Daily Papers

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs (y, g cdot y), where g is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group G:= (R_m times Z_n times Z_n), combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group O(n) and the general linear group GL(n). We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

We present GRAPE (Group RepresentAtional Position Encoding), a unified framework for positional encoding based on group actions. GRAPE brings together two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in SO(d) and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group GL. In Multiplicative GRAPE, a position n in Z (or t in R) acts as G(n)=exp(n,ω,L) with a rank-2 skew generator L in R^{d times d}, yielding a relative, compositional, norm-preserving map with a closed-form matrix exponential. RoPE is recovered exactly when the d/2 planes are the canonical coordinate pairs with log-uniform spectrum. Learned commuting subspaces and compact non-commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at O(d) and O(r d) cost per head, respectively. In Additive GRAPE, additive logits arise as rank-1 (or low-rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Altogether, GRAPE supplies a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases. Project Page: https://github.com/model-architectures/GRAPE.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory and corresponding assumptions on the form of data. We propose Neural Fourier Transform (NFT), a general framework of learning the latent linear action of the group without assuming explicit knowledge of how the group acts on data. We present the theoretical foundations of NFT and show that the existence of a linear equivariant feature, which has been assumed ubiquitously in equivariance learning, is equivalent to the existence of a group invariant kernel on the dataspace. We also provide experimental results to demonstrate the application of NFT in typical scenarios with varying levels of knowledge about the acting group.

Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.

Let V be a highest weight module over a Kac-Moody algebra g, and let conv V denote the convex hull of its weights. We determine the combinatorial isomorphism type of conv V, i.e. we completely classify the faces and their inclusions. In the special case where g is semisimple, this brings closure to a question studied by Cellini-Marietti [IMRN 2015] for the adjoint representation, and by Khare [J. Algebra 2016; Trans. Amer. Math. Soc. 2017] for most modules. The determination of faces of finite-dimensional modules up to the Weyl group action and some of their inclusions also appears in previous work of Satake [Ann. of Math. 1960], Borel-Tits [IHES Publ. Math. 1965], Vinberg [Izv. Akad. Nauk 1990], and Casselman [Austral. Math. Soc. 1997]. For any subset of the simple roots, we introduce a remarkable convex cone which we call the universal Weyl polyhedron, which controls the convex hulls of all modules parabolically induced from the corresponding Levi factor. Namely, the combinatorial isomorphism type of the cone stores the classification of faces for all such highest weight modules, as well as how faces degenerate as the highest weight gets increasingly singular. To our knowledge, this cone is new in finite and infinite type. We further answer a question of Michel Brion, by showing that the localization of conv V along a face is always the convex hull of the weights of a parabolically induced module. Finally, as we determine the inclusion relations between faces representation-theoretically from the set of weights, without recourse to convexity, we answer a similar question for highest weight modules over symmetrizable quantum groups.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

Orbit recovery problems are a class of problems that often arise in practice and various forms. In these problems, we aim to estimate an unknown function after being distorted by a group action and observed via a known operator. Typically, the observations are contaminated with a non-trivial level of noise. Two particular orbit recovery problems of interest in this paper are multireference alignment and single-particle cryo-EM modelling. In order to suppress the noise, we suggest using the method of moments approach for both problems while introducing deep neural network priors. In particular, our neural networks should output the signals and the distribution of group elements, with moments being the input. In the multireference alignment case, we demonstrate the advantage of using the NN to accelerate the convergence for the reconstruction of signals from the moments. Finally, we use our method to reconstruct simulated and biological volumes in the cryo-EM setting.

Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of arbitrary finite type, which are further shown to be preserved by the ibraid group action; this recovers the results of Lu-Pan in ADE type obtained earlier in a geometric approach. Moreover, we identify the dual canonical basis for the Drinfeld double quantum group of arbitrary finite type, which is realized via iHopf algebra on the double Borel, with Berenstein-Greenstein's double canonical basis, settling several of their conjectures.

There exist a number of well known multiplicative generating functions for series of Schur functions. Amongst these are some related to the dual Cauchy identity whose expansion coefficients are rather simple, and in some cases periodic in parameters specifying the Schur functions. More recently similar identities have been found involving expansions in terms of characters of the symplectic group. Here these results are extended and generalised to all classical Lie groups. This is done through the derivation of explicit recurrence relations for the expansion coefficients based on the action of the Weyl groups of both the symplectic and orthogonal groups. Copious results are tabulated in the form of explicit values of the expansion coefficients as functions of highest weight parameters. An alternative approach is then based on dual pairs of symplectic and/or orthogonal groups. A byproduct of this approach is that expansions in terms of spin orthogonal group characters can always be recovered from non-spin cases.

We consider stochastic sequential learning problems where the learner can observe the average reward of several actions. Such a setting is interesting in many applications involving monitoring and surveillance, where the set of the actions to observe represent some (geographical) area. The importance of this setting is that in these applications, it is actually cheaper to observe average reward of a group of actions rather than the reward of a single action. We show that when the reward is smooth over a given graph representing the neighboring actions, we can maximize the cumulative reward of learning while minimizing the sensing cost. In this paper we propose CheapUCB, an algorithm that matches the regret guarantees of the known algorithms for this setting and at the same time guarantees a linear cost again over them. As a by-product of our analysis, we establish a Ω(dT) lower bound on the cumulative regret of spectral bandits for a class of graphs with effective dimension d.

