Daily Papers

This technical white paper introduces the Interactive Agents Call Tree (IACT), a computational model designed to address the limitations of static, hard-coded agent workflows. Unlike traditional systems that require pre-defined graphs or specialized programming, IACT operates as a general-purpose autonomous system driven purely by user dialogue. Given a high-level objective, the system autonomously grows a dynamic, recursive agent topology incrementally tailored to the problem's structure. This allows it to scale its organizational complexity to match open-ended tasks. To mitigate the error propagation inherent in unidirectional function calls, IACT introduces interactional redundancy by replacing rigid invocations with bidirectional, stateful dialogues. This mechanism enables runtime error correction and ambiguity resolution. We describe the architecture, design principles, and practical lessons behind the production deployment of this model in the kragent.ai system, presenting qualitative evidence from real-world workflows rather than exhaustive benchmark results.

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely functional language with array operations. It is the first one to deliver a provably efficient, purely functional, and denotationally correct reverse-mode differentiation. We show that our transformation is semantically correct and verifies the cheap gradient principle. Inspired by PROPs and compilation to categories, we introduce a novel intermediate representation that we call 'unary form'. Our reverse-mode transformation is factored as a compilation scheme through this intermediate representation. We obtain provably efficient gradients by performing general partial evaluation optimizations after our reverse-mode transformation, as opposed to manually derived ones. For simple first-order programs, the obtained output programs resemble static-single-assignment (SSA) code. We emphasize the modularity of our approach and show how our language can easily be enriched with more optimized primitives, as required for some speed-ups in practice.

Large language models (LLMs) have recently shown tremendous promise in serving as the backbone to agentic systems, as demonstrated by their performance in multi-faceted, challenging benchmarks like SWE-Bench and Agent-Bench. However, to realize the true potential of LLMs as autonomous agents, they must learn to identify, call, and interact with external tools and application program interfaces (APIs) to complete complex tasks. These tasks together are termed function calling. Endowing LLMs with function calling abilities leads to a myriad of advantages, such as access to current and domain-specific information in databases and knowledge sources, and the ability to outsource tasks that can be reliably performed by tools, e.g., a Python interpreter or calculator. While there has been significant progress in function calling with LLMs, there is still a dearth of open models that perform on par with proprietary LLMs like GPT, Claude, and Gemini. Therefore, in this work, we introduce the GRANITE-20B-FUNCTIONCALLING model under an Apache 2.0 license. The model is trained using a multi-task training approach on seven fundamental tasks encompassed in function calling, those being Nested Function Calling, Function Chaining, Parallel Functions, Function Name Detection, Parameter-Value Pair Detection, Next-Best Function, and Response Generation. We present a comprehensive evaluation on multiple out-of-domain datasets comparing GRANITE-20B-FUNCTIONCALLING to more than 15 other best proprietary and open models. GRANITE-20B-FUNCTIONCALLING provides the best performance among all open models on the Berkeley Function Calling Leaderboard and fourth overall. As a result of the diverse tasks and datasets used for training our model, we show that GRANITE-20B-FUNCTIONCALLING has better generalizability on multiple tasks in seven different evaluation datasets.

Spiking Neural Networks (SNNs) promise energy-efficient vision, but applying them to RGB visual tracking remains difficult: Existing SNN tracking frameworks either do not fully align with spike-driven computation or do not fully leverage neurons' spatiotemporal dynamics, leading to a trade-off between efficiency and accuracy. To address this, we introduce SpikeTrack, a spike-driven framework for energy-efficient RGB object tracking. SpikeTrack employs a novel asymmetric design that uses asymmetric timestep expansion and unidirectional information flow, harnessing spatiotemporal dynamics while cutting computation. To ensure effective unidirectional information transfer between branches, we design a memory-retrieval module inspired by neural inference mechanisms. This module recurrently queries a compact memory initialized by the template to retrieve target cues and sharpen target perception over time. Extensive experiments demonstrate that SpikeTrack achieves the state-of-the-art among SNN-based trackers and remains competitive with advanced ANN trackers. Notably, it surpasses TransT on LaSOT dataset while consuming only 1/26 of its energy. To our knowledge, SpikeTrack is the first spike-driven framework to make RGB tracking both accurate and energy efficient. The code and models are available at https://github.com/faicaiwawa/SpikeTrack.

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at https://github.com/sail-sg/autofd .

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

While enabling large language models to implement function calling (known as APIs) can greatly enhance the performance of LLMs, function calling is still a challenging task due to the complicated relations between different APIs, especially in a context-learning setting without fine-tuning. This paper proposes a simple yet controllable target-driven approach called Reverse Chain to empower LLMs with capabilities to use external APIs with only prompts. Given that most open-source LLMs have limited tool-use or tool-plan capabilities, LLMs in Reverse Chain are only employed to implement simple tasks, e.g., API selection and argument completion, and a generic rule is employed to implement a controllable multiple functions calling. In this generic rule, after selecting a final API to handle a given task via LLMs, we first ask LLMs to fill the required arguments from user query and context. Some missing arguments could be further completed by letting LLMs select another API based on API description before asking user. This process continues until a given task is completed. Extensive numerical experiments indicate an impressive capability of Reverse Chain on implementing multiple function calling. Interestingly enough, the experiments also reveal that tool-use capabilities of the existing LLMs, e.g., ChatGPT, can be greatly improved via Reverse Chain.

Intelligent vehicle cockpits present unique challenges for API Agents, requiring coordination across tightly-coupled subsystems that exceed typical task environments' complexity. Traditional Function Calling (FC) approaches operate statelessly, requiring multiple exploratory calls to build environmental awareness before execution, leading to inefficiency and limited error recovery. We introduce VehicleWorld, the first comprehensive environment for the automotive domain, featuring 30 modules, 250 APIs, and 680 properties with fully executable implementations that provide real-time state information during agent execution. This environment enables precise evaluation of vehicle agent behaviors across diverse, challenging scenarios. Through systematic analysis, we discovered that direct state prediction outperforms function calling for environmental control. Building on this insight, we propose State-based Function Call (SFC), a novel approach that maintains explicit system state awareness and implements direct state transitions to achieve target conditions. Experimental results demonstrate that SFC significantly outperforms traditional FC approaches, achieving superior execution accuracy and reduced latency. We have made all implementation code publicly available on Github https://github.com/OpenMOSS/VehicleWorld.

Large Language Models (LLMs) have exhibited significant potential in performing diverse tasks, including the ability to call functions or use external tools to enhance their performance. While current research on function calling by LLMs primarily focuses on single-turn interactions, this paper addresses the overlooked necessity for LLMs to engage in multi-turn function calling--critical for handling compositional, real-world queries that require planning with functions but not only use functions. To facilitate this, we introduce an approach, BUTTON, which generates synthetic compositional instruction tuning data via bottom-up instruction construction and top-down trajectory generation. In the bottom-up phase, we generate simple atomic tasks based on real-world scenarios and build compositional tasks using heuristic strategies based on atomic tasks. Corresponding functions are then developed for these compositional tasks. The top-down phase features a multi-agent environment where interactions among simulated humans, assistants, and tools are utilized to gather multi-turn function calling trajectories. This approach ensures task compositionality and allows for effective function and trajectory generation by examining atomic tasks within compositional tasks. We produce a dataset BUTTONInstruct comprising 8k data points and demonstrate its effectiveness through extensive experiments across various LLMs.

Large language models have demonstrated impressive value in performing as autonomous agents when equipped with external tools and API calls. Nonetheless, effectively harnessing their potential for executing complex tasks crucially relies on enhancements in their function calling capabilities. This paper identifies a critical gap in existing function calling models, where performance varies significantly across benchmarks, often due to being misled by specific naming conventions. To address such an issue, we introduce Hammer, a novel family of foundation models specifically engineered for on-device function calling. Hammer employs an augmented dataset that enhances models' sensitivity to irrelevant functions and incorporates function masking techniques to minimize misleading. Our empirical evaluations reveal that Hammer not only outperforms larger models but also demonstrates robust generalization across diverse benchmarks, achieving sota results. Our open source contributions include a specialized dataset for irrelevance detection, a tuning framework for enhanced generalization, and the Hammer models, establishing a new standard for function calling performance.

Learning depth from spherical panoramas is becoming a popular research topic because a panorama has a full field-of-view of the environment and provides a relatively complete description of a scene. However, applying well-studied CNNs for perspective images to the standard representation of spherical panoramas, i.e., the equirectangular projection, is suboptimal, as it becomes distorted towards the poles. Another representation is the cubemap projection, which is distortion-free but discontinued on edges and limited in the field-of-view. This paper introduces a new framework to fuse features from the two projections, unidirectionally feeding the cubemap features to the equirectangular features only at the decoding stage. Unlike the recent bidirectional fusion approach operating at both the encoding and decoding stages, our fusion scheme is much more efficient. Besides, we also designed a more effective fusion module for our fusion scheme. Experiments verify the effectiveness of our proposed fusion strategy and module, and our model achieves state-of-the-art performance on four popular datasets. Additional experiments show that our model also has the advantages of model complexity and generalization capability.The code is available at https://github.com/alibaba/UniFuse-Unidirectional-Fusion.

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM usually requires hundreds of model evaluations, which is computationally expensive. Despite recent progress in designing high-order solvers for DPMs, there still exists room for further speedup, especially in extremely few steps (e.g., 5~10 steps). Inspired by the predictor-corrector for ODE solvers, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256times256 (conditional) with only 10 function evaluations. Code is available at https://github.com/wl-zhao/UniPC

Existing function-calling benchmarks focus on single-turn interactions. However, they overlook the complexity of real-world scenarios. To quantify how existing benchmarks address practical applications, we introduce DICE-SCORE, a metric that evaluates the dispersion of tool-related information such as function name and parameter values throughout the dialogue. Analyzing existing benchmarks through DICE-SCORE reveals notably low scores, highlighting the need for more realistic scenarios. To address this gap, we present DICE-BENCH, a framework that constructs practical function-calling datasets by synthesizing conversations through a tool graph that maintains dependencies across rounds and a multi-agent system with distinct personas to enhance dialogue naturalness. The final dataset comprises 1,607 high-DICE-SCORE instances. Our experiments on 19 LLMs with DICE-BENCH show that significant advances are still required before such models can be deployed effectively in real-world settings. Our code and data are all publicly available: https://snuhcc.github.io/DICE-Bench/.

Function calling is a core capability of large language models, essential for AI agents. Existing benchmarks such as the Berkeley Function Calling Leaderboard (BFCL), tau^2-Bench (arXiv:2506.07982), and ACEBench (arXiv:2501.12851) evaluate argument correctness but do not test adherence to format instructions embedded in parameter descriptions, such as enclosing values in double quotes or using ISO date formats. We introduce IFEval-FC, a benchmark inspired by IFEval (arXiv:2311.07911) that assesses precise instruction following in function calling. IFEval-FC encodes verifiable formats directly within JSON schema descriptions, for example specifying that a value must not contain punctuation. It includes 750 test cases, each consisting of a function with an embedded format for one of its input parameters and a corresponding user query. Evaluation is fully algorithmic, ensuring objectivity, reproducibility, and scalability. Our results show that even state-of-the-art proprietary models, including GPT-5 and Claude 4.1 Opus, frequently fail to follow basic formatting rules, highlighting a practical limitation for real-world agent systems. The complete codebase and data are publicly available at https://github.com/Skripkon/IFEval-FC.

