneous network datasets. In both transductive and inductive node classification tasks, LATTE can achieve state-of-the-art performance compared to existing approaches, all while offering a lightweight model. With extensive experimental analyses and visualizations, the framework can demonstrate the ability to extract informative insights on heterogeneous networks.

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in this field, much of the focus has been on single polygons, overlooking the intricate inner- and inter-polygonal relationships inherent in multipolygons. To address this gap, our study introduces a comprehensive framework specifically designed for learning representations of polygonal geometries, particularly multipolygons. Central to our approach is the incorporation of a heterogeneous visibility graph, which seamlessly integrates both inner- and inter-polygonal relationships. To enhance computational efficiency and minimize graph redundancy, we implement a heterogeneous spanning tree sampling method. Additionally, we devise a rotation-translation invariant geometric representation, ensuring broader applicability across diverse scenarios. Finally, we introduce Multipolygon-GNN, a novel model tailored to leverage the spatial and semantic heterogeneity inherent in the visibility graph. Experiments on five real-world and synthetic datasets demonstrate its ability to capture informative representations for polygonal geometries. Code and data are available at https://github.com/dyu62/PolyGNN{github.com/dyu62/PolyGNN}.

Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and consistently deliver state-of-the-art results across diverse applications. However, hyperbolic classifiers often grapple with computational challenges. Methods reliant on Riemannian optimization frequently exhibit sluggishness, stemming from the increased computational demands of operations on Riemannian manifolds. In response to these challenges, we present hyperDT, a novel extension of decision tree algorithms into hyperbolic space. Crucially, hyperDT eliminates the need for computationally intensive Riemannian optimization, numerically unstable exponential and logarithmic maps, or pairwise comparisons between points by leveraging inner products to adapt Euclidean decision tree algorithms to hyperbolic space. Our approach is conceptually straightforward and maintains constant-time decision complexity while mitigating the scalability issues inherent in high-dimensional Euclidean spaces. Building upon hyperDT we introduce hyperRF, a hyperbolic random forest model. Extensive benchmarking across diverse datasets underscores the superior performance of these models, providing a swift, precise, accurate, and user-friendly toolkit for hyperbolic data analysis.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Anomaly detection plays an important role in modern data-driven security applications, such as detecting suspicious access to a socket from a process. In many cases, such events can be described as a collection of categorical values that are considered as entities of different types, which we call heterogeneous categorical events. Due to the lack of intrinsic distance measures among entities, and the exponentially large event space, most existing work relies heavily on heuristics to calculate abnormal scores for events. Different from previous work, we propose a principled and unified probabilistic model APE (Anomaly detection via Probabilistic pairwise interaction and Entity embedding) that directly models the likelihood of events. In this model, we embed entities into a common latent space using their observed co-occurrence in different events. More specifically, we first model the compatibility of each pair of entities according to their embeddings. Then we utilize the weighted pairwise interactions of different entity types to define the event probability. Using Noise-Contrastive Estimation with "context-dependent" noise distribution, our model can be learned efficiently regardless of the large event space. Experimental results on real enterprise surveillance data show that our methods can accurately detect abnormal events compared to other state-of-the-art abnormal detection techniques.

Score-based generative models, commonly referred to as diffusion models, have proven to be successful at generating text and image data. However, their adaptation to mixed-type tabular data remains underexplored. In this work, we propose CDTD, a Continuous Diffusion model for mixed-type Tabular Data. CDTD is based on a novel combination of score matching and score interpolation to enforce a unified continuous noise distribution for both continuous and categorical features. We explicitly acknowledge the necessity of homogenizing distinct data types by relying on model-specific loss calibration and initialization schemes.To further address the high heterogeneity in mixed-type tabular data, we introduce adaptive feature- or type-specific noise schedules. These ensure balanced generative performance across features and optimize the allocation of model capacity across features and diffusion time. Our experimental results show that CDTD consistently outperforms state-of-the-art benchmark models, captures feature correlations exceptionally well, and that heterogeneity in the noise schedule design boosts sample quality. Replication code is available at https://github.com/muellermarkus/cdtd.

Despite advances in indoor 3D scene layout generation, synthesizing scenes with dense object arrangements remains challenging. Existing methods primarily focus on large furniture while neglecting smaller objects, resulting in unrealistically empty scenes. Those that place small objects typically do not honor arrangement specifications, resulting in largely random placement not following the text description. We present HSM, a hierarchical framework for indoor scene generation with dense object arrangements across spatial scales. Indoor scenes are inherently hierarchical, with surfaces supporting objects at different scales, from large furniture on floors to smaller objects on tables and shelves. HSM embraces this hierarchy and exploits recurring cross-scale spatial patterns to generate complex and realistic indoor scenes in a unified manner. Our experiments show that HSM outperforms existing methods by generating scenes that are more realistic and better conform to user input across room types and spatial configurations.

Spatial confounding poses a significant challenge in scientific studies involving spatial data, where unobserved spatial variables can influence both treatment and outcome, possibly leading to spurious associations. To address this problem, we introduce SpaCE: The Spatial Confounding Environment, the first toolkit to provide realistic benchmark datasets and tools for systematically evaluating causal inference methods designed to alleviate spatial confounding. Each dataset includes training data, true counterfactuals, a spatial graph with coordinates, and smoothness and confounding scores characterizing the effect of a missing spatial confounder. It also includes realistic semi-synthetic outcomes and counterfactuals, generated using state-of-the-art machine learning ensembles, following best practices for causal inference benchmarks. The datasets cover real treatment and covariates from diverse domains, including climate, health and social sciences. SpaCE facilitates an automated end-to-end pipeline, simplifying data loading, experimental setup, and evaluating machine learning and causal inference models. The SpaCE project provides several dozens of datasets of diverse sizes and spatial complexity. It is publicly available as a Python package, encouraging community feedback and contributions.

Federated Learning (FL) represents a paradigm shift in distributed machine learning (ML), enabling clients to train models collaboratively while keeping their raw data private. This paradigm shift from traditional centralized ML introduces challenges due to the non-iid (non-independent and identically distributed) nature of data across clients, significantly impacting FL's performance. Existing literature, predominantly model data heterogeneity by imposing label distribution skew across clients. In this paper, we show that label distribution skew fails to fully capture the real-world data heterogeneity among clients in computer vision tasks beyond classification. Subsequently, we demonstrate that current approaches overestimate FL's performance by relying on label/class distribution skew, exposing an overlooked gap in the literature. By utilizing pre-trained deep neural networks to extract task-specific data embeddings, we define task-specific data heterogeneity through the lens of each vision task and introduce a new level of data heterogeneity called embedding-based data heterogeneity. Our methodology involves clustering data points based on embeddings and distributing them among clients using the Dirichlet distribution. Through extensive experiments, we evaluate the performance of different FL methods under our revamped notion of data heterogeneity, introducing new benchmark performance measures to the literature. We further unveil a series of open research directions that can be pursued.

Client selection strategies are widely adopted to handle the communication-efficient problem in recent studies of Federated Learning (FL). However, due to the large variance of the selected subset's update, prior selection approaches with a limited sampling ratio cannot perform well on convergence and accuracy in heterogeneous FL. To address this problem, in this paper, we propose a novel stratified client selection scheme to reduce the variance for the pursuit of better convergence and higher accuracy. Specifically, to mitigate the impact of heterogeneity, we develop stratification based on clients' local data distribution to derive approximate homogeneous strata for better selection in each stratum. Concentrating on a limited sampling ratio scenario, we next present an optimized sample size allocation scheme by considering the diversity of stratum's variability, with the promise of further variance reduction. Theoretically, we elaborate the explicit relation among different selection schemes with regard to variance, under heterogeneous settings, we demonstrate the effectiveness of our selection scheme. Experimental results confirm that our approach not only allows for better performance relative to state-of-the-art methods but also is compatible with prevalent FL algorithms.

