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At least 1,189 records · Page 66Linked to original sources
arXiv2026

Multi-Teacher On-Policy Distillation for Flow-Based Vision-Language-Action Models

Specialized vision-language-action (VLA) policies acquire strong domain-specific skills, yet consolidating these skills into one shared policy remains challenging. On-policy distillation (OPD) transfers teacher knowledge on inputs induced by the student, addressing the distribution mismatch encountered during deployment. For flow-based VLAs, this mismatch arises at two levels: environment observations and intermediate action-generation states. We propose a two-level on-policy distillation framework that couples student-driven environment interaction with teacher velocity supervision along student-generated action flow trajectories. Frozen domain specialists jointly supervise one student. After each update, the student collects new environment experience and generates fresh action-flow trajectories. Starting from a joint supervised fine-tuning (SFT) initialization, Velocity Loss OPD yields absolute success-rate gains of 22.55% on LIBERO-40, 33.4% on CALVIN five-instruction sequences, and 22.6% on Meta-World MT50. Compared with Action Loss OPD and Teacher-rollout SFT, it achieves absolute success-rate gains of 6.4-9.5% on LIBERO-40, 9.7-18.3% on CALVIN, and 3.2-4.2% on Meta-World MT50. Analysis by sequence length further shows larger success-rate gains on longer CALVIN sequences. These results demonstrate effective multi-domain capability consolidation through two-level on-policy supervision, with a single student deployed across domains.

cs.RO↗
arXiv2026

Non-equilibrium Muon Dynamics Imitating Fractional Spin Excitations in a Quantum Spin Chain

Fractional spin excitations in low-dimensional and frustrated magnets are commonly associated with sporadic spin fluctuations, as observed in quantum spin liquids, spin ices, and other complex magnetic states. In this study, we investigate the spin dynamics in the amplitude-modulated magnetic ground state of AgCuVO$_4$, a spin-1/2 chain compound with competing intrachain interactions, by muon spectroscopy. Our data reveal a Gaussian decay of muon polarization that remains remarkably resilient against applied magnetic fields---a behavior often interpreted as evidence of emergent sporadic spin dynamics. However, density functional theory calculations of muon stopping sites and their quadrupolar level-crossing resonance spectra suggest an alternative mechanism: a two-state model where the muon randomly hops between two nearby sites, eventually equilibrating across both on a microsecond timescale via quantum delocalization. These findings provide a microscopic explanation for the field-resilient muon polarization and indicate that such behavior may not always stem from intrinsic spin fluctuations, but can also arise from non-equilibrium muon dynamics.

cond-mat.str-el↗
arXiv2026

Direct measures of black hole masses through cosmic time

Supermassive black holes (BHs) are thought to reside in all massive galaxies. They play a fundamental role in shaping galaxy evolution by suppressing star formation and halting the stellar growth of the most massive galaxies via feedback mechanisms. However, to date, measuring even their most basic property, their mass, is still challenging. The mass of BHs carries information on the growth history and the mutual interplay with the host galaxy. Uncertain BH masses leave many key questions on galaxy evolution wide open. Here we show that a transformational facility such as ALMA2040 would open a new window to measure BH mass by directly observing the kinematics of cold gas in galaxy cores from the local Universe up to very high redshift, irrespective of BH activity. This would revolutionise our understanding of BH formation, growth, and their role within galaxy evolution.

astro-ph.IM↗
arXiv2026

CriticaLLM: Using LLMs as Autonomous Game Master for Tabletop Role-Playing Games

Large Language Models (LLMs) have shown impressive capabilities across many tasks, including processing large amounts of text, following instructions, and generating ideas. This allows the use of such models in various contexts, including games and Tabletop Role-Playing Games (TTRPGs), such as Dungeons & Dragons. However, these games include many complex components, from crafting interesting stories to adhering to rules, while allowing some freedom in players' actions. In this work, we first highlight key components that LLMs should exhibit in the context of TTRPGs. Then, we introduce our framework, CriticaLLM, a fully automated Game Master that can run entire TTRPG games, from creating diverse and interesting stories to managing exploration and combat phases. We evaluate our framework with actual TTRPG players and examine the diversity of generated plots and antagonists across four LLMs of varying sizes. Overall, our framework appears to be a promising option for running entire TTRPG games.