This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC derives from the lambda-calculus by taking the standard operational perspective of a call-by-name stack machine as primary, and introducing two natural generalizations. One, "locations", introduces multiple stacks, which each may represent an effect and so enable effect operators to be encoded into the abstraction and application constructs of the calculus. The second, "sequencing", is known from kappa-calculus and concatenative programming languages, and introduces the imperative notions of "skip" and "sequence". This enables the encoding of reduction strategies, including call-by-value lambda-calculus and monadic constructs. The encoding of effects into generalized abstraction and application means that standard results from the lambda-calculus may carry over to effects. The main result is confluence, which is possible because encoded effects reduce algebraically rather than operationally. Reduction generates the familiar algebraic laws for state, and unlike in the monadic setting, reader/writer effects combine seamlessly. A system of simple types confers termination of the machine.

We introduce a method to generate temporally coherent human animation from a single image, a video, or a random noise. This problem has been formulated as modeling of an auto-regressive generation, i.e., to regress past frames to decode future frames. However, such unidirectional generation is highly prone to motion drifting over time, generating unrealistic human animation with significant artifacts such as appearance distortion. We claim that bidirectional temporal modeling enforces temporal coherence on a generative network by largely suppressing the motion ambiguity of human appearance. To prove our claim, we design a novel human animation framework using a denoising diffusion model: a neural network learns to generate the image of a person by denoising temporal Gaussian noises whose intermediate results are cross-conditioned bidirectionally between consecutive frames. In the experiments, our method demonstrates strong performance compared to existing unidirectional approaches with realistic temporal coherence.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Diffusion models have shown remarkable performance in image generation in recent years. However, due to a quadratic increase in memory during generating ultra-high-resolution images (e.g. 4096*4096), the resolution of generated images is often limited to 1024*1024. In this work. we propose a unidirectional block attention mechanism that can adaptively adjust the memory overhead during the inference process and handle global dependencies. Building on this module, we adopt the DiT structure for upsampling and develop an infinite super-resolution model capable of upsampling images of various shapes and resolutions. Comprehensive experiments show that our model achieves SOTA performance in generating ultra-high-resolution images in both machine and human evaluation. Compared to commonly used UNet structures, our model can save more than 5x memory when generating 4096*4096 images. The project URL is https://github.com/THUDM/Inf-DiT.

LLM-based function calling enables intelligent agents to interact with external tools and environments, yet autoregressive decoding imposes a fundamental latency bottleneck that limits real-time applications such as embodied intelligence, game AI, and interactive avatars (e.g., 10 Hz control frequency). We observe that function calling differs fundamentally from free-form text generation: structured outputs exhibit substantial token redundancy (delimiters, parameter names), and arguments exhibit weak causal dependencies. Crucially, these two properties must be exploited jointly to achieve real-time performance. We present SimpleTool, which introduces special tokens that serve a dual role: compressing low-entropy tokens (4-6x reduction) while acting as mode selectors that enable independent parallel generation of function name and arguments. This synergistic design achieves 3-6x end-to-end speedup (up to 9.6x) with only +8.2% parallelization overhead. Experiments on five benchmarks across Qwen-series models (0.5B-14B) demonstrate substantial speedup while maintaining competitive or improved accuracy. On Mobile Actions, ST-Qwen-0.5B outperforms Google's FunctionGemma in both accuracy and latency consistency. With quantization on consumer-grade GPU, SimpleTool achieves 61.2ms P50 latency, enabling 16 Hz real-time control at 4B model scale, bridging the gap between LLM function calling and latency-critical real-world deployment.

Function calling (FC) empowers large language models (LLMs) and autonomous agents to interface with external tools, a critical capability for solving complex, real-world problems. As this ability becomes increasingly central to advanced AI systems, the need for high-quality, multi-turn training data to develop and refine it cannot be overstated. Existing data synthesis methods, such as random environment sampling or multi-agent role-playing, are not powerful enough to generate high-quality data in real-world environments. Practical challenges come in three folds: targeted model training, isolation of tool architecture, and multi-turn logical dependency. To address these structural deficiencies, we present FunReason-MT, a novel data synthesis framework for real-world multi-turn tool use. FunReason-MT resolves the complexity barrier in multi-turn FC data by employing 1) Environment-API Graph Interactions to gather varied high-quality trajectories, 2) Advanced Tool-Query Synthesis to simplify hard query construction, and 3) Guided Iterative Chain for sophisticated CoT generation. Evaluations on Berkeley Function-Calling Leaderboard (BFCLv3) demonstrate the power of our framework: a 4B model built upon FunReason-MT generated data achieves state-of-the-art performance among comparable-sized models, outperforming most close-source models. Further performance improvements on BFCLv4 confirm that FunReason-MT provides a reliable and robust source for agentic learning.

We introduce UniGraspTransformer, a universal Transformer-based network for dexterous robotic grasping that simplifies training while enhancing scalability and performance. Unlike prior methods such as UniDexGrasp++, which require complex, multi-step training pipelines, UniGraspTransformer follows a streamlined process: first, dedicated policy networks are trained for individual objects using reinforcement learning to generate successful grasp trajectories; then, these trajectories are distilled into a single, universal network. Our approach enables UniGraspTransformer to scale effectively, incorporating up to 12 self-attention blocks for handling thousands of objects with diverse poses. Additionally, it generalizes well to both idealized and real-world inputs, evaluated in state-based and vision-based settings. Notably, UniGraspTransformer generates a broader range of grasping poses for objects in various shapes and orientations, resulting in more diverse grasp strategies. Experimental results demonstrate significant improvements over state-of-the-art, UniDexGrasp++, across various object categories, achieving success rate gains of 3.5%, 7.7%, and 10.1% on seen objects, unseen objects within seen categories, and completely unseen objects, respectively, in the vision-based setting. Project page: https://dexhand.github.io/UniGraspTransformer.

We introduce UniReal, a unified framework designed to address various image generation and editing tasks. Existing solutions often vary by tasks, yet share fundamental principles: preserving consistency between inputs and outputs while capturing visual variations. Inspired by recent video generation models that effectively balance consistency and variation across frames, we propose a unifying approach that treats image-level tasks as discontinuous video generation. Specifically, we treat varying numbers of input and output images as frames, enabling seamless support for tasks such as image generation, editing, customization, composition, etc. Although designed for image-level tasks, we leverage videos as a scalable source for universal supervision. UniReal learns world dynamics from large-scale videos, demonstrating advanced capability in handling shadows, reflections, pose variation, and object interaction, while also exhibiting emergent capability for novel applications.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

Despite recent progress made by large language models in code generation, they still struggle with programs that meet complex requirements. Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program. Yet, planning deep-inside requirements in advance can be challenging, and the tests need to be accurate to accomplish self-improvement. To this end, we propose FunCoder, a code generation framework incorporating the divide-and-conquer strategy with functional consensus. Specifically, FunCoder recursively branches off sub-functions as smaller goals during code generation, represented by a tree hierarchy. These sub-functions are then composited to attain more complex objectives. Additionally, we designate functions via a consensus formed by identifying similarities in program behavior, mitigating error propagation. FunCoder outperforms state-of-the-art methods by +9.8% on average in HumanEval, MBPP, xCodeEval and MATH with GPT-3.5 and GPT-4. Moreover, our method demonstrates superiority on smaller models: With FunCoder, StableCode-3b surpasses GPT-3.5 by +18.6% and achieves 97.7% of GPT-4's performance on HumanEval. Further analysis reveals that our proposed dynamic function decomposition is capable of handling complex requirements, and the functional consensus prevails over self-testing in correctness evaluation.

Hand motion plays a central role in human interaction, yet modeling realistic 4D hand motion (i.e., 3D hand pose sequences over time) remains challenging. Research in this area is typically divided into two tasks: (1) Estimation approaches reconstruct precise motion from visual observations, but often fail under hand occlusion or absence; (2) Generation approaches focus on synthesizing hand poses by exploiting generative priors under multi-modal structured inputs and infilling motion from incomplete sequences. However, this separation not only limits the effective use of heterogeneous condition signals that frequently arise in practice, but also prevents knowledge transfer between the two tasks. We present UniHand, a unified diffusion-based framework that formulates both estimation and generation as conditional motion synthesis. UniHand integrates heterogeneous inputs by embedding structured signals into a shared latent space through a joint variational autoencoder, which aligns conditions such as MANO parameters and 2D skeletons. Visual observations are encoded with a frozen vision backbone, while a dedicated hand perceptron extracts hand-specific cues directly from image features, removing the need for complex detection and cropping pipelines. A latent diffusion model then synthesizes consistent motion sequences from these diverse conditions. Extensive experiments across multiple benchmarks demonstrate that UniHand delivers robust and accurate hand motion modeling, maintaining performance under severe occlusions and temporally incomplete inputs.

This paper proposes a unified diffusion framework (dubbed UniDiffuser) to fit all distributions relevant to a set of multi-modal data in one model. Our key insight is -- learning diffusion models for marginal, conditional, and joint distributions can be unified as predicting the noise in the perturbed data, where the perturbation levels (i.e. timesteps) can be different for different modalities. Inspired by the unified view, UniDiffuser learns all distributions simultaneously with a minimal modification to the original diffusion model -- perturbs data in all modalities instead of a single modality, inputs individual timesteps in different modalities, and predicts the noise of all modalities instead of a single modality. UniDiffuser is parameterized by a transformer for diffusion models to handle input types of different modalities. Implemented on large-scale paired image-text data, UniDiffuser is able to perform image, text, text-to-image, image-to-text, and image-text pair generation by setting proper timesteps without additional overhead. In particular, UniDiffuser is able to produce perceptually realistic samples in all tasks and its quantitative results (e.g., the FID and CLIP score) are not only superior to existing general-purpose models but also comparable to the bespoken models (e.g., Stable Diffusion and DALL-E 2) in representative tasks (e.g., text-to-image generation).

