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All of arXiv

Tuesday 13 October

Strongly Correlated Electrons

A hierarchy of exact lower bounds on the Laughlin spectral gap

Michael G. Scheer and Eslam Khalaf

We develop a bootstrap approach to deriving lower bounds on the spectral gap of the first Haldane pseudopotential Hamiltonian on the sphere with $N_\Phi$ flux quanta for arbitrary $N_\Phi$, including in the thermodynamic limit $N_\Phi \to \infty$. Our approach can in principle be generalized to pseudopotentials describing other model wavefunctions such as the Moore-Read state or Read-Rezayi sequence. Our approach is based on Knabe's observation that if $H$ is a Hamiltonian with ground state energy $0$ then the spectral gap is at least $\epsilon > 0$ if and only if $H^2 \succeq \epsilon H$. To show this inequality, we split $H^2$ into two parts, one that can be analytically bounded and another that can be bounded using a finite semidefinite program (SDP). Crucially, the size of this program is determined only by cutoff parameters, and the program depends on $N_\Phi$ only parametrically, allowing us to obtain numerically exact (up to solver precision) lower bounds on the gap. In order to turn these numerical bounds into mathematically rigorous bounds, we introduce an algorithm that can produce nearly-optimal exact feasible points for large rational SDPs. We additionally provide an algorithm that establishes the rank stability of the semidefinite program in the limit $N_\Phi \to \infty$ which is needed to certify the bound in the thermodynamic limit. Beyond establishing the Laughlin gap and revealing a potential method for deriving spectral gap lower bounds for other pseudopotentials, our work provides a general method for turning numerical semidefinite programming bounds into rigorous mathematical proofs, which may have wide applicability.
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Machine Learning

Two Clocks: Why Larger Rollout Batches Learn Slower but Fail on Schedule in Reinforcement Learning with Verifiable Rewards

Yuante Li, Junwei Quan, Kai Qiu et al. (+2 more)

Reinforcement learning with verifiable rewards (RLVR) relies on costly model-generated responses, motivating larger rollout batches and square-root learning-rate scaling. Reported to approximately preserve progress per sample with one optimizer step per rollout, this rule is less understood in practical multi-step training. We develop a two-clock framework that separates the samples needed to make progress from those consumed before collapse. Under a local quadratic model, the square-root rule preserves first-order drift per sample but not progress: larger batches take fewer, longer updates and lose more to curvature, yielding a learning-rate-dependent critical batch beyond which sample efficiency degrades. A drift-threshold hypothesis predicts a complementary failure clock whose sample count remains approximately invariant along the square-root rule. Controlled GRPO experiments on Qwen2.5-Math-1.5B across a $16\times$ batch range support both predictions. Ratio clipping delays failure, especially for larger batches, but the progress gap persists without it. Widening the clip trades stability for a transient speed gain. The progress gap reappears on another dataset, a general-purpose checkpoint, and a 7B model. Finally, we use the two-clock framework to derive a simple multi-step RLVR schedule: start below the critical batch and switch to a larger batch before failure. Our code is available at: https://github.com/WinstonLiyt/two-clocks-rlvr.
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All authors Yuante Li, Junwei Quan, Kai Qiu, Kate Zhang, Yicheng Tao

Robotics

ForceWAM: Decoupling Future and Response Learning from Demo and Play Data for Contact-Rich Manipulation

Zijun Xu, Wendi Chen, Xinkai Wang et al. (+16 more)

Expert demonstrations show how to complete contact-rich tasks, but provide limited coverage of how interaction forces respond to different actions. Task-agnostic play provides broader experience of contact dynamics without specifying task goals. To fully leverage these two types of data, we introduce ForceWAM, a force world action model that decouples knowledge of task-compatible interaction outcomes from knowledge of how local actions change contact. A world model learns from successful demonstrations to jointly predict future video and six-axis force/torque trajectories. Together, these futures describe the expected evolution of motion and contact during the task. A separate inverse dynamics model (IDM) learns from both task and play, mapping current observations and recorded visual-wrench futures to their associated robot actions. Play data thus provide knowledge of force responses for goal-directed execution. At deployment, the IDM reactively translates generated futures into actions, reusing them with fresh wrench feedback between world-model updates. Across real-robot force-regulated sliding, box flipping with and without disturbances, and ring placement, ForceWAM achieves $85$-$95\%$ mean success, surpassing world-modeling and reactive baselines. Our experiments further show that adding task-agnostic play data improves success by $15$-$45$ percentage points, demonstrating its value for learning contact-rich execution. Project page and code are available at https://force-wam.github.io/.
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All authors Zijun Xu, Wendi Chen, Xinkai Wang, Jiachen Zou, Hongjin Chen, Hairuo Liu, Bokai Lin, Shihao Ma, Ke Ma, Zhiwei Zhang, Zhuohao Yan, Ke Wu, Haoming Song, Xueqi Li, Chuan Wen, Jieru Zhao, Wenchao Ding, Cewu Lu, Lixin Yang

Artificial Intelligence

MFG: Multi-turn Feedback Guided Molecular Optimization

Trieu Nguyen, Frazier N. Baker, Ruoxi Gao et al. (+2 more)

Multi-objective molecular optimization is a critical process in drug discovery that aims to modify a given molecule to simultaneously improve multiple properties while maintaining a similar overall structure. This process often requires iterative modifications guided by computational or experimental feedback. Recent large language model (LLM)-based methods have begun to explore this iterative approach; however, these methods are not explicitly trained to leverage such feedback, while existing approaches primarily focus on single-turn molecular optimization. To address this gap, we introduce Multi-turn Feedback Guided (MFG) molecular optimization, a reinforcement learning framework that trains an LLM to progressively optimize molecules using feedback from previous turns. MFG introduces a feedback vector capturing both property improvements and source molecule similarity, alongside a feedback-aligned reward function that promotes progressive improvement across turns. We apply MFG over $\text{GeLLM}^{3}\text{O}$, a state-of-the-art LLM model for multi-objective molecular optimization, evaluate $\text{GeLLM}^{3}\text{O-MFG}$ on ten multi-objective molecular optimization tasks. The results demonstrate that $\text{GeLLM}^{3}\text{O-MFG}$ achieves the highest average similarity-constrained success rate ($81.50%$), outperforming the base model $\text{GeLLM}^{3}\text{O}$ ($70.81%$).
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All authors Trieu Nguyen, Frazier N. Baker, Ruoxi Gao, Daniel Adu-Ampratwum, Xia Ning

