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arXiv cs.DC

Beyond Proof of Possession: A Relational Theory of Authority

arXiv:2611.07159v1 Announce Type: cross Abstract: Proof-of-Possession (PoP) establishes that an executor controls an artifact (key, token, credential, or capability), but such control alone determines neither the executor's relational profile nor the causal history of an execution occurrence. We separate PoP from Proof of Relationship (PoR), the semantic property that one execution occurrence validly continues another, and from authorization, which is occurrence-sensitive. The foundational change is in the semantic domain of authorization: from holders and authority-bearing artifacts to execution occurrences situated in causal histories. We give authorization models an observation-based occurrence verdict and a separate transition-admissibility relation; kernel inclusion yields a partial order on observation-kernel classes. Building on Provenance Identity Continuity (PIC) and Proof-of-Continuity (PoC), we classify executors by authorization-relevant equivalence relations whose quotients form relational profile spaces, with positive predicates over profile transitions forming a distributive lattice. This adds relational attenuation to authority attenuation: along a valid causal history, $C_{i+1}\subseteq C_i$ and $\rho_{i+1}\Rightarrow\rho_i$. We prove dual monotonicity, combined closure, and origin relational closure. Two occurrences of the same authenticated executor, with the same profile and possession evidence, need not be authorization-equivalent, and within a valid PIC lineage a deputy's independent authority cannot be imported outside the origin context. Finally, we prove that the executor-dependent decision factors through the relational profile and is invariant under sound mechanisms establishing it: successor-side PoP is a possible evidence mechanism, not a necessary premise of authorization. Under explicit Witness Assumptions, a boundary-witnessed checkpoint construction realizes the premises without successor-side PoP.

arXiv cs.LG

Finite-Time Convergence and Regret Guarantees for Neural Reinforcement Learning in POMDPs

arXiv:2611.07069v1 Announce Type: new Abstract: Reinforcement learning (RL) in Partially Observable Markov Decision Processes (POMDPs) is computationally challenging due to the curse of long-range dependence on history. Fortunately, recent studies have shown that a range of POMDPs that satisfy the filter stability assumption can be well approximated by a superstate Markov Decision Process (MDP) based on a truncated history in a finite-memory window, with a value gap that decays with the window length. However, existing finite-time convergence analyses on such superstate MDP surrogates are either limited to over-simplified linear function approximation or rely on an i.i.d. sampling oracle that is violated by POMDP trajectories, both of which severely limit the applicability of these theoretical results in practice. This motivates us to bridge the gap by investigating RL in POMDPs with nonlinear neural value function approximation. Our main contributions are threefold: i) We first establish a new finite-state MDP point-wise approximation error bound, which lays the foundation for our RL algorithm design and analysis in POMDPs; ii) By applying Temporal-Difference (TD) learning to POMDP-generated superstate transitions and targeting the Bellman fixed point of the superstate MDP, we prove a finite-time critic error bound with nonlinear neural value function approximation; and iii) By combining the neural critic function approximation error bound with the policy mirror descent framework, we obtain a finite-time sublinear regret against the optimal POMDP value. To the best of our knowledge, such a finite-time sublinear regret based on neural function approximation is the first in the literature for finite-memory POMDPs. Our numerical experiments also verify our theoretical results.

arXiv cs.AI

Formalizing inverse problems in the age of AI: possibilities, pitfalls, and an invitation

arXiv:2611.06962v1 Announce Type: new Abstract: Proof assistants such as Lean check mathematical proofs down to the axioms, and AI agents have recently made writing such proofs cheap. We describe AutoIP, a Lean library in which classical linear regularization theory, together with the functional analysis it rests on, has been autoformalized by AI agents. A machine-checked proof certifies only the formal statement it proves, so the remaining human task is to confirm that each formal statement says what was intended. We organize the library around this task: a reviewer compares the formal statements with their natural-language counterparts and never needs to read a proof. Our experience is that the risks lie in the statements rather than in the proofs, and that simple automated tests on the statements can expose problems even in the established literature. We illustrate this with a textbook theorem whose hypothesis is more restrictive than asserted. We invite the inverse problems community to extend and build on the library.

