Papers

We introduce the leap group of a graph, the subgroup of the symmetric group on the vertex set generated by graph derangements. We summarize historical results on graph derangements, which we call hops, and prove additional existence and complexity results. The leap groups of various canonical graphs are computed, and their behavior under basic graph operations is analyzed. We offer partial results on which groups can appear as leap groups, and study hops and leaps for infinite and directed graphs.

Readout scaling changes what a sparse autoencoder (SAE) learns, but the benefit of removing it depends on the data. We use readout-canonicalized decision-space (RC-DS) coordinates to remove singular-value gains while preserving retained decision information. At a fixed readout condition number, changing the generating distribution reverses which training coordinates recover known factors best. In our controlled coordinate-matching study, recovery is highest when training restores the space in which the factors were generated. When factors are generated before readout scaling, RC-DS increases mean sparse-factor recovery from 0.506 to 0.913 at condition number 100, compared with centered-logit training under the same budget. An exact wrapper reproduces RC-DS training to numerical precision, isolating training geometry rather than additional information. In neural policies, RC-DS improves mean logit reconstruction under the tested budgets. On three fixed language-model checkpoints, RC-DS has higher mean gain-free reconstruction in all 18 tested task-sparsity settings, while centered-logit SAEs reconstruct output logits better in 17. Small-label-head controls show that longer training reduces the reconstruction gap from 0.0198 to 0.0016. Together, these results show how readout scaling, the data distribution, and training shape sparse learning. RC-DS provides an information-preserving method for studying and controlling the readout's contribution. Separate label-detection and steering tests distinguish these reconstruction effects from task-specific feature usefulness.

Video subtitle removal (VSR) is an important video restoration task, yet existing evaluation remains limited by low-resolution datasets, fragmented test sets, and generic video-inpainting protocols that fail to adequately capture localized restoration errors, unintended modifications, temporal instability, and incomplete outputs. In this paper, we introduce MFVSR, a large-scale multi-style benchmark for fine-grained and reliability-aware video subtitle removal evaluation. MFVSR distinguishes itself through three key features: (1) Large-scale and diverse data, comprising 3,000 paired videos from Real-HQ, Real-LQ, and AI-Generated sources, with an auxiliary set of 953 in-the-wild real videos for real-world coverage analysis; (2) Controlled subtitle diversity, spanning 16 languages and four factors covering spatial layout, temporal behavior, visual style, and language mode; (3) Fine-grained evaluation, introducing an information-conditioned, spatially decoupled protocol that separates blind from mask-guided removal and measures Restoration Fidelity, Preservation Fidelity, Temporal Fidelity, coverage, and failures. Experiments on six representative methods reveal substantial discrepancies between local restoration, outside-region preservation, temporal consistency, and full-set reliability that are obscured by conventional full-frame metrics. MFVSR therefore provides a more comprehensive and diagnostic foundation for evaluating and advancing video subtitle removal methods.

The cosmic reheating is an important epoch in the very early Universe, and has significant impacts on the primordial black hole (PBH) abundance and the scalar-induced gravitational wave (SIGW) spectrum. The relevant energy scale and the constituents of cosmic medium are encoded in the reheating frequency $f_{\mathrm{reh}}$ and the equation of state parameter $w$. In this work, we perform a full parameter space Bayesian inference, using the NANOGrav 15-yr dataset to constrain the thermal history of reheating. Treating $f_{\mathrm{reh}}$ and $w$ as free parameters, we systematically investigate the Dirac $\delta$, narrow and broad log-normal primordial power spectra. Current pulsar timing array data can effectively constrain the peak frequency of the SIGW spectrum as $f_{\rm p}\sim 10^{-7.6}$–$10^{-7.0}$ Hz, along with $f_{\rm reh}\sim 10^{-9.0}$–$10^{-8.3}$ Hz and $w\sim 0.19$–$0.79$ (the $68\%$ confidence level), when the power spectrum has a relatively narrow width $\Delta \lesssim 1$. A broader power spectrum introduces a smoothing effect that obscures the characteristic frequency knee in the SIGW spectrum, leading to the loss of information about cosmic reheating. Furthermore, for the Dirac $\delta$ and narrow spectra, the PBH masses associated with the SIGWs are anchored at the planetary mass scale around $10^{-6}$–$10^{-4} M_{\odot}$. This establishes a consistent physical framework that naturally bridges the nanohertz gravitational wave background with the dark matter candidates implied by the Optical Gravitational Lensing Experiment microlensing events.