Robotics

Collaborative Planning for UAV-UGV Teams under Operational Constraints via Masked Error-bounded Neuro-Symbolic Diffusion

Zihao Deng, Qianhuang Li, Maggie Wigness et al. (+3 more)

Collaborative planning under operational constraints is essential for heterogeneous robot teams in large-scale missions. Unmanned Aerial Vehicles (UAVs) provide rapid area coverage but are limited by onboard energy, while Unmanned Ground Vehicles (UGVs) can serve as mobile recharging stations yet are constrained by road-network traversability. Effective collaboration must enforce operational constraints during execution while enabling parallel, coordinated actions. Masked Diffusion Models (MDMs) have shown promise through token unmasking but have two key limitations: entropy-guided scheduling assumes distributional alignment and reliance on differentiable constraints for diffusion-time optimization. We propose Masked Error-bounded Neuro-Symbolic Diffusion (MEND), which formulates collaborative planning as a conditional masked generative process to generate context-aware action sequences for UAV-UGV teams. MEND introduces a neuro-symbolic diffusion paradigm that constrains conditional masked diffusion policies at execution by reweighting the learned action distribution with a logic-induced admissibility indicator, thereby enforcing compliance with operational constraints. MEND introduces an error-bounded inference scheduling at execution that constructs the unmasking schedule by selecting positions with minimal predictive entropy over the constraint-aware action distribution, enhancing collaborative planning optimality under operational constraints. Extensive experimental results in simulation, on real-world maps, and with physical robot teams demonstrate that MEND advances UAV-UGV collaborative planning under operational constraints.
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All authors Zihao Deng, Qianhuang Li, Maggie Wigness, John Rogers, Donghyun Kim, Hao Zhang

Instrumentation and Detectors

Energy, vertex, and time response of a LiquidO detector with an opaque-scintillator target to Compton-tagged electrons

LiquidO Collaboration: S. Katz, J. T. Moffatt, G. Wendel et al. (+88 more)

LiquidO detectors confine scintillation light near its point of production by stochastic scattering in an opaque medium and collect it with a lattice of wavelength-shifting (WLS) fibers. The elementary signal of such a detector is the point-like sub-MeV energy deposition, yet the response to that signal at the center of the detector volume has not been measured against an event-by-event ground truth. To close this gap, we couple BPULSE, a 4-liter prototype LiquidO detector, to a Compton-coincidence calibration setup that selects electron recoils of known energy on a constrained beam axis. The prototype is a 160 mm cube of opaque scintillator with 64 WLS fibers in alternating orthogonal layers at a 20 mm pitch, read out by silicon photomultipliers. Compton scatters of collimated gamma-ray beams from $^{137}$Cs and $^{60}$Co sources are tagged by a NaI(Tl) spectrometer. For 373.4 keV electrons, tagged from $90^{\circ}$ scatters of the $^{137}$Cs beam, the detector collects $19.04 \pm 0.07$ photoelectrons (p.e.). Across four operating points, the two sources at two scattering angles, it responds linearly at $48.3 \pm 1.5$ p.e./MeV. The energy resolution of $(23.4 \pm 0.4)\%$ matches the Poisson statistics of the detected photoelectrons. Collection at both fiber ends and larger sensors would raise the light yield of this target to an estimated 108-124 p.e./MeV. Center-of-mass reconstruction locates each recoil to the width of the delivered 20 mm beam spot, which bounds the intrinsic localization of the detector from above. The arrival time response sets a lower bound of 1.5 ns on the single-scatter start time at the observed $\approx 19$ p.e. light level. This single-scatter response is the building block for reconstructing multi-site events. It constrains the light collection, confinement, and timing models on which reconstruction in future LiquidO detectors will rest.
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All authors LiquidO Collaboration: S. Katz, J. T. Moffatt, G. Wendel, D. F. Cowen, I. Jovanovic, S. Schoppmann, A. S. Wilhelm, J. Apilluelo, L. Asquith, N. P. Barradas, J. L. Beney, M. Berberan e Santos, X. de la Bernardie, T. J. C. Bezerra, M. Bongrand, C. Bourgeois, D. Breton, J. Busto, A. Cabrera, A. Cadiou, E. Calvo, M. de Carlos Generowicz, B. J. Cattermole, E. Chauveau, M. Chen, P. Chimenti, S. Kr. Das, S. Dusini, A. Earle, M. Felizardo, C. Frigerio Martins, J. Galán, J. A. García, A. Gibson-Foster, C. Girard-Carillo, J. J. Gómez-Cadenas, W. C. Griffith, K. Groomes, M. Guitière, F. Haddad, J. Hartnell, A. Holin, I. G. Irastorza, W. Keck, A. Kling, L. Koch, J. F. Le Du, F. Lefevre, P. Loaiza, J. A. Lock, T. Lux, G. Luzón, J. Maalmi, J. P. Malhado, F. Mantovani, J. G. Marques, C. Marquet, M. Martínez, D. Navas-Nicolás, H. Nunokawa, J. P. Ochoa-Ricoux, T. Palmeira, C. Palomares, D. Petyt, P. Pillot, A. Pin, M. S. Pravikoff, S. Richards, M. Roche, N. Rodrigues, R. Rosero, B. Roskovec, M. L. Sarsa, A. Serafini, C. Shepherd-Themistocleous, W. Shorrock, M. Silva, L. Simard, S. R. Soleti, D. Stocco, V. Strati, J. S. Stutzmann, F. Suekane, N. Tuccori, A. Verdugo, B. Viaud, S. M. Wakely, A. Weber, A. W. R. Wong, M. Yeh, F. Yermia