arXiv cs.DC

Full Provenance on the COSS Causal Axis: An Event-Level Closure of Causal Attribution and Confused-Deputy Exclusion

arXiv:2611.07164v1 Announce Type: cross Abstract: Provenance Identity Continuity (PIC) represents an authority-use event as an operation/resource behavior situated in a causal lineage, $(o,r,\ell)\in O\times R\times L$. We make the causal occurrence itself primitive: a represented security-relevant causal graph $(E,\to_c)$ in which each occurrence has a unique causal history, so the consistent event-lineage space is canonically isomorphic to $E$. The modeled execution has one causal partial order; distinct lineages are distinct causal histories inside it and may share a root while diverging into incomparable branches. PIC's $O\times R\times L$ is the authority-behavior projection of this space, and Causally Ordered Security-State (COSS) continuity generalizes it to an arbitrary behavior product over the same causal execution. On this semantics we prove an architecture-independent confused-deputy exclusion theorem. PIC continuation requires $C(e')\subseteq C(e)$ on every ordinary causal edge, so descendants are bounded by their ancestors; at an ordinary join, authority available on only one incoming branch cannot be resurrected, even when branches share a common root. Non-conservative combination must be an explicit authorized composition or relaxation event. With protected-effect mediation, an effect caused by request $q$ through an ordinary authority segment can exercise only authority in $C(q)$, so a confused-deputy state is contradictory. The result holds for any system whose protected request-to-effect causes are faithfully represented and whose ordinary authority transport satisfies PIC. We revisit Rajani, Garg, and Rezk: their value, control-flow, and initial-heap attacks are different witnesses of causal ancestry, so full provenance is an evidence mechanism for recovering edges of the causal graph, not the foundation of the PIC theorem. Finally we lift it to the COSS product of heterogeneous security-state coordinates.

arXiv cs.DC

Ab Initio Accuracy Beyond the Cutoff: Distributed Message-Passing Equivariant Attention at Tens-of-Millions-of-Atom Scale

arXiv:2611.06122v1 Announce Type: new Abstract: Molecular dynamics predicts molecular motion from atomic forces and trajectory integration. Density functional theory (DFT) provides first-principles forces, but its $O(N^3)$ cost limits simulations to thousands of atoms; empirical force fields scale to millions but miss bond breaking and charge transfer. Equivariant message-passing Transformers learn the ab initio potential at linear cost. Stacked layers propagate information beyond a single cutoff, giving four layers a receptive field up to 23{\AA}. At this frontier, scale is limited by communication: layers exchange boundary features across devices, force backpropagation repeats the exchange, and moving atoms change neighbor graphs and tensor shapes. We present Tessera, a distributed runtime that fixes workload shapes between rebuilds. It sorts atoms along a space-filling curve into equal-count shards, ensuring identical atom counts and tensor shapes per rank. Peer sets scale as $K^{0.5}$, not $K$. A conservative neighbor skin preserves topology across updates, enabling each rebuild interval to replay as one CUDA Graph. Fused kernels, three-level neighbor search, and overlapped All-to-All complete it. On 512 GPUs, Tessera sustains 30.7M atoms at 89.7% weak-scaling efficiency (77--90% across three per-GPU loads); per-step time rises 1.11--1.29x as machine and problem grow 16x. Graph reuse cuts full-step time $1.87\times$. Across an $8\times$ device increase, neighbor-search cost grows $1.7\times$, versus $3.0\times$ for Morton order. In a live $10.24$M-atom salt solution, NVE energy drift is $0.42\,\mu$eV/atom/ps over $10$ ps, and structure matches a serial reference. A 10.06M-atom Norovirus capsid sustains 100 ps of NVT at $\approx 8$ ps/day on 256 A100 GPUs. Over 200,000 steps, it has no broken bonds or anomalously close pairs and uses three compiled variants, with no graph breaks or eager fallbacks.

