Inverse reinforcement learning (IRL) recovers reward functions from observed behavior, yet traditional methods assume a single stationary reward that cannot capture goal switching within an episode. Recent multi-intention IRL methods address this by segmenting trajectories, but model intention transitions as either a memoryless Markov chain or via manual state augmentation with a fixed history window. We propose the Probabilistic Recurrent Intention Switching Model (PRISM), which replaces both mechanisms with a lightweight recurrent network that maps observation history to a per-step intention distribution. We prove that the resulting EM objective decomposes exactly into independent per-intention reward subproblems, each solvable in closed form, yielding an $\mathcal{O}(nK)$ E-step with no variational approximation. We evaluate PRISM on a non-Markovian gridworld, a mouse labyrinth, and BridgeData~V2 robotic manipulation, the first large-scale robotic application of multi-intention IRL. Across all settings PRISM achieves the highest held-out log-likelihood while recovering nameable, temporally coherent intentions from unlabeled demonstrations, suggesting that discrete goal switching is present in both biological and artificial agents.

Vision-language models (VLMs) may memorize undesirable information from training data, motivating growing interest in machine unlearning. In this work, we present the first systematic survey and robustness analysis of VLM unlearning. We provide a comprehensive taxonomy and review of existing VLM unlearning methods, together with unified evaluations under multiple prompt settings. We then propose three attack paradigms to examine whether forgotten multimodal knowledge can be reactivated through contextual prompting or downstream retraining. Extensive experiments show that many existing methods remain vulnerable under these attacks, indicating that current approaches often hide rather than fully remove target knowledge. Our study provides new insights into the robustness and limitations of current VLM unlearning methods and highlights the need for more reliable multimodal unlearning strategies. Code is available at https://github.com/XMUDeepLIT/VLM-UnL-Attack.

Collaboration is central to human behavior, enabling tasks beyond individual capability. This ability arises from coordinating actions through internal representations of others, a concept known as shared intelligence. Additionally, humans are characterized by physical bodies and cognitive abilities that are optimized in response to their environment, a phenomenon referred to as embodied cognition. Designing humanoid robots that collaborate safely and effectively with people requires unifying these principles. Here we propose an architecture that integrates shared intelligence and embodied cognition to enable robots to physically collaborate with humans, where robot hardware and control are optimized for human metrics, using representations of the human body and motion intelligence. The ultimate goal is to achieve a form of shared embodied intelligence. Specifically, our architecture optimizes robot hardware and physical intelligence parameters with respect to human ergonomic metrics. This is accomplished by modeling human-robot interaction as a function of hardware configurations and embedding human models into the robot's physical intelligence. As a concrete implementation, we present the humanoid robot ergoCub, whose morphology and control have been optimized for collaborative tasks with humans. Our approach provides a framework for designing humanoid robots that prioritize human ergonomics at both the hardware and physical intelligence levels, with applications in industrial and assistive robotics.

Tax evasion causes severe losses of government revenues and disturbs the economic order of fair competition. To help alleviate this problem, the latest tax evasion detection solutions utilize expert knowledge to extract features and then train classifiers to determine whether a company is suspected of tax evasion. However, existing solutions mainly focus on the statistical features of the company, but fail to exploit the rich interactive information in tax scenarios, which affect the detection performance. In this paper, we first model the tax scenario as a heterogeneous graph and study the tax evasion detection problem under the heterogeneous graph model. To improve the performance of tax evasion detection, a novel graph neural network model is proposed to extract the comprehensive information of heterogeneous graphs. Specifically, we use heterogeneous and complex related party transaction groups to filter low-level noise information. Moreover, a hierarchical attention mechanism is designed to capture the deeper structure and semantic information hidden in the related party transaction group. We apply our method to the real risk management system of the tax bureau, and evaluate it on two human-labeled real-world tax datasets. The results demonstrate that our method significantly outperforms the state-of-the-art in the tax evasion detection task.

