Papers

An LLM agent is defined by two things: the weights inside its model and the harness of components assembled around it. Harnesses are still handcrafted, and HarnessX, which evolves them automatically, starts each benchmark from a handcrafted harness, reports gains on the tasks it evolved on, and budgets 100 to 175 million meta-agent tokens per benchmark. We propose LiteEvo, a lightweight harness-evolution algorithm whose tool-free meta-agents mine agent trajectories for reusable components, curate them into a versioned library, and compose each round's harness from it, starting every benchmark from the same neutral harness and never naming the benchmark. Evolving on the graded tasks of five agentic benchmarks with a frozen Qwen3.5-9B, LiteEvo lifts pass@2 by 10.5 to 67.7pp and reaches comparable or higher pass@2 than a reproduction of HarnessX (71.0 against 67.3 on average) at 13.0 lower mean API cost. Harnesses evolved on train tasks keep their gains on unseen test tasks of four benchmarks, and LiteEvo also lifts Claude Code with Sonnet 4.6 by 1.2 to 71.4pp.

Constructing action targets from measured robot motion is an established approach in imitation learning. Under interaction constraints, however, command-state discrepancy may reflect control demands that motion alone does not capture. We investigate when this information matters and how to exploit it. Across three real-robot tasks, task and phase analyses reveal larger supervision gaps under constrained interaction, while selective command retention provides evidence of locally useful command information. Building on these findings, we propose Command-State Discrepancy Weighting (CSDW), which accounts for robot response times and combines subsequent progress, persistent unmet demand, and demand changes into continuous weights for command supervision. The method requires no task-phase annotations or changes to policy architecture or inference. CSDW improves over uniform command supervision on constrained tasks, while methods perform similarly in the less constrained task. Project page: https://seen-e.github.io/CSDW/.

Looped Transformers can generalize to reasoning chains longer than those encountered during training, but the computations enabling this behavior and limiting its extent remain unclear. We mechanistically compare two looped-Transformer configurations, which we call the Matched-Recurrence Looped Transformer (MR-Loop) and Decoupled-Recurrence Looped Transformer (DR-Loop), reflecting their respective recurrence-training schemes. We evaluate polynomial iteration, finite-state composition, and knowledge-graph traversal using detailed mechanistic analysis. Attention analysis, intermediate-state decoding, and causal interventions reveal distinct mechanisms learned under final-answer supervision. MR-Loop updates an intermediate state at a fixed readout while advancing relation selection through adjacent-token interactions and a transferable progress cue. DR-Loop instead propagates intermediate states across relation positions, forming an advancing computational frontier. However, both mechanisms become unreliable at greater depths: MR-Loop exhibits degradation of its readout state and progress cues, while DR-Loop exhibits declining reliability of state propagation. Limited self-correction allows local errors to persist and compound. Across both models, we uncover a common representational principle: recurrent states encode not only task-relevant content but also its computational status, whether that content remains in a form that can support subsequent computation. Transferable live-consumed and fresh-aged residual directions causally control whether represented information can participate in subsequent computation, including beyond the training horizon. We further show that length generalization need not rely on faithful step-by-step reasoning, as Looped Transformers can exploit task structure without explicitly representing every intermediate state.

Quarter-ahead revenue forecasting requires company-scale numerical accuracy, strict temporal validity, and company-specific interpretation of narrative disclosures. LLMs can distill textual evidence but can produce scale-misaligned forecasts, whereas history-based anchors are stable but miss forecast-time signals such as product transitions, supply constraints, and management guidance. We introduce CAME (Company-Aware Evidence-Memory Experts), a residual-forecasting framework that refines a no-leakage statistical anchor when current semantic evidence and prior error patterns justify an adjustment. On a development-inclusive rolling backtest of 336 company-quarters from 12 large public technology and platform firms, CAME achieves the lowest aggregate point-estimate error among the reported methods, with statistically supported macro-sMAPE gains over the matched Statistical Anchor, and outperforms History + Guidance on all six aggregate metrics. CAME also links adjustments to source-linked evidence cards and guarded memory traces, supporting forecast inspection, provenance, and failure localization.