External tools can extend the capabilities of small language models (SLMs), enabling their deployment in resource constrained environments. However, their limited capabilities make it difficult for SLMs to discover effective tool use behaviors through reinforcement learning alone, while direct teacher supervision suffers from teacher student behavioral distribution mismatch and may propagate erroneous preferences. To address these challenges, we propose Selective Teacher guided Policy Optimization (SeTPO), which coordinates student exploration with selective teacher guidance and persistent demonstration supervision. Specifically, SeTPO incorporates reverse KL derived token level teacher feedback into policy advantages on low reward trajectories, while auxiliary forward KL supervision preserves teacher demonstrated behaviors throughout training. Under an idealized bidirectional KL objective, we theoretically establish that the optimal policy achieves expected reward no lower than the teacher's while retaining a guaranteed fraction of the teacher's probability mass. Extensive experiments on BFCL v4 and API Bank demonstrate that SeTPO achieves superior overall performance over supervised fine tuning, reinforcement learning, and distillation baselines across all three student scales.

Modern image restoration methods increasingly rely on large-scale supervised training, yet clean targets are often prohibitively difficult to obtain in scientific imaging modalities such as hyperspectral imaging (HSI) and magnetic resonance imaging (MRI). Plug-and-play ADMM (PnP-ADMM) with pretrained diffusion priors offers a promising alternative, but the learned prior distribution can mismatch both the target scientific image distribution and the distribution of ADMM denoiser inputs induced by dual feedback. To mitigate these mismatches, we propose $\mathrm{S}^3$-PnP, a self-supervised plug-and-play restoration framework that learns a score prior directly from observation-derived ADMM intermediate states, without clean training targets or externally pretrained weights. Specifically, the learned score corrects the input to the analytical prior update, combining observation-driven corrections with analytical regularization. We further analyze the convergence and reconstruction error of the corrected ADMM algorithm assuming an ideal score and quadratic data fidelity. Experiments on reference-guided HSI restoration, single-image HSI denoising, and MRI denoising demonstrate consistent improvements over competing methods.

Large language model (LLM) agents are becoming an integral part of the software development lifecycle, and the capabilities granted to them allow an agent to act with the user's authority on any resource it can access. The reach that gives an agent its utility is equally available to an attacker who can steer it. Anything an agent ingests can carry an injected instruction, and since the model does not reliably distinguish instructions from data, indirect prompt injection should be mitigated by mediating the effects the agent produces. Such mediation faces a structural difficulty. Legitimate work and the first step of an attack often look alike when an individual action is observed, and what separates them lies later in the trace, so a monitor limited to allow and deny is forced to decide before the evidence accumulates. We present Kairos, a reference monitor at the isolation boundary of an unmodified, opaque agent, where a tool call, a shell command, and a script the agent writes all cross the boundary as the same file and network operations, so that confinement holds regardless of the agent's behavior. A declarative policy that states which sources are trusted decides most effects deterministically and defers the rest, which are held while the agent continues speculatively. A decision oracle with bounded authority, such as a language model or a human, releases or refuses each deferred effect on the trace. Across three benchmarks and three agent models, Kairos outperforms existing defenses in the trade-off between attack success and utility. In particular, on AgentDojo, it reduces attack success from 47.0% to 2.7% while its benign utility stays at the level of the undefended agent.