While scaling laws have transformed natural language processing and computer vision, 3D point cloud understanding has yet to reach that stage. This can be attributed to both the comparatively smaller scale of 3D datasets, as well as the disparate sources of the data itself. Point clouds are captured by diverse sensors (e.g., depth cameras, LiDAR) across varied domains (e.g., indoor, outdoor), each introducing unique scanning patterns, sampling densities, and semantic biases. Such domain heterogeneity poses a major barrier towards training unified models at scale, especially under the realistic constraint that domain labels are typically inaccessible at inference time. In this work, we propose Point-MoE, a Mixture-of-Experts architecture designed to enable large-scale, cross-domain generalization in 3D perception. We show that standard point cloud backbones degrade significantly in performance when trained on mixed-domain data, whereas Point-MoE with a simple top-k routing strategy can automatically specialize experts, even without access to domain labels. Our experiments demonstrate that Point-MoE not only outperforms strong multi-domain baselines but also generalizes better to unseen domains. This work highlights a scalable path forward for 3D understanding: letting the model discover structure in diverse 3D data, rather than imposing it via manual curation or domain supervision.

Federated learning (FL) is a distributed learning method that offers medical institutes the prospect of collaboration in a global model while preserving the privacy of their patients. Although most medical centers conduct similar medical imaging tasks, their differences, such as specializations, number of patients, and devices, lead to distinctive data distributions. Data heterogeneity poses a challenge for FL and the personalization of the local models. In this work, we investigate an adaptive hierarchical clustering method for FL to produce intermediate semi-global models, so clients with similar data distribution have the chance of forming a more specialized model. Our method forms several clusters consisting of clients with the most similar data distributions; then, each cluster continues to train separately. Inside the cluster, we use meta-learning to improve the personalization of the participants' models. We compare the clustering approach with classical FedAvg and centralized training by evaluating our proposed methods on the HAM10k dataset for skin lesion classification with extreme heterogeneous data distribution. Our experiments demonstrate significant performance gain in heterogeneous distribution compared to standard FL methods in classification accuracy. Moreover, we show that the models converge faster if applied in clusters and outperform centralized training while using only a small subset of data.

Ad-hoc Video Search (AVS) involves using a textual query to search for multiple relevant videos in a large collection of unlabeled short videos. The main challenge of AVS is the visual diversity of relevant videos. A simple query such as "Find shots of a man and a woman dancing together indoors" can span a multitude of environments, from brightly lit halls and shadowy bars to dance scenes in black-and-white animations. It is therefore essential to retrieve relevant videos as comprehensively as possible. Current solutions for the AVS task primarily fuse multiple features into one or more common spaces, yet overlook the need for diverse spaces. To fully exploit the expressive capability of individual features, we propose LPD, short for Learning Partially Decorrelated common spaces. LPD incorporates two key innovations: feature-specific common space construction and the de-correlation loss. Specifically, LPD learns a separate common space for each video and text feature, and employs de-correlation loss to diversify the ordering of negative samples across different spaces. To enhance the consistency of multi-space convergence, we designed an entropy-based fair multi-space triplet ranking loss. Extensive experiments on the TRECVID AVS benchmarks (2016-2023) justify the effectiveness of LPD. Moreover, diversity visualizations of LPD's spaces highlight its ability to enhance result diversity.

The efficiency of Federated Learning (FL) is often affected by both data and device heterogeneities. Data heterogeneity is defined as the heterogeneity of data distributions on different clients. Device heterogeneity is defined as the clients' variant latencies in uploading their local model updates due to heterogeneous conditions of local hardware resources, and causes the problem of staleness when being addressed by asynchronous FL. Traditional schemes of tackling the impact of staleness consider data and device heterogeneities as two separate and independent aspects in FL, but this assumption is unrealistic in many practical FL scenarios where data and device heterogeneities are intertwined. In these cases, traditional schemes of weighted aggregation in FL have been proved to be ineffective, and a better approach is to convert a stale model update into a non-stale one. In this paper, we present a new FL framework that leverages the gradient inversion technique for such conversion, hence efficiently tackling unlimited staleness in clients' model updates. Our basic idea is to use gradient inversion to get estimations of clients' local training data from their uploaded stale model updates, and use these estimations to compute non-stale client model updates. In this way, we address the problem of possible data quality drop when using gradient inversion, while still preserving the clients' local data privacy. We compared our approach with the existing FL strategies on mainstream datasets and models, and experiment results demonstrate that when tackling unlimited staleness, our approach can significantly improve the trained model accuracy by up to 20% and speed up the FL training progress by up to 35%.

Tabular data generation has become increasingly essential for enabling robust machine learning applications, which require large-scale, high-quality data. Existing solutions leverage generative models to learn original data distributions. However, real-world data are naturally heterogeneous with diverse distributions, making it challenging to obtain a universally good model for diverse data generation. To address this limitation, we introduce Diversity-Aware Tabular data gEnerator (DATE), a framework that (i) prepares high-quality and distributionally distinct examples for in-context learning by effectively partitioning the original heterogeneous data into multiple diverse subsets; (ii) harnesses Large Language Models (LLMs) to explore the diversity of the partitioned distribution with decision tree reasoning as feedback, generating high-quality labeled data for each subset. However, the massive generated data inherently involves a trade-off between diversity and quality. To integrate this issue, existing solutions greedily select the validation-best data. However, we prove that the selection in heterogeneous settings does not possess the greedy-choice property, and design a Multi-Arm Bandit-based sampling algorithm that balances the diversity and quality of generated data. Extensive experiments on tabular classification and regression benchmarks demonstrate that DATE consistently outperforms state-of-the-art GAN-based and LLM-based methods. On average, DATE achieves a 23.75% reduction in error rate with just 100 generated data. Empirically, we demonstrate that data generated by DATE can improve the accuracy of Direct Preference Optimization (DPO) and enhance the reasoning capability of LLMs on the target data. Code is available at https://github.com/windblow32/DATE.

Heterogeneous graph learning aims to capture complex relationships and diverse relational semantics among entities in a heterogeneous graph to obtain meaningful representations for nodes and edges. Recent advancements in heterogeneous graph neural networks (HGNNs) have achieved state-of-the-art performance by considering relation heterogeneity and using specialized message functions and aggregation rules. However, existing frameworks for heterogeneous graph learning have limitations in generalizing across diverse heterogeneous graph datasets. Most of these frameworks follow the "pre-train" and "fine-tune" paradigm on the same dataset, which restricts their capacity to adapt to new and unseen data. This raises the question: "Can we generalize heterogeneous graph models to be well-adapted to diverse downstream learning tasks with distribution shifts in both node token sets and relation type heterogeneity?'' To tackle those challenges, we propose HiGPT, a general large graph model with Heterogeneous graph instruction-tuning paradigm. Our framework enables learning from arbitrary heterogeneous graphs without the need for any fine-tuning process from downstream datasets. To handle distribution shifts in heterogeneity, we introduce an in-context heterogeneous graph tokenizer that captures semantic relationships in different heterogeneous graphs, facilitating model adaptation. We incorporate a large corpus of heterogeneity-aware graph instructions into our HiGPT, enabling the model to effectively comprehend complex relation heterogeneity and distinguish between various types of graph tokens. Furthermore, we introduce the Mixture-of-Thought (MoT) instruction augmentation paradigm to mitigate data scarcity by generating diverse and informative instructions. Through comprehensive evaluations, our proposed framework demonstrates exceptional performance in terms of generalization performance.