Generating a correct answer does not mean that a language model will select it. We separate factual recall into three steps: generating a correct candidate, ranking the available candidates, and selecting the final answer. Pre-generation readouts predict factual recall and which questions sampling will cover across three model families, but say little about whether an available correct answer will ultimately be selected. Explicit verification with $P(\mathrm{True})$ improves within-question ranking over mean log-likelihood in Gemma, Qwen3, and Llama, with AUROC gains of $0.08$–$0.12$. In a prospectively defined Gemma cohort, verification raises plurality accuracy by about $5$ points, and still gains about $2$ points over chat-template likelihood, a stronger generative baseline. The advantage is strongest for relations with common-answer priors and depends on access to the entity; masking the entity removes the ranking advantage in larger Qwen models. Finally, the measured benefit depends on how correctness is defined: recall-oriented reference matching can credit option lists favored by likelihood and substantially understate the improvement seen under human semantic judgments. Prior work shows that models can carry latent factual knowledge and judge candidate answers; we show that these capabilities do not collapse into a single notion of “knowing,” and trace where information is gained, lost, or mismeasured between availability, ranking, and final choice.

Agentic AI is increasingly being embedded in software applications to provide natural language interfaces to features and functionality. In most cases these agents are powered by enterprise (100+ billion parameter) or frontier class large language models that require substantial computational resources run and depend on cloud hosted inference to handle the task of transforming natural language inputs into actionable software operations. This reliance on cloud-hosted inference introduces substantial network latency on top of LLM inference times, creates data privacy concerns, and, given the costs of running these models, can rapidly escalate expenses associated with supporting agentic features. This paper introduces a novel means of converting the NL-to-Action problem from a generative one into a classification-centric formulation via on-device operation caches. These caches allow an agentic system to handle frequently occurring classes of actions completely on-device – reducing latency, enhancing privacy, and lowering operational costs. We show that for a classic NL-to-Formula task, generating Excel Formula in response to user requests, this approach reduces total inference cost by 56% when compared to cloud-only model-routing based inference and, on cache hits, reduces the latency to response latency by 5x.

The main purpose of this paper is to address an open problem posed by Huang, Rasila, and Zhu in [Anal. Math. 48(2022), 1069-1080]. We first establish a sharp Lipschitz continuity result for locally univalent harmonic Bloch mappings with respect to the pseudo hyperbolic metric. This result is then applied to demonstrate that harmonic $(K,K_0)$-quasiregular Bloch type mappings are Lipschitz continuous under the same metric, where $K\geq1$ and $K_{0}\geq0$. Moreover, the estimates obtained are asymptotically sharp as $K \to 1^+$ and $K_0 \to 0^+$. In particular, when $K_0 = 0$, our theorem provides a solution to the aforementioned open problem in the asymptotically sharp sense.

This paper studies communication-centric symbol-level precoding (SLP) for fronthaul-limited networked integrated sensing and communication (ISAC). SLP is attractive for exploiting constructive interference, but its data-dependent nature makes fronthaul-aware waveform design difficult because the transmit covariance used in conventional linear-precoding compression models is unavailable before the symbol block is formed. To address this issue, we develop a compression-aware SLP framework that relates the fronthaul requirement to the realized block energy. We further formulate a sensing-oriented joint design. To solve the resulted high-dimensional and nonconvex problem, we propose a tractable lower-bound method with a performance bound. Simulations show that the proposed SLP scheme improves sensing performance over linear-beamforming baselines under fronthaul constraints.

Recovering physical properties of unknown objects through non-prehensile interaction is challenging because no single manipulation primitive reveals all relevant parameters. Planar pushing couples mass and friction, while conventional tipping cannot recover friction and may fail entirely when low-friction or curved-base objects slide or rotate instead of tipping. We introduce a multi-modal estimation framework that combines a sliding interaction with a press-and-pull tipping primitive to recover object mass, center of mass height, and surface friction. The press-and-pull interaction increases the object-table sliding threshold and stabilizes the pivot, enabling controlled tipping without any prior geometric object model. Wrist force/torque sensing, RGB-D perception, and robot proprioception are fused to estimate the physical parameters from the two complementary interaction modes. Experiments on an ABB IRB120 across four objects with varied geometry, mass, center of mass, and friction achieve low relative error, while successfully operating on curved-base objects that fail under conventional forward tipping. The results demonstrate that complementary non-prehensile interactions can recover a compact set of physical parameters without grasping, a prior object model, or learned interaction dynamics.