Robotics

Contact Trajectory Prompting: In-Context Transfer of Contact-Rich Behaviors from a Single Demonstration

Xian Nie, Yujie Zang, Yuhang Zheng et al. (+8 more)

In-context robot learning enables robots to acquire new behaviors from demonstrations without test-time parameter updates. However, visual and kinematic specifications alone may not distinguish contact-rich behaviors that share similar motions but require different interaction intensities or patterns. We propose Contact Trajectory Prompting (CTP), a framework for one-shot transfer of contact-rich manipulation behaviors. CTP encodes motion and contact information from a single demonstration into an ordered contact trajectory prompt that captures their temporal evolution and specifies the desired physical interaction behavior. During execution, the policy uses online sensory feedback to retrieve interaction-relevant information from the prompt, conditioning closed-loop action generation on the demonstrated contact behavior. Across real-world wiping, rotation, and insertion tasks on objects excluded from training, CTP achieves 78.7% overall success, outperforming the strongest evaluated baseline by 13.0 percentage points. Changing only the reference demonstration enables CTP to follow contact specifications for both intensity and direction, including an intermediate wiping force level and clockwise or counterclockwise cap rotation. These results demonstrate that contact trajectories serve as effective behavioral specifications, extending in-context robot learning beyond motion imitation to physical interaction transfer. Project website: https://ctp-robotics.github.io/project_page.
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All authors Xian Nie, Yujie Zang, Yuhang Zheng, Yupeng Zheng, Songen Gu, Wendi Chen, Chuan Wen, Cewu Lu, Wenchao Ding, Junchi Yan, Shuicheng Yan

Probability

Superdiffusive Invariance Principle for the two-dimensional Asymmetric Simple Exclusion Process

Quentin Moulard

We consider the Asymmetric Simple Exclusion Process (ASEP) at its critical dimension $d=2$, started from the Bernoulli product measure with density $\rho \in (0,1)$. We first derive the sharp $\log(t)^{2/3}$ divergence of the bulk diffusivity, predicted via mode-coupling theory in [H. van Beijeren, R. Kutner, H. Spohn, Phys. Rev. Lett., 1985], including the exact prefactor, thereby removing the subleading diverging multiplicative corrections in the Tauberian bounds of [H.-T. Yau, Ann. of Math., 2004]. More importantly, we establish an invariance principle for the density fluctuation field on the corresponding superdiffusive scales. On the time scale $\tau$, we rescale space by $\sqrt{\tau} \log(\tau)^{1/3}$ in the direction of the drift and by $\sqrt{\tau}$ in the transverse direction, and prove functional convergence of the rescaled fluctuation process to the solution of a conservative stochastic heat equation with additive noise. This is the same explicit Gaussian Fixed Point obtained in [G. Cannizzaro, Q. Moulard, F. Toninelli, arXiv:2501.00344, 2025] for the two-dimensional Stochastic Burgers Equation (SBE). We also deduce a superdiffusive central limit theorem for the second-class particle under the same anisotropic rescaling. The result holds for any finite-range jump kernel with nonzero drift and uniaxial asymmetry. This is the first space-time scaling limit result for a nonequilibrium interacting particle system at the critical dimension, where Gaussian fluctuations emerge despite logarithmic corrections to the scaling. The proof uses an approximate fluctuation-dissipation relation, which is obtained by combining a sharp quantitative comparison between the ASEP and SBE generators with refined estimates on the SBE Ansatz. An additional key novelty is a tightness argument that overcomes the limitations of the Itô trick on superdiffusive scales.
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Computer Vision

WorldRecon: Generative Multi-View Mesh Reconstruction for Large-Scale 3D World

Mengchen Zhang, Yang Li, Chunshi Wang et al. (+2 more)

Reconstructing complete, high-quality meshes of large-scale scenes from unposed multi-view images requires faithful geometric grounding while plausibly completing surfaces that are unobserved or only sparsely captured. We present WorldRecon, a generative multi-view reconstruction framework for recovering complete, large-scale 3D scene meshes from unposed RGB images. WorldRecon uses a coarse, noisy global point cloud and camera poses estimated from the input images by a reconstruction model as a global scaffold for whole-scene generation and partitions it into overlapping spatial blocks. To robustly leverage these imperfect geometric priors, we equip the native 3D generative model TRELLIS.2 with a dedicated reconstruction-based conditioning architecture that generates each block from its local point-cloud crop and block-relevant image observations, producing sparse structure, detailed geometry, and PBR materials. To maintain scene-level coherence, we introduce neighbour-aware latent inpainting and a causal world-generation procedure that propagates structural, geometric, and material context across overlapping blocks. Together, these designs scale multi-view generative reconstruction to large-scale scenes, yielding coherent, unified meshes. Extensive experiments demonstrate that WorldRecon achieves state-of-the-art reconstruction performance, reducing Chamfer distance by 14.9% and 43.1% while improving F-score by 17.3% and 12.0% over the strongest baselines on synthetic and real-world indoor scenes, respectively, thereby demonstrating faithful and complete generative reconstruction as well as strong sim-to-real generalization. Project page: https://kszpxxzmc.github.io/WorldRecon-website/.
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All authors Mengchen Zhang, Yang Li, Chunshi Wang, Tong Wu, Chunchao Guo

Computer Vision

The Last Remote Sensing Model Built by Humans? Casting Any Earth Observation Task as Recursive Self-Improvement

Sijie Zhao, Zeqi Zhou, Heli Qi et al. (+6 more)

