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Computer Science

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Thursday 8 October

Computation and Language

Latent Core Tokenizer: Compress, but Meaningfully

Felermino D. M. A. Ali, Millicent Ochieng, Ogbemi Ekwejunor-Etchie et al. (+3 more)

Tokenizers are commonly optimized for compression, but a compact vocabulary does not necessarily distribute its capacity evenly across languages. We introduce the Latent Core Tokenizer (LCT), a language-agnostic approach that separates structural discovery from vocabulary construction. LCT uses Minimum Description Length, entropy-based boundary signals, and morphotactic constraints to identify reusable linguistic units before constructing a shared vocabulary. Across 104 languages with a 200K-token vocabulary, LCT achieves lower fertility and higher MorphScore than BPE, Unigram, and parity-aware BPE, while maintaining comparable cross-lingual disparity in tokenization cost. Across four multilingual downstream benchmarks, LCT improves aggregate score by 1.48, 1.83, and 2.00 points over BPE, Unigram, and parity-aware BPE, respectively. Our findings show that compression alone does not predict representation quality and highlight the importance of morphology-driven structural discovery and how frequency is used to allocate the final vocabulary across languages.
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All authors Felermino D. M. A. Ali, Millicent Ochieng, Ogbemi Ekwejunor-Etchie, Ade Famoti, Jacki O'Neill, Debjit Paul

Artificial Intelligence

OnTrack: Real-Time Monitoring and Intervention in LLM Agent Trajectories via Streaming Structure-Aware Optimal Transport

Babak Barazandeh, Connor Swanson, Chinmay Kulkarni et al. (+1 more)

Agents are deployed in applications from trip planners and stock trading to IT incident triage. In most cases, LLM agents work autonomously with minimal rule-based safeguarding, leading to cost and safety issues from irreversible actions. Recent works resolve this either by using a safeguard agent to monitor behavior or evaluating logs post-hoc. The first adds cost and latency to every step; the second delivers its verdict after the run, when tokens are burned and damage is done. To overcome this, we propose OnTrack, a streaming monitoring mechanism that compares an agent's steps and dependencies against recorded successful runs to alert users or block the agent in about a millisecond per step. We study this problem in three regimes of decreasing access: full reference access (historical runs and tool schemas), intermediate access (only tool schemas), and no prior knowledge (only step logs as generated). Expectation of OnTrack's monitoring capabilities reduces as data access drops, ranging from plan violation detection to identifying loops, stalls, and repeated tool calls. Finally, we evaluate OnTrack using SWE-bench trajectories. Based on the first 8 steps, our method ranks failing trajectories below succeeding ones better than content similarity approaches (+0.057 AUROC). With an abort policy, we save about 18% of compute that would be burned on failing runs, where 83% of interrupted runs were actually heading to failure (5 out of 6 aborts were correct).
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All authors Babak Barazandeh, Connor Swanson, Chinmay Kulkarni, Nikhil Mungel

Computer Vision

AgentGarten: Code Worlds for Evolving Agents

Jiawei Chi, Shangchen Miao, Zhiyuan Shi et al. (+12 more)

Interactive virtual worlds allow agents to learn through exploration and interaction. What agents can learn is bounded by the environments they practice in, which must be faithful, with consistent state, rules, and dynamics, and realistic, with observations that follow the real-world visual distributions. Achieving both across diverse worlds remains a bottleneck. We introduce AgentGarten, a framework that couples simulators and game engines with a shared neural renderer to build real-time interactive environments. Its simulation backends maintain persistent world state and execute program-defined interaction rules, while the renderer generates visual observations from structured conditions exported through a common interface. To build the neural renderer, we adapt a pretrained video model to geometry conditions, distill it with our proposed Adversarial Forcing, and optimize inference for real-time interaction. Adversarial Forcing makes history prefilling differentiable through exact replay, so that losses on later predictions update how the renderer encodes prior observations, and adds real-data adversarial supervision to improve its visual quality. In AgentGarten, agents perceive the world through visual observations, interact with it in real time, and improve by distilling each round of experience into playbooks that subsequent agents inherit and refine. Our empirical study demonstrates a substantial gain in learning efficiency, with agents learning from just 4 rounds compared with millions for a conventional reinforcement learning counterpart. As new worlds can be written as code and rendered through the same interface, environments can scale in both number and difficulty alongside their agents, a step toward agents that keep evolving through interactive experience.
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All authors Jiawei Chi, Shangchen Miao, Zhiyuan Shi, Kailu Wu, Hanyang Wang, Weiliang Chen, Qiyu Dai, Chengyang Li, Jinshan Ren, Jun Gao, Mingsheng Long, Yueqi Duan, Jiangran Lyu, Jialong Wu, Fangfu Liu

Graphics

FeatureZ: A General Framework for Feature-Preserving Compression via Pointwise Bounds and Star Classification

Nathaniel Gorski, Xin Liang, Hanqi Guo et al. (+1 more)

Geometric and topological features, such as isosurfaces, quantiles, merge trees, and Morse-Smale complexes, are central to the analysis and visualization of scientific data across diverse domains, including medical imaging, climate science, materials science, and astronomy. However, most lossy compressors for scientific data provide only pointwise error guarantees and do not preserve derived features. Existing feature-preserving compressors are often difficult to develop and typically tailored to a single feature. In this paper, we introduce FeatureZ, a lossy compression framework for structured volumetric scalar fields that can preserve a wide class of geometric and topological features. In particular, FeatureZ frames feature-preserving compression as preserving pointwise upper and lower bounds together with a consistent classification of each point's star (i.e., its incident cells) in the underlying structured mesh. Although not all notions of feature preservation fit this framework, many features and topological descriptors targeted by existing compressors do. FeatureZ provides an efficient implementation of feature-preserving compression under this formulation. In particular, FeatureZ operates as an augmentation layer that refines the output of an existing lossy compressor. It first applies quantization to enforce pointwise bounds, and then employs an iterative procedure to ensure consistent star classification. We demonstrate that FeatureZ preserves diverse features during compression with minimal overhead, achieving compression ratios comparable to or better than methods specialized for individual features.
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All authors Nathaniel Gorski, Xin Liang, Hanqi Guo, Bei Wang