Traditional fixed test sets fall short in evaluating open-ended capabilities of foundation models. To address this, we propose ONEBench(OpeN-Ended Benchmarking), a new testing paradigm that consolidates individual evaluation datasets into a unified, ever-expanding sample pool. ONEBench allows users to generate custom, open-ended evaluation benchmarks from this pool, corresponding to specific capabilities of interest. By aggregating samples across test sets, ONEBench enables the assessment of diverse capabilities beyond those covered by the original test sets, while mitigating overfitting and dataset bias. Most importantly, it frames model evaluation as a collective process of selecting and aggregating sample-level tests. The shift from task-specific benchmarks to ONEBench introduces two challenges: (1)heterogeneity and (2)incompleteness. Heterogeneity refers to the aggregation over diverse metrics, while incompleteness describes comparing models evaluated on different data subsets. To address these challenges, we explore algorithms to aggregate sparse measurements into reliable model scores. Our aggregation algorithm ensures identifiability(asymptotically recovering ground-truth scores) and rapid convergence, enabling accurate model ranking with less data. On homogenous datasets, we show our aggregation algorithm provides rankings that highly correlate with those produced by average scores. We also demonstrate robustness to ~95% of measurements missing, reducing evaluation cost by up to 20x with little-to-no change in model rankings. We introduce ONEBench-LLM for language models and ONEBench-LMM for vision-language models, unifying evaluations across these domains. Overall, we present a technique for open-ended evaluation, which can aggregate over incomplete, heterogeneous sample-level measurements to continually grow a benchmark alongside the rapidly developing foundation models.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

Deploying robots at scale demands robustness to the long tail of everyday situations. The countless variations in scene layout, object geometry, and task specifications that characterize real environments are vast and underrepresented in existing robot benchmarks. Measuring this level of generalization requires infrastructure at a scale and diversity that physical evaluation alone cannot provide. We introduce MolmoSpaces, a fully open ecosystem to support large-scale benchmarking of robot policies. MolmoSpaces consists of over 230k diverse indoor environments, ranging from handcrafted household scenes to procedurally generated multiroom houses, populated with 130k richly annotated object assets, including 48k manipulable objects with 42M stable grasps. Crucially, these environments are simulator-agnostic, supporting popular options such as MuJoCo, Isaac, and ManiSkill. The ecosystem supports the full spectrum of embodied tasks: static and mobile manipulation, navigation, and multiroom long-horizon tasks requiring coordinated perception, planning, and interaction across entire indoor environments. We also design MolmoSpaces-Bench, a benchmark suite of 8 tasks in which robots interact with our diverse scenes and richly annotated objects. Our experiments show MolmoSpaces-Bench exhibits strong sim-to-real correlation (R = 0.96, ho = 0.98), confirm newer and stronger zero-shot policies outperform earlier versions in our benchmarks, and identify key sensitivities to prompt phrasing, initial joint positions, and camera occlusion. Through MolmoSpaces and its open-source assets and tooling, we provide a foundation for scalable data generation, policy training, and benchmark creation for robot learning research.

There is increased interest in using generative AI to create 3D spaces for Virtual Reality (VR) applications. However, today's models produce artificial environments, falling short of supporting collaborative tasks that benefit from incorporating the user's physical context. To generate environments that support VR telepresence, we introduce SpaceBlender, a novel pipeline that utilizes generative AI techniques to blend users' physical surroundings into unified virtual spaces. This pipeline transforms user-provided 2D images into context-rich 3D environments through an iterative process consisting of depth estimation, mesh alignment, and diffusion-based space completion guided by geometric priors and adaptive text prompts. In a preliminary within-subjects study, where 20 participants performed a collaborative VR affinity diagramming task in pairs, we compared SpaceBlender with a generic virtual environment and a state-of-the-art scene generation framework, evaluating its ability to create virtual spaces suitable for collaboration. Participants appreciated the enhanced familiarity and context provided by SpaceBlender but also noted complexities in the generative environments that could detract from task focus. Drawing on participant feedback, we propose directions for improving the pipeline and discuss the value and design of blended spaces for different scenarios.

Collaborative perception aims to mitigate the limitations of single-agent perception, such as occlusions, by facilitating data exchange among multiple agents. However, most current works consider a homogeneous scenario where all agents use identity sensors and perception models. In reality, heterogeneous agent types may continually emerge and inevitably face a domain gap when collaborating with existing agents. In this paper, we introduce a new open heterogeneous problem: how to accommodate continually emerging new heterogeneous agent types into collaborative perception, while ensuring high perception performance and low integration cost? To address this problem, we propose HEterogeneous ALliance (HEAL), a novel extensible collaborative perception framework. HEAL first establishes a unified feature space with initial agents via a novel multi-scale foreground-aware Pyramid Fusion network. When heterogeneous new agents emerge with previously unseen modalities or models, we align them to the established unified space with an innovative backward alignment. This step only involves individual training on the new agent type, thus presenting extremely low training costs and high extensibility. To enrich agents' data heterogeneity, we bring OPV2V-H, a new large-scale dataset with more diverse sensor types. Extensive experiments on OPV2V-H and DAIR-V2X datasets show that HEAL surpasses SOTA methods in performance while reducing the training parameters by 91.5% when integrating 3 new agent types. We further implement a comprehensive codebase at: https://github.com/yifanlu0227/HEAL

Chemical language models (CLMs) are prominent for their effectiveness in exploring chemical space and enabling molecular engineering. However, while exploring chemical-linguistic space, CLMs suffer from the gap between natural language and molecular representations. This challenge is primarily due to the inherent modeling differences between molecules and texts: molecules operate unified modeling to learn chemical space, while natural language sequentially models the semantic space. Additionally, the limited availability of high-quality text-to-molecule datasets further exacerbates this challenge. To address the problem, we first verified the information bias in molecular representations from different perspectives. We then developed the Heterogeneous Molecular Encoding (HME) framework, a unified molecular encoder compressing the molecular features from fragment sequence, topology, and conformation with Q-learning. To better model chemical-linguistic space, we further constructed the MCMoD dataset, which contains over one million molecules with various conditions, including properties, fragments, and descriptions. Experimentally, HME promotes CLMs to achieve chemical-linguistic sharing space exploration: (1) chemical space exploration with linguistic guidance, where HME achieves significant improvements (+37.8\% FCD) for molecular design in multiple constraints, even in zero-shot scenarios; (2) linguistic space exploration with molecular guidance, where HME generates textual descriptions with high qualities (+11.6\% BLEU) for molecules. These results highlight the precision of HME in handling multi-objective and cross-domain tasks, as well as its remarkable generalization capability on unseen task combinations. HME offers a new perspective on navigating chemical-linguistic sharing space, advancing the potential of CLMs in both fundamental research and practical applications in chemistry.

The development of foundation models for embodied intelligence critically depends on access to large-scale, high-quality robot demonstration data. Recent approaches have sought to address this challenge by training on large collections of heterogeneous robotic datasets. However, unlike vision or language data, robotic demonstrations exhibit substantial heterogeneity across embodiments and action spaces as well as other prominent variations such as senor configurations and action control frequencies. The lack of explicit designs for handling such heterogeneity causes existing methods to struggle with integrating diverse factors, thereby limiting their generalization and leading to degraded performance when transferred to new settings. In this paper, we present HiMoE-VLA, a novel vision-language-action (VLA) framework tailored to effectively handle diverse robotic data with heterogeneity. Specifically, we introduce a Hierarchical Mixture-of-Experts (HiMoE) architecture for the action module which adaptively handles multiple sources of heterogeneity across layers and gradually abstracts them into shared knowledge representations. Through extensive experimentation with simulation benchmarks and real-world robotic platforms, HiMoE-VLA demonstrates a consistent performance boost over existing VLA baselines, achieving higher accuracy and robust generalization across diverse robots and action spaces. The code and models are publicly available at https://github.com/ZhiyingDu/HiMoE-VLA.

