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All of arXiv

Friday 2 October

Analysis of PDEs

Sign-changing solutions for the critical Neumann problem in the three-dimensional unit ball

Fei Wu

We consider the existence of nonradial sign-changing solutions to the problem $\Delta u-\mu u+|u|^4u=0$ with zero Neumann boundary conditions in the unit ball for an arbitrary fixed parameter $\mu>0$. We prove that, for every $\mu>0$, this problem admits infinitely many distinct nonradial sign-changing solutions. More precisely, for every sufficiently large even integer $K$, we construct a solution by gluing $K$ symmetrically arranged, suitably transformed copies of a sign-changing entire solution of the critical equation in $\mathbb{R}^3$. The construction combines an inner–outer gluing scheme with a finite-dimensional reduction. A detailed expansion of the reduced energy allows us to locate an interior critical point in the admissible parameter region and thereby complete the construction.
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Computation and Language

Adaptive Mutual Distillation for Balanced Multi-Task Post-Training of Large Language Models

Baohang Li, Xiaocheng Feng, Yichong Huang et al. (+6 more)

Multi-task post-training of large language models (LLMs) aims to improve performance across tasks with unequal amounts of training data. Existing methods focus primarily on balancing task contributions during single-model training. Different task-balancing strategies can produce models with complementary strengths, creating opportunities for mutual distillation. However, the usefulness of cross-model supervision can vary across tasks, transfer directions, and stages of training. We propose Adaptive Mutual Distillation (AMD), a collaborative post-training framework that jointly trains two models with different task-balancing strategies. AMD evaluates candidate adjustments to distillation weights through short training probes shared across tasks, then uses task-wise validation scores to select an adjustment for each task and transfer direction. Across six benchmarks and three LLM backbones, both AMD models achieve higher average benchmark scores than supervised fine-tuning (SFT) baselines trained with the same sampling strategies. They also outperform the task-balancing methods evaluated in our experiments. Merging the two trained models can further improve their average benchmark score while yielding a single model for inference. The merged models outperform multi-task SFT by an average of 2.91 points across the three backbones.
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All authors Baohang Li, Xiaocheng Feng, Yichong Huang, Chengpeng Fu, Wenshuai Huo, Zekun Zhou, Zekun Yuan, Tingjia Zhang, Bing Qin

High Energy Physics (Experiment)

First measurement of the low-momentum negative-muon beam for the muon-to-electron conversion experiment at J-PARC

The COMET Collaboration: K. Oishi, R. Abramishvili, G. Adamov et al. (+182 more)

The COMET Phase-$\alpha$ experiment, the initial beam-operation stage of the COMET muon-to-electron conversion programme at J-PARC, took place in 2023 and marked the first beam operation at the COMET facility. It served to commission the delivery of a bunched, slow-extracted 8 GeV proton beam and the muon beamline. Its objective was to demonstrate experimentally that low-momentum negative muons could be transported to the experimental area through the Transport Solenoid (TS). We report a measurement of the transported muon beam using the Range Counter, a dedicated detector that identifies stopped negative muons by detecting delayed electrons emitted after the muons stop in a copper absorber. From the measured decay-time spectra, we reconstruct the number of stopped muons, the corresponding momentum spectrum, and the transverse beam profile. The observation of the stopped-muon component demonstrates that slow negative muons were transported through the TS to the experimental area. The reconstructed momentum spectrum indicates that the transported beam is concentrated in the low-momentum region. The non-uniform transverse profile is qualitatively consistent with charge drift in the curved solenoidal magnetic field. A Geant4-based simulation reproduces the overall dependence on degrader thickness and detector position; the measured yields are systematically higher by roughly 30%. These results provide the first experimental benchmark of low-momentum negative-muon transport in COMET and establish the basis for future beam characterisation and production studies.
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All authors The COMET Collaboration: K. Oishi, R. Abramishvili, G. Adamov, J. C. Angelique, K. Aoki, M. Aoki, Y. Arimoto, A. N. B. Az, I. Bagaturia, D. Bauer, T. Bouillaud, L. Del Buono, C. Cârloganu, N. Chadeau, Y. Chen, P. Chetry, D. Chokheli, T. Clouvel, P. D. Dauncey, S. Dekkers, R. Derveni, G. Devidze, P. J. Dornan, M. T. Dubouchet, L. B. Epshteyn, I. Evtoukhovitch, P. Evtoukhovitch, G. Faure, S. Fayer, G. V. Fedotovich, Y. Fujii, Y. Fukao, E. George, E. L. Gillies, M. Gouzevitch, D. N. Grigoriev, E. Hamada, I. H. Hashim, S. Hashimoto, M. Higashide, Y. Higuchi, N. Hiroshima, Y. Igarashi, F. V. Ignatov, M. Iio, M. Ikeno, K. Ishibashi, T. Itahashi, A. Jansen, R. Jeena, O. Jeremy, X. Jiang, P. M. Jonsson, Y. Kageyama, V. Kalinnikov, E. Kaneva, F. Kapusta, K. Kawagoe, R. Kawashima, N. Kazak, A. Khvedelidze, Y. Kojima, A. N. Kozyrev, B. Krikler, Y. Kuno, S. Kuribayashi, Y. Kurochkin, N. Kurosawa, A. Kurup, K. Ladhams, P. Lebrun, M. J. Lee, H. Li, W. Li, R. P. Litchfield, D. Lomidze, I. Lomidze, G. Macharashvili, Y. Makida, S. Makimura, G. Matsumoto, S. Matsumoto, A. Melnik, H. Miao, S. Mihara, A. Miles, M. Miyataki, Y. Miyazaki, T. Mizuno, M. Moritsu, R. Muto, R. Nagai, H. Nagashima, Y. Nakai, T. Nakamoto, Y. Nakamura, Y. Nakatsugawa, Y. Nakazawa, J. Nash, M. A. S. Nasrullah, T. M. Nguyen, V. Niess, Y. S. Ning, H. Nishiguchi, M. Nishihara, K. Noguchi, N. H. M. Nor, N. Norjoharuddeen, T. Ogitsu, H. Ohata, N. Ohuchi, K. Okabe, T. Okamura, H. Okurano, M. Oonaka, J. Pasternak, A. Paulau, D. Pieters, V. Raspal, R. Razali, A. Razquin, W. Roth, B. Sabirov, T. Saito, H. Sakamoto, P. Sarin, K. I. Sasaki, R. Sasaki, A. Sato, J. Sato, H. Sendai, N. Shigyo, M. Shinjo, Z. Shioya, M. Shoji, Dz. Shoukavy, W. Da Silva, A. Simonenko, D. Stöckinger, N. Sumi, A. Sumimura, S. Sun, J. Suzuki, S. Takami, S. Tanaka, J. Tang, J. Tojo, M. Tomizawa, T. Toriashvili, N. Tran, Z. Tsamalaidze, N. Tsverava, T. Uchida, Y. Uchida, Y. Uchiyama, S. Ueda, K. Ueno, Y. Uesaka, D. Vasileuskaya, E. Velicheva, M. L. Wong, T. S. Wong, C. Wu, T. Xing, Y. Xu, C. Yamada, H. Yamaguchi, M. Yamanaka, Y. Yang, W. Yao, B. Yeo, H. Yoshida, M. Yoshida, M. Yoshii, D. Yoshikawa, T. Yoshioka, Y. Yuan, Yu. V. Yudin, N. Yussup, I. Yusuff, J. Zhang, Y. Zhang, Z. Zhang, Y. Zhou, K. Zuber