arXiv cs.AI

AGORA: Reliability-Aware Aggregation of LLM Judges via Item-Response Theory

arXiv:2611.05556v1 Announce Type: new Abstract: LLM-as-a-judge is a common substitute for costly human evaluation, and aggregating several judges is the standard remedy for any single judge's bias. Judge pools mix judges of very different reliability, while the human-labeled sets that validate them hold a few hundred items or fewer. In this regime the per-item mean weights weak judges as heavily as strong ones, and confusion-table models such as Dawid-Skene must estimate a per-judge error table from too few items. We propose AGORA (Aggregation Of Reliability-weighted Assessments), an item-response-theory aggregator that places every item on one latent quality scale and describes each judge by a sensitivity parameter and ordered rating thresholds, so judge reliability is learned from all items jointly and without human labels. Across three benchmarks, AGORA matches or exceeds Dawid-Skene on large evaluation sets, and its advantage widens as the set shrinks toward a few hundred items. It remains accurate as pools grow more uneven, a label-free dispersion statistic indicates in advance when trust weighting helps, and its learned trust weights track per-judge human validity.

arXiv cs.CL

Prospective Memory for Proactive LLM Agents

arXiv:2611.05731v1 Announce Type: new Abstract: Most memory systems for LLM agents are retrospective, preserving and retrieving past information to inform current decisions. Proactive agents, however, also require prospective memory: retaining future-directed intentions and realizing them when appropriate opportunities arise, even without explicit requests. Crucially, remembering the right intention does not guarantee acting at the right time: a related observation may call for waiting, while a later cue may make the same intention actionable. Inspired by cognitive theories of human prospective memory, we introduce Pro-Memory, a memory framework that separates maintaining future intentions from deciding when and how to realize them. Pro-Memory preserves pending objectives linked to their supporting evidence, assesses new observations against their original goals and activation conditions, and coordinates appropriate contributions with the agent's ongoing actions. It further updates intention states based on actions actually issued or evidence of resolution, while an experience memory distills feedback from completed episodes into guidance for future decisions. Experiments on two benchmarks spanning delayed-intention tasks and open-ended proactive assistance demonstrate consistent improvements in proactive task performance over representative memory approaches across multiple LLM backbones, while limiting unnecessary interventions.

arXiv cs.LG

Structured Priors: Towards an algebra of component priors for prior-data fitted networks

arXiv:2611.04056v1 Announce Type: new Abstract: Prior-data fitted networks are typically trained using synthetic data generated by a single, manually constructed generator. In cases where such a generator combines multiple components, e.g., in TabPFN, Mitra, or TabICLv2, this is achieved through a mixture using manually specified weights, the impact of which on the network only becomes apparent after pre-training. Instead of such a hand-built generator, this work proposes a structured prior: a small set of named component priors, linked by operators whose algebraic properties are formally proven and whose influence on the trained network has been validated. Within a measure-theoretic framework, the operators of mixture, convolution, amplitude scaling, local transform, and projection are defined. Their governing laws are proven. These operators are implemented in the macl2l software package. Experiments demonstrate that the implemented generators reproduce the identities within the resolution of a permutation test. Furthermore, it is shown that trained networks obey the distributive law; that a mixed prior composed of small components performs as well as or better than any individual component in seven out of eight open regression benchmarks; and that on two of these tables a structured prior reaches, with a ninth of the data budget, an error that a generic random-function prior does not reach even with the full budget. A theorem on model averaging demonstrates that networks trained on individual components constitute the Bayes predictor for the mixture, provided that the component networks are themselves the Bayes predictors for their respective priors. However, the pre-registered test of this averaged predictor with trained component networks failed, because the networks identify the generating component too rarely. The paper proposes a research program focused on the algebra of structured priors for prior-data fitted networks.

arXiv cs.CV

Convex Potential Learning for Optimal Transport Between Medical Images

arXiv:2610.37844v1 Announce Type: new Abstract: Computing optimal transport maps between medical images plays a fundamental role in morphological analysis. However, existing methods are either difficult to scale to large 3D medical images or rely on regularized formulations that provide only approximate transport maps. To improve the accuracy of downstream medical image analysis, we propose a novel approach for estimating optimal transport maps by parameterizing the convex potential function. By construction, the resulting transport map is guaranteed to be curl-free, consistent with Brenier's theorem. We evaluate the proposed method on both 2D and 3D medical imaging datasets. Experimental results demonstrate that our approach achieves lower transport estimation errors and produces higher-q