Machine Learning

Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders

Joel-Pascal Ntwali N'konzi, Feliks Nüske and Stefan Klus

Koopman operator theory provides a linear framework for analyzing nonlinear dynamical systems and has become a major tool for data-driven modeling. A central challenge, however, is that finite-dimensional approximations computed by methods such as extended dynamic mode decomposition (EDMD) require the dictionary to be specified a priori. Recent machine-learning approaches address this limitation by learning the dictionary from data, predominantly using artificial neural network (ANN) autoencoder architectures. Although kernel methods offer an alternative with greater interpretability and tractability for theoretical analysis, they have received little attention in this setting. We introduce extended dynamic mode decomposition with kernel-based dictionary learning (EDMD-kDL), a kernel-based method for learning finite-dimensional Koopman embeddings directly from data. The method combines ideas from collocation methods and bilevel optimization to simultaneously learn a kernel dictionary and the corresponding Koopman approximation. We evaluate EDMD-kDL against state-of-the-art ANN-based approaches on a range of numerical experiments, including global sea-surface-temperature forecasting and learning directly from video data. Across all tested settings, EDMD-kDL achieves performance comparable to or better than the ANN-based methods. Moreover, in contrast to standard kernel methods, the proposed approach is scalable to large datasets by design since the size of the required kernel matrices depends on the number of collocation points rather than the size of the training dataset.
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Robotics

Embodied Turing Machines: Stateful Code for Robot Recursive Self-Improvement

Kairui Hu, Siyuan Hu, Fangzhou Hong et al. (+2 more)

Most robot policies keep a model in the control loop: a VLA maps observations to actions, and an Agent Harness, such as Agent-as-Policy or Harness VLA queries a VLM for decision making at run time. We propose a different view: the embodied world is an Embodied Turing Machine, whose tape is the robot and environment state and rules are the policy. If this state can be represented accurately, the decision making can be written entirely in code. We therefore propose Code-Only-as-Policy (COAP): code measures and tracks the robot, environment, and task state from camera images and proprioception, and makes every decision from it. The same code applies across episodes, and different tasks share one library without a VLM or VLA in the loop. Compared with VLAs and Agent Harnesses, we analyze three advantages of COAP: (i) Explicit State: the state can be stored in code; (ii) Execution: code makes decision making controllable, recovers from failures flexibly, and runs fast and cheaply online; (iii) Extensibility: new tasks reuse, inherit, or extend the shared library, so capabilities can accumulate over tasks. These advantages make COAP a suitable medium for recursive self-improvement (RSI): coding agents develop the library in a closed loop, and each change is explicit and controllable. On RoboDojo's 42 bimanual tasks, the resulting library reaches a success rate of 70.24% without a model at test time. The upper bound of COAP lies in how accurately the state is represented for decision making and how robust the code logic is. We thus propose COAP as a new paradigm for embodied tasks; since it applies across episodes, it can also serve as an efficient data engine for VLAs and Agent Harnesses.
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All authors Kairui Hu, Siyuan Hu, Fangzhou Hong, Zhaoxi Chen, Ziwei Liu

Robotics

LiteNWM: Efficient Latent World Models for Onboard Visual Navigation in the Wild

Linkai Liu, Yuntian Zhang, Zhenshan Bing et al. (+5 more)

Direct visual navigation policies generate trajectories efficiently but do not explicitly evaluate their future consequences. Generative navigation world models provide this foresight through visual rollouts, which are costly when evaluating multiple candidates. We present LiteNWM, a latent navigation world model that shares visual encoding across candidates and jointly predicts their action-conditioned future representations at multiple horizons, while a learned scorer uses these predictions to select trajectories. In offline evaluations on RECON, SCAND, and SACSoN, LiteNWM reduces macro-averaged trajectory error by 17.56% relative to NoMaD+NWM-XL and achieves a 128.00-fold end-to-end speedup on an RTX 5090. The same evaluator transfers from NoMaD to MBRA without proposer-specific retraining, reducing MBRA's macro-averaged trajectory error by 16.2%. In real-robot experiments in unseen indoor and outdoor environments, LiteNWM improves navigation success from 43.3% to 83.3% relative to NoMaD. These results demonstrate that LiteNWM can be deployed for future-aware planning and closed-loop navigation on a physical robot.
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All authors Linkai Liu, Yuntian Zhang, Zhenshan Bing, Chen Chen, Lingjuan Lyu, Shangguang Wang, Mengwei Xu, Dongqi Cai

Computation and Language

Which Skill to Distill? SGUID: Selecting a Compact Skill Bank for Model-Skill Co-Evolution

Yuhan Liu, Xiyao Ma, Zhongkai Sun et al. (+4 more)