Earth observation (EO) models are still built by hand. For each new task, experts design a training recipe and tune it against a benchmark. We show that this loop can be handed to an agent. Any verifiable task can be cast as a harness and a verifier, where the harness defines what the agent may use and the verifier defines what counts as success. Every EO task can be made verifiable, through labeled benchmarks, independent sensors, physical models or the repeated observation of the same place. Given only these two components, a general-purpose coding agent builds the EO model and improves it recursively on its own outputs. Settings long treated as separate research problems, from learning with a handful of labels to adapting across domains, become choices of harness and verifier. On six EO benchmarks spanning optical, SAR and multispectral time-series imagery, with outputs that range from land-cover maps and ship instances to canopy heights and answers about large images, agent-built models surpass the state of the art on every one, and on land-cover mapping, they do so from 11% of the training labels. This establishes a new paradigm for EO, in which people design harnesses and verifiers and agents build the models, so EO models improve as agents do.
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All authors Sijie Zhao, Zeqi Zhou, Heli Qi, Xuanchao Fu, Zhuo Zheng, Junshi Xia, Junjue Wang, Weihao Xuan, Naoto Yokoya

Computer Vision

RepProbe: Can Video Language Models Count Repeated Actions? A Diagnostic Benchmark

Mahsa Khoshnoodi and Sarah Adel Bargal

Repetition counting requires identifying and enumerating action cycles over time. While state-of-the-art video language models describe actions fluently, they fail to reliably count how many times an action repeats. To investigate this limitation, we introduce RepProbe, a benchmark of 42K real and synthetic video clips containing exactly k in [1, 20] complete repetitions, with controls for clip position, temporal coverage, and duration. These controls allow us to study the counting failure directly and locate where in the model it arises. Counting accuracy collapses at high counts across the video language models we evaluate, and controlled experiments show this collapse is not explained by frame sampling alone. We compare model outputs with linear probes trained on the final-layer representations used to generate those outputs. We find a consistent representation-to-output dissociation: substantial count information remains linearly decodable even when models fail to report the correct count. Further analysis shows this failure arises primarily at the output stage, where answers concentrate on a small set of preferred numbers rather than the available count information. The dissociation holds on both real and synthetic videos and is not explained by clip duration, position, or scene content. These results indicate that models encode repetition structure but do not reliably report it in their outputs. Project page: https://arenaa.github.io/RepProbe-webpage/
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Robotics

LIBERO-RIG: A Hardware-Setup Robustness Benchmark for Vision-Language-Action Models

Andrea Yaoyun Cui, Hanyu Wang, Xinyi Wang et al. (+6 more)

Robot policies are expected to generalize across deployment environments, including variations in the robot itself: cameras are bumped and remounted, calibrations drift, controllers run at different rates, and end-effector pads wear down. We present LIBERO-RIG, a benchmark that perturbs only the robot's hardware and setup while holding every LIBERO task fixed. The benchmark spans eleven perturbation axes, including camera mounting and optics, camera-to-arm calibration, actuation gain, control rate, proprioceptive noise, base pose, table height, and gripper pads. Each axis has five severity levels, yielding 210 conditions across the four LIBERO suites. We evaluate nine recent vision-language-action models using 500 episodes per condition and substantiate each finding with rigorous statistical tests. Pooled success falls from 0.932 to 0.767 at the middle severity and 0.509 at the highest severity. Performance degradation varies substantially across perturbation axes and action interfaces, and training on visual perturbations does not mitigate faults that leave camera images unchanged. We release the benchmark together with manifests specifying the fixed perturbation parameters for each episode.
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All authors Andrea Yaoyun Cui, Hanyu Wang, Xinyi Wang, Bangzheng Li, Lin Zhang, Zhenggang Tang, Shyamal Buch, Dejia Xu, Matthew Tancik

Artificial Intelligence

Who Improves the Robot? Toward Physical Recursive Self-Improvement

Hai Zhou, Fan Yang, Zeyi Chen et al. (+27 more)

Robots are increasingly autonomous in task execution, yet their improvement remains largely human-driven. This study investigates Physical Recursive Self-Improvement (Physical RSI), in which physical experience guides lasting updates to both a robot's capabilities and its improvement procedure, making subsequent improvement more effective across tasks. Physical RSI faces challenges from noisy observations, continuous dynamics, costly trials, and irreversible consequences. We present an L0-L5 framework that differentiates capability-level from meta-level updates and within-task from across-task gains, reserving L5 for independently verified recursive gain. We study existing methods around harness adaptation and model training, alongside safety and control mechanisms that govern execution and successive updates. Our analysis reveals that, despite substantial progress in self-improvement, the surveyed literature does not yet demonstrate Physical RSI as defined by our framework. We identify research priorities in reliable feedback, causal attribution, safety preservation, and benchmarking, outlining a path toward robots that autonomously improve how they learn while ensuring safety. The GitHub repository for Physical RSI is available at https://github.com/SAIL-Research-Lab/Physical-RSI.
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All authors Hai Zhou, Fan Yang, Zeyi Chen, Lejun Zhang, Chenyang Fu, Jianping Li, Jiayi Zhu, Xianyang Liu, Yingxuan Yang, Lili Meng, Lu Wang, Xinyang Han, Jiankai Sun, Weirui Ye, Guanchu Wang, Wanhua Li, Ming Zhou, Boyi Li, Ming Jin, Kun Shao, Muhao Chen, Guang Chen, Lei Ma, Joey Tianyi Zhou, Costas Spanos, Xia Hu, Mac Schwager, Weinan Zhang, Qian Feng, Shangding Gu