Function-calling agents -- large language models that invoke tools and APIs -- require high-quality, domain-specific training data spanning executable environments, backing databases, and diverse multi-turn trajectories. We introduce EigenData, an integrated, self-evolving platform that automates the full data lifecycle through a multi-agent architecture. A top-level orchestrator, EigenCore, coordinates three specialized sub-systems: DatabaseAgent for realistic domain database construction, CodingAgent for verified executable environment generation with iterative test-debug loops, and DataAgent for multi-turn trajectory synthesis with self-evolving prompt optimization. Cross-component feedback ensures consistency across all artifacts. We apply EigenData to audit and repair the Berkeley Function-Calling Leaderboard (BFCL-V3), identifying systematic errors in function schemas, implementations, and reference trajectories, automatically correcting them through coordinated schema refinement, code-level bug fixes, and trajectory modification, and introducing an outcome-aware evaluation protocol that assesses task success via database-state correctness rather than turn-level trajectory matching. We demonstrate that the repaired benchmark, coupled with outcome-aware metrics, produces model rankings substantially better correlated with human judgments of functional correctness.

Large language models (LLMs) use function calls to interface with external tools and data source. However, the current approach to LLM function calling is inherently synchronous, where each call blocks LLM inference, limiting LLM operation and concurrent function execution. In this work, we propose AsyncLM, a system for asynchronous LLM function calling. AsyncLM improves LLM's operational efficiency by enabling LLMs to generate and execute function calls concurrently. Instead of waiting for each call's completion, AsyncLM introduces an interrupt mechanism to asynchronously notify the LLM in-flight when function calls return. We design an in-context protocol for function calls and interrupts, provide fine-tuning strategy to adapt LLMs to the interrupt semantics, and implement these mechanisms efficiently on LLM inference process. We demonstrate that AsyncLM can reduce end-to-end task completion latency from 1.6x-5.4x compared to synchronous function calling on a set of benchmark tasks in the Berkeley function calling leaderboard (BFCL). Furthermore, we discuss how interrupt mechanisms can be extended to enable novel human-LLM or LLM-LLM interactions.

Large language models (LLMs) have exhibited the ability to effectively utilize external tools to address user queries. However, their performance may be limited in complex, multi-turn interactions involving users and multiple tools. To address this, we propose Magnet, a principled framework for synthesizing high-quality training trajectories to enhance the function calling capability of large language model agents in multi-turn conversations with humans. The framework is based on automatic and iterative translations from a function signature path to a sequence of queries and executable function calls. We model the complicated function interactions in multi-turn cases with graph and design novel node operations to build reliable signature paths. Motivated by context distillation, when guiding the generation of positive and negative trajectories using a teacher model, we provide reference function call sequences as positive hints in context and contrastive, incorrect function calls as negative hints. Experiments show that training with the positive trajectories with supervised fine-tuning and preference optimization against negative trajectories, our 14B model, Magnet-14B-mDPO, obtains 68.01 on BFCL-v3 and 73.30 on ToolQuery, surpassing the performance of the teacher model Gemini-1.5-pro-002 by a large margin in function calling.

Sparse-view 3D modeling represents a fundamental tension between reconstruction fidelity and generative plausibility. While feed-forward reconstruction excels in efficiency and input alignment, it often lacks the global priors needed for structural completeness. Conversely, diffusion-based generation provides rich geometric details but struggles with multi-view consistency. We present UniRecGen, a unified framework that integrates these two paradigms into a single cooperative system. To overcome inherent conflicts in coordinate spaces, 3D representations, and training objectives, we align both models within a shared canonical space. We employ disentangled cooperative learning, which maintains stable training while enabling seamless collaboration during inference. Specifically, the reconstruction module is adapted to provide canonical geometric anchors, while the diffusion generator leverages latent-augmented conditioning to refine and complete the geometric structure. Experimental results demonstrate that UniRecGen achieves superior fidelity and robustness, outperforming existing methods in creating complete and consistent 3D models from sparse observations.

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a monoidal category. More recently, the notion of a learner has been proposed: these provide a compositional way of modelling supervised learning algorithms, and again form the morphisms of a monoidal category. In this paper, we show that the two concepts are tightly linked. We show both that there is a faithful, identity-on-objects symmetric monoidal functor embedding a category of asymmetric lenses into the category of learners, and furthermore there is such a functor embedding the category of learners into a category of symmetric lenses.

Function-calling language models are essential for agentic AI systems that translate natural language into executable structured actions, yet existing models exhibit severe structural instability when applied to Arabic. We present AISA-AR-FunctionCall, a production-oriented Arabic function-calling framework built on a 270M-parameter FunctionGemma backbone and trained through systematic dataset auditing, schema repair, tool-aware prompt restructuring, and full-parameter supervised fine-tuning. On a held-out test set, fine-tuning reduces parse failures from 87\% to below 1\%, improves function name accuracy by more than eightfold, and substantially enhances argument alignment across dialects and domains. Error analysis reveals a transition from structural collapse to semantic misalignment, suggesting that serialization stability and decision-level reasoning are separable challenges. We further explore a reasoning-augmented LoRA variant that introduces explicit intermediate reasoning prior to tool invocation. All datasets and models are publicly released under the AISA framework.

Function calling capabilities are crucial for deploying Large Language Models in real-world applications, yet current training approaches fail to develop robust reasoning strategies. Supervised fine-tuning produces models that rely on superficial pattern matching, while standard reinforcement learning methods struggle with the complex action space of structured function calls. We present a novel reinforcement learning framework designed to enhance group relative policy optimization through strategic entropy based exploration specifically tailored for function calling tasks. Our approach addresses three critical challenges in function calling: insufficient exploration during policy learning, lack of structured reasoning in chain-of-thought generation, and inadequate verification of parameter extraction. Our two-stage data preparation pipeline ensures high-quality training samples through iterative LLM evaluation and abstract syntax tree validation. Extensive experiments on the Berkeley Function Calling Leaderboard demonstrate that this framework achieves state-of-the-art performance among open-source models with 86.02\% overall accuracy, outperforming standard GRPO by up to 6\% on complex multi-function scenarios. Notably, our method shows particularly strong improvements on code-pretrained models, suggesting that structured language generation capabilities provide an advantageous starting point for reinforcement learning in function calling tasks. We will release all the code, models and dataset to benefit the community.

Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to O(d^{k}) scaling of the derivative tensor size and the O(2^{k-1}L) scaling in the computation graph, where d is the dimension of the domain, L is the number of ops in the forward computation graph, and k is the derivative order. In previous works, the polynomial scaling in d was addressed by amortizing the computation over the optimization process via randomization. Separately, the exponential scaling in k for univariate functions (d=1) was addressed with high-order auto-differentiation (AD). In this work, we show how to efficiently perform arbitrary contraction of the derivative tensor of arbitrary order for multivariate functions, by properly constructing the input tangents to univariate high-order AD, which can be used to efficiently randomize any differential operator. When applied to Physics-Informed Neural Networks (PINNs), our method provides >1000times speed-up and >30times memory reduction over randomization with first-order AD, and we can now solve 1-million-dimensional PDEs in 8 minutes on a single NVIDIA A100 GPU. This work opens the possibility of using high-order differential operators in large-scale problems.

This paper tackles optimization problems whose objective and constraints involve a trained Neural Network (NN), where the goal is to maximize f(Phi(x)) subject to c(Phi(x)) leq 0, with f smooth, c general and non-stringent, and Phi an already trained and possibly nonwhite-box NN. We address two challenges regarding this problem: identifying ascent directions for local search, and ensuring reliable convergence towards relevant local solutions. To this end, we re-purpose the notion of directional NN attacks as efficient optimization subroutines, since directional NN attacks use the neural structure of Phi to compute perturbations of x that steer Phi(x) in prescribed directions. Precisely, we develop an attack operator that computes attacks of Phi at any x along the direction nabla f(Phi(x)). Then, we propose a hybrid algorithm combining the attack operator with derivative-free optimization (DFO) techniques, designed for numerical reliability by remaining oblivious to the structure of the problem. We consider the cDSM algorithm, which offers asymptotic guarantees to converge to a local solution under mild assumptions on the problem. The resulting method alternates between attack-based steps for heuristic yet fast local intensification and cDSM steps for certified convergence and numerical reliability. Experiments on three problems show that this hybrid approach consistently outperforms standard DFO baselines.

Typical inverse rendering methods focus on learning implicit neural scene representations by modeling the geometry, materials and illumination separately, which entails significant computations for optimization. In this work we design a Unified Voxelization framework for explicit learning of scene representations, dubbed UniVoxel, which allows for efficient modeling of the geometry, materials and illumination jointly, thereby accelerating the inverse rendering significantly. To be specific, we propose to encode a scene into a latent volumetric representation, based on which the geometry, materials and illumination can be readily learned via lightweight neural networks in a unified manner. Particularly, an essential design of UniVoxel is that we leverage local Spherical Gaussians to represent the incident light radiance, which enables the seamless integration of modeling illumination into the unified voxelization framework. Such novel design enables our UniVoxel to model the joint effects of direct lighting, indirect lighting and light visibility efficiently without expensive multi-bounce ray tracing. Extensive experiments on multiple benchmarks covering diverse scenes demonstrate that UniVoxel boosts the optimization efficiency significantly compared to other methods, reducing the per-scene training time from hours to 18 minutes, while achieving favorable reconstruction quality. Code is available at https://github.com/freemantom/UniVoxel.

Large Language Models (LLMs) have shown remarkable results on various complex reasoning benchmarks. The reasoning capabilities of LLMs enable them to execute function calls, using user-provided functions to overcome their inherent limitations, such as knowledge cutoffs, poor arithmetic skills, or lack of access to private data. This development has expanded LLMs' scope to include multi-function calling, where LLMs are equipped with a variety of functions and select the proper functions based on the context. Multi-function calling abilities of LLMs have catalyzed LLM-based software development, allowing them to tackle more complex problems. However, current methods for multi-function calling often require sequential reasoning and acting for each function which can result in high latency, cost, and sometimes inaccurate behavior. To address this, we introduce LLMCompiler, which executes functions in parallel to efficiently orchestrate multi-function calling. Drawing from the principles of classical compilers, LLMCompiler streamlines parallel function calling with three components: (i) an LLM Planner, formulating execution strategies and dependencies; (ii) a Task Fetching Unit, dispatching function calling tasks; and (iii) an Executor, executing these tasks in parallel. LLMCompiler automatically computes an optimized orchestration for the function calls and can be used with open-source models such as LLaMA-2. We have benchmarked LLMCompiler on a range of tasks including cases with non-trivial inter-dependency between function calls, as well as cases that require dynamic replanning based on intermediate results. We observe consistent latency speedup of up to 3.7x, cost savings of up to 6.7x, and accuracy improvement of up to ~9% as compared to ReAct. Additionally, LLMCompiler achieves up to 1.35x latency gain over OpenAI's recent parallel function calling, while achieving similar accuracy.

Enhancing large language models (LLMs) with real-time APIs can help generate more accurate and up-to-date responses. However, evaluating the function calling abilities of LLMs in real-world scenarios remains under-explored due to the complexity of data collection and evaluation. In this work, we introduce ComplexFuncBench, a benchmark for complex function calling across five real-world scenarios. Compared to existing benchmarks, ComplexFuncBench encompasses multi-step and constrained function calling, which requires long-parameter filing, parameter value reasoning, and 128k long context. Additionally, we propose an automatic framework, ComplexEval, for quantitatively evaluating complex function calling tasks. Through comprehensive experiments, we demonstrate the deficiencies of state-of-the-art LLMs in function calling and suggest future directions for optimizing these capabilities. The data and code are available at https://github.com/THUDM/ComplexFuncBench.