Quantum Physics

Thermalization in a repeated-interaction model with memory effects

Kanji Nishii, Ryo Nagai and Yoshihiko Abe

We study how memory affects the thermalization of a qubit in a repeated-interaction model. In our model, a memory qubit interacts repeatedly with the system, while both qubits undergo collisions with fresh thermal ancillas. We derive exact closed evolution equations for their populations and mutual coherence, and demonstrate memory effects using a causal-break operation. Although the system converges to the target thermal state, the thermalization behavior shows non-monotonic approach. We also find a Mpemba-like reversal, in which the number of collisions required for thermalization depends non-monotonically on the temperature of the target state. Within the initial-state family considered, both phenomena require initial coherence between the system and memory or an imbalance in their excited-state populations.
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Artificial Intelligence

Bounded Reachability & Jailbreak Detection via Contraction-Constrained State Space Models

Omanshu Thapliyal

Safety heads are lightweight classifiers attached to pretrained language models for flagging harmful inputs before generation. Their empirical detection performance has been studied, but their formal robustness properties remain largely unexplored. We ask when a State Space Model (SSM)-based safety head can be certified to produce the same prediction for all inputs within a bounded embedding-space perturbation. We prove that the answer turns on a single condition: the $l_\infty$ norm of the state transition matrix must satisfy $\norm{A}_\infty<1$ (the contraction condition), which enables exact interval bound propagation (IBP) certification for linear time-invariant classifiers. When the contraction condition holds, the reachable output interval has bounded steady-state width and examples can be certified as robustly classified. When it fails, the interval grows exponentially with sequence length and certification is impossible at any practical perturbation radius. We enforce contraction with a hinge penalty and show on toxic comment data that certified fraction improves from 41% to 59%, with a sharp empirical phase transition at $\norm{A}_\infty=1$ matching the theory. Applying a contraction-regularized S4 head to jailbreak detection on JailbreakBench, we achieve a zero-shot transfer to AdvBench (DR=0.994) and HarmBench (DR=0.988). A logistic regression on mean-pooled Mamba-130M embeddings matches or exceeds the S4 head on every detection metric, confirming that harmful intent is already linearly separable in the embedding space. The S4 safety head's contribution is not superior discrimination but the formal certification that no probe-based approach provides.
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Rings and Algebras

Nilpotency and nil subvarieties of binary Zinbiel algebras

Nurken Smadyarov

An algebra is called binary Zinbiel if every subalgebra generated by at most two elements is a Zinbiel algebra. Over a field of characteristic zero, we prove that every finite-dimensional binary Zinbiel algebra is nilpotent. We also show that a subvariety of binary Zinbiel algebras is nil if and only if it does not contain the variety of all Zinbiel algebras. We further prove an analogue of Itô's theorem for binary Zinbiel algebras.
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Distributed Computing

ByteSplat: Efficient Distributed 3D Gaussian Splatting Training via Intra- and Inter-GPU communication reduction

Shuo Wu, He Zhu, Han Zhao et al. (+9 more)