Text-to-speech (TTS) evaluation for low-resource non-Latin-script languages can fail when it relies on a single ASR round-trip word error rate (WER). A system may produce no audio, speak a neighbouring language, preserve target script text only in an ASR transcript, or sound unnatural to native listeners. We introduce INSV (Intelligibility, Naturalness, Script fidelity, and Verification), a reporting framework that separates these cases. This paper reports INSV-A, the automated screening subset: synthesis completion, ASR WER/CER, transcript Script Fidelity Rate, and audio language identification. Native MOS and phonetic annotation are specified but not claimed in this release. We instantiate INSV-A as PashtoTTS-Bench, a dated benchmark for Pashto TTS. The April-May 2026 run evaluates Edge GulNawaz, Edge Latifa, OmniVoice clone, OmniVoice auto, and an Urdu negative control on 200 FLEURS and 200 filtered Common Voice 24 prompts. Under the independent omniASR_CTC_300M_v2, OmniVoice auto has the lowest WER (24.1% FLEURS, 27.4% CV24), followed by Edge GulNawaz (32.8%, 39.5%), Edge Latifa (35.6%, 47.7%), and OmniVoice clone (45.4%, 34.8%). WER below the natural-speech baseline reflects clean synthetic audio and should not be read as better than native speech. Whisper Large V3 returns 0.0% Pashto labels on checked Pashto TTS audio, while MMS-LID-4017 and SpeechBrain VoxLingua107 separate Pashto outputs from the Urdu control. The release provides provider metadata, per-sentence scores, LID audits, failure logs, and scripts for adding systems.

The Muon optimizer has recently demonstrated remarkable empirical success in training large language models. However, the theoretical understanding of its mechanisms remains limited. Current convergence guarantees for Muon rely heavily on smoothness assumptions, leaving its non-smooth convergence behavior largely unexplored. In this work, we take a step toward bridging this gap by investigating Spectral Descent (SD), a simplified variant of Muon, together with its truncated counterpart, Truncated Spectral Descent (TSD). Under convexity, Lipschitz continuity, and sharpness conditions, we establish global linear convergence for both SD and TSD in non-smooth convex formulations. We also study regularized variants equipped with decoupled weight decay and derive sublinear convergence guarantees through their connection with Frank-Wolfe methods. Finally, we apply our theoretical framework to robust low-rank matrix recovery under mixed sparse and dense noise regimes and provide rigorous recovery guarantees. Numerical experiments support the theoretical findings and demonstrate the effectiveness of Muon-type methods for non-smooth optimization.

The proliferation of Reinforcement Learning from Verifiable Rewards (RLVR) datasets has exacerbated provenance collapse due to unclear lineage among existing datasets. To bridge this fragmented RLVR data landscape, we propose Atomic-source Tracing via Lineage-Aware Search (ATLAS), a systematic framework for tracing RLVR datasets back to their atomic sources, attributing over 99.7% of 1.45M instances to 20 atomic sources. Our analysis reveals that most RLVR datasets are variants of a small set of shared upstream sources, with few introducing genuinely new data, and many facing data contamination risks. These findings naturally motivate us to curate a new RLVR dataset, DAPO++, and to benchmark existing datasets from a lineage-aware perspective. To this end, we propose Source-level Counterfactual Attribution (SCA) as a guiding principle to curate a decontaminated training dataset with concentrated learning signals. Essentially, SCA measures a sample's marginal utility by comparing per-atomic-source RL checkpoints against a shared base model. Building upon these attribution signals, we further design a composite dataset quality score Q that strongly correlates with downstream RLVR performance. Experiments on Qwen3 series models verify that DAPO++ consistently improves performance on held-out benchmarks, while Q reliably predicts downstream RLVR training effectiveness. Our code and data is available at https://github.com/Celine-hxy/ATLAS.