cs.AI↗
arXiv2026

On the Robustness of Gossip Protocols in Modern Blockchains

Modern platforms such as Ethereum and Polkadot nowadays execute Byzantine fault-tolerant consensus protocols over large validator committees, often comprising hundreds of nodes. At this scale, complete graph topologies for connecting nodes are impractical, leading systems to adopt various gossip mechanisms, often in an ad hoc manner. In this paper, we study the robustness of widely deployed gossip protocols used in committee-based blockchains against realistic network adversaries. We show, both analytically and through extensive empirical measurements, that the graph parameters commonly chosen to instantiate random graphs are insufficient to guarantee that enough honest nodes receive consensus messages for quorum formation in existing protocols. Motivated by this finding, we empirically assess the robustness of Bitcoin's Erdős-Rényi (ER) graphs, Polkadot's grid topology, Ethereum's GossipSub, and Solana's chunk- and tree-based disseminations. Our results reveal surprising tradeoffs: Solana's dynamic trees are bandwidth-efficient in benign settings but fragile under adaptive attacks; Polkadot's grid achieves strong robustness at the cost of high bandwidth overhead; GossipSub is both bandwidth-efficient and resilient to adaptive adversaries, yet highly sensitive to parameter choices; and ER graphs provide a strong robustness-efficiency tradeoff, e.g., when the (average) fanout degree exceeds 15 for networks up to 5000 nodes.

cs.CR↗
arXiv2026

Activation-Adjacent Layer Normalization: Effects on Approximation Power

Layer normalization (LN) and root mean square normalization (RMSNorm) depend on their inputs and remain nonlinear at inference. Inserting either next to an activation may therefore change the function a network represents. We study when shallow activation-normalized (AN) and preactivation-normalized (PN) networks can approximate a prescribed width-$N$ one-hidden-layer MLP. Viewing RMSNorm as input-dependent scaling, we use width augmentation to locally linearize normalization on compact feature sets. For AN networks, an unbounded activation range allows width $N+1$, while every continuous nonconstant activation admits width $N+r$ with error $O_f(r^{-1})$. For PN networks, affine parameters or, without them, degree-one positive homogeneity recover width $N+1$; general continuous activations admit width $N+r$ with error tending to zero. The corresponding LN constructions use centered coordinate pairs, yielding widths $N+2$ and $N+2r$, respectively. We prove that $N+1$ for RMSNorm and $N+2$ for LN are also the worst-case bound for approximations, and show that applicable universal-approximation theorems for ordinary MLPs transfer to these normalized architectures. Numerical experiments recover the predicted approximation rates for both normalizations across all five settings and illustrate the shifted-ReLU finite-width obstruction.

cs.LG↗
arXiv2026

Quantum Cosmology in Page-Wootters' Framework: Singularity Resolution and Clock Coherence

We investigate the fate of big-bang singularity and coherence between distinct clock states in a quantum cosmological setting within the Page-Wootters framework. With a canonically quantized plane-symmetric Bianchi I universe, we employ Dirac factorization of the Wheeler-DeWitt constraint and obtain a Schrodinger-like equation which is first-order in an internal clock variable. By constructing its solution as a Gaussian wave packet in the expanding branch, we derive the corresponding conditional state and probability density of the universe. We find that the conditional probability density vanishes in the zero-volume limit, indicating resolution of the big-bang singularity within this probabilistic framework. Another prespective of the study is provided by the construction of density matrix from the conditional states associated with different clock readings and the remaining degree of freedom. By tracing out the remaining subsystem, we obtain the reduced density matrix and analyze the resulting coherence as a function of separation between different clock states. These results provide a relational characterization of singularity resolution and demonstrate how the spectral properties of the quantum state govern the temporal coherence between different clock states in the Page-Wootters description.

gr-qc↗
arXiv2026

Frey-Mazur theorem for semistable elliptic curves over function fields

Let $k$ be a field, let $B/k$ be a smooth projective geometrically integral curve, and put $K=k(B)$. We prove a Frey--Mazur type theorem for nonisotrivial semistable elliptic curves over $K$. More precisely, after fixing the genus of $B$ and the characteristic of $k$, a sufficiently large prime-to-characteristic torsion representation determines the $K$-isogeny class.