3D Gaussian Splatting (3DGS) enables photorealistic scene reconstruction, but training large-scale scenes requires substantial memory and computation. Distributing training across multiple GPUs increases available memory capacity, yet its performance is strictly constrained by data movement. We identify two dominant bottlenecks: repeated off-chip memory accesses during forward and backward rasterization, and inter-GPU communication of partial Gaussian gradients. To address these bottlenecks, we present ByteSplat, a distributed 3DGS training framework that jointly reduces intra- and inter-GPU data movement. First, ByteSplat fuses forward rasterization and backward rasterization into a single GPU kernel, retaining intermediate results on-chip to eliminate redundant off-chip transfers. Second, to alleviate the increased on-chip storage by fused rasterization, ByteSplat introduces hardware-aware pruning that considers both rendering quality and per-tile shared-memory constraints, increasing the overall performance of fused execution. Lastly, ByteSplat exploits gradient sparsity to eliminate zero partial gradients from inter-GPU communication. GPU-efficient encoder and decoder kernels compact the remaining records and directly aggregate the received gradients on their owner GPUs, reducing both communication volume and local aggregation overhead. We evaluate ByteSplat across six datasets. Compared with the baseline, ByteSplat reduces intra-GPU off-chip traffic and backward inter-GPU communication volume by 63.4% and 65.8%, respectively. On eight GPUs, ByteSplat achieves up to 6.1$\times$ training speedup while preserving reconstruction quality.
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All authors Shuo Wu, He Zhu, Han Zhao, Xiaohui Zhang, Yaqian Zhao, Hui Wei, Ruyang Li, Hongzhi Shi, Lihua Lu, Jingwen Leng, Yu Feng, Minyi Guo

Probability

A PDE approach to quantitative asymptotic stability of the optimal filter in the linear detectable setting

Minh Van Hoang Nguyen and Sangmin Park

The filtering problem asks to estimate a signal process, the initial state of which is unknown, given its partial and noisy observations. From a probabilistic perspective, the best estimate at each time is the optimal filter, which is the conditional law of the signal given all observations up to the time. The problem of asymptotic stability of the optimal filter, which asks whether the filter initialized with the incorrect initial law converges to the correctly initialized filter, is of fundamental practical and theoretical importance. This paper studies the quantitative asymptotic stability of the optimal filter for signal-observation models with linear drift and additive Brownian noise. When the initial law is additionally assumed to be Gaussian, the optimal filter reduces to the celebrated Kalman-Bucy filter, for which the detectability condition on the signal and observation matrices is the sharp condition ensuring asymptotic stability. In the linear setting where the detectability condition holds but the initial law need not be Gaussian, we make the following contributions by studying the Zakai equation satisfied by the unnormalized filter. First, we study the asymptotic behavior of the deterministic part of the Zakai equation in the general case with nonlinear drift, and place the detectability condition in this context. Second, in the case of linear drift, we characterize the solution of the Zakai equation (hence the optimal filter) by a gauge transformation that separates the finite-dimensional stochastic dynamics from the infinite-dimensional deterministic dynamics. Third, we use this representation to establish asymptotic exponential filter stability in the $\chi^p$-divergence (with respect to a reference optimal filter), the total variation norm, and the $2$-Wasserstein distance.
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Soft Condensed Matter

Nonlocal, nonlinear electrostatics: like-charge attraction and asymmetric solvation

V. Stepanyan, Y. Sh. Mamasakhlisov and A. E. Allahverdyan

We study an equilibrium system, where linear molecules with a rigid charge distribution interact via the mean-field generated by the Coulomb coupling. We focus on the nonlinear regime, which is valid close to external charges immersed in the system. The finite molecular size in this regime leads to a nonlocal response at short distances. First, we show that the mean-field potential is non-monotonic, i.e., like charges can attract each other. Second, we show that the polarization induced by an external charge (and hence its solvation structure) depends on the sign of this charge, violating the effective C-symmetry of the macroscopic electrodynamics. We identify several scenarios of this effect, characterize it with the free energy and entropy differences, and compare it with analogous effects in asymmetric electrolytes described by nonlinear Poisson-Boltzmann equations.
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Robotics

Permutation Robustness Is Not Enough: Action Collapse in Multi-Agent Transformer Policies

Amit Thakur and Mukesh Singhal

Transformer policies are attractive for multi-agent robot learning because self-attention can model interactions among agents. However, multi-agent teams are unordered, while transformers typically process agents as ordered token sequences. We study how this mismatch affects cooperative navigation policies under agent-order permutations. Our results show that low permutation error alone can be misleading: policies may appear robust simply because all agents choose the same action. We therefore evaluate policies using both permutation-consistency metrics and action-collapse diagnostics, including action diversity, same-action fraction, and maximum action frequency. A PPO-ID baseline yields non-collapsed behavior but remains order-sensitive, while strong equivariance regularization can still induce homogeneous behavior. A weak equivariance penalty improves the robustness while preserving more diverse actions for teams with \(N=3\) agents, whereas teams with \(N=4\) agents require substantially smaller regularization weights. These findings suggest that multi-agent transformer policies should be evaluated not only by return and permutation robustness, but also by whether they maintain non-collapsed, differentiated multi-agent behavior.
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Multiagent Systems

Turnover-Orthogonal Credit Assignment for Open-Team Multi-Agent Reinforcement Learning

Amit Thakur and Mukesh Singhal

Open-team multi-agent reinforcement learning studies cooperative systems in which agents may join, leave, or be replaced during an episode. In such settings, the team return changes both because agents choose useful actions and because the active population itself changes. Standard centralized critics and shared advantages often mix these two effects into one scalar credit signal, allowing surviving agents to be rewarded or penalized for exogenous turnover events outside their control. We introduce turnover-orthogonal credit assignment (TOCA), a value decomposition for open teams that separates action effects, pure turnover effects, and action–turnover interactions. Under exogenous turnover, the event-conditioned value admits a centered decomposition whose event-conditioned baseline removes the pure turnover component while preserving credit for actions that make the team robust to future replacements. We instantiate this idea with a permutation-invariant centralized critic over variable-size agent sets and event tokens, and derive both a counterfactual per-agent credit signal and a softly weighted interaction variant, TOCA-$\beta$, for high-variance control environments. Controlled diagnostic experiments show that TOCA improves return over event-aware MAPPO-style critics and that removing interaction credit substantially hurts performance. In a replacement-only Dynamic Spread benchmark, TOCA-$\beta$ achieves the best mean return at high turnover rates and improves over its no-interaction ablation. These results suggest that explicitly separating turnover from action credit is a useful principle for robust learning in dynamic cooperative teams.
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Machine Learning