User modeling aims to use language models (LMs) to mimic an individual's behavior from a corpus of past context-action pairs (e.g., conversation turns), enabling the simulation of users in settings like behavioral science, human-AI collaboration, and market research. Recent approaches augment these corpora with synthesized reasoning traces, typically generated by conditioning on both context and action. However, such conditioning constitutes post-hoc rationalization rather than reasoning: the trace is guaranteed to justify the action, but may not encode the underlying latent causal decision paths. We propose Recon, which uses action reconstruction to score reasoning traces by their predictive power: given a context and candidate reasoning, a reconstruction model predicts the action, and reconstruction fidelity determines reasoning quality. Across four domains, Recon achieves a 54.7% win rate over Backward Synthesis, a standard post-hoc rationalization baseline. Further, we find that training a reasoning synthesis model with rewards derived from Recon improves downstream user modeling performance, achieving a win rate of up to 70.0% over baselines. We further show that Recon-synthesized reasoning transfers across models, and improves user modeling beyond the reconstruction model. Our work demonstrates that post-hoc rationalization is insufficient for reasoning synthesis, and that useful and interpretable reasoning should naturally elicit the action from the context.

Existing video captioning methods struggle to balance visual fidelity and redundancy: holistic captions are compact but lose fine-grained evidence, whereas segment-wise captions improve coverage but introduce heavy redundancy. We propose CodecCap, a codec-inspired framework for high-fidelity dense video captioning. Analogous to video codecs, CodecCap represents videos using keyframe and residual captions. Keyframe captions exhaustively encode stable visual context, while residual captions capture temporally only localized actions, motions and changes. This effectively preserves fine-grained visual evidence while reducing redundant descriptions. To quantify the fidelity of captions, we introduce VidCapQA, a caption-then-QA benchmark with 1,000 questions across 14 capability dimensions. Results on VidCapQA show that captions directly generated by strong VLMs still miss many visual details, highlighting caption representation as a critical bottleneck. Experiments show that CodecCap significantly surpasses direct captioning with the same underlying VLMs, suggesting keyframe-residual captioning a way for high-fidelity video-language supervision. We further use CodecCap to construct CodecVDC-100K, a large-scale dense captioning dataset with anchor, residual, scene-level, and video-level supervision.

Reinforcement learning in open-ended long-form generation is challenging because reliable reference answers and automatic metrics are often unavailable. Existing rubric-based methods typically rely on pointwise LLM-as-a-judge scoring, but absolute scores are difficult to calibrate across complex responses, may provide weak discrimination among same-query rollouts, and can become saturated during optimization. We propose Tournament-GRPO, a group-wise reward framework that converts rubric-guided LLM judgments into relative rewards through repeated multi-round tournaments among same-query rollouts. Tournament-GRPO compares candidates within groups, accumulates tournament outcomes, and normalizes them into group-wise rewards for GRPO training. Experiments on Deep Research Bench show that Tournament-GRPO consistently outperforms existing reward-design baselines, achieving a 4.52-point overall-score improvement over the strongest baseline. Further analyses show that tournament rewards provide a favorable effectiveness--efficiency trade-off and that tournament design affects training dynamics. These results suggest that rubric-guided tournament comparison provides an effective reward signal for reinforcement learning in open-ended long-form generation.

As large language models (LLMs) are increasingly deployed to users around the world, they are integrated into everyday tasks across diverse cultural contexts, from drafting personal communications to brainstorming creative ideas. These tasks are inherently cultural: they require contextual appropriateness, symbolic resonance, and tacit cultural expectations that native speakers draw on instinctively, meaning that a response can be factually plausible yet unmistakably wrong to a local reader. Existing cultural benchmarks have treated culture as a flat set of facts via fact verification or norm entailment methods, and have adopted LLM-as-a-Judge without examining whether they can capture such thick cultural errors. To address this gap, we present JuICE (Benchmark for LLM-Judge in Identifying Cultural Errors), a multilingual dataset of 7,470 span-level annotations of cultural and linguistic errors in long-form LLM responses. It covers 1,050 query-response pairs from four countries (the United States, South Korea, Indonesia, and Bangladesh), in both English and their countries' main languages. Using JuICE, we find that even the strongest LLM-judge achieves only an F1 of 0.52 in the erroneous span detection task. Furthermore, LLM-judges consistently miss thick cultural errors that local residents readily identify. Our findings suggest that robust cultural evaluation must move beyond surface-level detection toward frameworks that account for the depth and situatedness of cultural meaning.