Geometric Topology

Arithmetic hyperbolic manifolds with bounded rank

Matthew Zevenbergen

We prove that closed arithmetic hyperbolic $n$-manifolds of bounded rank have bounded adjoint trace field degree, and consequently have lower bounded injectivity radius. From this, we obtain a number of corollaries. In particular, we obtain that closed arithmetic hyperbolic $3$-manifolds of bounded rank are contained in finitely many commensurability classes, and describe these commensurability classes. Additionally, it follows that for closed arithmetic hyperbolic $3$-manifolds, Heegaard genus is equal to rank for all but finitely many manifolds of each rank.
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High Energy Astrophysical Phenomena

Seeing Double: The Theory Defying Twin Flares of TDE 2022dbl

Xinze Guo, Ryan Chornock, Raffaella Margutti et al. (+13 more)

Partial tidal disruption events, in which a star survives a close passage by a supermassive black hole and may be disrupted again on a subsequent encounter, provide a unique probe of supermassive black hole properties and accretion physics. We examine TDE 2022dbl, a partial tidal disruption event candidate that exhibits two separate UV/optical flares, using 11 new optical spectra, updated UV/optical photometry, and a Keck-II/ESI host-galaxy spectrum. We trace the evolution of the prominent blended N III + He II feature across both flares and find that the blend evolves from N III-dominated to He II-dominated emission, which may reflect changing ionization conditions and a declining efficiency of Bowen fluorescence. The two flares show similar thermal evolution and spectral features, supporting a partial-disruption scenario. The second flare exhibits a broader, plateau-like peak, a longer decline timescale, and less extreme line velocities than the first flare. We suggest that these differences arise from the interaction between debris from the second disruption and an accretion disk formed during the first flare. From the host-galaxy velocity dispersion, we infer a black hole mass of $\log_{10}(M_{\rm BH}/M_\odot)=6.01\pm0.45$. No third flare has been detected at the expected recurrence epoch, leading us to propose a new interpretation in which a positive-energy kick during ballistic core reformation delays the return of the surviving remnant.
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All authors Xinze Guo, Ryan Chornock, Raffaella Margutti, Yuhan Yao, Erica Hammerstein, Natalie LeBaron, S. Bradley Cenko, Matthew J. Graham, Dina Ibrahimzade, Itai Sfaradi, Jean Somalwar, Robert Stein, Eli Wiston, Joahan Castaneda Jaimes, Mansi M. Kasliwal, Russ R. Laher

Machine Learning

Fast Rates for Offline Q-Learning with KL Regularization

Yize Hao, Guangxin Jiang and Shuang Qiu

This paper investigates offline Q-learning for finite-horizon Markov decision processes with Kullback-Leibler (KL) regularization. Recent studies have shown that KL regularization can yield fast rates in offline decision-making problems. However, it remains unclear whether Q-learning, which adopts incremental stochastic approximation updates, can achieve such fast rates in the offline setting. We first propose KL-regularized Q-Learning (KLQ), a simple variant of classical Q-learning. By exploiting KL regularization, we prove that KLQ achieves a sample complexity of $\widetilde{O}(1/\epsilon)$ without explicit pessimism. This guarantee, however, has an exponential dependence on the KL regularization parameter and the horizon. To address this limitation, we further propose KL-regularized Pessimistic Q-Learning (KLPQ), which incorporates pessimism into KLQ. We prove that KLPQ retains the same \(\widetilde O(1/\epsilon)\) rate while removing the explicit exponential dependence, thereby further improving the sample complexity. To the best of our knowledge, these results establish the first fast-rate guarantees for offline Q-learning in tabular finite-horizon KL-regularized MDPs.
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Machine Learning

Scaling Online Optimal Transport Minibatches for Flow Matching

Peter Chen and Sergey Levine

A central challenge in scaling flow models is maintaining stability in training and integration. In flow matching, this stability depends critically on how source samples are paired with data. Independent random pairing introduces substantial stochasticity, motivating minibatch optimal transport (OT) to construct online source-target couplings that reduce this randomness (Tong et al., 2024). However, as applications extend to larger and higher-dimensional datasets, small minibatches can limit these benefits, while scaling the coupling to substantially larger minibatches at every iteration is computationally prohibitive. Moreover, how OT coupling affects the full stochastic gradient and integration remains theoretically unresolved. In this work, we develop a scalable online entropic OT approximation that enables substantially larger source-target couplings while preserving the benefits of OT. We close the theoretical gap for both unregularized and entropic OT by proving strict reductions in full stochastic-gradient variance and integration error relative to independent pairing, and further characterize how these improvements strengthen as the online coupling minibatch grows. Experiments on single-cell gene interpolation-flow and image-flow training validate these predictions, showing that larger online couplings consistently improve training stability and final generation performance.
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Numerical Analysis

Fully discrete multi-entropy-stable compact Runge–Kutta discontinuous Galerkin methods for hyperbolic conservation laws

Zheng Sun

We develop fully discrete multi-entropy-stable high-order compact Runge–Kutta discontinuous Galerkin (cRKDG) methods for hyperbolic conservation laws. Our main result is a weak cell entropy inequality for multi-dimensional systems after one full high-order Runge–Kutta (RK) time step. The proof exploits the cell-local intermediate stages of cRKDG: their perturbations are controlled by the initial in-cell variation. The analysis does not require a strong stability preserving decomposition or stagewise entropy correction. For a sufficiently dissipative Lax–Friedrichs flux and explicit RK methods with nonnegative output weights, the inequality holds under a suitable time-step restriction for strongly convex entropy pairs. For a prescribed, uniformly conditioned family of such entropies, common dissipation and time-step conditions ensure weak cell entropy stability for all entropy pairs. A single cell-average-preserving scaling at the end of each step then enforces all corresponding strong cell entropy inequalities simultaneously. We also prove a Lax–Wendroff-type theorem: under the stated assumptions, any strongly convergent sequence of numerical solutions converges to a weak solution satisfying all prescribed entropy inequalities. Numerical experiments in one and two dimensions demonstrate high-order accuracy, the benefit of multiple entropy constraints for nonconvex scalar problems, and robust performance on shock problems.
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Computer Vision

Plan-Bench: Can Existing VLMs Go Well Beyond Perception to Reason and Plan in Embodied Worlds?