Skeleton-based multi-entity action recognition is a challenging task aiming to identify interactive actions or group activities involving multiple diverse entities. Existing models for individuals often fall short in this task due to the inherent distribution discrepancies among entity skeletons, leading to suboptimal backbone optimization. To this end, we introduce a Convex Hull Adaptive Shift based multi-Entity action recognition method (CHASE), which mitigates inter-entity distribution gaps and unbiases subsequent backbones. Specifically, CHASE comprises a learnable parameterized network and an auxiliary objective. The parameterized network achieves plausible, sample-adaptive repositioning of skeleton sequences through two key components. First, the Implicit Convex Hull Constrained Adaptive Shift ensures that the new origin of the coordinate system is within the skeleton convex hull. Second, the Coefficient Learning Block provides a lightweight parameterization of the mapping from skeleton sequences to their specific coefficients in convex combinations. Moreover, to guide the optimization of this network for discrepancy minimization, we propose the Mini-batch Pair-wise Maximum Mean Discrepancy as the additional objective. CHASE operates as a sample-adaptive normalization method to mitigate inter-entity distribution discrepancies, thereby reducing data bias and improving the subsequent classifier's multi-entity action recognition performance. Extensive experiments on six datasets, including NTU Mutual 11/26, H2O, Assembly101, Collective Activity and Volleyball, consistently verify our approach by seamlessly adapting to single-entity backbones and boosting their performance in multi-entity scenarios. Our code is publicly available at https://github.com/Necolizer/CHASE .

The study of complex human interactions and group activities has become a focal point in human-centric computer vision. However, progress in related tasks is often hindered by the challenges of obtaining large-scale labeled datasets from real-world scenarios. To address the limitation, we introduce M3Act, a synthetic data generator for multi-view multi-group multi-person human atomic actions and group activities. Powered by Unity Engine, M3Act features multiple semantic groups, highly diverse and photorealistic images, and a comprehensive set of annotations, which facilitates the learning of human-centered tasks across single-person, multi-person, and multi-group conditions. We demonstrate the advantages of M3Act across three core experiments. The results suggest our synthetic dataset can significantly improve the performance of several downstream methods and replace real-world datasets to reduce cost. Notably, M3Act improves the state-of-the-art MOTRv2 on DanceTrack dataset, leading to a hop on the leaderboard from 10th to 2nd place. Moreover, M3Act opens new research for controllable 3D group activity generation. We define multiple metrics and propose a competitive baseline for the novel task. Our code and data are available at our project page: http://cjerry1243.github.io/M3Act.

We introduce a novel deep learning based group activity recognition approach called the Pose Only Group Activity Recognition System (POGARS), designed to use only tracked poses of people to predict the performed group activity. In contrast to existing approaches for group activity recognition, POGARS uses 1D CNNs to learn spatiotemporal dynamics of individuals involved in a group activity and forgo learning features from pixel data. The proposed model uses a spatial and temporal attention mechanism to infer person-wise importance and multi-task learning for simultaneously performing group and individual action classification. Experimental results confirm that POGARS achieves highly competitive results compared to state-of-the-art methods on a widely used public volleyball dataset despite only using tracked pose as input. Further our experiments show by using pose only as input, POGARS has better generalization capabilities compared to methods that use RGB as input.

Repurposing large vision-language models (LVLMs) as computer use agents (CUAs) has led to substantial breakthroughs, primarily driven by human-labeled data. However, these models often struggle with novel and specialized software, particularly in scenarios lacking human annotations. To address this challenge, we propose SEAgent, an agentic self-evolving framework enabling CUAs to autonomously evolve through interactions with unfamiliar software. Specifically, SEAgent empowers computer-use agents to autonomously master novel software environments via experiential learning, where agents explore new software, learn through iterative trial-and-error, and progressively tackle auto-generated tasks organized from simple to complex. To achieve this goal, we design a World State Model for step-wise trajectory assessment, along with a Curriculum Generator that generates increasingly diverse and challenging tasks. The agent's policy is updated through experiential learning, comprised of adversarial imitation of failure actions and Group Relative Policy Optimization (GRPO) on successful ones. Furthermore, we introduce a specialist-to-generalist training strategy that integrates individual experiential insights from specialist agents, facilitating the development of a stronger generalist CUA capable of continuous autonomous evolution. This unified agent ultimately achieves performance surpassing ensembles of individual specialist agents on their specialized software. We validate the effectiveness of SEAgent across five novel software environments within OS-World. Our approach achieves a significant improvement of 23.2% in success rate, from 11.3% to 34.5%, over a competitive open-source CUA, i.e., UI-TARS.

Large Language Model Powered Multi-Agent Systems (MASs) are increasingly employed to automate complex real-world problems, such as programming and scientific discovery. Despite their promising, MASs are not without their flaws. However, failure attribution in MASs - pinpointing the specific agent actions responsible for failures - remains underexplored and labor-intensive, posing significant challenges for debugging and system improvement. To bridge this gap, we propose FAMAS, the first spectrum-based failure attribution approach for MASs, which operates through systematic trajectory replay and abstraction, followed by spectrum analysis.The core idea of FAMAS is to estimate, from variations across repeated MAS executions, the likelihood that each agent action is responsible for the failure. In particular, we propose a novel suspiciousness formula tailored to MASs, which integrates two key factor groups, namely the agent behavior group and the action behavior group, to account for the agent activation patterns and the action activation patterns within the execution trajectories of MASs. Through expensive evaluations against 12 baselines on the Who and When benchmark, FAMAS demonstrates superior performance by outperforming all the methods in comparison.