Agentic reinforcement learning (RL) has proven effective for training LLM-based agents with external tool-use capabilities. However, we identify that agentic RL training induces increasing redundant tool calls and blurs the model's intrinsic knowledge boundary, where the model fails to distinguish when tools are needed versus when parametric knowledge suffices. Existing solutions based on reward shaping create coarse-grained optimization targets that tend to incentivize indiscriminate tool-call suppression, leading to reward hacking. In this paper, we propose AKBE (Agentic Knowledge Boundary Enhancement), an on-policy method that dynamically probes the model's intrinsic knowledge boundary through dual-path (with-tool and no-tool) rollouts during training. We define the knowledge boundary as the per-instance determination of whether tools are required and the minimum tool calls necessary. By comparing correctness across paths, AKBE categorizes trajectories and constructs targeted supervisory signals that guide efficient tool-use patterns for each question. These signals are integrated seamlessly into the agentic RL training loop. Experiments on seven QA benchmarks demonstrate that AKBE improves task accuracy by +1.85 on average and reduces tool calls by 18% over standard agentic RL, yielding 25% higher tool productivity without any accuracy-efficiency trade-off. Further analysis suggests its plug-and-play compatibility across different RL algorithms and the mechanism of each signal category. Our code is available at https://github.com/CuSO4-Chen/AKBE.

3D shape completion from partial scans remains challenging for unseen categories and noisy real-world observations, where geometry alone is often insufficient for inferring missing structure. We present DinoComplete, a deterministic and efficient shape completion framework that augments geometric reconstruction with voxel-aligned semantic priors distilled from DINO features. First, we construct multi-view DINO feature volumes aligned with ShapeNet data and train a student network to predict dense semantic features directly from incomplete shapes. These predicted features capture global structure and part-aware semantic context while remaining aligned with the underlying geometry. We then integrate these distilled features into a completion network, where geometric and semantic voxel representations are fused through voxel state-space modeling. To enable efficient long-range reasoning without sacrificing resolution, we introduce a multi-scale voxel Mamba module that refines the fused features by combining full-grid and chunk-wise sequence modeling. Experiments on unseen ShapeNet categories and ScanNet objects show that DinoComplete achieves stronger completion quality than prior deterministic and generative based completion methods while using fewer parameters, requiring lower memory, and achieving faster inference. Our results demonstrate that distilling semantic priors from visual foundation models improves generalization and robustness in 3D shape completion.

The problem of object pose and shape estimation has seen key advancements lately. Encoder-decoder (e.g., SAM3D, LRM, CRISP) and diffusion-based models (e.g., InstantMesh, Zero123, SceneComplete) have shown category-agnostic shape encoding capacity and open-set generalizability. In this work, we ask the question: Are the object pose and shape estimation methods mature enough, such that when used with antipodal grasp sampling, can outperform the end-to-end grasp synthesis methods? We explore this question in detail by scoping our study to parallel jaw grippers, 7-DoF grasps, and single-view RGB(-D) image as input. We implement and compare a state-of-the-art, end-to-end grasp synthesis method and three modular methods, which first estimate the object pose and shape for all objects in the scene, and generate grasps using antipodal sampling. We observe that the modular methods outperform the end-to-end method in all our experiments. The modular methods are able to synthesize plenty of grasps, even for small objects, where the end-to-end methods fail. The effectiveness of the modular methods is contingent on the accuracy of the pose and shape estimation, and suffers partial degradation in cluttered scenes - a limitation of the existing pose and shape estimation methods. We also analyze the failure modes and run-times for the three modular methods, which use two different ways of object pose and shape estimation: one based on an encoder-decoder model, while another a diffusion model. Finally, we demonstrate that the single-view object pose and shape estimation methods can be augmented with vision-language models to yield language-conditioned grasps from just single-view RGB-D image as input. We notice comparable performance to the state-of-the-art LERF-TOGO baseline.