Let ${S}_n(321)$ and ${S}_n(\underline{321})$ denote the sets of $n$-permutations avoiding the classical pattern $321$ and the consecutive pattern $\underline{321}$, respectively. Permutations are in bijection with Lehmer codes, a type of inversion sequence. Using Lehmer codes, we create the corresponding weighted posets ${L}_n(321)$ and ${L}_n(\underline{321})$, where the weight of a code is the inversion number of its permutation. We show that there are $2^{n-2}$ maximal elements of ${L}_n(321)$, while the maximal elements of ${L}_n(\underline{321})$ are enumerated by the Padovan numbers. We also show that when $n$ is even, each of these posets has a unique maximum weight element, and that when $n$ is odd, there are two maximum weight elements. These maximum weight Lehmer codes correspond to the pattern avoiding permutations with maximum inversion number.

On-policy distillation (OPD) trains a student to match a teacher's next-token distributions on student-generated trajectories. However, privileged information supplied to the teacher for OPD training may contain sensitive data. Whether the student leaks private information about the records supplied to the teacher during distillation remains poorly understood. To the best of our knowledge, we present the first systematic study of membership inference in this setting. We find that fresh student trajectories expose sparse membership signals that fixed reference-answer losses often miss. These signals are mixed with probability changes caused by training on other records. We introduce Leaky, which samples fresh trajectories from the target model and compares its token log-probabilities with the maximum across matched reference models trained without the candidate records. It applies Leaky ReLU to the resulting gaps, preserving positive gaps and downweighting negative gaps as an approximate correction for incidental positive gaps in non-members. Across fifteen targets spanning mathematics, medical question answering, and code generation, Leaky outperforms all evaluated baselines and achieves mean AUROC 0.875, compared with 0.614 for the strongest baseline on each target in the main evaluation. On the same sampled trajectories, the strongest baseline achieves mean AUROC 0.826. These results show that students trained through OPD can expose the membership of records used for teacher supervision, even when fixed reference-answer losses provide little evidence of membership.

Long-context LLM inference pushes modern GPU serving stacks into an attention-bound regime, where both compute and memory are dominated by the softmax-GEMM pipeline. On NVIDIA Blackwell GPUs, FP4 Tensor Cores offer high matmul throughput, but we find that fully FP4 attention often fails to translate this throughput into end-to-end speedups due to non-matmul costs: online quantization after softmax, tensor/shared-memory data movement, and contention on the softmax path. We present MpFA, a training-free FlashAttention kernel optimized for Blackwell. Guided by hardware characterization, MpFA uses mixed precision: NVFP4 for QK and FP8 for PV (QK4PV8). This preserves low-bit QK throughput while avoiding the conversion and scaling overheads of FP4 PV. To recover accuracy without further stressing the softmax pipeline, MpFA introduces rank-one smoothing compensation implemented as an additional Tensor Core MMA. MpFA further improves performance with a fine-grained asynchronous pipeline, tensor-memory reuse, and adaptive parallel partitioning across prefill and decode. On an NVIDIA SM100 GPU and across 16K-128K contexts, MpFA improves prefill throughput over state-of-the-art BF16/FP8 baselines and increases end-to-end output throughput by 2.81$\times$ over BF16 FA4 across Llama-3.1-8B and Qwen3-14B. Across five benchmark suites and two models, rank-one compensation recovers 62.5% of the accuracy loss with about 2.0% kernel overhead.