Skills, reusable procedural guidance added at inference, can substantially improve LLM downstream performance (Li et al., 2026). Prior work retrieves skills from a bank by semantic relevance, then uses them as inference-time patches or for model distillation. The individual utility of each skill, however, is largely neglected. We first show that, in on-policy distillation where skill-conditioned policies serve as teachers, fewer than 25% of retrieved skills provide useful distillation signals. We then propose SGUID, a method for selecting a compact subset of skills for distillation. SGUID retains a skill only if it consistently yields effective learning signals during training. The selected skills are then distilled to produce a better model. Our results show that not all skills are worth distilling. Across four models from the Olmo and Qwen families, distilling 6 selected skills matches or exceeds full-bank distillation in mean avg@12 on three of the four models, and on all four after a second round that distills 3 newly selected skills, while the full banks are up to 11x larger. Importantly, SGUID supports stable model-skill co-evolution: after a distillation round, a new candidate bank is curated from the updated model's rollouts, and SGUID selects which skills to internalize next. In the second round, this loop selects 3 new skills and improves Qwen3-8B from 64.3% to 66.3%. The selection step is essential for stability: on Qwen3-4B, naively updating the model with unfiltered skills degrades performance, including a 0.3 percentage point drop on HMMT25, whereas SGUID improves HMMT25 by 0.5 points after the first round and 1.1 points after the second. These results identify skill selection as the key mechanism for stable model-skill co-evolution.
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All authors Yuhan Liu, Xiyao Ma, Zhongkai Sun, Xu Han, Chengyuan Ma, Benjamin Z. Yao, Chenlei Guo

Artificial Intelligence

HANS: A Handwritten Answer Sheet Dataset for Noisy Hybrid Document Parsing

Xiazhen Wu, Wansong Qin, Yangbin Zheng et al. (+5 more)

Intelligent grading and automated scoring technologies constitute critical infrastructure for smart education. However, existing document parsing and handwriting recognition benchmarks are predominantly designed for well-structured printed documents or isolated mathematical expressions, lacking datasets that capture the complex characteristics inherent to student answer sheets, including multi-line derivation processes, heterogeneous mixtures of text and mathematical formulae, and noise artifacts such as strikethroughs. To address this gap, we introduce HANS, the first dataset explicitly constructed for real-world educational scenarios, encompassing mathematical expressions, natural language text, hand-drawn tables, and diverse noise patterns including corrections and deletions, accompanied by fine-grained annotations that establish a reliable foundation for robust recognition research. Building upon HANS, we propose NA-GOT, an end-to-end framework that achieves two-stage noise suppression through a lightweight noise suppression module operating at the feature level, complemented by a noiseaware attention mechanism incorporated into the decoding stage. Experimental results demonstrate that HANS poses substantial challenges to existing methods, while NA-GOT achieves significant improvements in both accuracy and stability for answer process recognition. The dataset will be made publicly available upon publication.
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All authors Xiazhen Wu, Wansong Qin, Yangbin Zheng, Liangda Fang, Zhan Li, Xiujie Huang, Liushen Zhou, Quanlong Guan

Machine Learning

Closing the Horizon Gap in Policy Optimization for Adversarial MDPs

Mingyi Li and Taira Tsuchiya

We consider policy optimization for online episodic tabular Markov decision processes (MDPs) with adversarial losses and bandit feedback. Policy optimization updates the policy locally at each state and avoids optimization over the occupancy-measure polytope, but its existing regret bounds are larger by a factor of the horizon $H$ than those of occupancy-measure-based algorithms. We close this gap by using regularized $Q$-functions, which allow us to control the stability of the local updates jointly over all state-action pairs rather than separately at each state. The resulting algorithm attains high-probability regret bounds of $\widetilde O(\sqrt{HS(H+A)T})$ for known transitions and $\widetilde O(HS\sqrt{AT})$ for unknown transitions, where $S$ is the number of states, $A$ the number of actions, and $T$ the number of episodes. Both bounds improve the horizon dependence of existing policy optimization bounds, and the latter matches the best-known bound. We further extend the algorithm to adversarial linear-mixture MDPs and obtain the same improvement in the horizon dependence.
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Artificial Intelligence

Cited but Not Consulted: A Counterfactual Audit of Legal Chain-of-Thought Faithfulness

Saisab Sadhu, Shreeyans Arora and Pratinav Seth

Large language models increasingly justify legal decisions by naming the statute or precedent behind a verdict, treated as evidence that the decision follows from it. We test this directly: holding case facts fixed, we substitute the named legal authority for an unrelated one and decode a model's evolving verdict from its hidden states. Across seven open-weight models (8B-70B) and four benchmarks spanning judicial and contractual reasoning, when explicitly required to justify a verdict by naming the governing authority, models name the correct one in 66.7%-100% of generations, while the verdict changing when the authority changes is far less consistent: 0.0%-21.7% on CaseHOLD, 30.0%-76.7% on ECHR and SCOTUS, and 43.3%-50.0% on ContractNLI. Neither scale nor a purpose-built legal-reasoning model (a best-effort LoRA reproduction; Section 6) closes this gap. A red-teaming evaluation on five core models finds compliance with an adversarial instruction hidden in the case facts (73.3%-96.4%) exceeds verdict-swap sensitivity by a wide margin, holding without exception across model rankings. Naming a legal authority is thus a poor proxy for a verdict's dependence on it, while the same verdict remains separately vulnerable to adversarial manipulation. Both findings replicate across checks ruling out prompt-wording noise and confounded sampling, and bear directly on the use of generated legal explanations as compliance or audit artefacts.
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Artificial Intelligence

Accurate but Not Humble: Evaluating Epistemic Humility in LLM Agents under Knowledge Conflict

Kaiser Sun, Bernal Jimenez Gutierrez, Hongjun Liu et al. (+4 more)