Large language models (LLMs) can support democratic deliberation at scales previously constrained by turn-taking and facilitation bandwidth. Recent work shows that LLM-generated group statements are often preferred over human-mediated outputs, while theoretical analyses argue that LLMs relax the simultaneity constraints limiting collective intelligence. Yet pure LLM mediation risks collapsing pluralism, over-optimizing for agreement, and undermining legitimacy when participants cannot contest how they are represented. We propose a symbiotic human-AI framework organized into three layers: observation and diversity amplification, facilitation with clause-level provenance, and human primacy for ratification. Our contributions include graded coverage, diversity, and erasure metrics with salience-aware weighting; a provenance pipeline combining cross-encoder similarity with causal knockout diagnostics; preference-conditioned trade-off control; equity-aware contestability workflows; adversarial robustness tests; and an evaluation protocol with ablation designs informed by evidence of LLM-as-judge limitations. The result is a testable blueprint for deliberation technology that scales collective intelligence while preserving agency and legitimacy.

Parametric knowledge in large language models (LLMs) is a cornerstone of their success, yet remains poorly understood. Existing knowledge benchmarks typically rely on predefined questions (e.g., "What is the birth date of M.L. King?"), evaluating only knowledge that benchmark designers explicitly choose to query, a problematic availability bias. In this paper, we introduce open knowledge evaluation, a new paradigm for LLM knowledge benchmarking. Instead of asking narrow questions, it evaluates models on the knowledge they choose to surface in response to open-ended elicitation prompts (e.g., "Tell me everything you know about M.L. King"). This shifts the focus from predefined answer retrieval toward characterizing the knowledge models naturally express. We instantiate this paradigm with BeQu (Beyond Questions), a benchmark of 10,000 entities paired with reference corpora for statement verification. Using BeQu, we evaluate a broad range of language models and analyze the effects of reasoning effort, model scale, prompt format, and knowledge domain. Data and leaderboard are available on this work's GitHub repository and at the benchmark's website.

Large language models have achieved strong performance across many NLP tasks, yet Urdu remains comparatively underexplored due to limited resources and fragmented evaluation settings. To address this gap, we introduce DunbaaBERT, a family of Urdu RoBERTa-base models trained from scratch with Byte-BPE vocabularies of 32k, 52k, and 96k tokens on a deduplicated 17GB Urdu corpus. We evaluate DunbaaBERT across intrinsic and downstream Urdu NLP benchmarks covering linguistic acceptability, news classification, offensive language detection, and sentiment analysis while analyzing vocabulary-size effects on performance and efficiency trade-offs. Across benchmarks, the DunbaaBERT variants achieve competitive performance against strong multilingual baselines while consistently maintaining favorable efficiency trade-offs. Interestingly, larger vocabularies do not consistently improve downstream effectiveness, with DunbaaBERT$_{\text{32k}}$ repeatedly providing the strongest overall efficiency profile. Overall, our results demonstrate that carefully curated Urdu-specific encoder models can remain highly competitive despite comparatively compact model and training scales. All models are released under the MIT license.

Reinforcement learning with verifiable rewards (RLVR) has become central to post-training reasoning models, yet a key limitation of existing studies is their narrow view of the reasoning space: difficulty is treated as reasoning depth alone, and reward is concentrated on forward deductive state tracking. We instead characterize the reasoning space along two dimensions. Difficulty. Beyond reasoning depth, we study environment complexity, where models must identify the correct path amid distractors and interacting structures. Rewarded reasoning form. We consider four abilities core to real-world reasoning: deductive state tracking, abductive recovery of hidden events or facts, inductive rule induction, and analogical transfer. To disentangle these factors, we construct a synthetic knowledge-graph environment with controlled pre- and post-training distributions, where each instance varies along depth, complexity, and task family. Three findings emerge: joint depth-complexity coverage outperforms single-axis recipes; reasoning families respond non-uniformly, with abductive reasoning degrading outside the RL-covered region and task correlations clustering into deductive-abductive and inductive-analogy pairs; and uniform mixing outperforms staged curricula under a fixed budget. We also find that recent off-the-shelf models exhibit the same deductive-over-abductive asymmetry, suggesting that this gap is not merely an artifact of our controlled setup.