math.NT↗
arXiv2026

The Bardos-Tartar Conjecture for the Navier-Stokes Equations

We consider the incompressible viscous Navier-Stokes equations in dimension $d=2,3$ with periodic boundary conditions and time-independent external forcing. When $d=2$, the Bardos-Tartar conjecture asks whether the set of solutions at any given positive time is dense in the Hilbert subspace of $L^2$ consisting of mean-zero divergence-free vector fields, with respect to the strong $L^2$ norm. We prove the Bardos-Tartar conjecture and, more generally, its analogue for the hyperviscous Navier-Stokes equations studied by Guo-Titi. In addition, for $d=2,3$ we show that any given initial condition is either backwards-extendable (i) for all values of viscosity $ν>0$, or (ii) only for viscosities that belong to a Lebesgue-null subset of $\mathbb{R}_+$. When (i) holds, we show the initial condition and forcing must be real-analytic (in fact, both belong to $D(e^{σA})$ for some $σ>0$, where $A$ is the Stokes operator). Furthermore, we show that (i) is extremely unstable under perturbations. In particular, given any initial condition we show that two Fourier modes can be perturbed so that (ii) holds.

math.AP↗
arXiv2026

Incremental Exact Vertex Connectivity

We study the problem of maintaining the vertex connectivity $κ$ of a graph under edge insertions. For undirected graphs, our algorithm uses $O(κ^4 \log^2 n)$ amortized time per edge insertion. After each edge insertion, the algorithm outputs the current value of $κ$, plus a set of $κ$ vertices whose removal disconnects the graph. Our algorithm is Monte-Carlo randomized and works with a randomness-adaptive adversary. The algorithm also works on directed graphs against an oblivious adversary, which is equivalent to an output-adaptive adversary if we only have to output the current value of $κ$. Previously, algorithms for maintaining the vertex connectivity with $o(n)$ time per edge insertion were only known for $κ\le 2$, and need $\tilde{O}(\log^2 n)$ and $O(\sqrt{n})$ time per edge insertion for $κ= 1,2$, respectively. Moreover, for $κ> 4$, no algorithm faster than recomputation from scratch was known. We complement our algorithm with a conditional lower bound: Under the OMv conjecture, any insertions-only algorithm that outputs the current value of $κ$ after every insertion needs $Ω(n^{1-\varepsilon})$ amortized time per edge insertion for $κ= Θ(n)$. Previous conditional lower bounds for this problem only apply to worst case running time, or algorithms that support both edge insertions and edge deletions.

cs.DS↗
arXiv2026

A ${}^{13}$CO Detection in a Massive Molecular Gas Flow in Abell 1795's Central Galaxy

We present new ALMA ${}^{13}$CO(2-1) observations of the central galaxy in the cool-core cluster Abell 1795, targeting the origin of extended molecular filaments. The filaments extend for 5--7 kpc and are closely drawn up around large radio bubbles inflated by jets from the central active galactic nucleus (AGN). Smooth velocity gradients along their lengths are consistent with entrained flows lifted by the expanding bubbles. Here we detect the northern molecular filament in the low-opacity molecular tracer ${}^{13}$CO(2-1), which can provide a more reliable measure of the molecular gas mass and conditions than ${}^{12}$CO. The velocity structure in ${}^{13}$CO(2-1) is consistent with that of the ${}^{12}$CO(2-1) emission. Using a range of plausible excitation temperatures and covering fractions, we thereby determine a filament molecular gas mass of (0.1--2) $\times \ 10^9 \ \text{M}_\odot$, or down to an order of magnitude below previous estimates. This implies a CO-to-H$_2$ conversion factor of $α_\text{CO} =$ 0.4--5 $\ \text{M}_\odot $ (K km s$^{-1}$ pc$^2)^{-1}$ in the filament, or $\sim$ 0.1--1 times the standard assumption of the Milky Way value. Direct entrainment by the N radio bubble is now plausible, as it can provide sufficient mechanical energy and buoyant support for the molecular gas flow. Similarly, measured X-ray cooling rates are also now consistent with in-situ condensation of uplifted, low-entropy hot gas. Both formation mechanisms require multiple generations of bubbles at higher filament masses.