Understanding Enrichment in Reinforcement Learning

Jinwoo Kim and Shraddha Barke

When rewards are sparse, reinforcement learning with verifiable rewards (RLVR) often uses hints or intermediate guidance to generate more successful rollouts. This enrichment biases policy-gradient updates unless corrected via importance weights, but existing methods omit correction or truncate importance weights in order to avoid the high variance of correction. It thus remains unclear what exactly is gained or lost in RLVR by correcting enriched rollouts. We show, mathematically, that omitted or truncated correction implicitly reweights the defined reward, and we decompose the resulting gradient error into scale, rotation, and variance to explain their distinct effects on learning. To make correction practical, we develop a novel sequential Monte Carlo (SMC) weight correction mechanism that, under stability and particle-order assumptions, tempers the exponential compounding of standard correction variance over the length of a sample to an additive accumulation. We then apply our analysis of enrichment to interpreting the results of a fine-tune of Qwen3-1.7B on a sparse band of OpenMathReasoning, establishing a concrete mechanism of how enrichment, both corrected and uncorrected, helps avoid collapse in sparse domains. Our main contribution is to understand, in general, how enrichment and correction can affect training, as opposed to claiming that either mode of operation is superior to unenriched RL.
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Chaotic Dynamics

An Arrow of Time in Stable Autonomous Generation

Zhixin Lu

Does stable autonomous generation select a direction of time? This question matters both for learning models that autonomously generate prescribed dynamics and for designing controllers that make an invariant set attracting without changing its dynamics. Periodic motion and quasiperiodic torus rotations admit stable generation in either direction. For a chaotic attractor, however, reversing the equations reproduces its backward trajectories while turning attraction into repulsion. Can additional latent variables or autonomous feedback restore attraction without changing the reversed motion? We prove an obstruction to such exact generation by finite-dimensional autonomous systems with $C^2$ vector fields, compact attracting sets, and continuous readouts. The result applies to the classical Lorenz attractor and, more generally, to dynamics with an ergodic invariant measure of positive metric entropy whose intrinsic local stable fibers are totally disconnected on a set of positive measure. The proof connects this geometry to an entropy contradiction: a hypothetical attracting realization would force the output entropy to vanish, contrary to the prescribed chaotic dynamics. We use reservoir-computing examples to illustrate the difficulty of stable autonomous generation for time-reversed chaos: both time directions are closely tracked while the networks are driven by data, but only the forward example retains Lorenz geometry during autonomous generation. The theorem identifies a class of dynamics that cannot be learned for exact, stable autonomous generation by finite-dimensional smooth models satisfying the stated assumptions, regardless of the learning procedure or the number of latent variables.
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Artificial Intelligence

DNAlign: Dynamic Null-Space Safe Alignment for LLMs

Jisheng Dang, Yushuo Zhao, Dewei Liu et al. (+6 more)

Ensuring the safe and reliable deployment of large language models (LLMs) remains a fundamental challenge. Existing safety alignment approaches either incur high computational cost or unintentionally disrupt the model's core knowledge, leading to degraded fluency and factual accuracy on benign tasks. This reveals a persistent trade-off between safety and utility. We propose DNAlign, a lightweight alignment framework that integrates control-theoretic optimization with null-space projection. By treating the LLM as a dynamic system, the proposed framework introduces controllable perturbations to steer generation toward safe behavior. A key component is the projection module, which restricts these perturbations to the harmful-related subspace derived from neutral hidden states, thereby preserving general knowledge and response quality. A value function trained on human preference data adaptively optimizes the control signals to align with human safety preferences. Extensive evaluations across multiple LLM backbones demonstrate that our framework consistently reduces harmful outputs while maintaining fluency, coherence, and factual utility. It achieves superior overall performance compared to prior alignment baselines without sacrificing generation diversity. These results indicate that the proposed framework provides an effective and practically deployable solution for safe LLM alignment. Code is available at https://anonymous.4open.science/r/DNAlign.
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All authors Jisheng Dang, Yushuo Zhao, Dewei Liu, Junfeng Fang, Bimei Wang, Tiantian Rao, Hong Peng, Bin Hu, Tat-Seng Chua

Signal Processing

On the Optimality of OFDM for Aperiodic Ranging

Yifeng Xiong, Fan Liu, Ya-Feng Liu et al. (+2 more)

We study the expected aperiodic autocorrelation sidelobes of random communication symbols transmitted through a unitary modulation matrix. We consider proper sub-Gaussian constellations, namely those with fourth absolute moment $\mu_4<2$ and zero pseudo-variance, including the commonly used uniform square quadrature amplitude modulation (QAM) and uniform phase-shift keying (PSK) constellations. For every prescribed lag, we determine the exact minimum expected sidelobe level (ESL) and a unitary modulation attaining it by applying a normalized inverse discrete Fourier transform (IDFT) separately on each chain of sample indices spaced by that lag. The full orthogonal frequency division modulation (OFDM) modulation attains this minimum if and only if the lag divides the block length $N$. Combining this criterion with the complete characterization of the minimizers at lag one, we show that a unitary modulation minimizes the ESL simultaneously over the first $r$ positive lags, called the prefix $\{1,\ldots,r\}$ with $1\le r<N$, if and only if every lag in that prefix divides $N$. In particular, simultaneous optimality over all positive lags is impossible for $N\ge 3$. We also prove that OFDM globally minimizes the partial expected integrated sidelobe level (EISL), defined as the sum of the ESLs over a selected subset of positive lags, for every such prefix. This also resolves the full EISL conjecture when $r=N-1$.
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All authors Yifeng Xiong, Fan Liu, Ya-Feng Liu, Shi Jin, Jianhua Zhang