When retrieved evidence contradicts an agent's prior beliefs, does it revise its answer, acknowledge uncertainty, or persist with an incorrect conclusion? Existing evaluations of agentic systems focus primarily on task success, offering limited insight into how agents handle such conflicts. We propose to evaluate agents on epistemic humility (EH): the agent's willingness to recognize, act on, and communicate uncertainty during task execution. We operationalize EH through three trajectory-level behavioral dimensions: Identify, Solve, and Escalate (ISE). Through knowledge conflict, situations where the backbone language model's parametric knowledge contradicts the evidence it encounters, or where two contextual sources disagree, we evaluate two conflict settings: (1) controlled conflict and (2) naturally occurring conflict during multi-step agentic execution, each paired with matched no-conflict controls. Evaluating four agents, we find that higher task accuracy does not necessarily correspond to greater epistemic humility: some high-accuracy configurations recognize conflicts during execution but do not communicate unresolved uncertainty in their incorrect final answers. Trajectory-level analysis further reveals that agents frequently detect conflicts in early steps of execution but fail to maintain or resolve them in later steps. Finally, we show that model-level interventions can improve EH, but often at the cost of task accuracy, suggesting that epistemic humility emerges from the interaction among the backbone model, agent harness, and evaluation environment.
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All authors Kaiser Sun, Bernal Jimenez Gutierrez, Hongjun Liu, Jingyu Zhang, Jie Gao, Mark Dredze, Daniel Khashabi

Information Theory · Cross-listed from math.PR

Subspace Uncertainty and Sharp Sampling Thresholds on the Boolean Cube

Thomas Weinberger

We study Gaussian regression under squared population $L_2$ loss in a known $m$-dimensional subspace of degree-at-most-$k$ functions on the $d$-dimensional Boolean cube. Random inputs can undersample regions essential for prediction, delaying the parametric rate even when the model is known. For fixed $q_0<1/2$, $1\le k\le q_0d$, and sufficiently large fixed $A$, the worst-subspace sample threshold for minimax error $A\sigma^2(m+t)/n$ with confidence $1-e^{-t}$, $t\ge\log4$, is \[ N=(m+t)\exp\{E_{d,k}+O(k^{1/3})\}, \quad E_{d,k}=d\Psi(k/d), \] where $\Psi(q)=\log2-\mathsf H(\tfrac12-\sqrt{q(1-q)})$ and $\mathsf H$ is binary entropy with natural logarithms. The upper bound holds for every feasible $m$; the matching lower bound holds when $m\le\binom d{\lfloor k^{1/3}\rfloor}$ or $t\ge m$. We sharpen the Polyanskiy–Samorodnitsky uncertainty principle in two respects. First, for fixed leakage $\rho\in(0,1)$, the smallest set carrying a fraction $1-\rho$ of a nonzero degree-at-most-$k$ polynomial's energy has probability $\exp\{-E_{d,k}+O_{\rho,q_0}(k^{1/3})\}$. An Airy-kernel construction proves that the remainder cannot be $o(k^{1/3})$ in general. Second, we construct a subspace of dimension $\binom d{\lfloor k^{1/3}\rfloor}$ such that every function in the subspace has at least a fraction $1-\rho$ of its energy on the same set, whose probability is at most $\exp\{-E_{d,k}+C_{\rho,q_0}k^{1/3}\}$. For sufficiently large $k$, this set is a Hamming ball. A striking consequence is an exponential cost of noise: the parametric rate can require $(m+t)4^k\exp\{-O(k^{1/3})\}$ samples, whereas $O((m+t)2^k)$ suffice for noiseless identification. As $k\to\infty$ with $k/d\to0$, the noisy threshold is $(m+t)\exp\{2k+o(k)\}$.
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Cryptography and Security · Cross-listed from quant-ph

Improved Local Leakage Resilience of Shamir Secret Sharing and Worst-Case Optimal Polynomial Intersection

Yihang Sun and Mary Wootters

We study two problems: Local Leakage Resilience (LLR) for Shamir secret sharing, and worst-case Optimal Polynomial Intersection (OPI). Both problems concern polynomials $Q(X)$ of degree less than $k$, over a prime-order finite field $\mathbb{F}_p$. In LLR for Shamir secret sharing, one asks how much one can learn about $Q(0)$ given a few bits leaked from each of $Q(\alpha_1), \ldots, Q(\alpha_n)$, for distinct non-zero evaluation points $\alpha_i \in \mathbb{F}_p$. In OPI, one is given input list $S_1, \ldots, S_n \subset \mathbb{F}_p$, and wants to find a polynomial $Q(X)$ of degree less than $k$ so that $Q(\alpha_i) \in S_i$ for as many $i$ as possible. Leveraging recent connection between these two problems due to (Sun, Wootters 2026), we improve the state-of-the-art for both problems. For LLR, we show that there is some constant $\delta > 0$ so that, as long as $R := k/n \geq 1/2 - \delta$, Shamir secret-sharing is one-bit locally leakage resilient (meaning that one can learn only a negligible amount about $Q(0)$). This is the first result to break the so-called "one-half barrier" for LLR, and improves over the previous best known result, requiring $R \geq 0.668$ (Kasser, 2025). For OPI, we give a quantum algorithm that finds a polynomial $Q(X)$ that agrees with at least a $\mathsf{SCL}_\rho(R)-\varepsilon$ fraction of the lists in expectation, for every fixed $\varepsilon>0$, where $\mathsf{SCL}_\rho$ is the semicircle law of (Jordan et al., 2025). This improves previous algorithmic (and existential) results of (Jo, 2026) and (Horinaga, Yamakawa, 2026). We also give further improved existential results. We also adapt the hardness result of (Yamakawa, Zhandry, 2024) to apply to OPI (rather than a folded version); over large fields, this gives an unconditional separation between the quantum and classical hardness of OPI relative to a membership oracle.
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Computer Vision

Distilling Routed 3D Privilege for Spatial Reasoning in Vision-Language Models

Hongxing Li, Yixin Li, Dingming Li et al. (+5 more)