Recent advances in group-based reinforcement learning (RL) have driven frontier large language models (LLMs) in single-turn tasks like mathematical reasoning. However, their scalability to long-horizon LLM agent training remains limited. Unlike static tasks, agent-environment interactions unfold over many steps and often yield sparse or delayed rewards, making credit assignment across individual steps significantly more challenging. In this work, we propose Group-in-Group Policy Optimization (GiGPO), a novel RL algorithm that achieves fine-grained credit assignment for LLM agents while preserving the appealing properties of group-based RL: critic-free, low memory, and stable convergence. GiGPO introduces a two-level structure for estimating relative advantage: (i) At the episode-level, GiGPO computes macro relative advantages based on groups of complete trajectories; (ii) At the step-level, GiGPO introduces an anchor state grouping mechanism that retroactively constructs step-level groups by identifying repeated environment states across trajectories. Actions stemming from the same state are grouped together, enabling micro relative advantage estimation. This hierarchical structure effectively captures both global trajectory quality and local step effectiveness without relying on auxiliary models or additional rollouts. We evaluate GiGPO on two challenging agent benchmarks, ALFWorld and WebShop, using Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct. Crucially, GiGPO delivers fine-grained per-step credit signals and achieves performance gains of > 12\% on ALFWorld and > 9\% on WebShop over the GRPO baseline: all while maintaining the same GPU memory overhead, identical LLM rollout, and incurring little to no additional time cost.

Supervised fine-tuning (SFT) has emerged as one of the most effective ways to improve the performance of large language models (LLMs) in downstream tasks. However, SFT can have difficulty generalizing when the underlying data distribution changes, even when the new data does not fall completely outside the training domain. Recent reasoning-focused models such as o1 and R1 have demonstrated consistent gains over their non-reasoning counterparts, highlighting the importance of reasoning for improved generalization and reliability. However, collecting high-quality reasoning traces for SFT remains challenging -- annotations are costly, subjective, and difficult to scale. To address this limitation, we leverage Reinforcement Learning (RL) to enable models to learn reasoning strategies directly from task outcomes. We propose a pipeline in which LLMs generate reasoning steps that guide both the invocation of tools (e.g., function calls) and the final answer generation for conversational agents. Our method employs Group Relative Policy Optimization (GRPO) with rewards designed around tool accuracy and answer correctness, allowing the model to iteratively refine its reasoning and actions. Experimental results demonstrate that our approach improves both the quality of reasoning and the precision of tool invocations, achieving a 1.5% relative improvement over the SFT model (trained without explicit thinking) and a 40% gain compared to the base of the vanilla Qwen3-1.7B model. These findings demonstrate the promise of unifying reasoning and action learning through RL to build more capable and generalizable conversational agents.

Off-policy reinforcement learning (RL) for large language models (LLMs) is attracting growing interest, driven by practical constraints in real-world applications, the complexity of LLM-RL infrastructure, and the need for further innovations of RL methodologies. While classic REINFORCE and its modern variants like Group Relative Policy Optimization (GRPO) are typically regarded as on-policy algorithms with limited tolerance of off-policyness, we present in this work a first-principles derivation for group-relative REINFORCE without assuming a specific training data distribution, showing that it admits a native off-policy interpretation. This perspective yields two general principles for adapting REINFORCE to off-policy settings: regularizing policy updates, and actively shaping the data distribution. Our analysis demystifies some myths about the roles of importance sampling and clipping in GRPO, unifies and reinterprets two recent algorithms -- Online Policy Mirror Descent (OPMD) and Asymmetric REINFORCE (AsymRE) -- as regularized forms of the REINFORCE loss, and offers theoretical justification for seemingly heuristic data-weighting strategies. Our findings lead to actionable insights that are validated with extensive empirical studies, and open up new opportunities for principled algorithm design in off-policy RL for LLMs. Source code for this work is available at https://github.com/modelscope/Trinity-RFT/tree/main/examples/rec_gsm8k.

Let X be an algebraic variety over C and G be an algebraic group acting on X whose action is closed. J. Poineau defined a compactification X^urcorner of X(C) by using hybrid Berkovich spaces. We will focus on the extension of the action of G on this compactification by characterising the set U subset X^urcorner where the action is well defined. We will also show that the quotient of U by the action of G is homeomorphic to (X/G)^urcorner, the compactification of (X/G)(C). We then apply these results to X = Rat_d, the space of rational maps and G = SL_2. It gives the results of C. Favre-C. Gong in a more general setting. Furthermore, we get a compactification of M_d = Rat_d/SL_2 where the boundary is made of orbits of non-archimedean rational maps. The results still holds if C is replaced by k a non-trivially valued field and complex analytic spaces by Berkovich spaces over k.

Action quality assessment (AQA) applies computer vision to quantitatively assess the performance or execution of a human action. Current AQA approaches are end-to-end neural models, which lack transparency and tend to be biased because they are trained on subjective human judgements as ground-truth. To address these issues, we introduce a neuro-symbolic paradigm for AQA, which uses neural networks to abstract interpretable symbols from video data and makes quality assessments by applying rules to those symbols. We take diving as the case study. We found that domain experts prefer our system and find it more informative than purely neural approaches to AQA in diving. Our system also achieves state-of-the-art action recognition and temporal segmentation, and automatically generates a detailed report that breaks the dive down into its elements and provides objective scoring with visual evidence. As verified by a group of domain experts, this report may be used to assist judges in scoring, help train judges, and provide feedback to divers. We will open-source all of our annotated training data and code for ease of reproducibility.

Large language models (LLMs) have demonstrated remarkable reasoning abilities in complex tasks, often relying on Chain-of-Thought (CoT) reasoning. However, due to their autoregressive token-level generation, the reasoning process is largely constrained to local decision-making and lacks global planning. This limitation frequently results in redundant, incoherent, or inaccurate reasoning, which significantly degrades overall performance. Existing approaches, such as tree-based algorithms and reinforcement learning (RL), attempt to address this issue but suffer from high computational costs and often fail to produce optimal reasoning trajectories. To tackle this challenge, we propose Plan-Then-Action Enhanced Reasoning with Group Relative Policy Optimization PTA-GRPO, a two-stage framework designed to improve both high-level planning and fine-grained CoT reasoning. In the first stage, we leverage advanced LLMs to distill CoT into compact high-level guidance, which is then used for supervised fine-tuning (SFT). In the second stage, we introduce a guidance-aware RL method that jointly optimizes the final output and the quality of high-level guidance, thereby enhancing reasoning effectiveness. We conduct extensive experiments on multiple mathematical reasoning benchmarks, including MATH, AIME2024, AIME2025, and AMC, across diverse base models such as Qwen2.5-7B-Instruct, Qwen3-8B, Qwen3-14B, and LLaMA3.2-3B. Experimental results demonstrate that PTA-GRPO consistently achieves stable and significant improvements across different models and tasks, validating its effectiveness and generalization.