This paper develops a hierarchical clustering algorithm for weighted projective spaces P_{q}, utilizing a Finsler metric d_F([z], [w]) and its rational analogue d_{F,Q}([z], [w]) to define distances that preserve the non-Euclidean geometry of these quotient manifolds. Defined via geodesic integrals of a scaling invariant Finsler norm weighted by the grades q = (q_0, q_1, dots, q_n), these metrics satisfy true metric properties including the triangle inequality, overcoming the limitations of the non-metric dissimilarity measure from prior work.

Manipulating objects with varying geometries and deformable objects is a major challenge in robotics. Tasks such as insertion with different objects or cloth hanging require precise control and effective modelling of complex dynamics. In this work, we frame this problem through the lens of a heterogeneous graph that comprises smaller sub-graphs, such as actuators and objects, accompanied by different edge types describing their interactions. This graph representation serves as a unified structure for both rigid and deformable objects tasks, and can be extended further to tasks comprising multiple actuators. To evaluate this setup, we present a novel and challenging reinforcement learning benchmark, including rigid insertion of diverse objects, as well as rope and cloth manipulation with multiple end-effectors. These tasks present a large search space, as both the initial and target configurations are uniformly sampled in 3D space. To address this issue, we propose a novel graph-based policy model, dubbed Heterogeneous Equivariant Policy (HEPi), utilizing SE(3) equivariant message passing networks as the main backbone to exploit the geometric symmetry. In addition, by modeling explicit heterogeneity, HEPi can outperform Transformer-based and non-heterogeneous equivariant policies in terms of average returns, sample efficiency, and generalization to unseen objects. Our project page is available at https://thobotics.github.io/hepi.

Due to domain shift, machine learning systems typically fail to generalize well to domains different from those of training data, which is what domain generalization (DG) aims to address. Although various DG methods have been developed, most of them lack interpretability and require domain labels that are not available in many real-world scenarios. This paper presents a novel DG method, called HMOE: Hypernetwork-based Mixture of Experts (MoE), which does not rely on domain labels and is more interpretable. MoE proves effective in identifying heterogeneous patterns in data. For the DG problem, heterogeneity arises exactly from domain shift. HMOE uses hypernetworks taking vectors as input to generate experts' weights, which allows experts to share useful meta-knowledge and enables exploring experts' similarities in a low-dimensional vector space. We compare HMOE with other DG algorithms under a fair and unified benchmark-DomainBed. Our extensive experiments show that HMOE can divide mixed-domain data into distinct clusters that are surprisingly more consistent with human intuition than original domain labels. Compared to other DG methods, HMOE shows competitive performance and achieves SOTA results in some cases.

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

Image diversity remains a fundamental challenge for text-to-image diffusion models. Low-diversity models tend to generate repetitive outputs, increasing sampling redundancy and hindering both creative exploration and downstream applications. A primary cause is that generation often collapses toward a strong mode in the learned distribution. Existing attempts to improve diversity, such as noise resampling, prompt rewriting, or steering-based guidance, often still collapse to dominant modes or introduce distortions that degrade image quality. In light of this, we propose Token-Prompt embedding Space Optimization (TPSO), a training-free and model-agnostic module. TPSO introduces learnable parameters to explore underrepresented regions of the token embedding space, reducing the tendency of the model to repeatedly generate samples from strong modes of the learned distribution. At the same time, the prompt-level space provides a global semantic constraint that regulates distribution shifts, preventing quality degradation while maintaining high fidelity. Extensive experiments on MS-COCO and three diffusion backbones show that TPSO significantly enhances generative diversity, improving baseline performance from 1.10 to 4.18 points, without sacrificing image quality. Code will be released upon acceptance.

With the current surge in spatial reasoning explorations, researchers have made significant progress in understanding indoor scenes, but still struggle with diverse applications such as robotics and autonomous driving. This paper aims to advance all-scale spatial reasoning across diverse scenarios by tackling two key challenges: 1) the heavy reliance on indoor 3D scans and labor-intensive manual annotations for dataset curation; 2) the absence of effective all-scale scene modeling, which often leads to overfitting to individual scenes. In this paper, we introduce a holistic solution that integrates a structured spatial reasoning knowledge system, scale-aware modeling, and a progressive training paradigm, as the first attempt to broaden the all-scale spatial intelligence of MLLMs to the best of our knowledge. Using a task-specific, specialist-driven automated pipeline, we curate over 38K video scenes across 5 spatial scales to create SpaceVista-1M, a dataset comprising approximately 1M spatial QA pairs spanning 19 diverse task types. While specialist models can inject useful domain knowledge, they are not reliable for evaluation. We then build an all-scale benchmark with precise annotations by manually recording, retrieving, and assembling video-based data. However, naive training with SpaceVista-1M often yields suboptimal results due to the potential knowledge conflict. Accordingly, we introduce SpaceVista-7B, a spatial reasoning model that accepts dense inputs beyond semantics and uses scale as an anchor for scale-aware experts and progressive rewards. Finally, extensive evaluations across 5 benchmarks, including our SpaceVista-Bench, demonstrate competitive performance, showcasing strong generalization across all scales and scenarios. Our dataset, model, and benchmark will be released on https://peiwensun2000.github.io/mm2km .

We present a dataset of large-scale indoor spaces that provides a variety of mutually registered modalities from 2D, 2.5D and 3D domains, with instance-level semantic and geometric annotations. The dataset covers over 6,000m2 and contains over 70,000 RGB images, along with the corresponding depths, surface normals, semantic annotations, global XYZ images (all in forms of both regular and 360{\deg} equirectangular images) as well as camera information. It also includes registered raw and semantically annotated 3D meshes and point clouds. The dataset enables development of joint and cross-modal learning models and potentially unsupervised approaches utilizing the regularities present in large-scale indoor spaces. The dataset is available here: http://3Dsemantics.stanford.edu/

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive C_{0}-semigroups under the topology of uniform weak operator convergence on compact subsets of R_{+}. Eisner and Serény raised in 2009 the open problem: Does this space constitute a Baire space? Observing that the subspace of unitary semigroups is completely metrisable and appealing to known density results, we solve this problem positively by showing that certain topological properties can in general be transferred from dense subspaces to larger spaces. The transfer result in turn relies upon classification of topological properties via infinite games. Our approach is sufficiently general and can be applied to other contexts, e.g. the space of contractions under the pw-topology.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

As AI evolves, collaboration among heterogeneous models helps overcome data scarcity by enabling knowledge transfer across institutions and devices. Traditional Federated Learning (FL) only supports homogeneous models, limiting collaboration among clients with heterogeneous model architectures. To address this, Heterogeneous Federated Learning (HtFL) methods are developed to enable collaboration across diverse heterogeneous models while tackling the data heterogeneity issue at the same time. However, a comprehensive benchmark for standardized evaluation and analysis of the rapidly growing HtFL methods is lacking. Firstly, the highly varied datasets, model heterogeneity scenarios, and different method implementations become hurdles to making easy and fair comparisons among HtFL methods. Secondly, the effectiveness and robustness of HtFL methods are under-explored in various scenarios, such as the medical domain and sensor signal modality. To fill this gap, we introduce the first Heterogeneous Federated Learning Library (HtFLlib), an easy-to-use and extensible framework that integrates multiple datasets and model heterogeneity scenarios, offering a robust benchmark for research and practical applications. Specifically, HtFLlib integrates (1) 12 datasets spanning various domains, modalities, and data heterogeneity scenarios; (2) 40 model architectures, ranging from small to large, across three modalities; (3) a modularized and easy-to-extend HtFL codebase with implementations of 10 representative HtFL methods; and (4) systematic evaluations in terms of accuracy, convergence, computation costs, and communication costs. We emphasize the advantages and potential of state-of-the-art HtFL methods and hope that HtFLlib will catalyze advancing HtFL research and enable its broader applications. The code is released at https://github.com/TsingZ0/HtFLlib.