Juntong Feng, Qingan Liu, Jingru Dong et al. (+8 more)

Vision-Language Models (VLMs) have achieved strong performance in visual perception and spatial reasoning, leading to growing interest in using them as high-level planners for embodied AI. However, physical tasks require models to integrate spatial information, reason over temporal states, and generate multi-step plans under various constraints, raising the question of whether current VLMs can reliably support such reasoning and planning independently of execution. We introduce Plan-Bench, a benchmark for evaluating the high-level reasoning and multi-step planning capabilities of VLMs relevant to embodied worlds, while isolating the influence of action execution. It covers three complementary dimensions, spanning 16 subclasses and 699 curated samples. Extensive evaluation of 28 VLMs reveals room for improvement, with even the strongest model achieving only 75.0% accuracy. We further find that model scaling generally improves these capabilities. Ablation studies also indicate larger models show increasing potential as high-level planners. Overall, Plan-Bench provides a lightweight probe for evaluating VLMs' reasoning and planning capabilities relevant to embodied environments and assessing their potential as decision makers for physical tasks. Our benchmark and code are available at https://github.com/MinneFeng/Plan-Bench.
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All authors Juntong Feng, Qingan Liu, Jingru Dong, Yue Zhu, Weiming Zheng, Yujie Cheng, Xinzhe Han, Shuai Hao, Yunzhi Zhuge, Haiwen Diao, Huchuan Lu

Robotics

RoboSimStudio: An Interactive Toolkit for Human and Agent Rapid Real2Sim of Robot Manipulation Tasks

Kaiyuan Chen, Shuangyu Xie, Uksang Yoo et al. (+9 more)

It has been difficult to accurately model the physics of the interaction between a robot and the objects it manipulates, including contact mechanics, coupled contact dynamics, deformations, stiffness and friction. We present RoboSimStudio (RSS), an interactive toolkit that makes choices of solver, contact model, and physical parameters explicit and editable, allowing both humans and coding agents to quickly create and iteratively refine simulations based on observed physical behavior. We implement RSS with the open Newton physics simulation system and describe experiments with human-guided real2sim using (1) visual evaluation, (2) force-feedback and (3) agentic Real2Sim2Real. Code, video and additional information can be found on the project website: https://robosimstudio.github.io
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All authors Kaiyuan Chen, Shuangyu Xie, Uksang Yoo, Xinyue Zhu, Cael Magner, Alvin Zhu, Daehwa Kim, Eric Heiden, Erwin Coumans, Miles Macklin, Spencer Huang, Ken Goldberg

Computer Vision

Game2Real-Bench: Do Toy Games Reveal and Transfer to Real-World Visual Reasoning?

Qingan Liu, Juntong Feng, Yue Zhu et al. (+6 more)

Visual reasoning is an important capability for vision-language models (VLMs) to understand visual evidence, spatial structure, constraints, and state changes. Existing evaluations mainly rely on real-world data or procedurally generated tasks. Real-world data preserve natural complexity, while procedural games provide controllable generation and verifiable solutions. However, it remains unclear whether abilities measured in toy games correspond to real-world visual reasoning and whether game examples can support transfer. We introduce Game2Real-Bench, a benchmark that studies these connections across four capability groups, including fine-grained perception, spatial reasoning, constraint reasoning, and sequential planning. We construct 1,000 procedurally generated game samples with executable verification and curate 400 real-world samples aligned by shared reasoning requirements rather than visual similarity. We evaluate 25 representative VLMs and observe strong game-to-real consistency, with Pearson and Spearman correlations of 0.935. We further study one-shot game-to-real transfer on four models. Constraint reasoning improves for several models, while fine-grained perception declines with game demonstrations. We also construct Game2Real-Dataset with nearly 24K verified game samples across 18 tasks and 65 QA families. Our benchmark, dataset, and code are available at https://github.com/QingAnLiu/Game2Real-Bench.
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All authors Qingan Liu, Juntong Feng, Yue Zhu, Yujie Cheng, Xinzhe Han, Shuai Hao, Yunzhi Zhuge, Haiwen Diao, Huchuan Lu

General Relativity and Quantum Cosmology

Testing compact binary nature in eccentric orbits with third-generation detectors

Syed U. Naqvi, Kaushik Paul and Chandra Kant Mishra

The spin-induced quadrupole moment (SIQM) of a compact object provides a direct null test of the Kerr hypothesis. Most existing gravitational-wave tests of SIQM assume quasi-circular binaries, although dynamical formation channels can produce measurable eccentricity that may persist in the sensitive band of third-generation (3G) detectors. We extend the symmetric SIQM test to eccentric, aligned-spin binaries using a post-Newtonian spinning-eccentric phasing model, and forecast its measurability with Cosmic Explorer (CE) and Einstein Telescope (ET). Single-event Fisher-matrix forecasts show that the impact of eccentricity on SIQM measurement precision depends on the binary parameters and detector configuration, rather than uniformly degrading the measurement. A population study with a truncated eccentric expansion indicates that ET's additional low-frequency eccentric cycles tighten $\Delta\kappa_s$ by roughly a factor of two relative to CE (median $0.11$ to $0.12$ versus $0.20$ to $0.23$); the absolute values are indicative only. We further show that quasi-circular template banks can lose significant effectualness for moderately eccentric signals, motivating the development of eccentric-spin template families. Accounting for eccentricity is therefore important both for SIQM measurements and for avoiding systematic losses in searches, and it strengthens tests of the nature of compact objects with 3G gravitational-wave detectors.
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Differential Geometry

Exterior free-boundary minimal surfaces of every topological type with at least two ends