We prove that for (compact) finite-rank median algebras the geometric rank equals the independence number of all (continuous) median-preserving functions to [0,1]. Combined with Rosenthal's dichotomy, this yields a generalized Helly selection principle: for finite-rank median algebras, the space of all median-preserving functions to [0,1] is sequentially compact in the pointwise topology. Generalizing joint results with E. Glasner on dendrons (rank-1), we establish that every continuous action of a topological group G by median automorphisms on a finite-rank compact median algebra is Rosenthal representable, hence dynamically tame. As an application, the Roller-Fioravanti compactification of finite-rank topological median G-algebras with compact intervals is often a dynamically tame G-system.

We define a cell complex with an action of the even spin mapping class group, and use it to obtain a finite presentation. We also obtain a finite presentation with Dehn twist generators.

Recent advancements in Vision-Language-Action (VLA) models have shown promise for end-to-end autonomous driving by leveraging world knowledge and reasoning capabilities. However, current VLA models often struggle with physically infeasible action outputs, complex model structures, or unnecessarily long reasoning. In this paper, we propose AutoVLA, a novel VLA model that unifies reasoning and action generation within a single autoregressive generation model for end-to-end autonomous driving. AutoVLA performs semantic reasoning and trajectory planning directly from raw visual inputs and language instructions. We tokenize continuous trajectories into discrete, feasible actions, enabling direct integration into the language model. For training, we employ supervised fine-tuning to equip the model with dual thinking modes: fast thinking (trajectory-only) and slow thinking (enhanced with chain-of-thought reasoning). To further enhance planning performance and efficiency, we introduce a reinforcement fine-tuning method based on Group Relative Policy Optimization (GRPO), reducing unnecessary reasoning in straightforward scenarios. Extensive experiments across real-world and simulated datasets and benchmarks, including nuPlan, nuScenes, Waymo, and CARLA, demonstrate the competitive performance of AutoVLA in both open-loop and closed-loop settings. Qualitative results showcase the adaptive reasoning and accurate planning capabilities of AutoVLA in diverse scenarios.

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been adapted to several manifolds, referred to as Riemannian normalization. Nonetheless, most of the existing Riemannian normalization methods have been derived in an ad hoc manner and only apply to specific manifolds. This paper establishes a unified framework for Riemannian Batch Normalization (RBN) techniques on Lie groups. Our framework offers the theoretical guarantee of controlling both the Riemannian mean and variance. Empirically, we focus on Symmetric Positive Definite (SPD) manifolds, which possess three distinct types of Lie group structures. Using the deformation concept, we generalize the existing Lie groups on SPD manifolds into three families of parameterized Lie groups. Specific normalization layers induced by these Lie groups are then proposed for SPD neural networks. We demonstrate the effectiveness of our approach through three sets of experiments: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/LieBN.git.

The recent DeepSeek-R1 has showcased the emergence of reasoning capabilities in LLMs through reinforcement learning (RL) with rule-based rewards. Building on this idea, we are the first to explore how rule-based RL can enhance the reasoning capabilities of multimodal large language models (MLLMs) for graphic user interface (GUI) action prediction tasks. To this end, we curate a small yet high-quality dataset of 136 challenging tasks, encompassing five common action types on mobile devices. We also introduce a unified rule-based action reward, enabling model optimization via policy-based algorithms such as Group Relative Policy Optimization (GRPO). Experimental results demonstrate that our proposed data-efficient model, UI-R1-3B, achieves substantial improvements on both in-domain (ID) and out-of-domain (OOD) tasks. Specifically, on the ID benchmark AndroidControl, the action type accuracy improves by 15%, while grounding accuracy increases by 10.3%, compared with the base model (i.e. Qwen2.5-VL-3B). On the OOD GUI grounding benchmark ScreenSpot-Pro, our model surpasses the base model by 6.0% and achieves competitive performance with larger models (e.g., OS-Atlas-7B), which are trained via supervised fine-tuning (SFT) on 76K data. These results underscore the potential of rule-based reinforcement learning to advance GUI understanding and control, paving the way for future research in this domain.

Large language models (LLMs) typically receive diverse natural language (NL) feedback through interaction with the environment. However, current reinforcement learning (RL) algorithms rely solely on scalar rewards, leaving the rich information in NL feedback underutilized and leading to inefficient exploration. In this work, we propose GOLF, an RL framework that explicitly exploits group-level language feedback to guide targeted exploration through actionable refinements. GOLF aggregates two complementary feedback sources: (i) external critiques that pinpoint errors or propose targeted fixes, and (ii) intra-group attempts that supply alternative partial ideas and diverse failure patterns. These group-level feedbacks are aggregated to produce high-quality refinements, which are adaptively injected into training as off-policy scaffolds to provide targeted guidance in sparse-reward regions. Meanwhile, GOLF jointly optimizes generation and refinement within a unified RL loop, creating a virtuous cycle that continuously improves both capabilities. Experiments on both verifiable and non-verifiable benchmarks show that GOLF achieves superior performance and exploration efficiency, achieving 2.2times improvements in sample efficiency compared to RL methods trained solely on scalar rewards. Code is available at https://github.com/LuckyyySTA/GOLF.