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arXiv cs.LG

A Mathematical Theory of the Jacobian Lens

arXiv:2610.31955v1 Announce Type: new Abstract: Recent work from Anthropic introduced a new interpretability tool, called the Jacobian lens (J-lens, Gurnee et al., 2026). This method identified linear directions in the hidden states of frontier language models that had properties reminiscent of working memory-like representations. However, it is unclear what mechanistic properties of such features make them detectable to the J-lens. To this end, we introduce a mathematical theory of the J-lens, and show that it preferentially identifies coherent features -- directions that act like leading, spatially coherent Lyapunov modes. Small perturbations along these directions amplify across layers, remain roughly constant across token positions, and are consistent across different contexts. While w

新闻源配图 · arXiv cs.LG
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arXiv cs.LG

PRISM: Promoting Sampling Diversity of Large Language Models with Implicit Stochastic Modulation

arXiv:2610.32101v1 Announce Type: new Abstract: Large language models (LLMs) exhibit mode collapse, where their output distribution concentrates on familiar semantic modes. When diversity disappears, repeated sampling becomes semantic repetition rather than discovery, making rare but stronger solutions unlikely to surface and leaving self-evolution and continual learning difficult to sustain. Most remedies intervene only at inference time, shaping sam- ples without making diversity a model capability. We propose PRISM, a training-time framework that internalizes diversity within the model. PRISM combines (i) submodular curation that pairs each prompt with diverse-yet-correct multi-teacher solutions, and (ii) stochastic embedding modulation, which turns special-token perturbations into impl

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arXiv cs.LG

Putting Transformer Theories to the Test

arXiv:2610.32104v1 Announce Type: new Abstract: Several formal theories have been developed to characterize the capabilities and limitations of the transformer architecture, each employing different abstractions that capture different features of the architecture. Due to the differences in their underlying assumptions and conceptual frameworks, these theories can disagree in their predictions about what tasks transformers find easy or hard. We map out seven theories of transformer capability (Star-free, $\mathsf{AC}^0$, $\mathsf{TC}^0$, C-RASP, MPC, BAPO, and Sensitivity) and translate their results into a common matrix of predictions across a suite of tasks covering different computational structures. We provide new theoretical results to complete this matrix. We then evaluate theoretical

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arXiv cs.LG

Collaborative In-Context Learning for Indoor Radio Map Estimation

arXiv:2610.31702v1 Announce Type: new Abstract: Indoor radio map estimation (RME) is essential for wireless applications such as coverage planning, localization, and network deployment. However, most existing methods follow a supervised learning paradigm that requires costly labeled data and task-specific model training. Moreover, indoor environments involve privacy-sensitive information, such as building layouts and structures, that often cannot be centralized. To address these challenges, we make the first attempt to formulate indoor RME as a collaborative in-context learning (ICL) problem. We propose Poly-Ripple, a framework in which multiple clients perform ICL using large autoregressive vision models (LAVMs) without model updates. Each client is prompted by its private demonstrations

Collaborative In-Context Learning for Indoor Radio Map Estimation
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arXiv cs.LG

When and How Does Muon Precondition? The Role of Structured Gradient Noise

arXiv:2610.31728v1 Announce Type: new Abstract: Muon has become a popular optimizer for large language model training, yet its theoretical foundations remain poorly understood. In this work, we study how gradient noise geometry shapes Muon's preconditioning benefits. We first show, theoretically and empirically, that under the classical isotropic noise assumption, Muon offers no acceleration beyond a rescaling of the learning rate. This motivates us to investigate structured noise arising from mini-batch sampling in associative memory with heterogeneous task frequencies. We establish an exact balancing threshold for two tasks and extend the analysis to multiple tasks, revealing how task coverage and gradient reliability jointly shape learning. Our analysis shows that Muon can soften the de

When and How Does Muon Precondition? The Role of Structured Gradient Noise
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