This work considers the category distribution heterogeneity in federated learning. This issue is due to biased labeling preferences at multiple clients and is a typical setting of data heterogeneity. To alleviate this issue, most previous works consider either regularizing local models or fine-tuning the global model, while they ignore the adjustment of aggregation weights and simply assign weights based on the dataset size. However, based on our empirical observations and theoretical analysis, we find that the dataset size is not optimal and the discrepancy between local and global category distributions could be a beneficial and complementary indicator for determining aggregation weights. We thus propose a novel aggregation method, Federated Learning with Discrepancy-aware Collaboration (FedDisco), whose aggregation weights not only involve both the dataset size and the discrepancy value, but also contribute to a tighter theoretical upper bound of the optimization error. FedDisco also promotes privacy-preservation, communication and computation efficiency, as well as modularity. Extensive experiments show that our FedDisco outperforms several state-of-the-art methods and can be easily incorporated with many existing methods to further enhance the performance. Our code will be available at https://github.com/MediaBrain-SJTU/FedDisco.

Diverse and realistic floor plan data are essential for the development of useful computer-aided methods in architectural design. Today's large-scale floor plan datasets predominantly feature simple floor plan layouts, typically representing single-apartment dwellings only. To compensate for the mismatch between current datasets and the real world, we develop Modified Swiss Dwellings (MSD) -- the first large-scale floor plan dataset that contains a significant share of layouts of multi-apartment dwellings. MSD features over 5.3K floor plans of medium- to large-scale building complexes, covering over 18.9K distinct apartments. We validate that existing approaches for floor plan generation, while effective in simpler scenarios, cannot yet seamlessly address the challenges posed by MSD. Our benchmark calls for new research in floor plan machine understanding. Code and data are open.

Federated learning (FL) is a distributed learning paradigm that enables multiple clients to learn a powerful global model by aggregating local training. However, the performance of the global model is often hampered by non-i.i.d. distribution among the clients, requiring extensive efforts to mitigate inter-client data heterogeneity. Going beyond inter-client data heterogeneity, we note that intra-client heterogeneity can also be observed on complex real-world data and seriously deteriorate FL performance. In this paper, we present a novel FL algorithm, i.e., FedIns, to handle intra-client data heterogeneity by enabling instance-adaptive inference in the FL framework. Instead of huge instance-adaptive models, we resort to a parameter-efficient fine-tuning method, i.e., scale and shift deep features (SSF), upon a pre-trained model. Specifically, we first train an SSF pool for each client, and aggregate these SSF pools on the server side, thus still maintaining a low communication cost. To enable instance-adaptive inference, for a given instance, we dynamically find the best-matched SSF subsets from the pool and aggregate them to generate an adaptive SSF specified for the instance, thereby reducing the intra-client as well as the inter-client heterogeneity. Extensive experiments show that our FedIns outperforms state-of-the-art FL algorithms, e.g., a 6.64\% improvement against the top-performing method with less than 15\% communication cost on Tiny-ImageNet. Our code and models will be publicly released.

Both biological and artificial neural networks inherently balance their performance with their operational cost, which balances their computational abilities. Typically, an efficient neuromorphic neural network is one that learns representations that reduce the redundancies and dimensionality of its input. This is for instance achieved in sparse coding, and sparse representations derived from natural images yield representations that are heterogeneous, both in their sampling of input features and in the variance of those features. Here, we investigated the connection between natural images' structure, particularly oriented features, and their corresponding sparse codes. We showed that representations of input features scattered across multiple levels of variance substantially improve the sparseness and resilience of sparse codes, at the cost of reconstruction performance. This echoes the structure of the model's input, allowing to account for the heterogeneously aleatoric structures of natural images. We demonstrate that learning kernel from natural images produces heterogeneity by balancing between approximate and dense representations, which improves all reconstruction metrics. Using a parametrized control of the kernels' heterogeneity used by a convolutional sparse coding algorithm, we show that heterogeneity emphasizes sparseness, while homogeneity improves representation granularity. In a broader context, these encoding strategy can serve as inputs to deep convolutional neural networks. We prove that such variance-encoded sparse image datasets enhance computational efficiency, emphasizing the benefits of kernel heterogeneity to leverage naturalistic and variant input structures and possible applications to improve the throughput of neuromorphic hardware.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

Information retrieval involves selecting artifacts from a corpus that are most relevant to a given search query. The flavor of retrieval typically used in classical applications can be termed as homogeneous and relaxed, where queries and corpus elements are both natural language (NL) utterances (homogeneous) and the goal is to pick most relevant elements from the corpus in the Top-K, where K is large, such as 10, 25, 50 or even 100 (relaxed). Recently, retrieval is being used extensively in preparing prompts for large language models (LLMs) to enable LLMs to perform targeted tasks. These new applications of retrieval are often heterogeneous and strict -- the queries and the corpus contain different kinds of entities, such as NL and code, and there is a need for improving retrieval at Top-K for small values of K, such as K=1 or 3 or 5. Current dense retrieval techniques based on pretrained embeddings provide a general-purpose and powerful approach for retrieval, but they are oblivious to task-specific notions of similarity of heterogeneous artifacts. We introduce Adapted Dense Retrieval, a mechanism to transform embeddings to enable improved task-specific, heterogeneous and strict retrieval. Adapted Dense Retrieval works by learning a low-rank residual adaptation of the pretrained black-box embedding. We empirically validate our approach by showing improvements over the state-of-the-art general-purpose embeddings-based baseline.

A comprehensive semantic understanding of a scene is important for many applications - but in what space should diverse semantic information (e.g., objects, scene categories, material types, texture, etc.) be grounded and what should be its structure? Aspiring to have one unified structure that hosts diverse types of semantics, we follow the Scene Graph paradigm in 3D, generating a 3D Scene Graph. Given a 3D mesh and registered panoramic images, we construct a graph that spans the entire building and includes semantics on objects (e.g., class, material, and other attributes), rooms (e.g., scene category, volume, etc.) and cameras (e.g., location, etc.), as well as the relationships among these entities. However, this process is prohibitively labor heavy if done manually. To alleviate this we devise a semi-automatic framework that employs existing detection methods and enhances them using two main constraints: I. framing of query images sampled on panoramas to maximize the performance of 2D detectors, and II. multi-view consistency enforcement across 2D detections that originate in different camera locations.

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping from its latent space to image space. To tackle this problem, we present Isometric Diffusion, equipping a diffusion model with a geometric regularizer to guide the model to learn a geometrically sound latent space of the training data manifold. This approach allows diffusion models to learn a more disentangled latent space, which enables smoother interpolation, more accurate inversion, and more precise control over attributes directly in the latent space. Our extensive experiments consisting of image interpolations, image inversions, and linear editing show the effectiveness of our method.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

Serving Large Language Models (LLMs) is a GPU-intensive task where traditional autoscalers fall short, particularly for modern Prefill-Decode (P/D) disaggregated architectures. This architectural shift, while powerful, introduces significant operational challenges, including inefficient use of heterogeneous hardware, network bottlenecks, and critical imbalances between prefill and decode stages. We introduce HeteroScale, a coordinated autoscaling framework that addresses the core challenges of P/D disaggregated serving. HeteroScale combines a topology-aware scheduler that adapts to heterogeneous hardware and network constraints with a novel metric-driven policy derived from the first large-scale empirical study of autoscaling signals in production. By leveraging a single, robust metric to jointly scale prefill and decode pools, HeteroScale maintains architectural balance while ensuring efficient, adaptive resource management. Deployed in a massive production environment on tens of thousands of GPUs, HeteroScale has proven its effectiveness, increasing average GPU utilization by a significant 26.6 percentage points and saving hundreds of thousands of GPU-hours daily, all while upholding stringent service level objectives.