Reasoning models generate long chains of thought before they answer, yet it is debated whether the content of these chains does real computational work or is largely decorative. We study this question by viewing a transformer as a shallow circuit. One forward pass through a fixed number of layers has constant depth, so any procedure that runs the model a constant number of times is a shallow circuit. We call the best accuracy that a shallow circuit can reach on a task the ceiling of the task, and a task is serial if its ceiling lies below one. We prove three results on serial tasks that hold for every transformer, no matter how it was trained. Necessity: replacing the chain by anything that does not depend on its content, such as filler tokens or a restatement of the question, drives the accuracy down to the ceiling, and on a maximally serial task down to chance. Depth: no shallow computation can write the chain of a model whose accuracy exceeds the ceiling, not even approximately. Locality: the answer is one shallow pass away from the finished chain, so all of the serial reasoning happens in the chain. On word problems of finite groups, whose ceilings are known, small transformers trained from scratch, with or without reinforcement learning, attain the predicted numbers: chain-trained models solve every input length and fall to chance when the chain is erased, chainless models collapse to the ceiling as the input length grows, and open-weight reasoning models given the same problem in words return to the baseline without their chain. On MATH-500 and AIME, erasing the chain costs open reasoning models 0.52 to 0.82 accuracy, a sentence shuffle is harmless, and a token shuffle is as harmful as erasing; the same holds for checkpoints trained by GRPO with a correct or a random reward. The ceiling of a task therefore answers when a transformer can succeed without its chain of thought.

Training long-context LLM policies with RL requires re-evaluating groups of sampled responses under the updated policy, an update-stage attention workload that differs sharply from pre-training: each group shares one long prompt that fans out into multiple response branches. Standard context parallelism (CP) flattens each prompt–response pair into a linear sequence, so the same prompt key–value (KV) states are recomputed—or repeatedly rotated through the network—once per response branch. We present AugTree, a CP execution scheme built around this replay stage. AugTree separates the replay into two phases: a prompt-prefill phase that computes the shared prompt KV state once, and a response-replay phase that schedules the independent response branches over a bounded set of replay lanes. The replay phase instantiates two communication semantics, chosen by a lightweight online planner that enumerates CP degrees, schedules, and placements before GPU dispatch: rotating KV shards within response-local lanes when responses dominate, and moving response queries to stationary prompt-KV owners with a partial-softmax reduction when prompts dominate. The shared prompt state remains fully differentiable—response losses backpropagate into it and the accumulated prompt gradients propagate through the original prefill graph—so AugTree preserves exact training semantics rather than performing detached, inference-style KV caching. On four real post-training workloads and up to 64 accelerators, AugTree improves average training-stage step time by 1.18$\times$ over dynamic CP (up to 2.23$\times$), 2.63$\times$ over a Megatron ring CP baseline with prompt reuse, and 7.08$\times$ over the baseline without reuse.

Recent advances in quantum computing are opening new opportunities for computationally intensive decision problems. This paper studies how quantum computing can improve Monte Carlo tree search (MCTS) in the fixed-confidence setting, where the goal is to identify a near-optimal move in a given game tree with high probability while minimizing query complexity. We first formulate MCTS under a quantum oracle model. We then develop a quantum MCTS algorithm (QMCTS) that combines threshold-based elimination on the search tree with quantum Monte Carlo estimation to reduce the cost of evaluating stochastic leaf values. We establish an instance-dependent lower bound on the query complexity and derive a corresponding upper bound for QMCTS. The lower-bound analysis introduces a new quantum phase-testing result that may also be useful beyond MCTS. We validate the theoretical results through simulation experiments and further demonstrate the feasibility of QMCTS on real quantum hardware.

Black-box Optimization (BO) is a powerful framework for optimizing expensive objective functions or unknown functions with a limited number of evaluations. A central step of standard BO such as Bayesian optimization is the optimization of a surrogate-based acquisition criterion, which is commonly performed using nonlinear optimization or heuristic search. Therefore, conventional black-box optimization generally does not guarantee global optimality in candidate selection. In this study, we propose Integer Linear Programming-based Black-box Optimization (ILP-BO), a quasi-Bayesian optimization framework that transforms kernel-based surrogate optimization over discrete domains into an Integer Linear Programming (ILP) problem. The key idea is to represent nonlinear kernel functions exactly on finite discrete distance levels by introducing binary one-hot auxiliary variables. This transformation converts the nonlinear surrogate into a linear objective with linear constraints and binary variables. To incorporate exploration while preserving the linear structure, we further introduce a Hamming-distance margin that excludes neighborhoods around previously observed points. We derive the proposed formulation for several standard kernels and obtain an analytical upper bound on the Hamming-distance threshold based on the measure in the binary search space. The resulting candidate-selection problem can be solved by integer programming solvers with certificates of optimality. Thus, our methodology has the potential to serve as a highly transparent black-box optimization framework. Experiments on synthetic and discrete optimization benchmarks show that ILP-BO achieves competitive optimization performance compared with practical Bayesian optimization methods.