AI-based cellular perturbation prediction is essential to accelerate drug discovery and therapeutic identification. However, perturbation-specific signals are generally obscured by cellular complexity, making it difficult for existing methods to correctly capture perturbation effects. To address this problem, we propose PerturbEnergy, which introduces a conditional energy-based prior over perturbation representations. It assigns lower energy (higher probability) to representations compatible with the given perturbation and higher energy to others, thereby explicitly tilting the latent space toward perturbation-preferred regions. Besides, PerturbEnergy can be integrated into autoencoder architectures as we find its Evidence Lower Bound (ELBO) is equivalent to the ELBO of the complete autoencoder. We further prove that optimizing PerturbEnergy increases the lower bound on the conditional mutual information between representation and perturbation. Extensive experiments on four benchmark datasets demonstrate the effectiveness of our PerturbEnergy: it improves perturbation recognition especially in latent space with improvement of up to 83.2%; It also achieves state-of-the-art performance for predicting top-50/100/200 differentially expressed gene(DEG) response and remaining competitive on highly variable gene(HVG) prediction. The code is provided: https://github.com/BlueWhaleLab/PerturbEnergy

Rapid advances in artificial intelligence-generated content (AIGC) have significantly promoted using text-to-image (T2I) models to generate images with specific affective intentions. However, the emotional effects conveyed by generated images frequently deviate from target expectations, and it remains unclear whether multimodal large language models (MLLMs) can reliably interpret the emotion of AI-generated visual content. Existing affective benchmarks are predominantly built on natural images, while affective studies of generated images have largely focused on emotions expressed in portraits, lacking a unified benchmark for studying the emotions expressed and evoked by generated images. We therefore introduce EmoGenie, a benchmark of emotion for AI-generated images that evaluates capabilities in T2I generation and MLLM understanding across expressed and evoked emotions. It comprises 6,400 images generated by eight T2I models using 800 emotion-targeted prompts, annotated with question-answer (QA) pairs, termed EmoGenie-QA, and continuous human ratings, termed EmoGenie-Assess. EmoGenie-QA contains 90,000 closed-set questions in single-image and image-pair settings, as well as 1,057 open-ended questions for emotion description. EmoGenie-Assess benchmarks continuous affective and aesthetic prediction using 13,175 mean opinion scores (MOSs) aggregated from human ratings in terms of valence, arousal, dominance, and aesthetic quality. We further develop EmoProbe, which combines emotion question answering with response-aligned, dimension-specific regression heads for continuous score prediction. Experimental results show that EmoProbe achieves superior results on emotion-related QA tasks, while its affective and aesthetic predictions correlate better with human ratings, demonstrating its state-of-the-art capabilities of unified coarse-to-fine affective understanding for AI-generated images.

Quantifying the capability and reliability of agentic systems in high-energy physics (HEP) requires repeated evaluations under controlled configurations. Establishing whether changes to models, tools, or harnesses improve performance also requires these components to be varied independently. We present the High Energy Physics Tool-and-Agent Benchmarking (HEPTABench) framework for portable and controlled evaluations of agentic systems, with separately configurable tasks, scaffolding, models, providers, harnesses, and domain capabilities. The framework combines HEP benchmark tasks and scientific rubrics with experiment execution and versioned tool interfaces. To support inspection, reproducibility, and post-hoc grading, the framework prioritizes recording and reporting complete experiment specifications, agent trajectories, and experiment artifacts. We demonstrate the framework in two benchmark campaigns. The first campaign evaluates a forward long-lived-particle reach calculation across four frontier coding-agent systems, comparing their built-in coding tools with the same tools supplemented by HEP domain tools. We show that including these HEP domain tools improves numerical accuracy and reduces trial-to-trial dispersion for every tested system. In a complementary campaign covering eight symbolic two-body decay tasks, we show that adding symbolic domain tools increases the fraction of successful trials for Claude Haiku 4.5 from $8\%$ to $79\%$, while GPT-5.5 succeeds in every trial with built-in tools alone. Through systematic evaluation of agentic systems, HEPTABench enables the identification of factors that improve the accuracy and reliability of their scientific work.