Federated Learning is a distributed learning paradigm with two key challenges that differentiate it from traditional distributed optimization: (1) significant variability in terms of the systems characteristics on each device in the network (systems heterogeneity), and (2) non-identically distributed data across the network (statistical heterogeneity). In this work, we introduce a framework, FedProx, to tackle heterogeneity in federated networks. FedProx can be viewed as a generalization and re-parametrization of FedAvg, the current state-of-the-art method for federated learning. While this re-parameterization makes only minor modifications to the method itself, these modifications have important ramifications both in theory and in practice. Theoretically, we provide convergence guarantees for our framework when learning over data from non-identical distributions (statistical heterogeneity), and while adhering to device-level systems constraints by allowing each participating device to perform a variable amount of work (systems heterogeneity). Practically, we demonstrate that FedProx allows for more robust convergence than FedAvg across a suite of realistic federated datasets. In particular, in highly heterogeneous settings, FedProx demonstrates significantly more stable and accurate convergence behavior relative to FedAvg---improving absolute test accuracy by 22% on average.

Few-shot image generation is a challenging task since it aims to generate diverse new images for an unseen category with only a few images. Existing methods suffer from the trade-off between the quality and diversity of generated images. To tackle this problem, we propose Hyperbolic Attribute Editing~(HAE), a simple yet effective method. Unlike other methods that work in Euclidean space, HAE captures the hierarchy among images using data from seen categories in hyperbolic space. Given a well-trained HAE, images of unseen categories can be generated by moving the latent code of a given image toward any meaningful directions in the Poincar\'e disk with a fixing radius. Most importantly, the hyperbolic space allows us to control the semantic diversity of the generated images by setting different radii in the disk. Extensive experiments and visualizations demonstrate that HAE is capable of not only generating images with promising quality and diversity using limited data but achieving a highly controllable and interpretable editing process.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

A key aspect of text-to-image personalization methods is the manner in which the target concept is represented within the generative process. This choice greatly affects the visual fidelity, downstream editability, and disk space needed to store the learned concept. In this paper, we explore a new text-conditioning space that is dependent on both the denoising process timestep (time) and the denoising U-Net layers (space) and showcase its compelling properties. A single concept in the space-time representation is composed of hundreds of vectors, one for each combination of time and space, making this space challenging to optimize directly. Instead, we propose to implicitly represent a concept in this space by optimizing a small neural mapper that receives the current time and space parameters and outputs the matching token embedding. In doing so, the entire personalized concept is represented by the parameters of the learned mapper, resulting in a compact, yet expressive, representation. Similarly to other personalization methods, the output of our neural mapper resides in the input space of the text encoder. We observe that one can significantly improve the convergence and visual fidelity of the concept by introducing a textual bypass, where our neural mapper additionally outputs a residual that is added to the output of the text encoder. Finally, we show how one can impose an importance-based ordering over our implicit representation, providing users control over the reconstruction and editability of the learned concept using a single trained model. We demonstrate the effectiveness of our approach over a range of concepts and prompts, showing our method's ability to generate high-quality and controllable compositions without fine-tuning any parameters of the generative model itself.

The interest in federated learning has surged in recent research due to its unique ability to train a global model using privacy-secured information held locally on each client. This paper pays particular attention to the issue of client-side model heterogeneity, a pervasive challenge in the practical implementation of FL that escalates its complexity. Assuming a scenario where each client possesses varied memory storage, processing capabilities and network bandwidth - a phenomenon referred to as system heterogeneity - there is a pressing need to customize a unique model for each client. In response to this, we present an effective and adaptable federated framework FedP3, representing Federated Personalized and Privacy-friendly network Pruning, tailored for model heterogeneity scenarios. Our proposed methodology can incorporate and adapt well-established techniques to its specific instances. We offer a theoretical interpretation of FedP3 and its locally differential-private variant, DP-FedP3, and theoretically validate their efficiencies.

In practical federated learning scenarios, the participating devices may have different bitwidths for computation and memory storage by design. However, despite the progress made in device-heterogeneous federated learning scenarios, the heterogeneity in the bitwidth specifications in the hardware has been mostly overlooked. We introduce a pragmatic FL scenario with bitwidth heterogeneity across the participating devices, dubbed as Bitwidth Heterogeneous Federated Learning (BHFL). BHFL brings in a new challenge, that the aggregation of model parameters with different bitwidths could result in severe performance degeneration, especially for high-bitwidth models. To tackle this problem, we propose ProWD framework, which has a trainable weight dequantizer at the central server that progressively reconstructs the low-bitwidth weights into higher bitwidth weights, and finally into full-precision weights. ProWD further selectively aggregates the model parameters to maximize the compatibility across bit-heterogeneous weights. We validate ProWD against relevant FL baselines on the benchmark datasets, using clients with varying bitwidths. Our ProWD largely outperforms the baseline FL algorithms as well as naive approaches (e.g. grouped averaging) under the proposed BHFL scenario.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Many real-world graphs frequently present challenges for graph learning due to the presence of both heterophily and heterogeneity. However, existing benchmarks for graph learning often focus on heterogeneous graphs with homophily or homogeneous graphs with heterophily, leaving a gap in understanding how methods perform on graphs that are both heterogeneous and heterophilic. To bridge this gap, we introduce H2GB, a novel graph benchmark that brings together the complexities of both the heterophily and heterogeneity properties of graphs. Our benchmark encompasses 9 diverse real-world datasets across 5 domains, 28 baseline model implementations, and 26 benchmark results. In addition, we present a modular graph transformer framework UnifiedGT and a new model variant, H2G-former, that excels at this challenging benchmark. By integrating masked label embeddings, cross-type heterogeneous attention, and type-specific FFNs, H2G-former effectively tackles graph heterophily and heterogeneity. Extensive experiments across 26 baselines on H2GB reveal inadequacies of current models on heterogeneous heterophilic graph learning, and demonstrate the superiority of our H2G-former over existing solutions. Both the benchmark and the framework are available on GitHub (https://github.com/junhongmit/H2GB) and PyPI (https://pypi.org/project/H2GB), and documentation can be found at https://junhongmit.github.io/H2GB/.

Recent NeRF methods on large-scale scenes have underlined the importance of scene decomposition for scalable NeRFs. Although achieving reasonable scalability, there are several critical problems remaining unexplored, i.e., learnable decomposition, modeling scene heterogeneity, and modeling efficiency. In this paper, we introduce Switch-NeRF++, a Heterogeneous Mixture of Hash Experts (HMoHE) network that addresses these challenges within a unified framework. It is a highly scalable NeRF that learns heterogeneous decomposition and heterogeneous NeRFs efficiently for large-scale scenes in an end-to-end manner. In our framework, a gating network learns to decomposes scenes and allocates 3D points to specialized NeRF experts. This gating network is co-optimized with the experts, by our proposed Sparsely Gated Mixture of Experts (MoE) NeRF framework. We incorporate a hash-based gating network and distinct heterogeneous hash experts. The hash-based gating efficiently learns the decomposition of the large-scale scene. The distinct heterogeneous hash experts consist of hash grids of different resolution ranges, enabling effective learning of the heterogeneous representation of different scene parts. These design choices make our framework an end-to-end and highly scalable NeRF solution for real-world large-scale scene modeling to achieve both quality and efficiency. We evaluate our accuracy and scalability on existing large-scale NeRF datasets and a new dataset with very large-scale scenes (>6.5km^2) from UrbanBIS. Extensive experiments demonstrate that our approach can be easily scaled to various large-scale scenes and achieve state-of-the-art scene rendering accuracy. Furthermore, our method exhibits significant efficiency, with an 8x acceleration in training and a 16x acceleration in rendering compared to Switch-NeRF. Codes will be released in https://github.com/MiZhenxing/Switch-NeRF.