Dexterous manipulation remains challenging due to the cost of collecting real-robot teleoperation data, the heterogeneity of hand embodiments, and the high dimensionality of control. We present UniDex, a robot foundation suite that couples a large-scale robot-centric dataset with a unified vision-language-action (VLA) policy and a practical human-data capture setup for universal dexterous hand control. First, we construct UniDex-Dataset, a robot-centric dataset over 50K trajectories across eight dexterous hands (6--24 DoFs), derived from egocentric human video datasets. To transform human data into robot-executable trajectories, we employ a human-in-the-loop retargeting procedure to align fingertip trajectories while preserving plausible hand-object contacts, and we operate on explicit 3D pointclouds with human hands masked to narrow kinematic and visual gaps. Second, we introduce the Function-Actuator-Aligned Space (FAAS), a unified action space that maps functionally similar actuators to shared coordinates, enabling cross-hand transfer. Leveraging FAAS as the action parameterization, we train UniDex-VLA, a 3D VLA policy pretrained on UniDex-Dataset and finetuned with task demonstrations. In addition, we build UniDex-Cap, a simple portable capture setup that records synchronized RGB-D streams and human hand poses and converts them into robot-executable trajectories to enable human-robot data co-training that reduces reliance on costly robot demonstrations. On challenging tool-use tasks across two different hands, UniDex-VLA achieves 81% average task progress and outperforms prior VLA baselines by a large margin, while exhibiting strong spatial, object, and zero-shot cross-hand generalization. Together, UniDex-Dataset, UniDex-VLA, and UniDex-Cap provide a scalable foundation suite for universal dexterous manipulation.

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Throughout, we show how the analysis extends to AD methods for computing higher order derivatives using a Taylor approximation.

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

Database systems incorporate an ever-growing number of functions in their kernels (a.k.a., database native functions) for scenarios like new application support and business migration. This growth causes an urgent demand for automatic database native function synthesis. While recent advances in LLM-based code generation (e.g., Claude Code) show promise, they are too generic for database-specific development. They often hallucinate or overlook critical context because database function synthesis is inherently complex and error-prone, where synthesizing a single function may involve registering multiple function units, linking internal references, and implementing logic correctly. To this end, we propose DBCooker, an LLM-based system for automatically synthesizing database native functions. It consists of three components. First, the function characterization module aggregates multi-source declarations, identifies function units that require specialized coding, and traces cross-unit dependencies. Second, we design operations to address the main synthesis challenges: (1) a pseudo-code-based coding plan generator that constructs structured implementation skeletons by identifying key elements such as reusable referenced functions; (2) a hybrid fill-in-the-blank model guided by probabilistic priors and component awareness to integrate core logic with reusable routines; and (3) three-level progressive validation, including syntax checking, standards compliance, and LLM-guided semantic verification. Finally, an adaptive orchestration strategy unifies these operations with existing tools and dynamically sequences them via the orchestration history of similar functions. Results show that DBCooker outperforms other methods on SQLite, PostgreSQL, and DuckDB (34.55% higher accuracy on average), and can synthesize new functions absent in the latest SQLite (v3.50).

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

We study distributionally robust expected values under optimal transport distance with a quadratic cost function. In general the duality method, for this computation for the payoff function f, requires the computation of the λc-transform f^{λc}. We show that under the quadratic cost function there exists an intuitive and easily implementable representation of f^{λc}, if f is convex and piecewise linear. We apply this to the robust expected shortfall under the risk-neutral measure of an unhedged call option, from the point of view of the writer, as well as that of a portfolio mixing underlying shares with a call and a put option.

The reference-based object segmentation tasks, namely referring image segmentation (RIS), few-shot image segmentation (FSS), referring video object segmentation (RVOS), and video object segmentation (VOS), aim to segment a specific object by utilizing either language or annotated masks as references. Despite significant progress in each respective field, current methods are task-specifically designed and developed in different directions, which hinders the activation of multi-task capabilities for these tasks. In this work, we end the current fragmented situation and propose UniRef++ to unify the four reference-based object segmentation tasks with a single architecture. At the heart of our approach is the proposed UniFusion module which performs multiway-fusion for handling different tasks with respect to their specified references. And a unified Transformer architecture is then adopted for achieving instance-level segmentation. With the unified designs, UniRef++ can be jointly trained on a broad range of benchmarks and can flexibly complete multiple tasks at run-time by specifying the corresponding references. We evaluate our unified models on various benchmarks. Extensive experimental results indicate that our proposed UniRef++ achieves state-of-the-art performance on RIS and RVOS, and performs competitively on FSS and VOS with a parameter-shared network. Moreover, we showcase that the proposed UniFusion module could be easily incorporated into the current advanced foundation model SAM and obtain satisfactory results with parameter-efficient finetuning. Codes and models are available at https://github.com/FoundationVision/UniRef.

Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the cost of restricting the functional forms. This poses a question on their representation power: are CF-INNs universal approximators for invertible functions? Without a universality, there could be a well-behaved invertible transformation that the CF-INN can never approximate, hence it would render the model class unreliable. We answer this question by showing a convenient criterion: a CF-INN is universal if its layers contain affine coupling and invertible linear functions as special cases. As its corollary, we can affirmatively resolve a previously unsolved problem: whether normalizing flow models based on affine coupling can be universal distributional approximators. In the course of proving the universality, we prove a general theorem to show the equivalence of the universality for certain diffeomorphism classes, a theoretical insight that is of interest by itself.

The integration of large language models (LLMs) with function calling has emerged as a crucial capability for enhancing their practical utility in real-world applications. However, effectively combining reasoning processes with accurate function execution remains a significant challenge. Traditional training approaches often struggle to balance the detailed reasoning steps with the precision of function calls, leading to suboptimal performance. To address these limitations, we introduce FunReason, a novel framework that enhances LLMs' function calling capabilities through an automated data refinement strategy and a Self-Refinement Multiscale Loss (SRML) approach. FunReason leverages LLMs' natural reasoning abilities to generate high-quality training examples, focusing on query parseability, reasoning coherence, and function call precision. The SRML approach dynamically balances the contribution of reasoning processes and function call accuracy during training, addressing the inherent trade-off between these two critical aspects. FunReason achieves performance comparable to GPT-4o while effectively mitigating catastrophic forgetting during fine-tuning. FunReason provides a comprehensive solution for enhancing LLMs' function calling capabilities by introducing a balanced training methodology and a data refinement pipeline. For code and dataset, please refer to our repository at GitHub https://github.com/BingguangHao/FunReason

Deploying massive diffusion models for real-time, infinite-duration, audio-driven avatar generation presents a significant engineering challenge, primarily due to the conflict between computational load and strict latency constraints. Existing approaches often compromise visual fidelity by enforcing strictly unidirectional attention mechanisms or reducing model capacity. To address this problem, we introduce SoulX-FlashTalk, a 14B-parameter framework optimized for high-fidelity real-time streaming. Diverging from conventional unidirectional paradigms, we use a Self-correcting Bidirectional Distillation strategy that retains bidirectional attention within video chunks. This design preserves critical spatiotemporal correlations, significantly enhancing motion coherence and visual detail. To ensure stability during infinite generation, we incorporate a Multi-step Retrospective Self-Correction Mechanism, enabling the model to autonomously recover from accumulated errors and preventing collapse. Furthermore, we engineered a full-stack inference acceleration suite incorporating hybrid sequence parallelism, Parallel VAE, and kernel-level optimizations. Extensive evaluations confirm that SoulX-FlashTalk is the first 14B-scale system to achieve a sub-second start-up latency (0.87s) while reaching a real-time throughput of 32 FPS, setting a new standard for high-fidelity interactive digital human synthesis.

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

In this paper, we unify more than 10 existing one-step diffusion distillation approaches, such as Diff-Instruct, DMD, SIM, SiD, f-distill, etc, inside a theory-driven framework which we name the \emph{Uni-Instruct}. Uni-Instruct is motivated by our proposed diffusion expansion theory of the f-divergence family. Then we introduce key theories that overcome the intractability issue of the original expanded f-divergence, resulting in an equivalent yet tractable loss that effectively trains one-step diffusion models by minimizing the expanded f-divergence family. The novel unification introduced by Uni-Instruct not only offers new theoretical contributions that help understand existing approaches from a high-level perspective but also leads to state-of-the-art one-step diffusion generation performances. On the CIFAR10 generation benchmark, Uni-Instruct achieves record-breaking Frechet Inception Distance (FID) values of \emph{1.46} for unconditional generation and \emph{1.38} for conditional generation. On the ImageNet-64times 64 generation benchmark, Uni-Instruct achieves a new SoTA one-step generation FID of \emph{1.02}, which outperforms its 79-step teacher diffusion with a significant improvement margin of 1.33 (1.02 vs 2.35). We also apply Uni-Instruct on broader tasks like text-to-3D generation. For text-to-3D generation, Uni-Instruct gives decent results, which slightly outperforms previous methods, such as SDS and VSD, in terms of both generation quality and diversity. Both the solid theoretical and empirical contributions of Uni-Instruct will potentially help future studies on one-step diffusion distillation and knowledge transferring of diffusion models.

Monocular 3D estimation is crucial for visual perception. However, current methods fall short by relying on oversimplified assumptions, such as pinhole camera models or rectified images. These limitations severely restrict their general applicability, causing poor performance in real-world scenarios with fisheye or panoramic images and resulting in substantial context loss. To address this, we present UniK3D, the first generalizable method for monocular 3D estimation able to model any camera. Our method introduces a spherical 3D representation which allows for better disentanglement of camera and scene geometry and enables accurate metric 3D reconstruction for unconstrained camera models. Our camera component features a novel, model-independent representation of the pencil of rays, achieved through a learned superposition of spherical harmonics. We also introduce an angular loss, which, together with the camera module design, prevents the contraction of the 3D outputs for wide-view cameras. A comprehensive zero-shot evaluation on 13 diverse datasets demonstrates the state-of-the-art performance of UniK3D across 3D, depth, and camera metrics, with substantial gains in challenging large-field-of-view and panoramic settings, while maintaining top accuracy in conventional pinhole small-field-of-view domains. Code and models are available at github.com/lpiccinelli-eth/unik3d .

In this paper, we provide a finite random iterated function system satisfying the open set condition, for which the random version of Bowen's formula fails to hold. This counterexample shows that analogous results established for random recursive constructions are not always obtained for random iterated function systems.