astro-ph.GA↗
arXiv2026

On the Solution Sets of the Cone-Volume Map

For a fixed set $U=(u_1,\ldots,u_m)$ of outer unit normals, we consider the cone-volume map which associates to a vector of support numbers $b\in\mathbb R^m_{> 0}$ the cone-volume vector $γ\in\mathbb R^m$ of the polytope \[ P(U,b)=\{x\in\mathbb{R}^n:U^\top x\leq b\}. \] We study its fibers $S(U,γ)$ over prescribed cone-volume vectors $γ$, with particular emphasis on finiteness and non-uniqueness. We give characterizations of the irreducibility of $U$ in terms of properties of the cone-volume map and its solution sets. In particular, for irreducible $U$, we show that $S(U,γ)$ is finite for all $γ$ outside a set of measure zero in the cone-volume cone, and we give an explicit upper bound for its cardinality. In the planar case, we prove that $S(U,γ)$ has semialgebraic dimension at most one for arbitrary $U$. Moreover, for every $U\in\mathcal{U}(2,m)$ with $m\geq 4$, there exists a cone-volume vector $γ$ for which $S(U,γ)$ contains at least two distinct elements. As a consequence, there exist two distinct smooth planar convex bodies with the same cone-volume measure. Finally, for $U$ in general position, we show that the number of solutions is odd for every cone-volume vector outside the exceptional set.

math.MG↗
arXiv2026

Attribution-Gated Joint Estimation of Intention and Capability for Assist-as-Needed Upper-Limb Robots

Assist-as-needed (AAN) control must distinguish between changes in intended motion and changes in effective voluntary torque capability, even though both can produce similar kinematic and interaction responses. A dual-measurand multimodal MHE-MPC architecture is developed as the base framework, in which the intended trajectory and the task-dependent effective voluntary torque capability are estimated online as distinct quantities, and both estimates are used to adapt robotic assistance. Building on this architecture, the ambiguity between the two update channels is formulated as a continuous credit-assignment problem and resolved by an attribution gate. A trajectory-change indicator is obtained from persistent corrective interaction, whereas a capability-change indicator is derived from the residual between normalized muscle activation and dynamics-reconstructed voluntary torque. Nine healthy participants completed factorial target-height-load trials and a pre-post fatigue cup-transport task. Without target-height input, the gated method generated correctly ordered Low-Middle-High references under every load: target changes were preferentially assigned to trajectory adaptation, whereas added load shifted adaptation toward the capability channel. It achieved the lowest RMSE in all nine conditions (0.017 rad versus 0.041 rad for ungated dual estimation and 0.127 rad for fixed-reference error-based AAN). Post-fatigue capability estimates decreased and assistance increased at all heights, supporting functional feasibility.

cs.RO↗
arXiv2026

Rectangular Symmetry for Catalan Functions

Katabolizable tableaux provide a combinatorial formula for the Schur coefficients of Catalan functions. We prove that a tableau involution preserves katabolizability under antidiagonal reflection of any upper root ideal. This involution complements shape and content in a fixed rectangle and preserves charge. We obtain a bijective proof of the rectangular symmetry of these coefficients.

math.CO↗
arXiv2026

It Takes Two Moments: Rigidity and Limits of Continuous Encoders for Over-the-Air Computation

We study over-the-air computation of functions, such as empirical variance, formed by combining two separately postprocessed sums of locally transformed observations. We consider continuous encoders subject to pointwise peak-power constraints over a single use of a complex multiple-access channel. With four or more transmitters, we identify conditions under which exact noiseless recovery forces every continuous encoder collection into a common affine structure that preserves both sums, reducing infinite-dimensional encoder design to selecting a finite set of coefficients. To quantify resilience against channel noise, we introduce a robustness score that measures the separation of noiseless received aggregates relative to variations in the desired function value. Within this characterized encoder family, we formulate robustness maximization as an exact convex semi-infinite program, eliminating rank constraints without a relaxation gap, and construct a decoder that attains the minimum uniform noise-amplification constant. For several function classes, including empirical variance, we derive closed-form robustness-optimal encoders and scores. Under mild regularity conditions, we also establish sharp limits on the Gaussian mean squared error at high signal-to-noise ratios and show how using the input distribution reduces average error at the expense of uniform robustness.