Unsupervised visual object tracking is a challenging task that requires following arbitrary targets in videos without training on ground-truth annotations. Despite considerable progress, existing state-of-the-art unsupervised trackers often struggle in scenarios that demand fine-grained understanding of semantic and visual structural information within video frames. Text-to-image diffusion models are well known for their ability to generate images that accurately reflect the semantics and structures described in the input prompt, demonstrating a strong grasp of visual semantics and structures. Building on this capability, we approach the unsupervised tracking from a new perspective by exploiting the rich semantic knowledge encoded in pretrained text-to-image diffusion models. To adapt the diffusion models, which are originally developed for image generation, to the tracking task, we reinterpret the models as a bridge between text and image modalities. This connection is realized through the cross-attention mechanism: when both text and an image are input into the models, they highlight the regions of the image that are semantically aligned with the text in the cross-attention maps. We therefore learn a prompt that represents the tracking target and activates its corresponding region in the cross-attention map for each frame, which enables object tracking with the diffusion model. Specifically, our method Diff-Tracking is composed of two main components: an initial prompt learner and an online prompt updater. The initial prompt learner generates a prompt that captures the target object in the first frame, allowing the diffusion model to identify the target. The online prompt updater refines the prompt based on motion information, enabling consistent tracking across video frames. We evaluate our approach on six challenging tracking datasets demonstrate the effectiveness of our approach.

Computing legal indicators from normative texts is a key task in legal monitoring and policy evaluation, but presents significant challenges due to the complexity, scale, and interpretive nature of legal language, as well as the variability in available document quality. Existing natural language processing techniques and generative models can assist in legal analysis, but often suffer from high risk of hallucinations and lack the interpretability and evidence grounding required for reliable indicator computation. This paper presents N2I-RAG (From Norms to Indicators), an agentic retrieval-augmented generation framework designed to automate the computation of legal indicators in a transparent and traceable way. We integrate adaptive retrieval, llm-based agents, and validation mechanisms in a modular pipeline, where each component performs a defined role in filtering, retrieving, and assessing evidence, and in producing binary legal outcomes linked to identifiable legal provisions. The framework emphasizes traceability by requiring explicit explanations of intermediate decisions and final indicator assignments. We evaluate N2I-RAG using an in-house constructed French marine environmental law corpus that includes both scanned and digital sources. Comparative experiments with multiple language model families demonstrate that the proposed approach consistently outperforms baseline systems, and generalizes well when tested on 2 different bans. The results indicate that agentic retrieval-augmented generation can bridge open-text legal language and standardized indicator computation, offering a foundation for transparent and scalable legal observatories.

Large language models (LLMs) have achieved remarkable progress, with post-training playing a crucial role in enhancing their reasoning capabilities. Among post-training paradigms, supervised fine-tuning (SFT) is widely used: it leverages external data to provide dense supervision and enables efficient training. However, directly fine-tuning on expert data can hurt generalization when the data distribution is mismatched with the target model's own distribution. In this work, we propose Data Adaptation for Reasoning Tuning (DART), which formulates the use of a fixed, potentially distributionally misaligned SFT dataset as an optimization problem over demonstration transformations. DART trains a mapper model with reinforcement learning to convert original SFT data into model-adapted supervision that better matches the target model's distribution and learning preferences. The transformed data are then used for SFT, allowing the target model to better exploit external supervision. Experiments across multiple models and datasets show that DART improves generalization, achieves higher training efficiency than direct RL, and helps models surpass standard SFT. Our code is available at https://anonymous.4open.science/r/DART525E50D.

Video generation models (VGMs) are rapidly entering classrooms, yet existing benchmarks evaluate only perceptual quality, intrinsic faithfulness, generic safety, or video as a reasoning medium, and none assesses whether the outputs are educationally valid. In this work, we present EduVideoBench, the first balanced benchmark in the education domain, grounded in the Knowledge-Skills-Attitude (KSA) framework so that pedagogical adequacy and educational safety are evaluated jointly rather than as ad-hoc quality dimensions. Across five frontier VGMs, our results show substantial room for improvement across knowledge, skills, and attitude before they are classroom-ready. We complement this with a qualitative analysis of expert comments, finding that educational validity is multi-component, where a single misaligned element such as pacing, legibility, or notation can invalidate an otherwise correct video. We hope EduVideoBench will guide the development of VGMs that are pedagogically grounded and safe for the classroom.