Unified multimodal models often struggle with complex synthesis tasks that demand deep reasoning, and typically treat text-to-image generation and image editing as isolated capabilities rather than interconnected reasoning steps. To address this, we propose UniReason, a unified framework that harmonizes these two tasks through a dual reasoning paradigm. We formulate generation as world knowledge-enhanced planning to inject implicit constraints, and leverage editing capabilities for fine-grained visual refinement to further correct visual errors via self-reflection. This approach unifies generation and editing within a shared representation, mirroring the human cognitive process of planning followed by refinement. We support this framework by systematically constructing a large-scale reasoning-centric dataset (~300k samples) covering five major knowledge domains (e.g., cultural commonsense, physics, etc.) for planning, alongside an agent-generated corpus for visual self-correction. Extensive experiments demonstrate that UniReason achieves advanced performance on reasoning-intensive benchmarks such as WISE, KrisBench and UniREditBench, while maintaining superior general synthesis capabilities.

This paper introduces UnDiff, a diffusion probabilistic model capable of solving various speech inverse tasks. Being once trained for speech waveform generation in an unconditional manner, it can be adapted to different tasks including degradation inversion, neural vocoding, and source separation. In this paper, we, first, tackle the challenging problem of unconditional waveform generation by comparing different neural architectures and preconditioning domains. After that, we demonstrate how the trained unconditional diffusion could be adapted to different tasks of speech processing by the means of recent developments in post-training conditioning of diffusion models. Finally, we demonstrate the performance of the proposed technique on the tasks of bandwidth extension, declipping, vocoding, and speech source separation and compare it to the baselines. The codes are publicly available.

Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual numbers, which are close to the formal specification of differentiation and hence easier to prove correct. But these papers have focussed on correctness not efficiency. Recently, it was shown how an approach using dual numbers could be made efficient through the right optimizations. Optimizations are highly dependent on order, as one optimization can enable another. It can therefore be useful to have fine-grained control over the scheduling of optimizations. One method expresses compiler optimizations as rewrite rules, whose application can be combined and controlled using strategy languages. Previous work describes the use of term rewriting and strategies to generate high-performance code in a compiler for a functional language. In this work, we implement dual numbers AD in a functional array programming language using rewrite rules and strategy combinators for optimization. We aim to combine the elegance of differentiation using dual numbers with a succinct expression of the optimization schedule using a strategy language. We give preliminary evidence suggesting the viability of the approach on a micro-benchmark.

Deepface generation has traditionally followed a task-driven paradigm, where distinct tasks (e.g., face transfer and hair transfer) are addressed by task-specific models. Nevertheless, this single-task setting severely limits model generalization and scalability. A unified model capable of solving multiple deepface generation tasks in a single pass represents a promising and practical direction, yet remains challenging due to data scarcity and cross-task conflicts arising from heterogeneous attribute transformations. To this end, we propose UniBioTransfer, the first unified framework capable of handling both conventional deepface tasks (e.g., face transfer and face reenactment) and shape-varying transformations (e.g., hair transfer and head transfer). Besides, UniBioTransfer naturally generalizes to unseen tasks, like lip, eye, and glasses transfer, with minimal fine-tuning. Generally, UniBioTransfer addresses data insufficiency in multi-task generation through a unified data construction strategy, including a swapping-based corruption mechanism designed for spatially dynamic attributes like hair. It further mitigates cross-task interference via an innovative BioMoE, a mixture-of-experts based model coupled with a novel two-stage training strategy that effectively disentangles task-specific knowledge. Extensive experiments demonstrate the effectiveness, generalization, and scalability of UniBioTransfer, outperforming both existing unified models and task-specific methods across a wide range of deepface generation tasks. Project page is at https://scy639.github.io/UniBioTransfer.github.io/

The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to embed computational effects, evaluation strategies, and control flow operations. The first instalment modelled sequential higher-order computation with global store, input/output, probabilities, and non-determinism, and embedded both the call-by-name and call-by-value lambda-calculus, as well as Moggi's computational metalanguage and Levy's call-by-push-value. The present paper extends the calculus from sequential to branching and looping control flow. This allows the faithful embedding of a minimal but complete imperative language, including conditionals, exception handling, and iteration, as well as constants and algebraic data types. The calculus is defined through a simple operational semantics, extending the (simplified) Krivine machine for the lambda-calculus with multiple operand stacks to model effects and a continuation stack to model sequential, branching, and looping computation. It features a confluent reduction relation and a system of simple types that guarantees termination of the machine and strong normalization of reduction (in the absence of iteration). These properties carry over to the embedded imperative language, providing a unified functional-imperative model of computation that supports simple types, a direct and intuitive operational semantics, and a confluent reduction semantics.

We generalise a technique of Bhat and Skeide (2015) to interpolate commuting families {S_{i}}_{i in I} of contractions on a Hilbert space H, to commuting families {T_{i}}_{i in I} of contractive C_{0}-semigroups on L^{2}(prod_{i in I}T) otimes H. As an excursus, we provide applications of the interpolations to time-discretisation and the embedding problem. Applied to Parrott's construction (1970), we then demonstrate for d in N with d geq 3 the existence of commuting families {T_{i}}_{i=1}^{d} of contractive C_{0}-semigroups which admit no simultaneous unitary dilation. As an application of these counter-examples, we obtain the residuality wrt. the topology of uniform wot-convergence on compact subsets of R_{geq 0}^{d} of non-unitarily dilatable and non-unitarily approximable d-parameter contractive C_{0}-semigroups on separable infinite-dimensional Hilbert spaces for each d geq 3. Similar results are also developed for d-tuples of commuting contractions. And by building on the counter-examples of Varopoulos--Kaijser (1973--74), a 0--1-result is obtained for the von Neumann inequality. Finally, we discuss applications to rigidity as well as the embedding problem, viz. that `typical' pairs of commuting operators can be simultaneously embedded into commuting pairs of C_{0}-semigroups, which extends results of Eisner (2009--10).

The advanced function-calling capabilities of foundation models open up new possibilities for deploying agents to perform complex API tasks. However, managing large amounts of data and interacting with numerous APIs makes function calling hardware-intensive and costly, especially on edge devices. Current Large Language Models (LLMs) struggle with function calling at the edge because they cannot handle complex inputs or manage multiple tools effectively. This results in low task-completion accuracy, increased delays, and higher power consumption. In this work, we introduce Less-is-More, a novel fine-tuning-free function-calling scheme for dynamic tool selection. Our approach is based on the key insight that selectively reducing the number of tools available to LLMs significantly improves their function-calling performance, execution time, and power efficiency on edge devices. Experimental results with state-of-the-art LLMs on edge hardware show agentic success rate improvements, with execution time reduced by up to 70% and power consumption by up to 40%.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

Multimodal generative models that can understand and generate across multiple modalities are dominated by autoregressive (AR) approaches, which process tokens sequentially from left to right, or top to bottom. These models jointly handle images, text, video, and audio for various tasks such as image captioning, question answering, and image generation. In this work, we explore discrete diffusion models as a unified generative formulation in the joint text and image domain, building upon their recent success in text generation. Discrete diffusion models offer several advantages over AR models, including improved control over quality versus diversity of generated samples, the ability to perform joint multimodal inpainting (across both text and image domains), and greater controllability in generation through guidance. Leveraging these benefits, we present the first Unified Multimodal Discrete Diffusion (UniDisc) model which is capable of jointly understanding and generating text and images for a variety of downstream tasks. We compare UniDisc to multimodal AR models, performing a scaling analysis and demonstrating that UniDisc outperforms them in terms of both performance and inference-time compute, enhanced controllability, editability, inpainting, and flexible trade-off between inference time and generation quality. Code and additional visualizations are available at https://unidisc.github.io.

Grasping is a fundamental capability for robots to interact with the physical world. Humans, equipped with two hands, autonomously select appropriate grasp strategies based on the shape, size, and weight of objects, enabling robust grasping and subsequent manipulation. In contrast, current robotic grasping remains limited, particularly in multi-strategy settings. Although substantial efforts have targeted parallel-gripper and single-hand grasping, dexterous grasping for bimanual robots remains underexplored, with data being a primary bottleneck. Achieving physically plausible and geometrically conforming grasps that can withstand external wrenches poses significant challenges. To address these issues, we introduce UltraDexGrasp, a framework for universal dexterous grasping with bimanual robots. The proposed data-generation pipeline integrates optimization-based grasp synthesis with planning-based demonstration generation, yielding high-quality and diverse trajectories across multiple grasp strategies. With this framework, we curate UltraDexGrasp-20M, a large-scale, multi-strategy grasp dataset comprising 20 million frames across 1,000 objects. Based on UltraDexGrasp-20M, we further develop a simple yet effective grasp policy that takes point clouds as input, aggregates scene features via unidirectional attention, and predicts control commands. Trained exclusively on synthetic data, the policy achieves robust zero-shot sim-to-real transfer and consistently succeeds on novel objects with varied shapes, sizes, and weights, attaining an average success rate of 81.2% in real-world universal dexterous grasping. To facilitate future research on grasping with bimanual robots, we open-source the data generation pipeline at https://github.com/InternRobotics/UltraDexGrasp.

This paper investigates the global convergence of stepsized Newton methods for convex functions. We propose several simple stepsize schedules with fast global convergence guarantees, up to O (k^{-3}), nearly matching lower complexity bounds Omega (k^{-3.5}) of second-order methods. For cases with multiple plausible smoothness parameterizations or an unknown smoothness constant, we introduce a stepsize backtracking procedure that ensures convergence as if the optimal smoothness parameters were known.

Which functions can be used as activations in deep neural networks? This article explores families of functions based on orthonormal bases, including the Hermite polynomial basis and the Fourier trigonometric basis, as well as a basis resulting from the tropicalization of a polynomial basis. Our study shows that, through simple variance-preserving initialization and without additional clamping mechanisms, these activations can successfully be used to train deep models, such as GPT-2 for next-token prediction on OpenWebText and ConvNeXt for image classification on ImageNet. Our work addresses the issue of exploding and vanishing activations and gradients, particularly prevalent with polynomial activations, and opens the door for improving the efficiency of large-scale learning tasks. Furthermore, our approach provides insight into the structure of neural networks, revealing that networks with polynomial activations can be interpreted as multivariate polynomial mappings. Finally, using Hermite interpolation, we show that our activations can closely approximate classical ones in pre-trained models by matching both the function and its derivative, making them especially useful for fine-tuning tasks. These activations are available in the torchortho library, which can be accessed via: https://github.com/K-H-Ismail/torchortho.