In this paper, we study a new variant of the ants walk: a model of reinforced random walks for the phenomenon of a colony of ants being able to find the shortest path between their nest and a source of food. In this model, the nest and the source of food are two distinguished nodes in a finite graph. The ants perform successive random walks on this graph, started at the nest and stopped when they first hit the food source; the transition probabilities of each random walk depends on the trajectories of the previous ants, through some edge-weights that represent the amount pheromones deposited on each edge. In our new variant of the model, the ant (1) forgets loops made on the way to the food as soon as they are made, and (2) comes back to the nest following this loop-erased version of its forward trajectory, and deposits pheromone on the edges it crosses by doing so (i.e. adds one to these edges' weights). We say that the ants "find the shortest path" if, almost surely as the number of ants tends to infinity, the proportion of ants that travel along a graph-geodesic path from the nest to the food tends to one and the proportion of ants that travel along the remaining edges tends to zero. We are able to prove that this new variant of the model finds the shortest path when the graph distance between the nest and the source is at most 2. The strength of our result is that there is no other assumption on the shape of the graph. We prove this result using stochastic approximation theory, the electrical network method for random walks on weighted graphs, and the theory of weighted uniform spanning trees (WUSTs). In particular, the link with WUSTs is unique to the model studied in this paper due to the way the ant erases loops on the outward journey.

Giant graviton expansions express finite-rank corrections to supersymmetric indices in terms of indices for wrapped D3-branes. We give detailed algebraic proofs of two previously proposed relations for four-dimensional $\mathcal N=4$ $U(N)$ super-Yang–Mills theory. The first is the Gaiotto–Lee single-sum expansion of the full superconformal index, proved by Hall–Littlewood orthogonality and an elementary calculation of operator traces. The second is the symmetric double-sum expansion of the flavored Schur index, proved by factorizing its exact free-fermion mode product. We specify the analytic continuation of the brane indices and justify the sums coefficient by coefficient. The two proofs apply to different expansion prescriptions and do not establish the full three-species expansion of Imamura. We discuss the additional physical and mathematical questions raised by that expansion and by the modular properties of the Schur index.

Large-scale expert parallelism (EP) has become the standard deployment configuration for Mixture-of-Experts (MoE) models in production. Meanwhile, the highly dynamic nature of LLM workloads requires providers to continuously adjust serving capacity to match fluctuating demand. Scaling MoE serving cannot be efficiently achieved by simply adding or removing serving instances; instead, it often requires resizing the EP group within an existing instance, which we refer to as intra-instance scaling.Existing inference engines primarily rely on instance-level scaling, which destroys and reconstructs entire serving instances, incurring substantial scaling overhead. We present FastEEP (Fast Elastic Expert Parallel), a fast intra-instance scaling system for MoE serving based on the principle of Partial Reuse. FastEEP reuses existing runtime state across worker execution, GPU memory, and communication by separating reusable execution structures from the resources activated by the current EP configuration. This separation enables coordinated resource reclamation and reconfiguration while preserving costly-to-reconstruct state, allowing fast EP scaling without full instance teardown and reconstruction. Our evaluation shows that FastEEP achieves 4.5x–11.7x faster scaling than the existing vLLM-based approach across different models, enabling efficient, fine-grained scaling of MoE serving.

This paper develops a three-axis Rydberg atomic receiver model for direction-of-arrival (DoA) estimation of the radio frequency (RF) signal source. Three nominally orthogonal RF local oscillators (LOs), each assigned a distinct frequency offset, project the weak incident RF field into resolvable complex beat coefficients in the optical readout. A beat-vector observation is obtained by adopting a response calibration mechanism that maps the coefficients onto the three axes of the Cartesian coordinate system. For a known circularly polarised RF signal, this observation induces a direction-dependent Rydberg steering vector, enabling maximum-likelihood DoA estimation. The pro posed procedure translates the Rydberg beat-vector front end into a highly sensitive RF field DoA sensor. Simulation results show that trace-level beat extraction supports the proposed DoA sensing workflow and provides a basis for comparison with a traditional vector antenna (VA) benchmark.