LLM-generated peer reviews are increasingly common at major venues, yet their deficiencies are hard to detect because they are uniformly fluent and well-structured. Existing work either classifies authorship without judging quality, or scores quality with features designed for human-written reviews; no prior system detects deficiencies in LLM-generated reviews at the level of individual defect types. To bridge the gap, we introduce TADDLE, a Tool-Augmented Agent for Detecting Deficient LLM-Generated Peer Reviews, together with the first expert-annotated benchmark for this task. Our benchmark comprises 1,800 reviews on 50 ICLR 2025 papers, multi-label-annotated by 18 domain experts against a taxonomy of six defect categories (plus a non-deficient label). TADDLE decomposes detection into four specialized analysis tools -- Verify, Correct, Complete, and Transform -- orchestrated by an agent; an integrator synthesizes their outputs into binary and multi-label classifications via two-stage semi-supervised learning. Extensive experiments show that TADDLE performs strongly on both binary detection and the multi-label classification task. We release the benchmark and code at https://github.com/AquariusAQ/TADDLE.

Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain sizes. A central building block for the exploitation of indistinguishable objects in factor graphs is the identification of commutative factors, i.e., factors whose output values are invariant under permutations of input values assigned to a subset of their arguments. In this paper, we revisit the theoretical foundations underlying the state-of-the-art algorithm to detect commutative factors. Specifically, we show that in its current form, the state-of-the-art algorithm relies on a central theorem that is mistakenly regarded as a sufficient condition to identify commutative factors, while it actually only implies necessary condition. Consequently, the state of the art might, as we show in this paper, deliver incorrect results. To fix the flaws currently present in the state of the art, we prove a slightly modified version of the aforementioned theorem, which serves as a necessary condition to identify commutative factors. Moreover, we present a corrected version of the state-of-the-art algorithm, which keeps its efficiency while ensuring correctness and introduce a complementary algorithm with tighter worst-case bounds.

A fundamental open question in self-supervised learning (SSL) is the explicit characterization of the optimal geometry of the learned representations. Recently, LeJEPA identified isotropic Gaussian embeddings as optimal for minimizing downstream prediction risk in Euclidean spaces. However, the corresponding problem for distributions supported on lower-dimensional manifolds, such as the hypersphere, remains unexplored. In this work, we demonstrate that extending this minimax analysis to smooth distributions on Riemannian manifolds fundamentally changes the optimal solution. We show that, under a worst-case formulation, both k-nearest neighbors and kernel ridge regression induce hyperspherical uniformity. More precisely, we show that uniform distributions on manifolds are optimal for k-nearest neighbors, and that the uniform distribution on the sphere is optimal for kernel ridge regression with both the exponential dot-product kernel and the linear kernel. This theoretical insight reveals a fundamental limitation of Gaussian embeddings: their non-uniform density induces anisotropic k-NN neighborhoods, severely biasing the estimator. To correct this, we introduce SPHERE-JEPA, a theoretically grounded SSL framework. We adapt LeJEPA's Cram{é}r-Wold projection mechanism to enforce hyperspherical uniformity rather than a Gaussian prior. Empirically, SPHERE-JEPA yields significant improvements, boosting texture retrieval mAP by over 6%, while consistently matching or outperforming LeJEPA on standard benchmarks-including a +1.8% linear probing gain on ImageNet-1K (ViT-B/14).