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

Vision-Language-Action (VLA) models excel in robotic manipulation but are constrained by their heavy reliance on expert demonstrations, leading to demonstration bias and limiting performance. Reinforcement learning (RL) is a vital post-training strategy to overcome these limits, yet current VLA-RL methods, including group-based optimization approaches, are crippled by severe reward sparsity. Relying on binary success indicators wastes valuable information in failed trajectories, resulting in low training efficiency. To solve this, we propose Self-Referential Policy Optimization (SRPO), a novel VLA-RL framework. SRPO eliminates the need for external demonstrations or manual reward engineering by leveraging the model's own successful trajectories, generated within the current training batch, as a self-reference. This allows us to assign a progress-wise reward to failed attempts. A core innovation is the use of latent world representations to measure behavioral progress robustly. Instead of relying on raw pixels or requiring domain-specific fine-tuning, we utilize the compressed, transferable encodings from a world model's latent space. These representations naturally capture progress patterns across environments, enabling accurate, generalized trajectory comparison. Empirical evaluations on the LIBERO benchmark demonstrate SRPO's efficiency and effectiveness. Starting from a supervised baseline with 48.9% success, SRPO achieves a new state-of-the-art success rate of 99.2% in just 200 RL steps, representing a 103% relative improvement without any extra supervision. Furthermore, SRPO shows substantial robustness, achieving a 167% performance improvement on the LIBERO-Plus benchmark.

Vision-Language-Action (VLA) models aim to unify perception, language understanding, and action generation, offering strong cross-task and cross-scene generalization with broad impact on embodied AI. However, current VLA models often lack explicit step-by-step reasoning, instead emitting final actions without considering affordance constraints or geometric relations. Their post-training pipelines also rarely reinforce reasoning quality, relying primarily on supervised fine-tuning with weak reward design. To address these challenges, we present VLA-R1, a reasoning-enhanced VLA that integrates Reinforcement Learning from Verifiable Rewards (RLVR) with Group Relative Policy Optimization (GRPO) to systematically optimize both reasoning and execution. Specifically, we design an RLVR-based post-training strategy with verifiable rewards for region alignment, trajectory consistency, and output formatting, thereby strengthening reasoning robustness and execution accuracy. Moreover, we develop VLA-CoT-13K, a high-quality dataset that provides chain-of-thought supervision explicitly aligned with affordance and trajectory annotations. Furthermore, extensive evaluations on in-domain, out-of-domain, simulation, and real-robot platforms demonstrate that VLA-R1 achieves superior generalization and real-world performance compared to prior VLA methods. We plan to release the model, code, and dataset following the publication of this work. Code: https://github.com/GigaAI-research/VLA-R1. Website: https://gigaai-research.github.io/VLA-R1.

Existing efforts in building Graphical User Interface (GUI) agents largely rely on the training paradigm of supervised fine-tuning on Large Vision-Language Models (LVLMs). However, this approach not only demands extensive amounts of training data but also struggles to effectively understand GUI screenshots and generalize to unseen interfaces. The issue significantly limits its application in real-world scenarios, especially for high-level tasks. Inspired by Reinforcement Fine-Tuning (RFT) in large reasoning models (e.g., DeepSeek-R1), which efficiently enhances the problem-solving capabilities of large language models in real-world settings, we propose \name, the first reinforcement learning framework designed to enhance the GUI capabilities of LVLMs in high-level real-world task scenarios, through unified action space rule modeling. By leveraging a small amount of carefully curated high-quality data across multiple platforms (including Windows, Linux, MacOS, Android, and Web) and employing policy optimization algorithms such as Group Relative Policy Optimization (GRPO) to update the model, \name achieves superior performance using only 0.02\% of the data (3K vs. 13M) compared to previous state-of-the-art methods like OS-Atlas across eight benchmarks spanning three different platforms (mobile, desktop, and web). These results demonstrate the immense potential of reinforcement learning based on unified action space rule modeling in improving the execution capabilities of LVLMs for real-world GUI agent tasks.

Vision-Language-Action (VLA) models enable instruction-following embodied control, but their large compute and memory footprints hinder deployment on resource-constrained robots and edge platforms. While reducing weights to 1-bit precision through binarization can greatly improve efficiency, existing methods fail to narrow the distribution gap between binarized and full-precision weights, causing quantization errors to accumulate under long-horizon closed-loop execution and severely degrade actions. To fill this gap, we propose HBVLA, a VLA-tailored binarization framework. First, we use a policy-aware enhanced Hessian to identify weights that are truly critical for action generation. Then, we employ a sparse orthogonal transform for non-salient weights to induce a low-entropy intermediate state. Finally, we quantize both salient and non-salient weights in the Harr domain with group-wise 1-bit quantization. We have evaluated our approach on different VLAs: on LIBERO, quantized OpenVLA-OFT retains 92.2% of full-precision performance; on SimplerEnv, quantized CogAct retains 93.6%, significantly outperforming state-of-the-art binarization methods. We further validate our method on real-world evaluation suite and the results show that HBVLA incurs only marginal success-rate degradation compared to the full-precision model, demonstrating robust deployability under tight hardware constraints. Our work provides a practical foundation for ultra-low-bit quantization of VLAs, enabling more reliable deployment on hardware-limited robotic platforms.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a surprising and counter-intuitive result: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