AI agents for autonomous scientific discovery must decide which experiments to run under a limited budget. Most benchmarks for science agents provide fixed datasets, while others that support active experimentation largely rely on simulation. We introduce Autonomous Science Bench, an initial release comprising six budgeted design-build-test-learn campaigns grounded in published experiments across biology, chemistry, and materials science. Agents select batches of designs, receive measurements from a lab service, and use the results to guide subsequent experiments before delivering a predictive model. Success requires passing two calibrated gates: a discovery gate, which evaluates the designs the agent measured, and a learning gate, which evaluates its model's ranking of held-out designs. In a pilot evaluation of eight agent-model configurations and 144 trials, the best configuration succeeds in 67% of trials, while the hardest campaign is solved in only three of 24 attempts. The two gates reveal different weaknesses: some agents build accurate rankings but find too few promising designs, while others find promising designs but fail to predict which unseen designs will perform well. These differences are obscured by overall success rates alone. We release version 0.1 of the campaigns, lab runtime, and public leaderboard at https://yibow.me/autonomous-science-bench.

Yttrium oxyhydride (YHO) thin films are synthesised by reactive magnetron sputtering of e̱ta}-YHx precursor films onto single-crystalline yttria-stabilised zirconia (YSZ) (111) and (100) substrates at 200 {\deg}C, followed by post-deposition oxidation in air. For comparison, reference films are also prepared on amorphous SiO2 and soda-lime glass substrates at both 200 {\deg}C and room temperature (RT). The structural (X-ray diffraction and scanning electron microscopy), compositional (elastic recoil detection analysis), and optical properties, including photochromic behaviour, of the films are systematically investigated. The results reveal a strong influence of substrate orientation on the film microstructure and crystallographic texture, leading to epitaxial-like growth with a mosaic spread of ~3-4{\deg}. YHO deposited on YSZ(100) exhibits larger crystallite sizes (10-20 nm) than YHO grown on YSZ(111) (~8 nm) and exhibits residual in-plane compressive strain while remaining largely relaxed with respect to the substrate. Compositional analysis revealed that the O/Y and O/H atomic ratios ranged from 0.71 to 0.82 and from 0.33 to 0.44, respectively, for films deposited under optimised conditions. These films exhibit photochromic behaviour under solar simulator illumination, with relative transmittance changes ranging from 7 to 22 % after 10 min of illumination. Despite the pronounced structural differences, the epitaxial-like films show no systematic improvement in photochromic response, indicating that the effect is governed primarily by composition. The study shows that the bleaching time constant increases exponentially with increasing contrast reached during illumination, rather than representing an intrinsic material constant of YHO.

World models have emerged as a promising paradigm for embodied AI, yet existing systems often remain fragmented in the modalities they model and the functions they support. In particular, visual dynamics, geometric structure, and executable action are commonly coupled through separate interfaces or downstream modules rather than being jointly represented and evolved within a shared dynamics model. In this work, we present Thinker-WM, a unified multimodal world model that jointly models and generates RGB, metric depth, and robot action through a shared intermediate Unified Dynamics Transformer with modality-specific encoders and decoders. The model performs multimodal unification at the representation level: appearance, geometry, and action are transformed into a common dynamic representation and jointly evolved by shared parameters, while their distinct output structures are preserved. The same parameterization supports multiple functions, including joint video-action generation, world prediction, policy inference, action-conditioned generation, video-to-action generation, and inverse dynamics. To examine whether the shared representation captures action-related information, we introduce a lightweight motion probe that shows the frozen visual representation contains recoverable motion information. Thinker-WM is trained on a heterogeneous corpus comprising approximately 20K hours of egocentric video, 10K hours of real-robot data, and 1K hours of simulation data, including approximately 4K hours of real-robot data with aligned depth supervision. Extensive experiments demonstrate strong performance across embodied world-model evaluations. Thinker-WM ranks first on EWMBench, WorldOlympiad and WorldArena, while controlled studies further demonstrate the benefits of action conditioning, geometric interaction, and multi-function training within the shared representation.

We present CoTL, a framework that learns a compact set of tokens that preserves scene geometry and appearance from unposed multi-view images. Our encoder compresses the input images into small per-view sets of latent tokens that aggregate information across views to form a view-consistent scene representation. Each additional view expands the representation with only a small, resolution-independent set of tokens, allowing its capacity to grow with the available observations. To force this compact bottleneck to retain sufficient scene information, a query-based Gaussian decoder uses scene-independent queries to attend to the learned tokens and recover an explicit, renderable set of 3D Gaussian primitives. Novel-view rendering supervision trains the compact representation end to end through the reconstructed Gaussian scene. Experiments on RealEstate10K and ACID show that the resulting compact, unstructured token set supports competitive novel-view synthesis and can serve as the latent space of a generative model for 3D Gaussian scene generation. Together, these results show that 3D Gaussian reconstruction is an effective objective for compact scene representation learning and the learned token space provides a basis for broader downstream tasks in 3D vision.