Igor Kozyrev

An exterior free-boundary minimal surface is a properly immersed minimal surface in the complement of the open unit ball of $\mathbb{R}^3$ whose boundary lies on the unit sphere and meets it orthogonally. We prove that for all integers $\ell\geq2$, $b\geq1$ and $\gamma\geq0$ there is a connected, orientable, properly embedded exterior free-boundary minimal surface with $\ell$ ends, $b$ boundary components and genus $\gamma$. Its total curvature is finite, and its ends are parallel catenoidal ends of multiplicity one. By the theorem of Mazet and Mendes, a surface of this kind with one end is a rotational annulus. Hence the topological types of such embedded surfaces are exactly the annulus with one end and all types with at least two ends. There are two gluing constructions. For $\ell\geq3$ we stack $\ell$ sheets over a stable catenoidal annulus that meets the sphere along a circle of radius $4/5$, and we join adjacent sheets by half-catenoidal bridges sitting on the sphere. The sheets are small normal graphs over this annulus whose displacements contain different multiples of the Jacobi field of the family of such annuli, so their boundary circles and the logarithmic growth of their ends differ slightly. For $\ell=2$ we double a catenoidal annulus near the critical angle $\pi/4$, where it acquires a bounded rotationally invariant Jacobi field; the distance to the critical annulus is coupled to the size of the bridges. In gluing constructions inside the unit ball that double or stack a compact surface, the bridges themselves must balance the sheets, which forces many bridges. Here the logarithmic growth of the ends absorbs this balancing. A fixed number of bridges therefore suffices, and every topological type is reached, including the small ones.
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Cryptography and Security

AegisAsync: Symbolic Async-Event Simulation for Risks in Python Asynchronous Programs

Baihong Chen and Wen Li

Security and robustness risks in Python async programs depend on event order, object identity, and execution after exceptions or cancellation. Detecting these risks requires connecting related operations across function calls and tracking their effects along execution paths. We present AegisAsync, a bytecode-based analysis of Python async risks for CPython 3.10-3.14. Its Async Event Transition Graph combines bytecode control flow, resolved calls, async events, and symbolic object relations. Bounded path-local simulation tracks event order and object states and explores cancellation at await suspensions. Six detector plugins evaluate the resulting traces and states to produce candidates with supporting witnesses. On AsyncBench, our benchmark of 180 labeled risks, AegisAsync detects all labeled risks with zero false positives on each of the five versions. Across five path budgets on 2,500 PyPI package versions, source review confirms 457 of 910 AegisAsync candidate records (50.2%), representing 457 unique bugs; across three flake8-async samples, 70 of 2,187 review judgments are confirmed (3.2%). By submission, 166 PoCs reproduce AegisAsync findings, and we have reported 157 bugs to developers, of which 16 have been confirmed and fixed.
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Nuclear Theory

A 4D $T^\prime$-expanded lattice QCD equation of state with a multi-dimensional 3D-Ising-type critical contribution

Francesco Di Clemente, Prachi Garella, Johannes Jahan et al. (+5 more)

Inferring the possible existence and location of a critical point on the QCD phase diagram through experimental observations requires equations of state that include both lattice QCD constraints and critical behavior. In this manuscript, we present the first four-dimensional equation of state in the $(T,\mu_B,\mu_Q,\mu_S)$ space combining the lattice 4D $T^\prime$-Expansion Scheme with a critical contribution mapped from the 3D Ising model. We extend the earlier two-dimensional construction, the so-called Ising 2D-TExS in the $(T, \mu_B)$ plane, promoting the critical point to a parametrizable critical surface in the full four-dimensional thermodynamic space. Our framework provides a family of equations of state to systematically study the effects of criticality in realistic hydrodynamic simulations with $BQS$ conserved charges, going beyond the case of strangeness neutrality, by varying the geometry of the critical surface and the strength of criticality at finite $\mu_B$, $\mu_Q$ and $\mu_S$ separately.
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All authors Francesco Di Clemente, Prachi Garella, Johannes Jahan, Micheal Kahangirwe, Jamie M. Karthein, Jacquelyn Noronha-Hostler, Claudia Ratti, Mikhail Stephanov

Computer Vision

OmniCompass: A Holistic Benchmark for Omni-Modal Video Grounding and Understanding

Xuyang Liu, Shihao Wang, Xinyu Wei et al. (+5 more)

With the rapid development of multimodal large language models (MLLMs), evaluating their video understanding capabilities has become increasingly important. Existing video understanding benchmarks cover only part of the evaluation dimensions, limiting systematic diagnosis of omni-modal video understanding. We introduce OmniCompass, a holistic benchmark for omni-modal video grounding and understanding. OmniCompass defines two evaluation tracks: OmniCompass-VL assesses vision-language models on tasks requiring visual evidence, while OmniCompass-AV assesses omni-modal models on tasks requiring joint audio-visual evidence. Each track includes three complementary tasks: temporal grounding (TG), spatial grounding (SG), and question answering (QA), assessing when a referenced target appears, where it is, and what happens. QA covers five perception and three reasoning categories in OmniCompass-VL, and three perception and two reasoning categories in OmniCompass-AV. OmniCompass-VL contains 820 videos and 2,460 instances across domains and three duration types: short, medium, and long. A narrative- and audio-rich subset forms OmniCompass-AV with 240 videos and 720 instances. Each instance is evaluated under two paired settings: text-only and text+image, specifying the same target through text and visual-language guidance. All instances are manually annotated with multi-round quality verification. Evaluations of 50 MLLMs show that open-source models still lag behind proprietary counterparts, particularly in audio-visual understanding. Precise temporal and spatial grounding remains challenging even for leading models, and their predictions still exhibit inconsistencies across the paired target specifications.
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All authors Xuyang Liu, Shihao Wang, Xinyu Wei, Minghan Li, Zeqing Wang, Zuhao Yang, Zichen Wen, Lei Zhang