Pose-based action recognition is predominantly tackled by approaches which treat the input skeleton in a monolithic fashion, i.e. joints in the pose tree are processed as a whole. However, such approaches ignore the fact that action categories are often characterized by localized action dynamics involving only small subsets of part joint groups involving hands (e.g. `Thumbs up') or legs (e.g. `Kicking'). Although part-grouping based approaches exist, each part group is not considered within the global pose frame, causing such methods to fall short. Further, conventional approaches employ independent modality streams (e.g. joint, bone, joint velocity, bone velocity) and train their network multiple times on these streams, which massively increases the number of training parameters. To address these issues, we introduce PSUMNet, a novel approach for scalable and efficient pose-based action recognition. At the representation level, we propose a global frame based part stream approach as opposed to conventional modality based streams. Within each part stream, the associated data from multiple modalities is unified and consumed by the processing pipeline. Experimentally, PSUMNet achieves state of the art performance on the widely used NTURGB+D 60/120 dataset and dense joint skeleton dataset NTU 60-X/120-X. PSUMNet is highly efficient and outperforms competing methods which use 100%-400% more parameters. PSUMNet also generalizes to the SHREC hand gesture dataset with competitive performance. Overall, PSUMNet's scalability, performance and efficiency makes it an attractive choice for action recognition and for deployment on compute-restricted embedded and edge devices. Code and pretrained models can be accessed at https://github.com/skelemoa/psumnet

We introduce Talk2Move, a reinforcement learning (RL) based diffusion framework for text-instructed spatial transformation of objects within scenes. Spatially manipulating objects in a scene through natural language poses a challenge for multimodal generation systems. While existing text-based manipulation methods can adjust appearance or style, they struggle to perform object-level geometric transformations-such as translating, rotating, or resizing objects-due to scarce paired supervision and pixel-level optimization limits. Talk2Move employs Group Relative Policy Optimization (GRPO) to explore geometric actions through diverse rollouts generated from input images and lightweight textual variations, removing the need for costly paired data. A spatial reward guided model aligns geometric transformations with linguistic description, while off-policy step evaluation and active step sampling improve learning efficiency by focusing on informative transformation stages. Furthermore, we design object-centric spatial rewards that evaluate displacement, rotation, and scaling behaviors directly, enabling interpretable and coherent transformations. Experiments on curated benchmarks demonstrate that Talk2Move achieves precise, consistent, and semantically faithful object transformations, outperforming existing text-guided editing approaches in both spatial accuracy and scene coherence.

Understanding human social behaviour is crucial in computer vision and robotics. Micro-level observations like individual actions fall short, necessitating a comprehensive approach that considers individual behaviour, intra-group dynamics, and social group levels for a thorough understanding. To address dataset limitations, this paper introduces JRDB-Social, an extension of JRDB. Designed to fill gaps in human understanding across diverse indoor and outdoor social contexts, JRDB-Social provides annotations at three levels: individual attributes, intra-group interactions, and social group context. This dataset aims to enhance our grasp of human social dynamics for robotic applications. Utilizing the recent cutting-edge multi-modal large language models, we evaluated our benchmark to explore their capacity to decipher social human behaviour.

Purpose: Surgical performance depends not only on surgeons' technical skills but also on team communication within and across the different professional groups present during the operation. Therefore, automatically identifying team communication in the OR is crucial for patient safety and advances in the development of computer-assisted surgical workflow analysis and intra-operative support systems. To take the first step, we propose a new task of detecting communication briefings involving all OR team members, i.e. the team Time-out and the StOP?-protocol, by localizing their start and end times in video recordings of surgical operations. Methods: We generate an OR dataset of real surgeries, called Team-OR, with more than one hundred hours of surgical videos captured by the multi-view camera system in the OR. The dataset contains temporal annotations of 33 Time-out and 22 StOP?-protocol activities in total. We then propose a novel group activity detection approach, where we encode both scene context and action features, and use an efficient neural network model to output the results. Results: The experimental results on the Team-OR dataset show that our approach outperforms existing state-of-the-art temporal action detection approaches. It also demonstrates the lack of research on group activities in the OR, proving the significance of our dataset. Conclusion: We investigate the Team Time-Out and the StOP?-protocol in the OR, by presenting the first OR dataset with temporal annotations of group activities protocols, and introducing a novel group activity detection approach that outperforms existing approaches. Code is available at https://github.com/CAMMA-public/Team-OR.

Propaganda is the expression of an opinion or an action by an individual or a group deliberately designed to influence the opinions or the actions of other individuals or groups with reference to predetermined ends, which is achieved by means of well-defined rhetorical and psychological devices. Propaganda techniques are commonly used in social media to manipulate or to mislead users. Thus, there has been a lot of recent research on automatic detection of propaganda techniques in text as well as in memes. However, so far the focus has been primarily on English. With the aim to bridge this language gap, we ran a shared task on detecting propaganda techniques in Arabic tweets as part of the WANLP 2022 workshop, which included two subtasks. Subtask~1 asks to identify the set of propaganda techniques used in a tweet, which is a multilabel classification problem, while Subtask~2 asks to detect the propaganda techniques used in a tweet together with the exact span(s) of text in which each propaganda technique appears. The task attracted 63 team registrations, and eventually 14 and 3 teams made submissions for subtask 1 and 2, respectively. Finally, 11 teams submitted system description papers.