Optimization and Control

When Can an Infinite-Stream Evaluation Support Dynamic Programming? Compatibility, Recursive Compression, and Generalized Summation

Yingzhe Xu

Dynamic programming for nonstandard infinite-horizon criteria requires more than finite stream values: one-step control substitutions must remain evaluable, and continuation information must propagate recursively. For expected stage-reward streams, we separate domain admissibility, finite-dimensional continuous autonomous realizability, scalar sufficiency, and contextual order consistency. For absolutely summable weighted criteria, we prove that the minimum Euclidean dimension of an exact continuous autonomous continuation state equals the temporal Hankel rank. Thus finite Hankel rank exactly characterizes when temporal nonstationarity can be replaced by finite endogenous state augmentation; the lower bound applies even to nonlinear continuous encoders and already holds in a one-state MDP. For literal Candelpergher Ramanujan summation, the same common-continuation test fails earlier: changing only the current action can leave the evaluation domain. Abel summation provides a contrasting prefix-closed benchmark.
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Computation and Language

How Robust Is Multimodal Claim Verification to LLM Rewriting?

Yun-Ang Wu, Xanh Ho, Andre Greiner-Petter et al. (+4 more)

LLMs are known to introduce stylistic changes into generated text, yet how these stylistic shifts affect model decisions on scientific tasks remains underexplored. In this paper, we focus on multimodal claim verification, where the goal is to determine whether a textual claim is grounded in a given piece of evidence. We apply two rewriting strategies: natural rewriting, which simulates how researchers routinely use LLMs to polish academic text, and controlled injection, which inserts a single LLM-associated word to isolate the effect of vocabulary choice. We evaluate 11 open-weight models spanning five VLM families and ranging from 2B to 38B parameters. We find that models are robust to these modifications: most show no significant drop in accuracy, and compared to prior work on review-score manipulation, verification appears far more stable. However, consistent probability shifts do occur. Hedging-oriented conditions produce significant shifts across nearly all models, while boosting conditions show a weaker effect and general polishing conditions (e.g., grammar correction, fluency improvement) have little effect.
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All authors Yun-Ang Wu, Xanh Ho, Andre Greiner-Petter, Sunisth Kumar, Tian Cheng Xia, Florian Boudin, Akiko Aizawa

Robotics

PointWAM: 3D World Action Modeling for Dexterous Robotic Manipulation

Chunghyun Park, Beomjun Kim, Seungcheol Park et al. (+5 more)

World action models jointly learn to forecast world dynamics and predict robot actions, such that the learned internal world dynamics guide accurate actions. Existing approaches typically represent the world as RGB frames or latent counterparts while predicting actions as end-effector poses or joint angles, but they often struggle to capture the 3D spatial structure and contact geometry central to dexterous manipulation. We introduce Point World Action Model (PointWAM), a 3D world action model that decomposes the world into a scene (i.e., environment) and hands (i.e., actor), and jointly forecasts both as 3D point trajectories within a shared space-time coordinate frame. This explicit, disentangled representation enables effective pre-training on large-scale human demonstration videos without requiring any task-specific object or keypoint selection. Given a colored point cloud and a language instruction, PointWAM predicts how the scene and hands co-evolve in 3D space over time, then retargets the forecast hand motion to robot actions. Pre-training on human videos improves average DexJoCo success by 56.9 percentage points, and scene-trajectory supervision adds 10.9 points over forecasting the hands alone. With both, PointWAM surpasses the prior state of the art on ten DexJoCo tasks by 11.7 points and outperforms strong VLAs on a real robot.
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All authors Chunghyun Park, Beomjun Kim, Seungcheol Park, Heeseung Kwon, Yashu Shukla, Seunghoon Sim, Jinwoo Shin, Minsu Cho

Machine Learning

To Explore The Strange New World Beyond Data Distribution: System Behavior, Causality Tax, and Non-causal Base Model

Xianzhi Zeng, Jiangneng Li and Gao Cong

We show that the causality of language models (LMs) may not be necessary nor optimal. This is the case when system behavior (denoted as $S$) is incorporated as a first-principle Bayesian feature. Here, $S$ refers to extra dominant factors beyond the data space, and they involve coupled effects. Despite being the de facto foundation of modern architecture, recent studies indicate persistent mismatches and contradictions with causality. These issues largely stem from system behavior rather than the data distribution. We therefore propose the SBD framework, which incorporates $S$ as an irreducible component of the evidence lower bound (ELBO). SBD theoretically reveals a counter-intuitive Causality Tax phenomenon, where causality emerges as a suboptimal approximation with an additional structural error, due to the obliviousness to $S$. To address the challenge of latent variable analysis, we validate the SBD-predicted impact of $S$ via implicit measurements, theoretical-bound-guided controls, and Neural Tangent Kernel (NTK) evaluations. In particular, we construct Green Shell (GSH) to show the possibility of reducing Causality Tax. GSH is a non-causal variational family, and it replaces the sequential dependency chain of $S$ components with a divide-and-conquer partition. NTK spectra in the lazy-training regime confirm that GSH always achieves significantly tighter error bounds than causality, with $7dB+$ improvement in signal-to-noise ratio. In the relatively later stage of lazy-training, GSH further leads to superior generalization (up to $20\%$ richer multi-scale fitting capabilities). Taken together, SBD establishes system behavior as a complementary theoretical abstraction besides causality and distribution fitting, opening new research avenues such as designing and optimizing LM base models.
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Trading and Market Microstructure