Achieving general-purpose robotic manipulation requires robots to seamlessly bridge high-level semantic intent with low-level physical interaction in unstructured environments. However, existing approaches falter in zero-shot generalization: end-to-end Vision-Language-Action (VLA) models often lack the precision required for long-horizon tasks, while traditional hierarchical planners suffer from semantic rigidity when facing open-world variations. To address this, we present UniManip, a framework grounded in a Bi-level Agentic Operational Graph (AOG) that unifies semantic reasoning and physical grounding. By coupling a high-level Agentic Layer for task orchestration with a low-level Scene Layer for dynamic state representation, the system continuously aligns abstract planning with geometric constraints, enabling robust zero-shot execution. Unlike static pipelines, UniManip operates as a dynamic agentic loop: it actively instantiates object-centric scene graphs from unstructured perception, parameterizes these representations into collision-free trajectories via a safety-aware local planner, and exploits structured memory to autonomously diagnose and recover from execution failures. Extensive experiments validate the system's robust zero-shot capability on unseen objects and tasks, demonstrating a 22.5% and 25.0% higher success rate compared to state-of-the-art VLA and hierarchical baselines, respectively. Notably, the system enables direct zero-shot transfer from fixed-base setups to mobile manipulation without fine-tuning or reconfiguration. Our open-source project page can be found at https://henryhcliu.github.io/unimanip.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from O(L^6) to O(L^3), where L is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

A supervised learning algorithm searches over a set of functions A to B parametrised by a space P to find the best approximation to some ideal function fcolon A to B. It does this by taking examples (a,f(a)) in Atimes B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding with a polyharmonic spline. However, a direct application of that solution is limited by O(N^3) computational cost and by a breakdown of the original theoretical assumptions when the input space has excessive dimensionality. This paper proposes a cascade architecture built from packages of polyharmonic splines that simultaneously addresses scalability and is theoretically justified for problems with unknown intrinsic low dimensionality. Efficient matrix procedures are presented for forward computation and end-to-end differentiation through the cascade.

This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its standard call-by-name stack machine in two directions. One, "locations", introduces multiple stacks, which enable effect operators to be encoded into the abstraction and application constructs. The second, "sequencing", introduces the imperative notions of "skip" and "sequence", similar to kappa-calculus and concatenative programming languages. The key observation of the RMC is that the first-order fragment of the FMC exhibits a latent duality which, given a simple decomposition of the relevant constructors, can be concretely expressed as an involution on syntax. Semantically, this gives rise to a sound and complete calculus for string diagrams of Frobenius monoids. We consider unification as the corresponding symmetric generalization of beta-reduction. By further including standard operators of Kleene algebra, the RMC embeds a range of computational models: the kappa-calculus, logic programming, automata, Interaction Nets, and Petri Nets, among others. These embeddings preserve operational semantics, which for the RMC is again given by a generalization of the standard stack machine for the lambda-calculus. The equational theory of the RMC (which supports reasoning about its operational semantics) is conservative over both the first-order lambda-calculus and Kleene algebra, and can be oriented to give a confluent reduction relation.

Image demoiréing poses one of the most formidable challenges in image restoration, primarily due to the unpredictable and anisotropic nature of moiré patterns. Limited by the quantity and diversity of training data, current methods tend to overfit to a single moiré domain, resulting in performance degradation for new domains and restricting their robustness in real-world applications. In this paper, we propose a universal image demoiréing solution, UniDemoiré, which has superior generalization capability. Notably, we propose innovative and effective data generation and synthesis methods that can automatically provide vast high-quality moiré images to train a universal demoiréing model. Our extensive experiments demonstrate the cutting-edge performance and broad potential of our approach for generalized image demoiréing.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Bimanual dexterous manipulation is a critical yet underexplored area in robotics. Its high-dimensional action space and inherent task complexity present significant challenges for policy learning, and the limited task diversity in existing benchmarks hinders general-purpose skill development. Existing approaches largely depend on reinforcement learning, often constrained by intricately designed reward functions tailored to a narrow set of tasks. In this work, we present a novel approach for efficiently learning diverse bimanual dexterous skills from abundant human demonstrations. Specifically, we introduce BiDexHD, a framework that unifies task construction from existing bimanual datasets and employs teacher-student policy learning to address all tasks. The teacher learns state-based policies using a general two-stage reward function across tasks with shared behaviors, while the student distills the learned multi-task policies into a vision-based policy. With BiDexHD, scalable learning of numerous bimanual dexterous skills from auto-constructed tasks becomes feasible, offering promising advances toward universal bimanual dexterous manipulation. Our empirical evaluation on the TACO dataset, spanning 141 tasks across six categories, demonstrates a task fulfillment rate of 74.59% on trained tasks and 51.07% on unseen tasks, showcasing the effectiveness and competitive zero-shot generalization capabilities of BiDexHD. For videos and more information, visit our project page https://sites.google.com/view/bidexhd.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Large language models (LLMs) have significantly advanced autonomous agents, particularly in zero-shot tool usage, also known as function calling. This research delves into enhancing the function-calling capabilities of LLMs by exploring different approaches, including prompt formats for integrating function descriptions, blending function-calling and instruction-following data, introducing a novel Decision Token for conditional prompts, leveraging chain-of-thought reasoning, and overcoming multilingual challenges with a translation pipeline. Our key findings and contributions are as follows: (1) Instruction-following data improves both function-calling accuracy and relevance detection. (2) The use of the newly proposed Decision Token, combined with synthetic non-function-call data, enhances relevance detection. (3) A tailored translation pipeline effectively overcomes multilingual limitations, demonstrating significant improvements in Traditional Chinese. These insights highlight the potential for improved function-calling capabilities and multilingual applications in LLMs.

Advanced agentic intelligence is a prerequisite for deploying Large Language Models in practical, real-world applications. Diverse real-world APIs demand precise, robust function-calling intelligence, which needs agents to develop these capabilities through interaction in varied environments. The breadth of function-calling competence is closely tied to the diversity of environments in which agents are trained. In this work, we scale up environments as a step towards advancing general agentic intelligence. This gives rise to two central challenges: (i) how to scale environments in a principled manner, and (ii) how to effectively train agentic capabilities from experiences derived through interactions with these environments. To address these, we design a scalable framework that automatically constructs heterogeneous environments that are fully simulated, systematically broadening the space of function-calling scenarios. We further adapt a two-phase agent fine-tuning strategy: first endowing agents with fundamental agentic capabilities, then specializing them for domain-specific contexts. Extensive experiments on agentic benchmarks, tau-bench, tau2-Bench, and ACEBench, demonstrate that our trained model, AgentScaler, significantly enhances the function-calling capability of models.

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising weight-space models that are equivariant to the permutation symmetries of simple feedforward networks. However, they are not applicable to general architectures, since the permutation symmetries of a weight space can be complicated by recurrence or residual connections. This work proposes an algorithm that automatically constructs permutation equivariant models, which we refer to as universal neural functionals (UNFs), for any weight space. Among other applications, we demonstrate how UNFs can be substituted into existing learned optimizer designs, and find promising improvements over prior methods when optimizing small image classifiers and language models. Our results suggest that learned optimizers can benefit from considering the (symmetry) structure of the weight space they optimize. We open-source our library for constructing UNFs at https://github.com/AllanYangZhou/universal_neural_functional.

We present a high-performance system for automatic differentiation (AD) of functions defined on triangle meshes that exploits the inherent sparsity and locality of mesh-based energy functions to achieve fast gradient and Hessian computation on the GPU. Our system is designed around per-element forward-mode differentiation, enabling all local computations to remain in GPU registers or shared memory. Unlike reverse-mode approaches that construct and traverse global computation graphs, our method performs differentiation on the fly, minimizing memory traffic and avoiding global synchronization. Our programming model allows users to define local energy terms while the system handles parallel evaluation, derivative computation, and sparse Hessian assembly. We benchmark our system on a range of applications--cloth simulation, surface parameterization, mesh smoothing, and spherical manifold optimization. We achieve a geometric mean speedup of 6.2x over optimized PyTorch implementations for second-order derivatives, and 2.76x speedup for Hessian-vector products. For first-order derivatives, our system is 6.38x, 2.89x, and 1.98x faster than Warp, JAX, and Dr.JIT, respectively, while remaining on par with hand-written derivatives.

This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limited expressive capabilities of the individual network itself. Specifically, we prove by construction that L_2circ g^{circ r}circ mathcal{L}_1 can approximate 1-Lipschitz continuous functions on [0,1]^d with an error O(r^{-1/d}), where g is realized by a fixed-size ReLU network, mathcal{L}_1 and L_2 are two affine linear maps matching the dimensions, and g^{circ r} denotes the r-times composition of g. Furthermore, we extend such a result to generic continuous functions on [0,1]^d with the approximation error characterized by the modulus of continuity. Our results reveal that a continuous-depth network generated via a dynamical system has immense approximation power even if its dynamics function is time-independent and realized by a fixed-size ReLU network.

Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics and prove that different ways of composing the building blocks of BFFG correspond to equivalent optics.

In the era of Large Language Models (LLMs), tremendous strides have been made in the field of multimodal understanding. However, existing advanced algorithms are limited to effectively utilizing the immense representation capabilities and rich world knowledge inherent to these large pre-trained models, and the beneficial connections among tasks within the context of text-rich scenarios have not been sufficiently explored. In this work, we introduce UniDoc, a novel multimodal model equipped with text detection and recognition capabilities, which are deficient in existing approaches. Moreover, UniDoc capitalizes on the beneficial interactions among tasks to enhance the performance of each individual task. To implement UniDoc, we perform unified multimodal instruct tuning on the contributed large-scale instruction following datasets. Quantitative and qualitative experimental results show that UniDoc sets state-of-the-art scores across multiple challenging benchmarks. To the best of our knowledge, this is the first large multimodal model capable of simultaneous text detection, recognition, spotting, and understanding.

Neural 3D scene representations have shown great potential for 3D reconstruction from 2D images. However, reconstructing real-world captures of complex scenes still remains a challenge. Existing generic 3D reconstruction methods often struggle to represent fine geometric details and do not adequately model reflective surfaces of large-scale scenes. Techniques that explicitly focus on reflective surfaces can model complex and detailed reflections by exploiting better reflection parameterizations. However, we observe that these methods are often not robust in real unbounded scenarios where non-reflective as well as reflective components are present. In this work, we propose UniSDF, a general purpose 3D reconstruction method that can reconstruct large complex scenes with reflections. We investigate both view-based as well as reflection-based color prediction parameterization techniques and find that explicitly blending these representations in 3D space enables reconstruction of surfaces that are more geometrically accurate, especially for reflective surfaces. We further combine this representation with a multi-resolution grid backbone that is trained in a coarse-to-fine manner, enabling faster reconstructions than prior methods. Extensive experiments on object-level datasets DTU, Shiny Blender as well as unbounded datasets Mip-NeRF 360 and Ref-NeRF real demonstrate that our method is able to robustly reconstruct complex large-scale scenes with fine details and reflective surfaces. Please see our project page at https://fangjinhuawang.github.io/UniSDF.

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.