Normalization layers in modern large language models (LLMs) consist of a deterministic normalization operation and a learnable scale vector. While the normalization operation has been extensively studied, the scale vector remains poorly understood despite its ubiquitous use. In this work, we present a systematic study of scale vectors in LLMs from the perspectives of expressivity, optimization, and architectural structure. First, we show empirically that although scale vectors constitute only a negligible fraction of model parameters, removing them substantially degrades LLM pre-training. Our theory further shows that, in Pre-Norm architectures, scale vectors do not increase expressivity; instead, they improve optimization through a self-amplifying preconditioning effect on subsequent linear mappings. Second, we investigate the role of weight decay for scale vectors. By distinguishing Input-Norm and Output-Norm layers, we theoretically show that weight decay is beneficial for the former but harmful for the latter, due to their distinct roles in optimization and expressivity. Third, motivated by this understanding, we propose three lightweight and complementary improvements to scale vectors: branch-specific heterogeneity, improved placement around linear mappings, and magnitude-direction reparameterization. Both theory and experiments show that each improvement yields consistent gains. Finally, we combine these improvements into a unified scale-vector strategy and evaluate it through extensive LLM pre-training experiments on dense and mixture-of-experts models ranging from 0.12B to 2B parameters, across multiple optimizers and learning rate schedules, under industrial-scale token budgets. The unified strategy consistently achieves lower terminal loss than well-tuned baselines and exhibits more favorable scaling behavior, while adding negligible parameter and computational overhead.

In point clouds, noise directly perturbs point coordinates that encode both spatial location and geometry, making one-to-one correspondence construction more challenging than in images. Existing methods impose statistical mappings across noisy variants via noise or optimal transport, but suffer from correspondence ambiguity. In this work, we propose Self-Induced Mirror-Point Consistency (SIMPC) to learn deterministic correspondences between points and the underlying surface in an unsupervised manner. For each noisy point, SIMPC generates a mirror-point on the opposite side of the underlying surface, guided by geometric priors during the denoising process. By encouraging consistency between the denoising targets of the original point and its mirror counterpart, SIMPC effectively localizes the position of underlying surface. Extensive experiments on synthetic and real-world datasets demonstrate that SIMPC significantly outperforms state-of-the-art unsupervised methods and surpasses several strong supervised counterparts.

Chain-of-Thought (CoT) reasoning has advanced large language models (LLMs), but outcome-based supervision leads to pervasive post-hoc rationalization, producing plausible yet unfaithful reasoning chains. Most prior faithfulness assessment methods are either unscalable, expensive, or unreliable. We propose GeoFaith, a spatio-temporal framework that leverages latent geometric structure and entropy dynamics to diagnose and enforce faithful reasoning. We develop a scalable bootstrapping pipeline expanding step-level annotations from 1k to 20k samples across four domains, train an 8B faithfulness detector outperforming GPT-5 on standard benchmarks, and design a faithfulness-aware reinforcement learning framework jointly optimizing outcome correctness, process faithfulness, and trajectory consistency. Experiments show the proposed method achieves superior performance on both faithfulness detection and downstream reasoning, producing shorter, more interpretable chains without sacrificing accuracy. Our code will be made available publicly.

Human motion recovered from monocular videos often appears overly smooth or dynamically inconsistent, even when joint positions are numerically accurate. We observe that this limitation stems from the absence of reliable high-order temporal cues -- velocity and acceleration -- which are essential for reconstructing motion that exhibits realistic momentum, timing, and high-frequency detail. We introduce HTD-Refine, a post-processing framework that augments existing Human Motion Recovery (HMR) pipelines using explicitly estimated high-order temporal dynamics. At the core of our system is PVA-Net, a temporal transformer that infers per-joint 2D positions, 3D velocities, and 3D accelerations directly from a monocular video. These predicted dynamics serve as soft yet informative constraints in a global optimization procedure that refines world-space trajectories, significantly reducing jitter, suppressing over-smoothing, and restoring physically plausible motion. Extensive experiments on challenging in-the-wild benchmarks show that HTD-Refine consistently improves state-of-the-art HMR methods, yielding more accurate global trajectories and substantially more natural motion dynamics. Our results highlight the critical role of high-order temporal modeling in advancing monocular human motion recovery.

Multi-stakeholder tasks require one output to satisfy users with conflicting preferences. Holistic LLM judges conflate utility estimation and utility aggregation, yielding unstable implicit weights. We show empirically and theoretically that this aggregation-specific \emph{weighting noise} can create large score shifts when stakeholder satisfaction is dispersed; in our experiments, these weight-induced shifts also increase with stakeholder count. We propose \textsc{DecompR}: counterfactual-calibrated weights are fixed from query structure before candidate scoring, while per-role utilities are estimated independently, removing candidate-dependent weight drift and reducing estimation noise.