Recently, Heterogeneous Federated Learning (HtFL) has attracted attention due to its ability to support heterogeneous models and data. To reduce the high communication cost of transmitting model parameters, a major challenge in HtFL, prototype-based HtFL methods are proposed to solely share class representatives, a.k.a, prototypes, among heterogeneous clients while maintaining the privacy of clients' models. However, these prototypes are naively aggregated into global prototypes on the server using weighted averaging, resulting in suboptimal global knowledge which negatively impacts the performance of clients. To overcome this challenge, we introduce a novel HtFL approach called FedTGP, which leverages our Adaptive-margin-enhanced Contrastive Learning (ACL) to learn Trainable Global Prototypes (TGP) on the server. By incorporating ACL, our approach enhances prototype separability while preserving semantic meaning. Extensive experiments with twelve heterogeneous models demonstrate that our FedTGP surpasses state-of-the-art methods by up to 9.08% in accuracy while maintaining the communication and privacy advantages of prototype-based HtFL. Our code is available at https://github.com/TsingZ0/FedTGP.

Data heterogeneity is an inherent challenge that hinders the performance of federated learning (FL). Recent studies have identified the biased classifiers of local models as the key bottleneck. Previous attempts have used classifier calibration after FL training, but this approach falls short in improving the poor feature representations caused by training-time classifier biases. Resolving the classifier bias dilemma in FL requires a full understanding of the mechanisms behind the classifier. Recent advances in neural collapse have shown that the classifiers and feature prototypes under perfect training scenarios collapse into an optimal structure called simplex equiangular tight frame (ETF). Building on this neural collapse insight, we propose a solution to the FL's classifier bias problem by utilizing a synthetic and fixed ETF classifier during training. The optimal classifier structure enables all clients to learn unified and optimal feature representations even under extremely heterogeneous data. We devise several effective modules to better adapt the ETF structure in FL, achieving both high generalization and personalization. Extensive experiments demonstrate that our method achieves state-of-the-art performances on CIFAR-10, CIFAR-100, and Tiny-ImageNet.

Diffusion models degrade images through noise, and reversing this process reveals an information hierarchy across timesteps. Scale-space theory exhibits a similar hierarchy via low-pass filtering. We formalize this connection and show that highly noisy diffusion states contain no more information than small, downsampled images - raising the question of why they must be processed at full resolution. To address this, we fuse scale spaces into the diffusion process by formulating a family of diffusion models with generalized linear degradations and practical implementations. Using downsampling as the degradation yields our proposed Scale Space Diffusion. To support Scale Space Diffusion, we introduce Flexi-UNet, a UNet variant that performs resolution-preserving and resolution-increasing denoising using only the necessary parts of the network. We evaluate our framework on CelebA and ImageNet and analyze its scaling behavior across resolutions and network depths. Our project website ( https://prateksha.github.io/projects/scale-space-diffusion/ ) is available publicly.

Universal graph pre-training has emerged as a key paradigm in graph representation learning, offering a promising way to train encoders to learn transferable representations from unlabeled graphs and to effectively generalize across a wide range of downstream tasks. However, recent explorations in universal graph pre-training primarily focus on homogeneous graphs and it remains unexplored for heterogeneous graphs, which exhibit greater structural and semantic complexity. This heterogeneity makes it highly challenging to train a universal encoder for diverse heterogeneous graphs: (i) the diverse types with dataset-specific semantics hinder the construction of a unified representation space; (ii) the number and semantics of meta-paths vary across datasets, making encoding and aggregation patterns learned from one dataset difficult to apply to others. To address these challenges, we propose a novel Meta-path-aware Universal heterogeneous Graph pre-training (MUG) approach. Specifically, for challenge (i), MUG introduces a input unification module that integrates information from multiple node and relation types within each heterogeneous graph into a unified representation.This representation is then projected into a shared space by a dimension-aware encoder, enabling alignment across graphs with diverse schemas.Furthermore, for challenge (ii), MUG trains a shared encoder to capture consistent structural patterns across diverse meta-path views rather than relying on dataset-specific aggregation strategies, while a global objective encourages discriminability and reduces dataset-specific biases. Extensive experiments demonstrate the effectiveness of MUG on some real datasets.

Simulations are the best approximation to experimental laboratories in astrophysics and cosmology. However, the complexity, richness, and large size of their outputs severely limit the interpretability of their predictions. We describe a new, unbiased, and machine learning based approach to obtaining useful scientific insights from a broad range of simulations. The method can be used on today's largest simulations and will be essential to solve the extreme data exploration and analysis challenges posed by the Exascale era. Furthermore, this concept is so flexible, that it will also enable explorative access to observed data. Our concept is based on applying nonlinear dimensionality reduction to learn compact representations of the data in a low-dimensional space. The simulation data is projected onto this space for interactive inspection, visual interpretation, sample selection, and local analysis. We present a prototype using a rotational invariant hyperspherical variational convolutional autoencoder, utilizing a power distribution in the latent space, and trained on galaxies from IllustrisTNG simulation. Thereby, we obtain a natural Hubble tuning fork like similarity space that can be visualized interactively on the surface of a sphere by exploiting the power of HiPS tilings in Aladin Lite.

We present a method for generating arrangements of indoor furniture from human-designed furniture layout data. Our method creates arrangements that target specified diversity, such as the total price of all furniture in the room and the number of pieces placed. To generate realistic furniture arrangement, we train a generative adversarial network (GAN) on human-designed layouts. To target specific diversity in the arrangements, we optimize the latent space of the GAN via a quality diversity algorithm to generate a diverse arrangement collection. Experiments show our approach discovers a set of arrangements that are similar to human-designed layouts but varies in price and number of furniture pieces.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

We investigate the construction of latent spaces through self-supervised learning to support semantically meaningful operations. Analogous to operational amplifiers, these "operational latent spaces" (OpLaS) not only demonstrate semantic structure such as clustering but also support common transformational operations with inherent semantic meaning. Some operational latent spaces are found to have arisen "unintentionally" in the progress toward some (other) self-supervised learning objective, in which unintended but still useful properties are discovered among the relationships of points in the space. Other spaces may be constructed "intentionally" by developers stipulating certain kinds of clustering or transformations intended to produce the desired structure. We focus on the intentional creation of operational latent spaces via self-supervised learning, including the introduction of rotation operators via a novel "FiLMR" layer, which can be used to enable ring-like symmetries found in some musical constructions.

This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of k+1 reference points. As this definition relies on points and not on tangent vectors, it can also be extended to geodesic spaces which are not Riemannian. For instance, in stratified spaces, it naturally allows principal subspaces that span several strata, which is impossible in previous generalizations of PCA. We show that barycentric subspaces locally define a submanifold of dimension k which generalizes geodesic subspaces.Second, we rephrase PCA in Euclidean spaces as an optimization on flags of linear subspaces (a hierarchy of properly embedded linear subspaces of increasing dimension). We show that the Euclidean PCA minimizes the Accumulated Unexplained Variances by all the subspaces of the flag (AUV). Barycentric subspaces are naturally nested, allowing the construction of hierarchically nested subspaces. Optimizing the AUV criterion to optimally approximate data points with flags of affine spans in Riemannian manifolds lead to a particularly appealing generalization of PCA on manifolds called Barycentric Subspaces Analysis (BSA).