Axient: Manifest-Bound Evidence for On-Chain Financial Protocols: Seven-Layer Derivation, Correlation, Tamper Rejection, and Reproducible Claim Promotion

Maksym Nechepurenko

Hybrid on-chain financial protocols are frequently evaluated with evidence that is individually useful but collectively insufficient: a unit test, transaction receipt, screenshot, service response, or several matching hashes may be presented as proof of a complete workflow even when the layers share one generated source or omit the financial authority that matters. This paper develops a manifest-bound evidence architecture for such systems. A sealed execution manifest binds declared system identities, roles, schemas, and release identity. Seven evidence layers are retained with registered derivations and linked by a common correlation identity. A conjunctive claim-promotion rule requires provenance, predicate-specific root conditions, negative controls, reproducible packaging, historical replay, and independent review in addition to hash equality. We formalize the evidence graph, prove that copied hashes cannot establish independent derivation, show how collision-resistant commitments make specified tampering detectable, define exactly-once financial-effect evidence, and distinguish original historical identities from later reproducibility attestations. The registered local case study records twelve parent Financial Interaction Assertions in one accepted cohort: 84 retained ACTUAL_EVIDENCE positions, two clean materializations with one byte-identical file index, a deterministic strict archive accepted by a separate verifier, and a selected ordered replay bound to that archive. FIA-011 is conjunctive and retains both stale-before-admission and book-epoch-change-mid-position subcases. The result demonstrates a reviewable chain of custody from financial assertion to replay-bound package while preserving the difference between observed evidence, interpretation, and future hypotheses.
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Sound

How Far Back Should a Transformer Look? Repetition and Copying in Music Sequence Models

Amir Fathi

We investigate how predictive performance depends on the maximum context available to an autoregressive model of symbolic music, and what information long-context models exploit. A small causal Transformer is trained separately at each context length T in {6, 18, 48, 96, 192, 336} and evaluated on the same target positions, both over raw tokens and over non-overlapping binary latent codes. On Nottingham folk tunes, the token predictor's test NLL decreases by 71% (0.986 bits per token) between 6 and 336 tokens, and by 71% on the O'Neill's tunes long enough for the same sweep (129 of 302 test tunes). Most of the long-context gain is explained by exact copying: the improvement appears when an earlier occurrence of the target's 16-token history enters the available context; overwriting that occurrence removes the gain, whereas equally large unrelated corruption does not; and a simple copy baseline recovers 94% of the reduction. A trained 336-token model likewise loses most of this gain when its history is restricted to recent tokens at test time. Because many repeats arise from written repeat signs expanded in the score, this result pertains specifically to these rendered score representations. By contrast, on MAESTRO performances and MusicNet scores, where exact repeats are substantially less frequent, the reduction is smaller (9% and 18%) and is largely attained by 96 tokens. Finally, an audit of an earlier draft that reported saturation at 16 tokens identified split leakage, overlapping latent receptive fields, an averaging predictor, and a per-file tempo grid; we present these as methodological checks for context-length measurements.
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Sound

Correlation-Based Distillation Yields More Mergeable Speech-Music Encoders

Fabian Ritter-Gutierrez

A single compact encoder for both speech and music removes the need to maintain a separate model per domain. A practical recipe distils a speech teacher and a music teacher into two small students, then merges them into one model. Two merging algorithms exist: interpolating the student weights from a shared initialisation, or permuting their channels into alignment before averaging. Prior work fixed the distillation loss in both, leaving open whether the loss itself affects how well the students merge. We show that it does. Holding architecture and evaluation fixed, we replace the DistilHuBERT loss \Lkd{} with a correlation-based loss \Lcl{}. Under weight interpolation, \Lcl{} students stay closer to their own better endpoint in $17$ of $18$ comparisons and lead on the speech tasks at every interpolated weight. Under activation permutation, they need fewer channels rearranged at three layers, their matched channels correlate more strongly, and they again lead on speech. The two merging algorithms share no mechanism, yet both improve under the same loss substitution. This suggests that the gain lies in the representation \Lcl{} produces rather than in either algorithm.
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Machine Learning

All Work And No Play Makes Jack a Dull Boy: Understanding and Preventing Catastrophic Strategy Collapse in RLVR

Qiyuan Huang, Tianshi Xu and Meng Li

During post-training of large language models (LLMs) with Reinforcement Learning with Verifiable Rewards (RLVR), GRPO-style algorithms can exhibit severe late-stage collapse. Prompt-based probing reveals that this is not benign strategic pruning, but a harmful contraction of effective strategy capacity that makes distinct reasoning strategies increasingly inaccessible. To characterize this phenomenon, we define strategies through trajectory-level policy-update interactions and develop a unified theoretical framework combining optimization dynamics and information theory. We prove that major RLVR objectives progressively concentrate probability mass onto a single strategy, while sustaining nontrivial task accuracy requires a minimum strategy capacity. The conflict between these two results provides a mechanistic explanation for catastrophic collapse. We further derive the {Mirrored Entanglement Index (MEI)} as a lightweight online warning signal. To prevent collapse, we propose Mesh Learning, which exposes multiple reasoning strategies and prevents any single strategy from dominating optimization. Across AIME26, AIME25, MATH-500, GPQA, and LiveCodeBench, Mesh Learning consistently outperforms strong baselines across Qwen and Phi model families, with gains of up to 13.4 pp and 11.5 pp, respectively. These results establish strategy preservation as a key principle for stable RLVR. Code is available at https://github.com/Ayanami-0123/Open-Mesh-Learning.
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Trading and Market Microstructure