cs.IT↗
arXiv2026

Functional Subnetwork Localization for Efficient Continual Learning in Large Language Models

Biological intelligence continually adapts to new information while retaining prior skills through localized plasticity. In contrast, continual learning in large language models (LLMs) remains vulnerable to catastrophic forgetting. A promising direction is to identify functionally specialized subnetworks within LLMs that enable targeted and resource-efficient adaptation. Using gradient-attribution profiling, we localize cognition-associated functional subnetworks exhibiting extremely low mutual overlap. Building on this finding, we propose Function-isolated Memory-Efficient Optimization (CiMEO), a continual learning framework that routes each training example to its corresponding functional subnetwork, restricting parameter updates and optimizer states to selected regions. Across 1.4 million sequential instructions, CiMEO achieves the highest average performance among the compared methods on five generative benchmarks spanning programming, examination-style tasks, and mathematical reasoning, while mitigating catastrophic forgetting. Subspace-overlap and principal-angle analyses further indicate that localized updates help preserve pre-trained representations, highlighting functional subnetwork localization as a practical approach to efficient and stable continual learning in LLMs.

cs.AI↗
arXiv2026

Agent Status Protocol (ASP): A Lightweight Specification for State Reporting in Multi-Agent Systems

The Agent Status Protocol (ASP) defines a lightweight way for heterogeneous AI agents to report their operational state to a status server, and for observers such as dashboards to receive that state as soon as it changes. Agents push small JSON events over HTTP POST; the server exposes the aggregated state to observers over Server-Sent Events (SSE). Because an agent that has crashed, hung or been compromised cannot be trusted to report its own failure, ASP does not rely on self-reports alone: the server infers liveness from missed heartbeats, can detect agents that are alive but no longer making progress, and accepts observations from supervisors, guardrails, operators and peers, some of which take precedence over what the agent says about itself while others are shown alongside it. ASP models state along independent dimensions (lifecycle, health, task, floor, governance), so that an agent can be, for example, online, degraded, working on a task and waiting for the floor at the same time. It reuses existing vocabularies: task states from the Agent2Agent (A2A) protocol, floor states from the Open Floor Protocol (OFP), and attribute conventions from the OpenTelemetry GenAI semantic conventions. This paper presents version 0.1 of ASP as a proposal, not as an approved standard. It is a working draft intended to open a discussion, and the authors invite comments, alternative proposals and independent implementations from the community.

cs.AI↗
arXiv2026

Reinforcement Learning-driven Diffusion Models: Language, Vision, and Beyond

Diffusion models (DMs) have steadily demonstrated outstanding performance in high-fidelity, controllable generation across diverse scenarios, following the "pretraining-finetuning" paradigm established in LLMs. Despite these advances, conventional DMs still face critical limitations in sophisticated reasoning, autonomous exploration of generation pathways, and adaptability to complex, human-aligned objectives. Inspired by RLHF's success in LLMs, RL has recently emerged as a pivotal post-training mechanism to iteratively refine DMs through reward-driven trajectory optimization. This paper presents the first comprehensive review of RL-driven DMs and an empirical analysis of how RL reshapes the diffusion process towards experience-centric, goal-directed generation. We propose a novel technical panorama elucidating RL's multifaceted roles in diffusion-based language, multimodal, robotic, and scientific models, with a granular focus on diffusion trajectory optimization and reward engineering. Through extensive experiments on multiple task-specific benchmarks, we systematically evaluate representative methods to intuitively highlight the advantages of different RL post-training strategies. Furthermore, we reveal and dissect three crucial bottlenecks that currently hinder the real-world deployment of RL-driven DMs: reward design fragility, exploration-exploitation trade-off in high-dimensional generation spaces, and training instability under sparse rewards. Based on these perspectives, we provide a principled roadmap for the integration of RL into DMs and outline promising future research directions for robust, interpretable RL-diffusion systems. We also construct a public repository to continuously track the latest developments in this rapidly evolving field: https://github.com/MAIR-Lab-HUST/Awesome-RL-for-Diffusion-Models.

cs.AI↗