We investigate spaces of symplectic embeddings of nleq 4 balls into the complex projective plane. We prove that they are homotopy equivalent to explicitly described algebraic subspaces of the configuration spaces of n points. We compute the rational homotopy type of these embedding spaces and their cohomology with rational coefficients. Our approach relies on the comparison of the action of PGL(3,C) on the configuration space of n ordered points in CP^2 with the action of the symplectomorphism group Symp(CP^2) on the space of n embedded symplectic balls.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly GRPO, has become the standard for eliciting LLM reasoning. However, its efficiency in exploration and difficulty adaptation remains an open challenge. In this work, we argue that these bottlenecks stem from an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE). This symmetry induces two critical limitations: (i) at the group level, strict symmetry in weights between correct and incorrect trajectories leaves unsampled action logits unchanged, thereby hindering exploration of novel correct solution. (ii) at the sample level, the algorithm implicitly prioritizes medium-difficulty samples, remaining agnostic to the non-stationary demands of difficulty focus. Through controlled experiments, we reveal that this symmetric property is sub-optimal, yielding two pivotal insights: (i) asymmetrically suppressing the advantages of correct trajectories encourages essential exploration. (ii) learning efficiency is maximized by a curriculum-like transition-prioritizing simpler samples initially before gradually shifting to complex ones. Motivated by these findings, we propose Asymmetric GRAE (A-GRAE), which dynamically modulates exploration incentives and sample-difficulty focus. Experiments across seven benchmarks demonstrate that A-GRAE consistently improves GRPO and its variants across both LLMs and MLLMs.

Given a complex of groups G(Y) = (G_sigma, psi_a, g_{a,b}) where all G_sigma are relatively hyperbolic, the psi_a are inclusions of full relatively quasiconvex subgroups, and the universal cover X is CAT(0) and delta--hyperbolic, we show pi_1(G(Y)) is relatively hyperbolic. The proof extends the work of Dahmani and Martin by constructing a model for the Bowditch boundary of pi_1(G(Y)). We prove the model is a compact metrizable space on which G acts as a geometrically finite convergence group, and a theorem of Yaman then implies the result. More generally, this model shows how any suitable action of a relatively hyperbolic group on a simply connected cell complex encodes a decomposition of the Bowditch boundary into the boundary of the cell complex and the boundaries of cell stabilizers. We hope this decomposition will be helpful in answering topological questions about Bowditch boundaries.

World models simulate dynamic environments, enabling agents to interact with diverse input modalities. Although recent advances have improved the visual quality and temporal consistency of video world models, their ability of accurately modeling human-specified actions remains under-explored. Reinforcement learning presents a promising approach for directly improving the suboptimal action-following capability of pre-trained models, assuming that an appropriate reward function can be defined. However, transferring reinforcement learning post-training methods to world model is impractical due to the prohibitive cost of large-scale preference annotations and the infeasibility of constructing rule-based video verifiers. To address this gap, we propose Reinforcement Learning with Inverse Rewards (RLIR), a post-training framework that derives verifiable reward signals by recovering input actions from generated videos using an Inverse Dynamics Model. By mapping high-dimensional video modality to a low-dimensional action space, RLIR provides an objective and verifiable reward for optimization via Group Relative Policy Optimization. Experiments across autoregressive and diffusion paradigms demonstrate 5-10% gains in action-following, up to 10% improvements in visual quality, and higher human preference scores, establishing RLIR as the first post-training method specifically designed to enhance action-following in video world models.

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in three dimensions to make predictions about novel images. However, imposing SO(3)-equivariance on two-dimensional inputs is difficult because the group of three-dimensional rotations does not have a natural action on the two-dimensional plane. Specifically, it is possible that an element of SO(3) will rotate an image out of plane. We show that an algorithm that learns a three-dimensional representation of the world from two dimensional images must satisfy certain geometric consistency properties which we formulate as SO(2)-equivariance constraints. We use the induced and restricted representations of SO(2) on SO(3) to construct and classify architectures which satisfy these geometric consistency constraints. We prove that any architecture which respects said consistency constraints can be realized as an instance of our construction. We show that three previously proposed neural architectures for 3D pose prediction are special cases of our construction. We propose a new algorithm that is a learnable generalization of previously considered methods. We test our architecture on three pose predictions task and achieve SOTA results on both the PASCAL3D+ and SYMSOL pose estimation tasks.

We study a class of Z^{d}-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of Z^{d}. We prove that any measurable factor map and even any homomorphism associated to a matrix commuting with the expansion matrix, induces a continuous one. We also get strong restrictions on the normalizer group, proving that any endomorphism is invertible, the normalizer group is virtually generated by the shift action and the quotient of the normalizer group by the automorphisms is restricted by the digit tile of the substitution.

Deploying GRPO on Flow Matching models has proven effective for text-to-image generation. However, existing paradigms typically propagate an outcome-based reward to all preceding denoising steps without distinguishing the local effect of each step. Moreover, current group-wise ranking mainly compares trajectories at matched timesteps and ignores within-trajectory dependencies, where certain early denoising actions can affect later states via delayed, implicit interactions. We propose TurningPoint-GRPO (TP-GRPO), a GRPO framework that alleviates step-wise reward sparsity and explicitly models long-term effects within the denoising trajectory. TP-GRPO makes two key innovations: (i) it replaces outcome-based rewards with step-level incremental rewards, providing a dense, step-aware learning signal that better isolates each denoising action's "pure" effect, and (ii) it identifies turning points-steps that flip the local reward trend and make subsequent reward evolution consistent with the overall trajectory trend-and assigns these actions an aggregated long-term reward to capture their delayed impact. Turning points are detected solely via sign changes in incremental rewards, making TP-GRPO efficient and hyperparameter-free. Extensive experiments also demonstrate that TP-GRPO exploits reward signals more effectively and consistently improves generation. Demo code is available at https://github.com/YunzeTong/TurningPoint-GRPO.

Consider a topological surface Σ. We introduce the spectrum of a representation from the fundamental group of Σ to SL(2,R), which is a subset of projective measured lamination on the surface, which captures the directions along which the representation fails to be Fuchsian, and which characterizes the action of the mapping class group on this representation. In the case of the once-punctured torus, we show that the spectrum of a generic representation is a Cantor set, and that it completely describes the dynamics of the familly of locally constant cocycles above interval exchange transformations associated to the representation.