Axient: Canonical Protocol-Graph Composition for Leveraged Event Markets: Single State Authority, Atomic Composition, Durable Sagas, and Exactly-Once Recovery

Maksym Nechepurenko

A modular leveraged event-market protocol can contain individually correct contracts for risk approval, positions, debt, settlement evidence, credit pools, junior backstops, reserves, liquidation, and governance while still lacking one authoritative financial execution path. This paper develops a canonical protocol graph in which every financial domain has one storage authority and composition components coordinate transitions without recreating balances, debt, positions, evidence receipts, queues, reserves, pause state, or terminal scenario state. The architecture formalizes atomic position origination, a settlement-confirmed debt saga, trader residual release, an ordered reserve-backstop-Senior loss waterfall, loss-participating withdrawal queues, capability-conditioned execution, protocol-wide pause and timelocked recovery, deterministic deployment manifests, canonical state projection, and exactly-once reconstruction after a chain-confirmed checkpoint. We prove composition-level authority uniqueness, atomic closure, loss conservation and priority, receipt-idempotent settlement, legal no-go safety, capability-transition safety, and no-financial-reexecution recovery under explicit assumptions. The implementation is evaluated through twelve parent Financial Interaction Assertions (FIA-001-FIA-012), including mandatory FIA-011A/B capability subcases. The registered local cohort contains twelve uniquely correlated scenario records and 84 retained ACTUAL_EVIDENCE layer positions, two clean materializations with one byte-identical file index, a deterministic strict archive accepted by a separate verifier, and a selected ordered replay bound to that archive. The result connects the formal protocol graph to a reproducible evidence chain while preserving explicit boundaries between the observed engineering result and future external-operation hypotheses.
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Combinatorics

Resolving Erdős-Ulam Monochromatic Union-Closed Family Conjectures

Deep Bhattacharjee, Priyabrata Mandal and Ushashi Bhattacharya

We prove both Erdős-Ulam conjectures on monochromatic union-closed families. Every two-colouring of the subsets of a finite set contains a monochromatic union-closed family whose size grows faster than any fixed power of the size of the set, while suitable colourings admit no monochromatic union-closed family of exponential size. Both results hold for any number of colours and are verified in Lean.
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Robotics

FastOPD: On-Policy Distillation for Lightweight VLA Deployment

Yoojin Oh, Jeongsol Kim, Yeonwoo Seo et al. (+7 more)

Vision-Language-Action (VLA) foundation models have scaled rapidly to enhance manipulation performance and generalizability, but this scaling incurs high computational costs that render real-world deployment increasingly challenging. Existing approaches typically mitigate this issue by designing smaller architectures or reducing the iterative denoising steps in flow-based policies. In this work, we propose FastOPD, a foundation-to-lightweight VLA framework that enables the practical deployment of large-scale VLAs through efficient on-policy distillation. Specifically, FastOPD adapts a flow map for single-state teacher supervision and combines it with a self-consistency objective to construct a compact student that learns the teacher dynamics. Furthermore, we theoretically demonstrate that minimizing this objective allows the distilled student to recover a distribution on par with that induced by an ideal few-step teacher model. We evaluate FastOPD across diverse foundation policies in simulation and real-world experiments. On LIBERO, FastOPD retains 84% of the performance of $\pi_{0.5}$ with only two inference steps, reducing inference latency by 78.1% while outperforming existing few-step distillation baselines in average success rate. With LingBot-VLA as the teacher, FastOPD improves the single-step success rate over the base student by 15.9 percentage points on RoboTwin 2.0. We further demonstrate its applicability to a World Action Model (WAM) and deploy a compact student distilled from MolmoAct2 on a real robot.
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All authors Yoojin Oh, Jeongsol Kim, Yeonwoo Seo, Jangho Park, Seonghyun Jin, Sunwoo Park, Youngmin Kim, Youngjun Jun, Kyumin Choi, Jong Chul Ye

Artificial Intelligence

AMBER: Multi-View Adaptive Budget Allocation for Listwise Vision-Language Reranking

Wenteng Chen, Jiachen Zhu, Rong Shan et al. (+10 more)

Vision-language models (VLMs) are powerful listwise rerankers for multimodal retrieval, but high inference costs restrict them to evaluating small local candidate views. Existing multi-call strategies rely on fixed schedules, wasting expensive VLM calls on uninformative candidate pairs and easy queries. To address this, we propose Adaptive Multi-view Budgeted Elo Reranking (AMBER), an online, budgeted multi-view reranking framework that dynamically optimizes global resource allocation. AMBER treats fragmented listwise VLM outputs as local tournaments, using continuous Elo updates to maintain a lightweight global ranking state. Building on this, it allocates computation at two levels: dynamically constructing candidate views with high score ambiguity, and scheduling queries to maximize expected information gain. We show that each Elo update corresponds to a stochastic gradient ascent step on the Bradley-Terry log-likelihood, and provide a submodular information-theoretic motivation for the query-level allocation strategy. Experiments on CIRR, CIRCO, and PhotoBench demonstrate that AMBER achieves the strongest overall performance among the compared multi-call VLM reranking methods under comparable VLM-call budgets, while remaining effective in lower-budget settings. Our code is publicly available at https://github.com/wnlfc/AMBER.
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All authors Wenteng Chen, Jiachen Zhu, Rong Shan, Tianyi Xu, Yuxiang Chen, Congmin Zheng, Teng Wang, Junjie Wu, Weiwen Liu, Changwang Zhang, Weinan Zhang, Jun Wang, Jianghao Lin