We introduce UniMuMo, a unified multimodal model capable of taking arbitrary text, music, and motion data as input conditions to generate outputs across all three modalities. To address the lack of time-synchronized data, we align unpaired music and motion data based on rhythmic patterns to leverage existing large-scale music-only and motion-only datasets. By converting music, motion, and text into token-based representation, our model bridges these modalities through a unified encoder-decoder transformer architecture. To support multiple generation tasks within a single framework, we introduce several architectural improvements. We propose encoding motion with a music codebook, mapping motion into the same feature space as music. We introduce a music-motion parallel generation scheme that unifies all music and motion generation tasks into a single transformer decoder architecture with a single training task of music-motion joint generation. Moreover, the model is designed by fine-tuning existing pre-trained single-modality models, significantly reducing computational demands. Extensive experiments demonstrate that UniMuMo achieves competitive results on all unidirectional generation benchmarks across music, motion, and text modalities. Quantitative results are available in the https://hanyangclarence.github.io/unimumo_demo/{project page}.

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.

Spiking Neural Networks (SNNs) offer energy-efficient, biologically plausible computation but suffer from non-differentiable spike generation, necessitating reliance on heuristic surrogate gradients. This paper introduces UltraLIF, a principled framework that replaces surrogate gradients with ultradiscretization, a mathematical formalism from tropical geometry providing continuous relaxations of discrete dynamics. The central insight is that the max-plus semiring underlying ultradiscretization naturally models neural threshold dynamics: the log-sum-exp function serves as a differentiable soft-maximum that converges to hard thresholding as a learnable temperature parameter eps to 0. Two neuron models are derived from distinct dynamical systems: UltraLIF from the LIF ordinary differential equation (temporal dynamics) and UltraDLIF from the diffusion equation modeling gap junction coupling across neuronal populations (spatial dynamics). Both yield fully differentiable SNNs trainable via standard backpropagation with no forward-backward mismatch. Theoretical analysis establishes pointwise convergence to classical LIF dynamics with quantitative error bounds and bounded non-vanishing gradients. Experiments on six benchmarks spanning static images, neuromorphic vision, and audio demonstrate improvements over surrogate gradient baselines, with gains most pronounced in single-timestep (T{=}1) settings on neuromorphic and temporal datasets. An optional sparsity penalty enables significant energy reduction while maintaining competitive accuracy.

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.

Recent large language models (LLMs) have enabled the development of advanced agentic systems that can integrate various tools and APIs to fulfill user queries through function calling. However, the deployment of these LLMs on the edge has not been explored since they typically require cloud-based infrastructure due to their substantial model size and computational demands. To this end, we present TinyAgent, an end-to-end framework for training and deploying task-specific small language model agents capable of function calling for driving agentic systems at the edge. We first show how to enable accurate function calling for open-source models via the LLMCompiler framework. We then systematically curate a high-quality dataset for function calling, which we use to fine-tune two small language models, TinyAgent-1.1B and 7B. For efficient inference, we introduce a novel tool retrieval method to reduce the input prompt length and utilize quantization to further accelerate the inference speed. As a driving application, we demonstrate a local Siri-like system for Apple's MacBook that can execute user commands through text or voice input. Our results show that our models can achieve, and even surpass, the function-calling capabilities of larger models like GPT-4-Turbo, while being fully deployed at the edge. We open-source our dataset, models, and installable package and provide a demo video for our MacBook assistant agent.

Egocentric human motion generation and forecasting with scene-context is crucial for enhancing AR/VR experiences, improving human-robot interaction, advancing assistive technologies, and enabling adaptive healthcare solutions by accurately predicting and simulating movement from a first-person perspective. However, existing methods primarily focus on third-person motion synthesis with structured 3D scene contexts, limiting their effectiveness in real-world egocentric settings where limited field of view, frequent occlusions, and dynamic cameras hinder scene perception. To bridge this gap, we introduce Egocentric Motion Generation and Egocentric Motion Forecasting, two novel tasks that utilize first-person images for scene-aware motion synthesis without relying on explicit 3D scene. We propose UniEgoMotion, a unified conditional motion diffusion model with a novel head-centric motion representation tailored for egocentric devices. UniEgoMotion's simple yet effective design supports egocentric motion reconstruction, forecasting, and generation from first-person visual inputs in a unified framework. Unlike previous works that overlook scene semantics, our model effectively extracts image-based scene context to infer plausible 3D motion. To facilitate training, we introduce EE4D-Motion, a large-scale dataset derived from EgoExo4D, augmented with pseudo-ground-truth 3D motion annotations. UniEgoMotion achieves state-of-the-art performance in egocentric motion reconstruction and is the first to generate motion from a single egocentric image. Extensive evaluations demonstrate the effectiveness of our unified framework, setting a new benchmark for egocentric motion modeling and unlocking new possibilities for egocentric applications.

Diffusion Transformers (DiT) excel in video generation but encounter significant computational challenges due to the quadratic complexity of attention. Notably, attention differences between adjacent diffusion steps follow a U-shaped pattern. Current methods leverage this property by caching attention blocks, however, they still struggle with sudden error spikes and large discrepancies. To address these issues, we propose UniCP a unified caching and pruning framework for efficient video generation. UniCP optimizes both temporal and spatial dimensions through. Error Aware Dynamic Cache Window (EDCW): Dynamically adjusts cache window sizes for different blocks at various timesteps, adapting to abrupt error changes. PCA based Slicing (PCAS) and Dynamic Weight Shift (DWS): PCAS prunes redundant attention components, and DWS integrates caching and pruning by enabling dynamic switching between pruned and cached outputs. By adjusting cache windows and pruning redundant components, UniCP enhances computational efficiency and maintains video detail fidelity. Experimental results show that UniCP outperforms existing methods in both performance and efficiency.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

Function calling enables large language models (LLMs) to interact with external systems by leveraging tools and APIs. When faced with multi-step tool usage, LLMs still struggle with tool selection, parameter generation, and tool-chain planning. Existing methods typically rely on manually designing task-specific demonstrations, or retrieving from a curated library. These approaches demand substantial expert effort and prompt engineering becomes increasingly complex and inefficient as tool diversity and task difficulty scale. To address these challenges, we propose a self-guided method, Stepwise Experience Recall (SEER), which performs fine-grained, stepwise retrieval from a continually updated experience pool. Instead of relying on static or manually curated library, SEER incrementally augments the experience pool with past successful trajectories, enabling continuous expansion of the pool and improved model performance over time. Evaluated on the ToolQA benchmark, SEER achieves an average improvement of 6.1% on easy and 4.7% on hard questions. We further test SEER on τ-bench, which includes two real-world domains. Powered by Qwen2.5-7B and Qwen2.5-72B models, SEER demonstrates substantial accuracy gains of 7.44% and 23.38%, respectively.

This study investigates language models' generative capabilities in tool-use dialogs. We categorize the models' outputs in tool-use dialogs into four distinct types: Tool Call, Answer Completion, Slot Question, and Relevance Detection, which serve as aspects for evaluation. We introduce FunctionChat-Bench, comprising 700 evaluation items and automated assessment programs. Using this benchmark, we evaluate several language models that support function calling. Our findings indicate that while language models may exhibit high accuracy in single-turn Tool Call scenarios, this does not necessarily translate to superior generative performance in multi-turn environments. We argue that the capabilities required for function calling extend beyond generating tool call messages; they must also effectively generate conversational messages that engage the user.

While multitask representation learning has become a popular approach in reinforcement learning (RL) to boost the sample efficiency, the theoretical understanding of why and how it works is still limited. Most previous analytical works could only assume that the representation function is already known to the agent or from linear function class, since analyzing general function class representation encounters non-trivial technical obstacles such as generalization guarantee, formulation of confidence bound in abstract function space, etc. However, linear-case analysis heavily relies on the particularity of linear function class, while real-world practice usually adopts general non-linear representation functions like neural networks. This significantly reduces its applicability. In this work, we extend the analysis to general function class representations. Specifically, we consider an agent playing M contextual bandits (or MDPs) concurrently and extracting a shared representation function phi from a specific function class Phi using our proposed Generalized Functional Upper Confidence Bound algorithm (GFUCB). We theoretically validate the benefit of multitask representation learning within general function class for bandits and linear MDP for the first time. Lastly, we conduct experiments to demonstrate the effectiveness of our algorithm with neural net representation.

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training pipelines. We avoid the recursive computation in BP and develop a unified likelihood ratio (ULR) method for gradient estimation with just one forward propagation. Not only can ULR be extended to train a wide variety of neural network architectures, but the computation flow in BP can also be rearranged by ULR for better device adaptation. Moreover, we propose several variance reduction techniques to further accelerate the training process. Our experiments offer numerical results across diverse aspects, including various neural network training scenarios, computation flow rearrangement, and fine-tuning of pre-trained models. All findings demonstrate that ULR effectively enhances the flexibility of neural network training by permitting localized module training without compromising the global objective and significantly boosts the network robustness.

Large language models demonstrate the intriguing ability to perform unseen tasks via in-context learning. However, it remains unclear what mechanisms inside the model drive such task-level generalization. In this work, we approach this question through the lens of off-by-one addition (i.e., 1+1=3, 2+2=5, 3+3=?), a two-step, counterfactual task with an unexpected +1 function as a second step. Leveraging circuit-style interpretability techniques such as path patching, we analyze the models' internal computations behind their performance and present three key findings. First, we uncover a function induction mechanism that explains the model's generalization from standard addition to off-by-one addition. This mechanism resembles the structure of the induction head mechanism found in prior work and elevates it to a higher level of abstraction. Second, we show that the induction of the +1 function is governed by multiple attention heads in parallel, each of which emits a distinct piece of the +1 function. Finally, we find that this function induction mechanism is reused in a broader range of tasks, including synthetic tasks such as shifted multiple-choice QA and algorithmic tasks such as base-8 addition. Overall, our findings offer deeper insights into how reusable and composable structures within language models enable task-level generalization.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category 2-Optic(C) whose 2-cells explicitly track optics' internal configuration. We show that the 1-category Optic(C) arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Newton-Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Deep implicit functions have been found to be an effective tool for efficiently encoding all manner of natural signals. Their attractiveness stems from their ability to compactly represent signals with little to no off-line training data. Instead, they leverage the implicit bias of deep networks to decouple hidden redundancies within the signal. In this paper, we explore the hypothesis that additional compression can be achieved by leveraging the redundancies that exist between layers. We propose to use a novel run-time decoder-only hypernetwork - that uses no offline training data - to better model this cross-layer parameter redundancy. Previous applications of hyper-networks with deep implicit functions have applied feed-forward encoder/decoder frameworks that rely on large offline datasets that do not generalize beyond the signals they were trained on. We instead present a strategy for the initialization of run-time deep implicit functions for single-instance signals through a Decoder-Only randomly projected Hypernetwork (D'OH). By directly changing the dimension of a latent code to approximate a target implicit neural architecture, we provide a natural way to vary the memory footprint of neural representations without the costly need for neural architecture search on a space of alternative low-rate structures.