Magnetic symmetry can generate momentum-dependent spin-split electronic bands even in the absence of spin-orbit coupling (SOC), giving rise to the recently discovered class of altermagnets. Here, we establish a unified symmetry framework for collinear antiferromagnets in orthorhombic Pbnm perovskites by combining spin and magnetic group theory with first-principles calculations. We show that the irreducible representation of the magnetic order uniquely determines the momentum-space planes supporting altermagnetic spin splitting, the form of the effective low-energy Hamiltonian, the orientation of SOC-induced weak ferromagnetic canting, and the allowed anomalous Hall conductivity (AHC) tensor components. These predictions are validated in eight experimentally realized orthorhombic perovskite oxides spanning both insulating and metallic regimes. In particular, LaTiO3 and CaCrO3 exhibit sizable anomalous Hall conductivities of approximately 38 and 205 S/cm, respectively, despite nearly vanishing net magnetization. We further show that SOC gaps symmetry-protected altermagnetic band crossings, generating large Berry curvature, while the Hall response is fundamentally rooted in the underlying non-relativistic spin splitting. Our work establishes a predictive symmetry-based framework for discovering and engineering altermagnetic materials with tunable spin-dependent electronic and transport properties.

As the bridge between protein modality and discrete modeling, protein structure tokenization still largely relies on heavily engineered training objectives tailored to specific downstream tasks and large training datasets, which hinders its transfer to broader application scenarios. To address this issue, we propose ProFiT, a lightweight flow matching tokenizer. With simple training strategies that encourage healthy codebook utilization, ProFiT can be trained efficiently and naturally learns semantically meaningful representations without any manual semantic alignment, while achieving reconstruction quality and generalization that match or surpass those of substantially larger tokenizers. We conduct extensive evaluations across a wide range of settings and demonstrate that ProFiT is a plug-and-play tokenizer adaptable to diverse downstream tasks. This study further reveals the significant potential of the flow matching tokenizer paradigm. Our code is publicly available at https://github.com/QDKStorm/ProFiT.

Hyun, Kim, Wu and Yue constructed optimal and minimal binary linear codes from order ideals of hierarchical posets with two levels. Two different generalizations of the underlying antichain (simplicial complex) setting to odd characteristic are known: down-sets of $\mathbb{F}_p^n$ under the componentwise order, and support-closed subsets of $\mathbb{F}_q^m$. No generalization of the poset setting itself has appeared. We introduce generalized order ideals of a poset of order $p-1$, obtained by attaching multiplicities in ${0,\dots,p-1}$ to the elements of a poset, and study the two natural notions of order ideal that arise for hierarchical posets with two levels. Whenever the ideal meets the upper level, the resulting defining sets are neither down-sets nor support-closed. We determine the weight distributions of the associated complement codes, exhibit a family of Griesmer codes in which the upper element carries an arbitrary multiplicity, and, via the characteristic function of a generalized order ideal, obtain an infinite family of minimal $p$-ary codes of length $p^n-1$ and dimension $n+1$ violating the Ashikhmin–Barg condition.