Automating AI research creates a positive feedback loop between software capability and research effort. We study a stochastic realisation of this loop in which independent, positive, multiplicative improvements arrive at a rate proportional to a power of current capability. Within this model, randomness leaves the deterministic explosion threshold unchanged but replaces the blow-up date by an explicit distribution. For equal-sized improvements the explosion time is a geometrically weighted sum of independent exponentials; its $q$-series representation gives its transforms, moments and tail behaviour, including a two-term small-time asymptotic. For Lomax-distributed improvement sizes the explosion time is exactly Gamma distributed. Self-similarity implies that, with parameters known, the relative uncertainty about the remaining time does not vanish as explosion approaches. We formulate a fixed-sample test between constant and geometrically increasing idea-arrival rates. If the baseline rate and the alternative log-rate increment $\ell$ are known, the minimum sample size at error level $\alpha$ is asymptotic to $(12z_\alpha^2)^{1/3}\ell^{-2/3}$, where $z_\alpha$ is the upper-$\alpha$ standard normal quantile. Uncertainty about the growth exponent near its critical value produces a $1/t$ tail with an explicit constant, and hence an infinite conditional mean waiting time, although explosion is certain given a positive exponent. Separate extensions show that a fixed deployment delay prevents explosion in the specified delayed-feedback models, that power-law diversion of effort shifts the growth threshold, and that in a deterministic oversight race a fixed allocation share does not change the asymptotic regime, except at a critical equality of exponents. Numerical illustrations, which are not empirical forecasts, show how timing and detectability depend on the granularity of improvements.

Disaggregated LLM serving moves each request's KV cache from a prefill GPU to a decode GPU before the response begins, and a coding-agent turn often moves the KV of its whole long context. Behind an oversubscribed packet fabric this transfer adds to time to first token (TTFT). An optical circuit switch (OCS) can give every transfer a full-rate circuit for less than an oversubscribed packet fabric costs, but a mechanical OCS needs tens of milliseconds to reconfigure. We hide this delay inside the prefill. A reservation scheduler commits each circuit while the prefill is still computing, so the circuit is ready when the KV is, and each GPU reaches the OCS over its own wavelength-multiplexed (WDM) optics on one fiber pair. In simulations of GPU clusters on real serving traces with measured prefill times on H100 GPUs, this optical KV cache network matches 400G packet fabrics with adaptive routing at 0.55 to 0.78 times the cost of a 2:1 fabric and tolerates the 50 ms reconfiguration delay of a 384-port mechanical OCS.

The fidelity of teleoperated demonstrations used for imitation learning is determined by how faithfully a robot hand can replicate the operator's posture. The posture retargeting law that the robot will execute is typically selected only once the hardware has been finalized, and conventional hand designs often neglect human-like grasping postures. We introduce PACT, an optimization based on human grasping postures that jointly optimizes the mechanical parameters of a 17-servo robot hand (link lengths, joint offsets, mounting angles, and base placements) and its nonlinear posture retargeter (a linear human-to-robot joint map, per-joint posture-IK weights, and damping). The optimization enforces full-finger correspondence (MCP, PIP, DIP, and tip of each finger) to human poses from the DexYCB dataset, and is constrained by servo interference, assembly clearances, and flat-hand protrusion, so the resulting design can be physically assembled. We fabricate the PACT Hand and validate it through teleoperation experiments and an imitation-learning demonstration. The hand reproduces all human hand keypoints with a kinematic RMSE of 3.9 mm, compared to 12.8 mm for the LEAP Hand baseline, and keeps all fingertips within 10 mm on every grasping posture, while the baseline achieves this for only 21.6% of the poses. Under matched per-joint torque limits, it lifts twice the baseline payload, 2 kg against 1 kg, and deforms a held paper cup seven times less, reaching a deformation level comparable to a human hand. It also achieves an 86% grasping success rate on YCB daily objects, compared to 64% for the baseline. Finally, as a demonstration, an imitation-learning policy trained on demonstrations collected with the PACT Hand achieved a 75% success rate at held-out placements in a can pick-and-place task. Project page: https://pact-hand-2027.github.io