Data Structures and Algorithms

Settling the Approximability of Submodular Facility Location

Adam N. Elmachtoub, Bento Natura and Meike Neuwohner

In submodular facility location (SFL), introduced by Svitkina and Tardos (SODA 2006), clients $\cal C$ in a metric space are assigned to facilities $\cal F$. A facility serving a set $S \subseteq \cal C$ of clients incurs cost $g(S)$, where $g$ is a monotone submodular function common to all facilities. The best known approximation factor for SFL is $O(\log\log|\cal C|)$, due to Abbasi, Adamczyk, Bosch-Calvo, Byrka, Grandoni, Sornat, and Tinguely (ICALP 2024), improving on the $O(\log|\cal C|)$-approximation of Svitkina and Tardos. We show that this is best possible up to a constant factor in the value-oracle model by showing that there exists no algorithm with only polynomially many queries to $g$ with approximation ratio $o(\log\log|\cal C|)$. This bound holds for algorithms with unlimited computation time, and when $g$ is restricted to matroid rank functions. We also show that the natural linear programming relaxation has an integrality gap of $\Theta(\log\log|\cal C|)$. Our lower bound follows by constructing an extension of Vondrák's symmetry-gap approach (FOCS 2009) for matroid rank functions.
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2610.18828 · 13 Oct · An initial proof of a constant-factor lower bound was obtained using ChatGPT 6.1 Astra. The stronger result shown in the paper was obtained in conversations with Claude Opus 5.5 and ChatGPT 6.1 Astra. The authors have improved the presentation and simplified the arguments. 25 pages, 2 figures

Abstract PDF $ALGO ×2$SYMM ×1

Quantum Physics

Gaussian entanglement and quantum communication: geodesic optimization and multimode bounds

Hemant K. Mishra and Mark M. Wilde

Loss and noise limit the use of light to distribute entanglement, transmit quantum information, and establish secret keys. Gaussian states have a compact description in terms of means and covariance matrices, but their entanglement still requires global optimization. We develop a framework for computing Gaussian-restricted versions of the relative entropy of entanglement and Rains entanglement. An integral representation reveals a convex geometry under matrix geometric means and reduces Gaussian Rains entanglement to relative entropy minimized over Gaussian states with positive partial transpose. We obtain unique optimal reference states and additivity for independent Gaussian input states. Our convex-majorization algorithm has an explicit geometric convergence rate, uniform in the faithful regularization parameter and valid for pure input states. Controlled numerical integration and approximate convex subproblem solutions give a bit-complexity bound that is polynomial in accuracy bits for each fixed rational input covariance matrix, with explicit dependence on covariance size. These calculations bound extractable entanglement and, through the relative entropy of entanglement, extractable secret key. Teleportation simulation, energy allocation, and a convex optimization of passive-basis loss cores give bounds on quantum and private communication under an input-energy constraint, allowing arbitrary two-way classically assisted protocols. Two- and three-mode examples compare the bounds with achievable rates, including matching pure-loss benchmarks. Finally, we separate the Gaussian-restricted quantities from their unrestricted counterparts and give a photon-number truncation method with controlled error for computing the latter.
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Robotics

WorldOracle: Benchmarking Action-Conditioned World Models against Real-World Executions

Haoyi Duan, Liliang Chen, Nan Wang et al. (+13 more)

We introduce WorldOracle, a benchmark specifically designed to evaluate action-conditioned world models (ACWMs) against paired real-world executions. Given the same initial observation and low-level action sequence, WorldOracle asks whether a predicted rollout reproduces what happens in the real world, including physical consequences and task-state transitions. We evaluate models along four complementary dimensions: physical state correctness, interaction spatial alignment, key interaction area fidelity, and multi-view action coherence. To support this evaluation, we curate real-world training and evaluation suites that cover different interaction dynamics and embodiments. The evaluation suite contains long, multi-segment episodes with both successful and failed executions, enabling evaluation across varied action outcomes and behavior distributions. Experiments on seven representative ACWMs reveal distinct model strengths and failure modes. WorldOracle provides a systematic foundation for measuring and advancing action-conditioned world modeling for manipulation. We will release the datasets, evaluation code, and leaderboard.
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All authors Haoyi Duan, Liliang Chen, Nan Wang, Yang Zhang, Yuhang Lu, Xiaotong Chen, Wei-Cheng Tseng, Shenyuan Gao, Zhaoshuo Li, Jingyi Jin, Pooya Jannaty, Dhruv Shah, Yuke Zhu, Ming-Yu Liu, Maoqing Yao, Guanghui Ren

Machine Learning (Statistics)

Joint Neural Posterior Estimation and Model Selection for Chemical Reaction Networks

J. Arturo Esquivel, Jorge A. Campos-Gonzalez-Angulo, Sergio Pablo-García et al. (+2 more)

Simulation-based Bayesian inference for Chemical Reaction Networks (CRNs) must simultaneously solve two computationally demanding problems: discriminating between overlapping reaction pathways and estimating reaction rate constants. Classical approaches, such as Sequential Monte Carlo ABC, rely on handcrafted summary statistics and scale poorly across large parameter spaces. To overcome this, we introduce a neural inference architecture. Our pipeline utilizes shared 1D-CNNs and a permutation-invariant Set Attention mechanism to learn low-dimensional summary statistics from variable-length, multi-experiment time-series data. These statistics simultaneously condition a model selection network to compute posterior model probabilities and model-specific conditional Invertible Neural Networks (cINNs) that estimate parameter posterior distributions. We demonstrate the practical utility of our approach on a real protodeboronation example, illustrating how it handles structural ambiguity and extracts kinetic parameters from competing catalyst deactivation pathways.
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All authors J. Arturo Esquivel, Jorge A. Campos-Gonzalez-Angulo, Sergio Pablo-García, Alán Aspuru-Guzik, Vianey Leos-Barajas