Offline-to-Online Reinforcement Learning (O2O RL) has emerged as a practical paradigm that pre-trains the policy using static offline datasets and subsequently adapts the policy through online interactions. Existing O2O methods primarily address the transition through value calibration, while generally treating the offline-trained policy as a given initialization. We instead study O2O adaptation from the perspective of network plasticity, asking whether the offline-trained policy remains sufficiently adaptable for online learning. Controlled experiments show that prolonged optimization on static offline data progressively reduces network plasticity even after offline performance has largely saturated, and that lower plasticity is associated with weaker subsequent online improvement. Motivated by these observations, we propose REstoring plasticity via Fresh Initialization and policy Transfer (REFIT), a lightweight model-level method for the O2O transition. Before online fine-tuning, REFIT distills the offline policy into a freshly initialized student while temporarily freezing a random subset of student units, transferring the learned offline behavior to a more plastic policy initialization. Extensive experiments on D4RL and OGBench demonstrate that REFIT consistently achieves higher aggregate performance than existing O2O plug-in methods across both Cal-QL and IQL backbones, while plasticity diagnostics and ablations provide further evidence of restored network plasticity.

Group-relative reinforcement learning (RL) relies on reward variation among sampled responses to estimate informative relative advantages. As language models become increasingly capable, existing training data can become reward-saturated: all sampled responses to the same problem might receive equally high rewards, where the group-relative learning signals vanish and leave previously useful data obsolete. In this work, we investigate whether useful learning signals can be recovered from such saturated data. We study interventions at four levels of group-policy RL pipelines—data, rollout, reward, and advantage—and conduct extensive RL training on saturated reasoning data only. While standard GRPO on saturated data would almost always yield near-0 advantages and near-noise signals, diverse interventions successfully recycle and repurpose such data: among the proposed strategies, interventions at rollout generation are consistently most effective: nudging the policy to generate “high-quality”, incorrect solutions introduces rollouts with poor rewards into saturated groups as negative samples, which turns out to improve GRPO by 6.4% to 9.0% across Qwen3-1.7B and 4B. Other interventions such as increasing rollout temperature or adding auxiliary rewards can also restore non-zero advantages, but yield less consistent gains. Further analyses show that effective negative rollouts require informative negative trajectories, that the method remains effective alongside unsaturated data, and that it supports iterative recycling of newly saturated examples. While increasingly stronger LLMs would render more data as saturated, our results demonstrate that don't waste your saturated data: with the right strategies they can be recycled into useful RL training signals in an increasingly data-scarce world.

Co-training offers a straightforward way to build a multi-task vision-language-action (VLA) policy, but can fall short of the performance achieved by training each task independently. The challenge is to retain these task-specific gains in a multi-task policy without joint post-training. Combining independently trained experts through model merging is a natural approach, yet strong individual experts do not necessarily yield a strong merged policy. We identify one source of this incompatibility: task-specific changes to the action interface, comprising action normalization and the action encoder and decoder. We propose PolicyWeave, combining merge-compatible post-training with context-guided sparse merging. During post-training, all experts retain the common base policy's action interface, while task adaptation is restricted to LoRA updates in the hidden layers of the action model. This makes the experts more compatible with existing model merging methods. However, merging all experts can still introduce interference from unrelated tasks at deployment. PolicyWeave scores each expert's LoRA updates using the initial visual-language context, determines the expert set through leave-one-layer-out ranking stability, and forms a sparse weighted merge of the selected updates that remains fixed for current task. We evaluate PolicyWeave with GR00T N1.5 on 18 RoboCasa365 tasks, using only 10% of the target-task demonstrations for supervised fine-tuning (SFT). Preserving the shared action interface raises the average success rate across four static merging methods from 17.0% to 52.8%. PolicyWeave achieves 64.7% success with these SFT experts and 74.1% after task-specific reinforcement learning (RL), compared with 60.7% for joint RL. Further evaluations on LIBERO-10 and an AgileX Piper arm support the deployment of independently learned skills in long-horizon and real-world manipulation.

We prove an $e$-positive formula for the chromatic symmetric function of proper circular arc graphs solving the $q=1$ case of a conjecture of Ellzey and of Alexandersson and Panova. In doing so, we provide a new proof of the $e$-positivity of unit interval graphs, which alongside Guay-Paquet's reduction gives a new proof of the Stanley–Stembridge conjecture. We define color matrices, which count proper colorings, and tableau matrices, whose entries are nonnegative rational numbers and ratios of elementary symmetric functions. We prove the two matrices are related by a single family of change of basis matrices, which become invertible after restricting to finitely many colors, and we show the chromatic symmetric function of proper circular arc graphs comes from taking the trace of these matrices. Using Hikita's tableaux, this gives an explicit formula for the chromatic symmetric function of a proper circular arc graph as a weighted sum over tableaux whose first and last $k$ vertices lie in the same columns.