In search engines and assistants, long-form RAG answers can mislead readers with claims their sources do not support. Faithfulness rewards, the share of supported sentences, train models toward fewer such claims. We show that these rewards are hacked by copying. A sentence copied from the passages is supported almost by construction, so trained models learn to copy rather than ground what they write. Common defenses only move the hack: a KL or copy penalty leaves copying in place or trades it for shorter, emptier answers and refusals. GRPO, the standard RL algorithm, makes it worse by giving every sentence its answer's advantage, reinforcing copied and grounded sentences alike. We propose Authored-Sentence Credit (ASC) , which fixes both by moving GRPO's reward and advantage from the answer to the sentence level. The reward credits only sentences that are authored rather than copied, say more than the question, and are supported by the passages. The advantage compares each sentence with every sentence sampled for the question, so one that earns no credit ranks last and is never reinforced. Across four models and two in-domain, three held-out corpora, only ASC lowers the error rate of authored sentences and writes more supported ones in every setting, by 38% and 46% at the median under held-out evaluators, giving readers more grounded information. It takes none of these shortcuts, and two LLM judges comparing whole answers prefer no baseline to the base model but rate ASC's answers on par with it. We conclude that a faithfulness reward should credit what a model writes, not what it copies.

We identify exact altermagnetic ground states of a classical Heisenberg model on a quasicrystal. Considering the Ammann–Beenker tiling as an example, we determine the ground states by exploiting the parity structure of its parent four-dimensional hypercubic lattice. The ground state hosts coplanar altermagnetic order characterized by the preserved spin-group symmetry $[C_{2x}\parallel C_{8z}]$. Without translational symmetry, the momentum-space spin splitting that usually identifies altermagnets is not directly accessible. We instead couple the spins to itinerant electrons and show spin-resolved transport with $g$-wave symmetry, confirming the altermagnetic nature in a nonperiodic system. Our results establish a geometric route to altermagnetic order in quasicrystals, connecting exact magnetic ground states to their spin-resolved transport signatures.

The Sachdev–Ye–Kitaev (SYK) model is a quantum many-body model of Majorana fermions with all-to-all random interactions. It has attracted wide interest in condensed matter and high-energy physics as a solvable model of non-Fermi liquids and holography. Fix an even integer $q\geq4$, and let $Z_N(\beta)$ be the partition function of the Gaussian $q$-body SYK model. We prove that for all sufficiently small inverse temperatures $\beta > 0$, there exists $\rho=\rho(\beta)>0$ such that \[ N^{q/2 -1}(\log Z_N(\beta)-\mathbb{E}[\log Z_N(\beta)]) \Longrightarrow \mathcal{N}(0,\rho^2). \] In addition to the mathematical results, we discuss how the proofs were developed and refined through interaction between human researchers and AI, and we describe the subsequent formalization of the main arguments in Lean 4. This work thus serves as a case study of a research workflow that integrates human insight, AI-assisted exploration, iterative proof refinement, and formal verification.

Although language is predominantly spoken, empirical tests of surprisal theory rely almost entirely on written text. In practice, surprisal is estimated using language models (LMs) trained on text and applied to transcriptions, creating a text bottleneck that limits evaluation of the theory in the spoken modality. We remove this bottleneck by estimating surprisal directly from the speech signal using a speech LM. This raises a key question: should surprisal be defined over realization-specific acoustic inputs or over abstract linguistic units? Since a single unit can have many distinct acoustic realizations, each assigned a different probability by the model, defining surprisal over abstract units is difficult. To address this, we introduce an importance sampling estimator that approximates the probability of an abstract unit by marginalizing over realizations generated by a text-to-speech model. Using pupillometry data from a listening study, we evaluate surprisal theory in this text-free setting at multiple levels of granularity. Obtaining surprisal from several speech LMs, we consistently find that surprisal estimated via importance sampling better predicts pupil dilation than realization-specific surprisal for words. We also find that surprisal values for sub-lexical units are predictive of pupil dilation. While we find that surprisal can be estimated without recourse to text, and that marginalizing over distinct realizations of words is more predictive of lexical processing effort, surprisal as a whole is not a strong predictor of change in pupil size, regardless of its source.