Spatial reasoning remains a persistent weakness of vision-language models (VLMs), because RGB inputs do not directly provide geometric evidence. Existing remedies either inject 3D into the model at inference, paying architecture and latency costs, or train with outcome rewards that supervise only the final answer. Spatial errors originate in perception: a misjudged depth or direction can be corrected only by the scene's true geometry, which the 3D-scanned sources of spatial training corpora already provide. We propose GPD (Geometry-Privileged Distillation), which makes geometric evidence the privilege in on-policy self-distillation (OPSD). For each question, depth, semantic, and bird's-eye-view (BEV) cues are rendered as compact text and routed to the teacher alongside the reference answer; a privileged KL, applied only to incorrect trajectories, augments GRPO, and the deployed model remains RGB-only. On the 4B backbone, GPD achieves 57.1 on VSI-Bench and 37.6 average across MindCube, SPARBench, MMSI-Bench, and ViewSpatial, outperforming both GRPO and answer-privileged OPSD across spatial reasoning benchmarks. Ablations confirm the complementarity of 3D and answer privilege, the advantage of question-conditioned routing over full-context injection, and the benefit of restricting distillation to incorrect trajectories.
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All authors Hongxing Li, Yixin Li, Dingming Li, Zixuan Wang, Yuchen Yan, Wenqi Zhang, Weiming Lu, Yongliang Shen

Machine Learning

SplitJEPA: Learning Invariant and Variant Latent Worlds without Reconstruction

Ruijin Hua, Zichuan Liu, Zhuokai Zhao et al. (+1 more)

Understanding a dynamical world calls for more than a latent state that summarizes its observations: the state should also be organized into the factors that stay shared across related observations and the factors that vary between them. For example, a robot pushing a cube to a goal should take the same action when the camera shifts or the lights dim, since nothing in the scene has moved. Existing approaches to this decomposition commonly obtain it through reconstruction, so the latent variables must first explain the entire observational world before their organization can be trusted. Joint embedding predictive architectures (JEPAs) model the latent state directly and never reconstruct, yet no existing result recovers the invariant and variant parts of the state they learn. How to learn the invariant-variant structure of the latent world without paying for its reconstruction therefore remains open. To close this gap, we introduce SplitJEPA, a JEPA that jointly recovers the latent state and its invariant and variant organization directly in representation space, without any reconstruction. We prove that, under stationary Gaussian predictive dynamics and a full-rank variation condition, SplitJEPA identifies the invariant and variant subspaces up to independent block-wise isometries, without introducing an observation decoder. Since the guarantee needs no decoder, the result extends reconstruction-free latent recovery to invariant-variant block identification. Experiments on synthetic nonlinear systems and robotic manipulation tasks support the theoretical results and show their practical value for both robustness and efficiency.
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All authors Ruijin Hua, Zichuan Liu, Zhuokai Zhao, Yujia Zheng

Numerical Analysis

Volume Sampling and Spectral Equalization in Randomized Alternating Projections

Alireza Entezari, Arunava Banerjee and Leila Kalantari

We study a family of randomized alternating projection methods that alternate among subspaces spanned by subsets of \(n\) vectors from a prescribed set. We derive an explicit characterization of performance bounds when these subspaces are sampled with probabilities proportional to the volumes subtended by the vectors in their corresponding subsets. For each \(n\), the bound is obtained through an explicit nonlinear transformation of the spectrum of an associated matrix. Our analysis reveals an explicit spectral equalization mechanism that drives the spectrum toward improved conditioning as $n$ increases, establishing an unexpected connection between volume sampling and the Cayley-Hamilton theorem. Furthermore, we introduce a computationally efficient uniform sampling scheme that achieves comparable theoretical guarantees through a specific relaxation strategy. Empirical results show that this relaxation method achieves convergence rates comparable to, and often better than, volume sampling, while avoiding the infeasibility of volume sampling at large scale. Besides the randomized Kaczmarz, these results also directly apply to randomized Gauss-Seidel and coordinate descent methods.
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Artificial Intelligence

Overcoming Prior Barriers: Supervised Fine-Tuning under Long-Tail Distribution

Haohui Wang, Jiahao Xu, Wangzhi Zhan et al. (+9 more)

Supervised fine-tuning (SFT) adapts pretrained large language models (LLMs) to downstream tasks, but the required concepts can receive substantially different levels of pretrained support. Frequent concepts are more likely to be well learned, whereas rare concepts may remain weakly represented. We introduce a novel notion named prior barrier to quantify how strongly the pretrained model supports competing concepts over the target concept. We observe that prior barriers follow a long-tail distribution, placing head and tail concepts at different starting points for SFT: head concepts face lower prior barriers, whereas tail concepts require additional instructions to overcome their higher prior barriers. Our theoretical analysis further derives a predictive risk bound for SFT under long-tail prior barriers, explicitly characterizing how the prior barrier and accumulated SFT evidence jointly determine predictive performance. Motivated by this prior barrier-dependent demand, we propose PASS, an adaptive SFT instruction selection method that constructs reference-derived concepts and estimates the distinguishing evidence provided by each instruction, and adaptively allocates the selection budget toward concepts that remain insufficiently covered under the current selection. In this way, PASS jointly considers which instructions can provide useful evidence and where additional supervision is needed under a limited budget. Experiments show that our method consistently outperforms seven state-of-the-art instruction selection methods on four backbone-budget settings. An ablation study further shows that PASS's adaptive allocation consistently improves over uniform allocation.
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All authors Haohui Wang, Jiahao Xu, Wangzhi Zhan, Tong Zeng, Dongqi Fu, Hong Li, Swastik Roy, Naren Ramakrishnan, Chris North, Jian Kang, Yujun Yan, Dawei Zhou

Computer Vision

Reasoning-Informed Visual Editing

Xue Yang, Peiyuan Zhang, Yilun Zhu et al. (+12 more)