Self-evolving agent harnesses continually update persistent components such as memory, prompts, skills, and tools. We call this process harness evolution. However, such evolution could introduce unexpected safety risks. Existing work studies harness misevolution and validates candidate harnesses or attributed individual component updates, leaving safety analysis of cross-component update interactions largely unexamined. To address this gap, we study compositional safety failures in harness evolution, where interactions among individually safe and utility-preserving component updates can produce undesirable or unsafe agent behavior, revealing a safety risk intrinsic to harness evolution. Across three safety-related benchmarks, we identify 43 pairwise and 18 irreducible 3-way compositional safety failures. Conventional solution incurs combinatorial complexity in validating cross-component interactions, leaving the safety checking impractical as the harness evolves. To solve this, we introduced a typed hypergraph that represents component states as nodes and safety-relevant higher-order interactions as hyperedges. When the harness changes, the hypergraph updates only the interaction neighborhood of the changed states rather than reconstructing the global composition space. Building on that, we develop a hypergraph-guided runtime monitoring mechanism. Experiments show that our method effectively mitigates compositional safety risks while preserving task utility and reducing interaction-checking costs, and further reveal an empirical safety-utility-cost trade-off across different safety mechanisms.

Persistent homology and persistent Laplacians have become effective descriptors of large molecular binding interactions, the latter encoding multiscale geometry and spectral information beyond the harmonic subspace. Both, however, are built on undirected graphs and pairwise contracts, while the interactions that determine binding are often directional and involve more than two atoms at once. We introduce persistent hyperdigraph learning (PHL), which represents these directed, many-body interactions directly. Because hyperdigraph Laplacian spectra become costly to compute at higher topological orders, we further use stochastic trace estimation to develop a matrix-free formulation(MFPHL) that estimates Laplacian trace statistics from probe-based quadratic forms evaluated through sparse boundary operators, without assembling or diagonalizing. The number of probes required for a target relative accuracy of the trace estimate is independent of matrix dimension, and per-probe cost scales with operator sparsity. On protein-protein binding affinity benchmarks, MFPHL reduces feature-generation time by roughly two orders of magnitude relative to the eigenvalue-based pipeline. Its predictive accuracy matches that of spectral PHL on the P2P wild-type set within training-seed variability but is lower on the two larger datasets. This dataset-dependent trade-off brings higher-order hyperdigraph features within practical reach.

Computational methods have consistently struggled to determine the dominant temporal orientation of a sentence. This difficulty is especially pronounced when a sentence contains multiple embedded clauses with competing tense and aspectual information. To address this difficulty, we propose an alternative approach for identifying a sentence's past, present, or future global reference interval. Our method does not use any form of pretrained embeddings. We rather encode sentences using fixed-length inventory vectors that are comprised of part-of-speech counts, dependency relation counts, and explicit futurate pattern counts. We term this inventory vector of a sentence a "Morphosyntacton". The method does not use any padding, sequence models, or large language models. Evaluation on 1,799 syntactically complex English sentences, annotated as past, present or future, shows balanced and high accuracy multiclass classification, achieving an overall multi-class accuracy of 92%.

Electrical distribution grid operations require inference across heterogeneous networks from sparse, noisy, and incomplete time series measurements. In this work, we identify challenges and explore solutions towards a unified model that can perform diverse tasks grounded in the physics of the electric grid and generalize to unseen distribution networks. We define a unified grid ontology that represents variable sized distribution networks as heterogeneous graphs while preserving native topology, asset types, and electrical relationships across networks. We develop a physics based data simulation pipeline that combines reference and procedurally generated distribution networks with network reconfigurations, fault scenarios, and configurable sensing conditions. We present Mycelium, a heterogeneous graph transformer with structure aware communication edges and electrical reference features that encode network position and nominal phase orientation, together with task specific temporal readouts which generate per task outputs. We train Mycelium on reference as well as synthetic grids, and study its generalization on benchmark networks completely excluded from training and validation. Mycelium is observed to outperform task specific neural baselines on most reported benchmark metrics. Architectural ablations and the aforementioned studies reveal Mycelium's capability to learn representations of the underlying physics which serves to enhance cross-task performance, thereby addressing a significant challenge in unified grid models.