The study of social emergence has long been a central focus in social science. Traditional modeling approaches, such as rule-based Agent-Based Models (ABMs), struggle to capture the diversity and complexity of human behavior, particularly the irrational factors emphasized in behavioral economics. Recently, large language model (LLM) agents have gained traction as simulation tools for modeling human behavior in social science and role-playing applications. Studies suggest that LLMs can account for cognitive biases, emotional fluctuations, and other non-rational influences, enabling more realistic simulations of socio-economic dynamics. In this work, we introduce TwinMarket, a novel multi-agent framework that leverages LLMs to simulate socio-economic systems. Specifically, we examine how individual behaviors, through interactions and feedback mechanisms, give rise to collective dynamics and emergent phenomena. Through experiments in a simulated stock market environment, we demonstrate how individual actions can trigger group behaviors, leading to emergent outcomes such as financial bubbles and recessions. Our approach provides valuable insights into the complex interplay between individual decision-making and collective socio-economic patterns.

Autonomous language-model agents increasingly rely on installable skills and tools to complete user tasks. Static skill auditing can expose capability surface before deployment, but it cannot determine whether a particular invocation is unsafe under the current user request and runtime context. We therefore study skill invocation auditing as a continuous-risk estimation problem: given a user request, candidate skill, and runtime context, predict a score that supports ranking and triage before a hard intervention is applied. We introduce STARS, which combines a static capability prior, a request-conditioned invocation risk model, and a calibrated risk-fusion policy. To evaluate this setting, we construct SIA-Bench, a benchmark of 3,000 invocation records with group-safe splits, lineage metadata, runtime context, canonical action labels, and derived continuous-risk targets. On a held-out split of indirect prompt injection attacks, calibrated fusion reaches 0.439 high-risk AUPRC, improving over 0.405 for the contextual scorer and 0.380 for the strongest static baseline, while the contextual scorer remains better calibrated with 0.289 expected calibration error. On the locked in-distribution test split, gains are smaller and static priors remain useful. The resulting claim is therefore narrower: request-conditioned auditing is most valuable as an invocation-time risk-scoring and triage layer rather than as a replacement for static screening. Code is available at https://github.com/123zgj123/STARS.

Vision-language model-based mobile agents have gained the ability to not only understand complex instructions and mobile screenshots, but also optimize their action outputs via thinking and reasoning, benefiting from reinforcement learning, such as Group Relative Policy Optimization (GRPO). However, existing research centers on offline reinforcement learning training or online optimization using action-level rewards, which limits the agent's dynamic interaction with the environment. This often results in agents settling into local optima, thereby weakening their ability for exploration and error action correction. To address these challenges, we introduce an approach called Mobile-R1, which employs interactive multi-turn reinforcement learning with task-level rewards for mobile agents. Our training framework consists of three stages: initial format finetuning, single-step online training via action-level reward, followed by online training via task-level reward based on multi-turn trajectories. This strategy is designed to enhance the exploration and error correction capabilities of Mobile-R1, leading to significant performance improvements. Moreover, we have collected a dataset covering 28 Chinese applications with 24,521 high-quality manual annotations and established a new benchmark with 500 trajectories. We will open source all resources, including the dataset, benchmark, model weight, and codes: https://mobile-r1.github.io/Mobile-R1/.

Large Language Model (LLM)-driven Multi-agent systems (Mas) have recently emerged as a powerful paradigm for tackling complex real-world tasks. However, existing Mas construction methods typically rely on manually crafted interaction mechanisms or heuristic rules, introducing human biases and constraining the autonomous ability. Even with recent advances in adaptive Mas construction, existing systems largely remain within the paradigm of semi-autonomous patterns. In this work, we propose MasHost, a Reinforcement Learning (RL)-based framework for autonomous and query-adaptive Mas design. By formulating Mas construction as a graph search problem, our proposed MasHost jointly samples agent roles and their interactions through a unified probabilistic sampling mechanism. Beyond the accuracy and efficiency objectives pursued in prior works, we introduce component rationality as an additional and novel design principle in Mas. To achieve this multi-objective optimization, we propose Hierarchical Relative Policy Optimization (HRPO), a novel RL strategy that collaboratively integrates group-relative advantages and action-wise rewards. To our knowledge, our proposed MasHost is the first RL-driven framework for autonomous Mas graph construction. Extensive experiments on six benchmarks demonstrate that MasHost consistently outperforms most competitive baselines, validating its effectiveness, efficiency, and structure rationality.

Is it possible to understand or imitate a policy maker's rationale by looking at past decisions they made? We formalize this question as the problem of learning social welfare functions belonging to the well-studied family of power mean functions. We focus on two learning tasks; in the first, the input is vectors of utilities of an action (decision or policy) for individuals in a group and their associated social welfare as judged by a policy maker, whereas in the second, the input is pairwise comparisons between the welfares associated with a given pair of utility vectors. We show that power mean functions are learnable with polynomial sample complexity in both cases, even if the comparisons are social welfare information is noisy. Finally, we design practical algorithms for these tasks and evaluate their performance.

Society is characterized by the presence of a variety of social norms: collective patterns of sanctioning that can prevent miscoordination and free-riding. Inspired by this, we aim to construct learning dynamics where potentially beneficial social norms can emerge. Since social norms are underpinned by sanctioning, we introduce a training regime where agents can access all sanctioning events but learning is otherwise decentralized. This setting is technologically interesting because sanctioning events may be the only available public signal in decentralized multi-agent systems where reward or policy-sharing is infeasible or undesirable. To achieve collective action in this setting we construct an agent architecture containing a classifier module that categorizes observed behaviors as approved or disapproved, and a motivation to punish in accord with the group. We show that social norms emerge in multi-agent systems containing this agent and investigate the conditions under which this helps them achieve socially beneficial outcomes.