Large Multi-modality Models (LMMs) have made significant progress in visual understanding and generation, but still face challenges in visual editing, particularly in following complex instructions, preserving appearance consistency, and supporting flexible input formats. To study this gap, we introduce RISEBench, the first benchmark for evaluating Reasoning-Informed viSual Editing (RISE), and extend it to RISEBench++, a more comprehensive and fine-grained benchmark for this emerging task. RISEBench++ extends the taxonomy into a hierarchical scheme spanning six reasoning dimensions: Temporal, Causal, Spatial, Logical, and Counterfactual Reasoning, together with Hybrid Reasoning integrating multiple reasoning types across multi-turn edits. These dimensions are further decomposed into 12 subcategories and 65 fine-grained task types. We expand input formats to include multi-image conditioning and scale the benchmark to 1000 human-annotated test cases, released in English and Chinese. We also improve our evaluation framework, assessing Instruction Reasoning, Appearance Consistency, and Visual Plausibility with human judges and an LMM-as-a-judge approach for more reliable and calibrated judgements. Beyond benchmarking, we introduce RISE-Agent, a training-free agentic framework integrating reasoning-driven planning, tool-augmented execution, and verifier-guided refinement, outperforming most strong existing approaches across diverse RISE tasks. We evaluate 58 visual editing approaches, including 34 open-source models, 19 closed-source models, and 5 agentic methods. The results reveal substantial challenges in reasoning-based visual editing, with even the strongest evaluated approach, GPT-Image-2.5 Sunburst, achieving only 56.6% accuracy. RISEBench++ highlights the limitations of contemporary editing models, provides insights, and indicates future directions for reasoning-aware visual editing.
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All authors Xue Yang, Peiyuan Zhang, Yilun Zhu, Qihao Yang, Mingxin Liu, Xiangyu Zhao, Ziqian Fan, Zhaokai Wang, Yan Li, Yifan Yang, Xu Yang, Xiaosong Jia, Yue Zhou, Zhihang Zhong, Junchi Yan

Artificial Intelligence

Can AI Agents Learn Their Way to the Top? Evaluating Heuristic Learning in a Long-Running Game Agent Competition

Kaisen Yang, Qingle Liu, Kejin Wang et al. (+24 more)

Adversarial games have driven advances from heuristic search to reinforcement learning, yet learning and adapting strategies from limited samples remain challenging. AI agents offer an alternative by turning game experience into revisions of executable policies. Building on heuristic learning (HL), we formalize Adversarial Heuristic Learning (AHL), a paradigm that uses AI agents as learning engines to refine game policies and supporting software while keeping model weights fixed. We introduce AAArena, a benchmark comprising 12 authentic adversarial games and 1,920 archived human programs, with an evaluation protocol modeled on real-world game competitions. Agents interpret rules, choose opponents, analyze replays, and revise game agents to achieve their highest ranking within fixed match and evaluation budgets. We evaluate \val{completedmodels} model and harness configurations: Opus5.5 with Claude Code earns 6 gold medals, while no evaluated configuration tops the remaining 6 human ladders. Performance is generally weaker in games with more complex rule specifications. Further experiments show that opponent selection and dense feedback support policy improvement, and that agents learn from both on-policy replays of their own matches and off-policy replays of other players' matches. These results highlight HL's potential in adversarial games and identify persistent challenges in game understanding, strategy implementation, and long-horizon policy development.
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All authors Kaisen Yang, Qingle Liu, Kejin Wang, Yicheng Zhao, Jieming Li, Shenghan Zheng, Ruize Yang, Bojun Yang, Heng Gong, Xiang Gao, Lanyue Zhang, Kaiyu Zhong, Zhuo Liu, Shaoxuan Li, Chengxi Li, Yong Yan, Weixuan Zhang, Tianwei Luo, Situ Wang, Youjie Zheng, Sihan Zhao, Shengyuan Wang, Huan-ang Gao, Jiazheng Xu, Xiaohui Xie, Wentao Han, Hongning Wang

Machine Learning

Ambient Discrete Diffusion: Using the Wrong Data at the Right Time for Data Efficient Learning

Julian Kleutgens, Mauricio Tec, Claudio Battiloro et al. (+2 more)

We introduce RefineMix, a framework for training discrete diffusion models under severe data scarcity, a common constraint in scientific applications. RefineMix uses out-of-distribution data at selected diffusion times to improve generalization without biasing the sampling distribution. Although this strategy has been explored in continuous diffusion, discrete diffusion presents a distinct challenge: unlike Gaussian noise, masking preserves domain information in surviving tokens, limiting the use of related data at high noise levels. At low noise levels, however, the domains effectively disjoint supports become an advantage, allowing the model to learn from both in-domain and out-of-distribution data without biasing the sampler. We formalize these intuitions and provide a theoretical analysis for the proposed method. Experimentally, across five domain-shift settings, RefineMix matches or outperforms in-domain finetuning and data mixing. For protein sequence generation, finetuning with just 197 in-domain examples nearly doubles the fraction of generated proteins that are simultaneously novel, foldable, and in-family compared to standard finetuning.
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All authors Julian Kleutgens, Mauricio Tec, Claudio Battiloro, Francesca Dominici, Giannis Daras

Computation and Language

VFold: Symmetry-Aware Cross-Layer Value Cache Compression

Neha Verma, Sungwon Kim, Kenton Murray et al. (+1 more)

While caching key-value (KV) states accelerates Large Language Model (LLM) decoding, this cache can dominate memory usage at long context lengths. One solution is to compress this memory by exploiting inter-layer cache similarities. However, most existing techniques necessitate architectural changes to LLMs and incur substantial overhead. In this work, we propose a symmetry-aware value cache merging strategy that reduces cache memory while avoiding both harmful performance degradation and architectural overhead during decoding. Furthermore, we show that this approach can be exploited alongside existing cache compression techniques, composing with high-ratio quantization or key cache pruning to reach compression ratios that neither method reaches alone, with minimal additional cost. Ultimately, our findings reveal a major source of underutilized capacity in the value cache, offering a simple yet highly effective direction for scaling context windows under memory constraints.
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All authors Neha Verma, Sungwon Kim, Kenton Murray, Kevin Duh