Medical question answering spans diverse specialties and modalities, and individual medical large language models (LLMs) exhibit distinct strengths across tasks and domains. This heterogeneity suggests that combining specialists may enable broader coverage of medical questions than relying on any single model. However, existing LLM routing methods primarily seek to balance answer quality and inference cost, leaving open how to exploit differences in specialist competence to improve medical reasoning. In this paper, we introduce MedRouter, an agentic system that uses an embedding-based multi-label router to select and query specialist LLMs, then passes their responses to a generator to produce the final answer. We further propose SCALE (Specialist Competence-Aware Learning), a two-stage training framework that first trains the Router with specialist correctness supervision and then optimizes its selections through reinforcement learning. The second stage uses a Performance Gain Reward (PGR) that measures how specialist information affects the generator's answer correctness relative to answering without that information. Experiments on eight text-based and multimodal medical QA benchmarks show that MedRouter outperforms the strongest routing baseline by 8% in average accuracy. Our analysis of specialist outputs further reveals distinct strengths and complementary question-level coverage, motivating learned routing to combine these capabilities for more comprehensive medical reasoning.

We construct maximal subgroups of topological full groups and their commutator subgroups using factor maps and wide open subgroupoids of minimal effective ample groupoids with Cantor unit spaces, assuming almost finiteness or pure infiniteness. For two-to-one coverings and prime factor maps with principal target and fibers of cardinality at most two, surjectivity and injectivity of the same induced map on full-group abelianizations characterize maximality of the factor full group and factor commutator subgroup, respectively. For subgroupoids arising from prime-order cyclic actions free on the unit space, the normalizer of the smaller commutator subgroup in the ambient full group is a semidirect product, maximal exactly when the inclusion induces a surjection on full-group abelianizations. In both constructions, the embedded commutator subgroup has a unique maximal overgroup in the ambient commutator subgroup, namely its normalizer. For Cantor minimal systems, the factor construction yields partition stabilizers of the type in the Grigorchuk-Vorobets conjecture. The subgroupoid normalizers act topologically primitively. Groupoid homology makes the criteria computable for these systems and shifts of finite type. Examples include finitely generated nonsimple and locally finite simple maximal subgroups of infinite index in finitely generated infinite simple amenable groups.

Multimodal large language models (MLLMs) can now interpret a standard ten-second, twelve-lead electrocardiogram (ECG) with clinically grounded, reward-verified reasoning. Real cardiac monitoring is different. Ambulatory (Holter) and telemetry recordings span hours to days and are read as they stream in, and their clinically decisive findings are paroxysmal, brief episodes buried in an otherwise unremarkable trace. Such a recording cannot be held in one context at diagnostic resolution, and its future has not yet happened, so a reader must work online, deciding what to measure now, committing evidence to memory as it passes, and reporting events as they occur. We recast long-duration ECG interpretation as a long-horizon, online (streaming, causal) sequential decision process and introduce ECG-Scroll. As a benchmark, long ambulatory recordings are streamed to an agent chunk by chunk, and it must localize, quantify, and promptly flag paroxysmal events without access to future signal; because the underlying signal is retained, every answer is checkable against objective ground truth, giving rule-based rather than judge-based rewards, and the streaming formulation adds a metric batch evaluation cannot express, the detection latency between an event's onset and the moment the agent records it. As an agent environment, it is a fixed, gym-style interaction layer that exercises three competencies single-glance ECG models never touch: Memory, Tool use through signal-grounded measurement rather than reading pixels, and Planning of what to measure now and when to commit. We release 390 whole-recording instances spanning 2,536 hours of two-lead ambulatory ECG and evaluate a signal-threshold rule agent alongside off-the-shelf LLM agents online, characterizing how they use memory, tools, and planning and where the benchmark's head-room lies.