While prior domain generalization (DG) benchmarks consider train-test dataset heterogeneity, we evaluate Federated DG which introduces federated learning (FL) specific challenges. Additionally, we explore domain-based heterogeneity in clients' local datasets - a realistic Federated DG scenario. Prior Federated DG evaluations are limited in terms of the number or heterogeneity of clients and dataset diversity. To address this gap, we propose an Federated DG benchmark methodology that enables control of the number and heterogeneity of clients and provides metrics for dataset difficulty. We then apply our methodology to evaluate 13 Federated DG methods, which include centralized DG methods adapted to the FL context, FL methods that handle client heterogeneity, and methods designed specifically for Federated DG. Our results suggest that despite some progress, there remain significant performance gaps in Federated DG particularly when evaluating with a large number of clients, high client heterogeneity, or more realistic datasets. Please check our extendable benchmark code here: https://github.com/inouye-lab/FedDG_Benchmark.

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geometry, mostly because of the absence of corresponding hyperbolic neural network layers. This makes it hard to use hyperbolic embeddings in downstream tasks. Here, we bridge this gap in a principled manner by combining the formalism of Möbius gyrovector spaces with the Riemannian geometry of the Poincaré model of hyperbolic spaces. As a result, we derive hyperbolic versions of important deep learning tools: multinomial logistic regression, feed-forward and recurrent neural networks such as gated recurrent units. This allows to embed sequential data and perform classification in the hyperbolic space. Empirically, we show that, even if hyperbolic optimization tools are limited, hyperbolic sentence embeddings either outperform or are on par with their Euclidean variants on textual entailment and noisy-prefix recognition tasks.

Recent unsupervised domain adaptation methods have utilized vicinal space between the source and target domains. However, the equilibrium collapse of labels, a problem where the source labels are dominant over the target labels in the predictions of vicinal instances, has never been addressed. In this paper, we propose an instance-wise minimax strategy that minimizes the entropy of high uncertainty instances in the vicinal space to tackle the stated problem. We divide the vicinal space into two subspaces through the solution of the minimax problem: contrastive space and consensus space. In the contrastive space, inter-domain discrepancy is mitigated by constraining instances to have contrastive views and labels, and the consensus space reduces the confusion between intra-domain categories. The effectiveness of our method is demonstrated on public benchmarks, including Office-31, Office-Home, and VisDA-C, achieving state-of-the-art performances. We further show that our method outperforms the current state-of-the-art methods on PACS, which indicates that our instance-wise approach works well for multi-source domain adaptation as well. Code is available at https://github.com/NaJaeMin92/CoVi.

Despite high semantic alignment, modern text-to-image (T2I) generative models still struggle to synthesize diverse images from a given prompt. This lack of diversity not only restricts user choice, but also risks amplifying societal biases. In this work, we enhance the T2I diversity through a geometric lens. Unlike most existing methods that rely primarily on entropy-based guidance to increase sample dissimilarity, we introduce Geometry-Aware Spherical Sampling (GASS) to enhance diversity by explicitly controlling both prompt-dependent and prompt-independent sources of variation. Specifically, we decompose the diversity measure in CLIP embeddings using two orthogonal directions: the text embedding, which captures semantic variation related to the prompt, and an identified orthogonal direction that captures prompt-independent variation (e.g., backgrounds). Based on this decomposition, GASS increases the geometric projection spread of generated image embeddings along both axes and guides the T2I sampling process via expanded predictions along the generation trajectory. Our experiments on different frozen T2I backbones (U-Net and DiT, diffusion and flow) and benchmarks demonstrate the effectiveness of disentangled diversity enhancement with minimal impact on image fidelity and semantic alignment.

Training transformer models requires substantial GPU compute and memory resources. In homogeneous clusters, distributed strategies allocate resources evenly, but this approach is inefficient for heterogeneous clusters, where GPUs differ in power and memory. As high-end GPUs are costly and limited in availability, heterogeneous clusters with diverse GPU types are becoming more common. Existing methods attempt to balance compute across GPUs based on capacity but often underutilize compute due to memory constraints. We present Cephalo, a system that optimizes compute and memory usage by decoupling compute distribution from training state assignment. Cephalo outperforms state-of-the-art methods by achieving significantly higher training throughput while supporting larger models and batch sizes.

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets which clearly show the superiority of the discrete latent space and obtain state of the art graph generative performance, making GLAD the first latent space graph generative model with competitive performance. Our source code is published at: https://github.com/v18nguye/GLAD.

SAM3D enables scalable, open-world 3D reconstruction from complex scenes, yet its deployment is hindered by prohibitive inference latency. In this work, we conduct the first systematic investigation into its inference dynamics, revealing that generic acceleration strategies are brittle in this context. We demonstrate that these failures stem from neglecting the pipeline's inherent multi-level heterogeneity: the kinematic distinctiveness between shape and layout, the intrinsic sparsity of texture refinement, and the spectral variance across geometries. To address this, we present Fast-SAM3D, a training-free framework that dynamically aligns computation with instantaneous generation complexity. Our approach integrates three heterogeneity-aware mechanisms: (1) Modality-Aware Step Caching to decouple structural evolution from sensitive layout updates; (2) Joint Spatiotemporal Token Carving to concentrate refinement on high-entropy regions; and (3) Spectral-Aware Token Aggregation to adapt decoding resolution. Extensive experiments demonstrate that Fast-SAM3D delivers up to 2.67times end-to-end speedup with negligible fidelity loss, establishing a new Pareto frontier for efficient single-view 3D generation. Our code is released in https://github.com/wlfeng0509/Fast-SAM3D.

In this work, we present a panoramic metric depth foundation model that generalizes across diverse scene distances. We explore a data-in-the-loop paradigm from the view of both data construction and framework design. We collect a large-scale dataset by combining public datasets, high-quality synthetic data from our UE5 simulator and text-to-image models, and real panoramic images from the web. To reduce domain gaps between indoor/outdoor and synthetic/real data, we introduce a three-stage pseudo-label curation pipeline to generate reliable ground truth for unlabeled images. For the model, we adopt DINOv3-Large as the backbone for its strong pre-trained generalization, and introduce a plug-and-play range mask head, sharpness-centric optimization, and geometry-centric optimization to improve robustness to varying distances and enforce geometric consistency across views. Experiments on multiple benchmarks (e.g., Stanford2D3D, Matterport3D, and Deep360) demonstrate strong performance and zero-shot generalization, with particularly robust and stable metric predictions in diverse real-world scenes. The project page can be found at: https://insta360-research-team.github.io/DAP_website/ {https://insta360-research-team.github.io/DAP\_website/}

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Real-world datasets follow an imbalanced distribution, which poses significant challenges in rare-category object detection. Recent studies tackle this problem by developing re-weighting and re-sampling methods, that utilise the class frequencies of the dataset. However, these techniques focus solely on the frequency statistics and ignore the distribution of the classes in image space, missing important information. In contrast to them, we propose FRActal CALibration (FRACAL): a novel post-calibration method for long-tailed object detection. FRACAL devises a logit adjustment method that utilises the fractal dimension to estimate how uniformly classes are distributed in image space. During inference, it uses the fractal dimension to inversely downweight the probabilities of uniformly spaced class predictions achieving balance in two axes: between frequent and rare categories, and between uniformly spaced and sparsely spaced classes. FRACAL is a post-processing method and it does not require any training, also it can be combined with many off-the-shelf models such as one-stage sigmoid detectors and two-stage instance segmentation models. FRACAL boosts the rare class performance by up to 8.6% and surpasses all previous methods on LVIS dataset, while showing good generalisation to other datasets such as COCO, V3Det and OpenImages. We provide the code at https://github.com/kostas1515/FRACAL.