Systems and Control

On BESS-Backed Trading on the Continuous Intraday Electricity Market

Leo Semmelmann, Runyao Yu, Joseph Cary et al. (+1 more)

Battery energy storage systems (BESS) on the continuous intraday market (IDC) often trade according to a rolling intrinsic algorithm, a myopic strategy which repeatedly opens and unwinds positions according to current prices throughout the trading session, before dispatching as delivery approaches. This paper introduces a novel trading strategy for storage, in which forecast-driven round trip trading takes priority and the BESS supplies a second route for closing out positions that the market would otherwise close at a distressed price. The agent uses price quantile forecasts to open positions on the IDC, and closes these positions closer to delivery. The market can move against these trades, and the BESS intervenes only when a position would have to be settled at a price that the forecast predicts to be highly improbable, absorbing or serving that volume physically and restoring its state of charge at ordinary prices afterwards. The position itself remains loss-making; what the asset changes is the price at which it is closed, by transferring the terminal settlement price through time. Four quantile forecasting models of increasing complexity supply the thresholds, and all strategies are backtested on realised EPEX SPOT transactions for the German market area in 2024. A 40 MWh BESS in this role earns EUR 2.06m against EUR 1.77m for a rolling intrinsic benchmark and EUR 1.37m for a perfect-foresight day-ahead benchmark, while consuming 167 instead of 365 available equivalent full cycles. Hence, the novel backstop strategy yields higher profits, while using the underlying BESS less, leaving capacity for other trading opportunities.
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All authors Leo Semmelmann, Runyao Yu, Joseph Cary, Derek Bunn

Computation and Language

Clinical Concept Centers in LLMs

Aishik Nagar, Abhishek Vaidyanathan, Arun-Kumar Kaliya-Perumal et al. (+2 more)

Large language models are increasingly used in clinical settings. However, research into the reliability and performance of these models has focused almost entirely on the language substrate, scoring what the model says. Mechanistic interpretability has found that the latent space carries a higher fidelity of representation than the text: internal representations not only encode substantially more than the output verbalizes, but the stated reasoning also systematically omits features that causally drive the answer. An evaluation of model behavior in terms of mechanistic interpretability has not been explored in clinical decision support. In this work, we extend behavioral evaluation into the latent space and ask whether clinical concepts exist as locatable, causally used representations inside open-weight LLMs. We find dedicated clinical concept centers in the latent space of all eleven open models we test. These concept centers are interpretable, firing only on their aligned clinical narratives, and meaningfully and causally drive model behavior in both constrained and open-ended settings. They are not just analytical representations, but circuits that can be utilized in clinical practice, and we explore their use from the perspective of both evaluation and performance. From the evaluation standpoint, models stay internally coherent and keep using the relevant concept centers even under adversarial role-based priming, while aligned priming improves downstream clinical performance. From a performance perspective, we simulate realistic deployment settings and find that steering models along these centers leads to meaningful downstream improvements. Finally, we conduct a blinded clinician validation and find the activation and usage of these concept centers predicts clinicians preferences.
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All authors Aishik Nagar, Abhishek Vaidyanathan, Arun-Kumar Kaliya-Perumal, Elijah Tzen Hsuen Boey, Stefan Winkler

Artificial Intelligence

FSPO: Policy-Consistent Risk and Pareto-Feasible Control for Budgeted LLM RL Post-Training

Miaobo Hu, Shuhao Hu, Xiaobo Guo et al. (+3 more)

Adaptive LLM reinforcement-learning post-training changes multiple training actuators online, including rollout temperature, group size, clipping, KL regularization, verifier allocation, and update budget. Three coupled issues remain unresolved. A future-risk model trained from behavior trajectories need not estimate the risk induced by the controller that will be deployed; a score calibrated on logged state-action pairs can become miscalibrated after selective action choice; and independent per-resource minimum costs do not in general certify a feasible multi-resource continuation. We introduce FSPO, a feedback-state controller for budgeted LLM RL post-training that addresses these issues jointly. FSPO learns a policy-consistent risk-to-go model whose Bellman target follows the same frozen controller used for future decisions, together with a long-horizon utility model. Decision-conditioned trajectory calibration (DCTC) calibrates risk on cross-fitted trajectories generated by actions selected by provisional controllers. A Pareto resource continuation certificate (PRCC) admits an action only when a non-dominated cumulative reservation remains feasible over the residual horizon. Under a matched GRPO resource envelope, FSPO reaches 66.11% held-out and 59.43% OOD accuracy, compared with 64.47% and 57.03% for PB2, the strongest evaluated adaptive baseline. Three paired training seeds give gains of +2.42 and +3.19 percentage points over the contextual bandit on held-out and OOD evaluation. Under high behavior-deployment mismatch, policy-consistent risk lowers selected-decision ECE from 0.108 to 0.053; DCTC lowers it from 0.039 to 0.022 at matched acceptance; PRCC removes false-feasible admissions on an 18-action catalog ($0.197\rightarrow0.000$); and enabling all three components reduces trajectory failure from 0.181 to 0.083 in a factorial ablation.
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All authors Miaobo Hu, Shuhao Hu, Xiaobo Guo, Xin Wang, Bokun Wang, Daren Zha