Molecular fragments provide chemically meaningful units, but existing molecular languages rarely make their locations and connections explicit for editing. Here we introduce STAMP (Sequential Tree Attachment-based Motif-Preserving representation), a topology-aware molecular language that connects fragment-level representation learning with precise structural editing. STAMP separately encodes motif identity, attachment sites and tree topology, making fragments reusable across contexts and subtrees directly accessible. Learned representations capture motif similarity and recurring transformations, and lower activity-cliff prediction error on 23 of 30 targets versus a matched SMILES encoder. Compatible subtree operations support scaffold-preserving optimization, ranking first among six methods on 15 of 23 benchmark objectives. A deterministic compiler enables frozen language models to act on indexed fragments, improving molecular editing, optimization, transformation transfer and change identification by 9 to 56 percentage points over plain SMILES. Together, these results establish an executable molecular language in which learned chemical units remain directly operable during design.

This paper deals with the optimal control problem for the general mean-field stochastic differential equations, in which the coefficients depend on both the state process as well as on its law. We focus on the connection between the general maximum principle and the dynamic programming principle for such a control problem. We establish the relationship between the value function of the mean-field optimal control problem and the adjoint equations in the maximum principle. We also give a general mean-field stochastic verification theorem. Some examples are solved explicitly to illustrate our results.

We prove that, for every $c>0$, the image of the generalized Markov-Krein transform on probability measures with finite logarithmic moment is closed under classical additive convolution and under the Mellin convolution. This resolves the positivity conjecture for the additive high-temperature convolution, a one-parameter interpolation between classical and free convolution arising in random matrix theory and representation theory in the regime $N\to\infty, N\beta_N/2\to c$. Our proof relies on a convolution theorem for universally prestarlike functions.

Referees increasingly use large language models (LLMs), while finance and accounting journals disagree about whether to allow it. We ask which part of a referee's job the models can do. GPT-4o, whose training data end before the 2024 conference season, referees the papers presented at the 2024 AFA and NBER finance meetings, and we compare its verdicts with publication in the top-three finance journals over the next two years. Papers the model scores one standard deviation higher are 44% more likely to be published, net of author reputation. The result is not driven by look-ahead bias, as the model does not recall the outcomes. The information comes from its judgements of correctness and exposition. Its judgements of originality and significance carry none, and a referee guide that stresses importance does not help. The split between correctness and contribution holds for accounting papers and for a newer model, GPT-5. LLMs can check whether research is right, but not whether it matters. The technical check can go to the model, while the judgement of contribution stays with people.

Expected improvement based on stochastic kriging (SK) surrogate is widely used in continuous simulation optimization, but unknown heteroscedastic noise makes three basic design choices consequential: the incumbent to define improvement, replication allocation, and final recommendation. Existing methods typically either assume the noise levels are known or choose these components separately through heuristic rules or empirical calibration. We instead derive a high-probability upper bound on the simple regret and systematically choose the three components within general rule classes to tighten this bound. We first establish a finite-sample confidence bound for the SK predictor as a foundation for the three design choices. Within general posterior-quantile rule classes, tightening the regret certificate selects a lower-quantile incumbent and an upper-quantile recommendation among sampled designs. The opposing quantiles reflect the different roles of exploratory experiments and the final implemented decision. Under mild conditions satisfied by common kernels, minimizing a tractable kernel-specific bound yields a logarithmic replication order. Based on these design choices, the resulting simple regret matches the existing results under known homoscedastic noise up to logarithmic factors. To our knowledge, this is the first simple-regret guarantee of this form for a continuous-domain EI-type simulation optimization method that learns unknown heteroscedastic variances through replications.