Computer Vision

ContiLNN: Mitigating Slice Sampling Discontinuity with Liquid Neural Networks for Medical Image Restoration

Jialei He, Enhe Liu, Sifan Song et al. (+10 more)

Anatomical continuity provides complementary information for medical image restoration, but its use requires accounting for local anatomy and variations in slice sampling. We introduce ContiLNN, which augments two-dimensional restoration backbones with bidirectional closed-form continuous-time (Bi-CfC) modules for cross-slice modeling while retaining in-plane feature extraction. Slice-index intervals modulate gates determined by local features and hidden states, enabling propagation to respond to sampling variations without numerical ODE integration. Reference-guided consistency aligns first- and second-order cross-slice intensity differences to preserve anatomical variation, while distillation from a frozen backbone helps retain in-plane fidelity. Across five training seeds, ContiLNN improves mean PSNR over Restore-RWKV by 0.1907, 1.0176, and 1.2482 dB for CT denoising, MRI super-resolution, and reduced-count PET restoration, respectively, with lower RMSE in all three tasks. CT results are descriptive for one held-out patient. PET ablations support ordered propagation beyond additional pointwise capacity. Under contiguous training, Bi-CfC achieves higher fidelity than a Bi-GRU with similar parameter counts and arithmetic costs across all tested sampling conditions. Matched seven-slice profiling shows 52.8% lower latency and 57.0% lower peak GPU memory use than Bi-GRU. Mixed-gap training improves sparse and irregular-context performance for both operators, without a uniform ranking across metrics and contexts. Experiments with fewer training patients and a second backbone further support data efficiency and backbone compatibility.
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All authors Jialei He, Enhe Liu, Sifan Song, Pengfei Jin, Jionglong Su, Hongbin Wang, Zhixiang Lu, Yanhao Huang, Anteng Cai, Zhengyong Jiang, Jiaman Ding, S. Kevin Zhou, Jinfeng Wang

Mathematical Software

asdex: Automatic Sparse Differentiation in JAX

Adrian Hill and Guillaume Dalle

Many tasks in scientific computing and machine learning require the Jacobian or Hessian matrix of a function. Automatic differentiation (AD) computes these derivatives to machine precision, but materializing a dense $m \times n$ Jacobian requires $n$ forward-mode or $m$ reverse-mode AD passes, one per column or row. For a large class of functions, each output depends on only a few inputs, making the derivative matrix sparse. Automatic sparse differentiation (ASD) exploits this structure in four steps: detection of the input-agnostic sparsity pattern, coloring of a graph to group columns or rows that can share an AD pass, compressed differentiation to compute a compressed derivative matrix with one AD pass per color, and finally decompression into the original sparsity pattern. The number of colors, and hence of AD passes, is often independent of the problem dimension: a banded Jacobian with $b$ contiguous bands, for instance, only ever requires $b$ colors, regardless of its size. asdex offers the first standalone ASD toolkit in the popular JAX ecosystem. With $\texttt{asdex.jacobian}$ and $\texttt{asdex.hessian}$, it provides sparse drop-in replacements for $\texttt{jax.jacobian}$ and $\texttt{jax.hessian}$.
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Computer Vision

RiCo: Neural Simulation of Rigid-Body Interactions via Local Contact Reasoning

Ruixiang Ouyang, Guanren Qiao, Fansen Meng et al. (+4 more)

Accurate simulation of rigid-body interactions is essential for predictive physical world models. Despite recent progress in modeling object dynamics, capturing how local contacts between surfaces shape object motion remains challenging. While end-to-end world models predict interactions across entire scenes or objects, in practice, rigid-body contact is inherently local, and only nearby surfaces can directly exchange contact forces. Motivated by this observation, we introduce Rigid-body Contact Reasoning (RiCo), which represents interactions between objects through sparse neighborhoods of contact surface points. RiCo combines each point's state with the relative geometry, motion, and physical properties of nearby surfaces, then reasons across the object's points to determine how these local contacts jointly affect its motion. By confining cross-object reasoning to nearby surfaces while propagating contact information within each rigid body, RiCo retains fine-grained interaction details without the cost of modeling every pair of scene points. Such properties enable RiCo a higher accuracy and contact fidelity. Experiments on MOVi-benchmark demonstrate that RiCo reduces 100-frame position and orientation errors by 31-35% and approximately 38%, respectively, compared with baselines. Moreover, RiCo achieves high contact fidelity, with ground-truth-relative penetration-time and mean-depth differences of 11.0% and 2.22 mm, respectively. RiCo further generalizes zero-shot from small-scale training scenarios to scenes containing 270 objects. Our real-world multi-ball collision experiments further provide preliminary evidence of sim-to-real transfer.
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All authors Ruixiang Ouyang, Guanren Qiao, Fansen Meng, Yueci Deng, Ruixing Jin, Kui Jia, Guiliang Liu

Artificial Intelligence · Cross-listed from stat.ML

Prediction-Powered Data Fusion for Treatment Effect Estimation

Yonghan Jung and Shu Yang

Randomized controlled trials (RCTs) identify treatment effects without confounding but are often small, whereas observational studies (OBS) are large but may be confounded. Many estimators combining a small RCT with a large OBS have been developed for the average treatment effect (ATE) and the conditional ATE (CATE). However, existing ATE estimators either make assumptions on the OBS or do not borrow enough power from them. The CATE has been studied less than the ATE. Existing CATE methods either assume the OBS are unconfounded, rely on a model of the confounding function, or accept bias in exchange for lower variance. We therefore propose a framework that, without special assumptions on the OBS, fuses the OBS and the RCT by preserving the unbiasedness of RCT-based estimation while borrowing power from the large OBS to boost precision. Applying this principle, we build an ATE estimator, AIPW-Fusion, with closed-form weights and confidence intervals, and two CATE learners, DR-Fusion and R-Fusion. Experiments corroborate our findings.
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Machine Learning