Large language models (LLMs) have demonstrated powerful decision-making and planning capabilities in solving complicated real-world problems. LLM-based autonomous agents can interact with diverse tools (e.g., functional APIs) and generate solution plans that execute a series of API function calls in a step-by-step manner. The multitude of candidate API function calls significantly expands the action space, amplifying the critical need for efficient action space navigation. However, existing methods either struggle with unidirectional exploration in expansive action spaces, trapped into a locally optimal solution, or suffer from exhaustively traversing all potential actions, causing inefficient navigation. To address these issues, we propose ToolChain*, an efficient tree search-based planning algorithm for LLM-based agents. It formulates the entire action space as a decision tree, where each node represents a possible API function call involved in a solution plan. By incorporating the A* search algorithm with task-specific cost function design, it efficiently prunes high-cost branches that may involve incorrect actions, identifying the most low-cost valid path as the solution. Extensive experiments on multiple tool-use and reasoning tasks demonstrate that ToolChain* efficiently balances exploration and exploitation within an expansive action space. It outperforms state-of-the-art baselines on planning and reasoning tasks by 3.1% and 3.5% on average while requiring 7.35x and 2.31x less time, respectively.

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative L_{1} error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

Code generation models based on the pre-training and fine-tuning paradigm have been increasingly attempted by both academia and industry, resulting in well-known industrial models such as Codex, CodeGen, and PanGu-Coder. To evaluate the effectiveness of these models, multiple existing benchmarks are proposed, including only cases of generating a standalone function, i.e., a function that may invoke or access only built-in functions and standard libraries. However, non-standalone functions, which typically are not included in the existing benchmarks, constitute more than 70% of the functions in popular open-source projects, and evaluating models' effectiveness on standalone functions cannot reflect these models' effectiveness on pragmatic code generation scenarios. To help bridge the preceding gap, in this paper, we propose a benchmark named CoderEval, consisting of 230 Python and 230 Java code generation tasks carefully curated from popular real-world open-source projects and a self-contained execution platform to automatically assess the functional correctness of generated code. CoderEval supports code generation tasks from six levels of context dependency, where context refers to code elements such as types, APIs, variables, and consts defined outside the function under generation but within the dependent third-party libraries, current class, file, or project. CoderEval can be used to evaluate the effectiveness of models in generating code beyond only standalone functions. By evaluating three code generation models on CoderEval, we find that the effectiveness of these models in generating standalone functions is substantially higher than that in generating non-standalone functions. Our analysis highlights the current progress and pinpoints future directions to further improve a model's effectiveness by leveraging contextual information for pragmatic code generation.

We study the code generation behavior of instruction-tuned models built on top of code pre-trained language models when they could access an auxiliary function to implement a function. We design several ways to provide auxiliary functions to the models by adding them to the query or providing a response prefix to incorporate the ability to utilize auxiliary functions with the instruction-following capability. Our experimental results show the effectiveness of combining the base models' auxiliary function utilization ability with the instruction following ability. In particular, the performance of adopting our approaches with the open-sourced language models surpasses that of the recent powerful proprietary language models, i.e., gpt-4o.

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal goal-reaching strategies are rarely reversible (symmetrical). Distance functions supported on these asymmetrical structures are called quasimetrics. Despite their common appearance, little research has been done on the learning of quasimetrics. Our theoretical analysis reveals that a common class of learning algorithms, including unconstrained multilayer perceptrons (MLPs), provably fails to learn a quasimetric consistent with training data. In contrast, our proposed Poisson Quasimetric Embedding (PQE) is the first quasimetric learning formulation that both is learnable with gradient-based optimization and enjoys strong performance guarantees. Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines.

Recent advances in unified multimodal models indicate a clear trend towards comprehensive content generation. However, the auditory domain remains a significant challenge, with music and speech often developed in isolation, hindering progress towards universal audio synthesis. This separation stems from inherent task conflicts and severe data imbalances, which impede the development of a truly unified audio generation model. To address this challenge, we propose UniMoE-Audio, a unified speech and music generation model within a novel Dynamic-Capacity Mixture-of-Experts (MoE) framework. Architecturally, UniMoE-Audio introduces a Top-P routing strategy for dynamic expert number allocation, and a hybrid expert design comprising routed experts for domain-specific knowledge, shared experts for domain-agnostic features, and null experts for adaptive computation skipping. To tackle data imbalance, we introduce a three-stage training curriculum: 1) Independent Specialist Training leverages original datasets to instill domain-specific knowledge into each "proto-expert" without interference; 2) MoE Integration and Warmup incorporates these specialists into the UniMoE-Audio architecture, warming up the gate module and shared expert using a subset of balanced dataset; and 3) Synergistic Joint Training trains the entire model end-to-end on the fully balanced dataset, fostering enhanced cross-domain synergy. Extensive experiments show that UniMoE-Audio not only achieves state-of-the-art performance on major speech and music generation benchmarks, but also demonstrates superior synergistic learning, mitigating the performance degradation typically seen in naive joint training. Our findings highlight the substantial potential of specialized MoE architecture and curated training strategies in advancing the field of universal audio generation. Homepage: https://mukioxun.github.io/Uni-MoE-site/home.html

Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been computationally expensive and challenging to use in inverse problems, whereas Neural solvers aim to address both concerns through machine learning. We propose a general formulation for continuous convolutions using separable basis functions as a superset of existing methods and evaluate a large set of basis functions in the context of (a) a compressible 1D SPH simulation, (b) a weakly compressible 2D SPH simulation, and (c) an incompressible 2D SPH Simulation. We demonstrate that even and odd symmetries included in the basis functions are key aspects of stability and accuracy. Our broad evaluation shows that Fourier-based continuous convolutions outperform all other architectures regarding accuracy and generalization. Finally, using these Fourier-based networks, we show that prior inductive biases, such as window functions, are no longer necessary. An implementation of our approach, as well as complete datasets and solver implementations, is available at https://github.com/tum-pbs/SFBC.

Language models have shown effectiveness in a variety of software applications, particularly in tasks related to automatic workflow. These models possess the crucial ability to call functions, which is essential in creating AI agents. Despite the high performance of large-scale language models in cloud environments, they are often associated with concerns over privacy and cost. Current on-device models for function calling face issues with latency and accuracy. Our research presents a new method that empowers an on-device model with 2 billion parameters to surpass the performance of GPT-4 in both accuracy and latency, and decrease the context length by 95\%. When compared to Llama-7B with a RAG-based function calling mechanism, our method enhances latency by 35-fold. This method reduces the latency to levels deemed suitable for deployment across a variety of edge devices in production environments, aligning with the performance requisites for real-world applications.

The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an evolutionary search method, which samples multiple candidate solutions from a large space and evaluates the quality of each candidate through a long training process. As a result, the search tends to be slow. In this paper, we show that large efficiency gains can be obtained by employing a fast unified functional hash, especially through the functional equivalence caching technique, which we also present. The central idea is to detect by hashing when the search method produces equivalent candidates, which occurs very frequently, and this way avoid their costly re-evaluation. Our hash is "functional" in that it identifies equivalent candidates even if they were represented or coded differently, and it is "unified" in that the same algorithm can hash arbitrary representations; e.g. compute graphs, imperative code, or lambda functions. As evidence, we show dramatic improvements on multiple AutoML domains, including neural architecture search and algorithm discovery. Finally, we consider the effect of hash collisions, evaluation noise, and search distribution through empirical analysis. Altogether, we hope this paper may serve as a guide to hashing techniques in AutoML.

State-of-the-art neural algorithmic reasoners make use of message passing in graph neural networks (GNNs). But typical GNNs blur the distinction between the definition and invocation of the message function, forcing a node to send messages to its neighbours at every layer, synchronously. When applying GNNs to learn to execute dynamic programming algorithms, however, on most steps only a handful of the nodes would have meaningful updates to send. One, hence, runs the risk of inefficiencies by sending too much irrelevant data across the graph -- with many intermediate GNN steps having to learn identity functions. In this work, we explicitly separate the concepts of node state update and message function invocation. With this separation, we obtain a mathematical formulation that allows us to reason about asynchronous computation in both algorithms and neural networks.

The rapid growth of stereoscopic displays, including VR headsets and 3D cinemas, has led to increasing demand for high-quality stereo video content. However, producing 3D videos remains costly and complex, while automatic Monocular-to-Stereo conversion is hindered by the limitations of the multi-stage ``Depth-Warp-Inpaint'' (DWI) pipeline. This paradigm suffers from error propagation, depth ambiguity, and format inconsistency between parallel and converged stereo configurations. To address these challenges, we introduce UniStereo, the first large-scale unified dataset for stereo video conversion, covering both stereo formats to enable fair benchmarking and robust model training. Building upon this dataset, we propose StereoPilot, an efficient feed-forward model that directly synthesizes the target view without relying on explicit depth maps or iterative diffusion sampling. Equipped with a learnable domain switcher and a cycle consistency loss, StereoPilot adapts seamlessly to different stereo formats and achieves improved consistency. Extensive experiments demonstrate that StereoPilot significantly outperforms state-of-the-art methods in both visual fidelity and computational efficiency. Project page: https://hit-perfect.github.io/StereoPilot/.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.

Achieving machine autonomy and human control often represent divergent objectives in the design of interactive AI systems. Visual generative foundation models such as Stable Diffusion show promise in navigating these goals, especially when prompted with arbitrary languages. However, they often fall short in generating images with spatial, structural, or geometric controls. The integration of such controls, which can accommodate various visual conditions in a single unified model, remains an unaddressed challenge. In response, we introduce UniControl, a new generative foundation model that consolidates a wide array of controllable condition-to-image (C2I) tasks within a singular framework, while still allowing for arbitrary language prompts. UniControl enables pixel-level-precise image generation, where visual conditions primarily influence the generated structures and language prompts guide the style and context. To equip UniControl with the capacity to handle diverse visual conditions, we augment pretrained text-to-image diffusion models and introduce a task-aware HyperNet to modulate the diffusion models, enabling the adaptation to different C2I tasks simultaneously. Trained on nine unique C2I tasks, UniControl demonstrates impressive zero-shot generation abilities with unseen visual conditions. Experimental results show that UniControl often surpasses the performance of single-task-controlled methods of comparable model sizes. This control versatility positions UniControl as a significant advancement in the realm of controllable visual generation.

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form h = g circ p where p : R^d rightarrow R is a degree k polynomial and g: R rightarrow R is a degree q polynomial. This function class generalizes the single-index model, which corresponds to k=1, and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree k polynomials p, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target h up to vanishing test error in mathcal{O}(d^k) samples and polynomial time. This is a strict improvement over kernel methods, which require widetilde Theta(d^{kq}) samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of p being a quadratic. When p is indeed a quadratic, we achieve the information-theoretically optimal sample complexity mathcal{O}(d^2), which is an improvement over prior work~nichani2023provable requiring a sample size of widetildeTheta(d^4). Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature p with mathcal{O}(d^k) samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce a canonical representation of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for many groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis is that learning a neural network to perform canonicalization is better than using predefined heuristics. Our results show that learning the canonicalization function indeed leads to better results and that the approach achieves excellent performance in practice.