Composite Online-to-Nonconvex Conversion with Optimal Oracle Complexity

Mingyi Li, Taira Tsuchiya and Kenji Yamanishi

We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks. The objective is the sum of a possibly nonsmooth nonconvex Lipschitz function and a convex regularizer, and the function is accessed through stochastic gradients or function values. The goal is to find a point that satisfies a Goldstein-type stationarity condition designed for composite objectives. To our knowledge, no oracle complexity bound for this setting is known under first-order access, and existing complexities under zeroth-order access are suboptimal. To handle this issue, we employ the framework of online-to-nonconvex conversion, which chooses update directions by an online learner and is known to achieve optimal rates for noncomposite problems. We extend the framework to our composite scenario by introducing new losses for the learner, which contain the regularizer itself rather than its linearization and for which a variant of online mirror descent achieves low regret. We show that the resulting algorithm finds such a point with $O(\delta^{-1}\varepsilon^{-3})$ stochastic gradient queries or $O(d\delta^{-1}\varepsilon^{-3})$ function-value queries, where $\delta$ is the Goldstein radius, $\varepsilon$ is the stationarity tolerance, and $d$ is the dimension. These rates match the optimal ones for noncomposite nonsmooth nonconvex optimization, demonstrating that the additional convex regularizer does not worsen the oracle complexity. We also give rates for the smooth case and present numerical experiments.
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Machine Learning

SparseDecoding: Decoding-Aware Pruning for Accurate and Efficient LLM Inference

Qitong Wang, Xinwei Niu, Mingluo Su et al. (+3 more)

The memory-bound nature of the decoding stage of large language model (LLM) inference incurs significant latency. Layer-wise training-free network pruning approaches guided by the Hessian have been a prominent solution to this problem, as pruning reduces the number of nonzero parameters read from memory during decoding. Nevertheless, typical methods in this line compute the Hessian using pre-collected natural sequences, whereas the model is fed self-generated tokens during decoding, creating a distribution shift between the two sequences. The Hessian calculated on the natural sequence is different from that calculated on the generated sequence. We observe that this discrepancy causes the activation distribution during generation to deviate from that used for pruning, further hurting the pruned model performance. Moreover, most existing LLM pruning methods that bring actual speedup primarily target the sparse matrix-matrix (SpMM) multiplication, providing limited support for the sparse matrix-vector (SpMV) operations, which dominate decoding. To solve these problems, we introduce SparseDecoding, a principled decoding-aware pruning framework tailored for accurate and efficient LLM decoding. Specifically, at the algorithmic axis, SparseDecoding constructs calibration matrices from layer-wise activations collected during the dense-model autoregressive generation, excluding prefill, thereby aligning the pruning objective with the decoding activations. At the system axis, we develop an optimized N:M sparse matrix-vector kernel with bitmask indexing and fixed-step traversal. Substantial empirical results on representative LLMs (Llama-3.1-8B, Llama-3.3-70B, Qwen3-14B / 32B) demonstrate that our method consistently outperforms standard fixed-text calibration on the long-form generation benchmarks while achieving up to 1.48x end-to-end wall-clock decoding speedup on A100 GPUs.
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All authors Qitong Wang, Xinwei Niu, Mingluo Su, Shanwei Zhao, Shiai Zhu, Huan Wang

Artificial Intelligence

Prior or Feedback? What an LLM Uses When Adapting Neural Operators

Julian Chan and Javier Mora Jimenez

Do LLM scientific agents rely only on their initial task context, or do they adapt their decisions in response to experimental feedback? We study this question in neural operator adaptation, where a large language model (LLM) selects fine-tuning configurations under a limited trial budget. Across transfers within and between partial differential equation (PDE) families, the LLM achieves lower held-out test nRMSE than random search and Bayesian optimisation in nearly every matched comparison. Endpoint performance alone cannot distinguish what happens, so we verify each attribution with controlled interventions. Before observing any validation score, the LLM's first configuration already ranks near the top of the corresponding random-search pool, indicating a useful initial bias. A complementary cold-start intervention shows that the selected base learning rate shifts with the PDE description. Once feedback becomes available, reassigning validation scores among evaluated configurations changes the next proposal in every case tested, whereas a value-preserving rewrite produces no comparable aggregate effect. These interventions establish that the LLM's decision-level actions respond to the given task and observed outcomes, showing that it combines a task-dependent prior with sensitivity to experimental feedback.
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Systems and Control

Convex Safety Filtering via Spectral Selection for Nonconvex Safe Sets

Juan Augusto Paredes Salazar, James Usevitch and Ankit Goel

The discrete-time control barrier function condition for a safe set that is a union of convex sets is nonconvex in the control input. For safe sets defined by a matrix concave function through the number of its nonnegative eigenvalues, this paper shows that the set is a union of convex sets, and that the nonconvexity arises because at least one member of the union must hold, not every member. Selecting eigenvectors of the matrix function at the current state yields a convex input constraint that acts only on the eigenvalues determining membership in the set. This constraint is implied by the matrix-wide condition of prior work, and it guarantees a geometric lower bound on each of those eigenvalues along closed-loop trajectories. A double-integrator simulation with a polytope obstacle and a spectrahedron obstacle compares the proposed filter with the matrix-wide condition.
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