Papers

Post-training is central to mathematical reasoning in modern large language models (LLMs), but endpoint pass@1 alone underidentifies what has changed. Gains may reflect newly reachable solutions, cheaper sampling of latent solutions, surface robustness, or memorisation. We compare three post-training paths under a common diagnostic readout: our sufficiently trained off-policy distillation trajectories, released Qwen3 off-policy-plus-on-policy distillation endpoints, and a released DeepSeek-Math endpoint trained with Group Relative Policy Optimisation (GRPO). Our probe uses cross-surface pass@K over verbatim prompts, paraphrases, numerical isomorphisms, and translations, plus consistency, distribution-shape, and verified supervised-fine-tuning (SFT) membership analyses. We find two regimes. On easier AMC problems, large-K ceilings are near saturation, so post-training mainly compresses sample cost. On harder AIME problems, post-training expands the large-K ceiling over the base model: sufficient off-policy distillation already raises this ceiling, Qwen3 released endpoints raise it further, and DeepSeek-Math GRPO does not dominate sufficient off-policy distillation at large K. English-dominant distillation improves non-English reasoning but preserves language-tier gaps. A controlled-overfit audit finds limited sensitivity in current SFT-membership probes. Compression is one regime of post-training, not a universal explanation.

Decision-making under uncertainty often relies on predicted parameters, yet accurate prediction does not necessarily lead to good operational decisions. Aligning prediction with downstream optimization requires learning from the consequences of the decisions those predictions induce. We introduce RL-PaO, a reinforcement learning framework that integrates system formulation, optimization, and decision execution into a single environment. This yields a Markov decision process in which prediction is regarded as action: it shifts the environment to produce subsequent context and reward that explicitly aligns prediction error with realized cost, and learning the optimal policy does not require differentiating through the black-box solver. We evaluate RL-PaO on day-ahead energy scheduling using real historical data. On the test year, RL-PaO achieves the lowest annual cost among the non-oracle baselines, achieving on average $10\%$ cost reduction. Moreover, RL-PaO is capable of further analyses to provide strong interpretability both from the policy evolution perspective and the cost-accuracy trade-off.

AI models trained on the same data can disagree about patient risk, with disagreement potentially concentrated in clinically important subgroups. We propose V(S), a statistically grounded vulnerability index combining an observable lower-bound witness of model disagreement with clinical severity, and develop inference and multiplicity-adjustment procedures for auditing prespecified subgroups. We applied the framework to two large critical-care cohorts, MIMIC-IV (n = 65,078) for model development and eICU-CRD (n = 188,230 admissions, 208 hospitals) for external validation, comparing a random forest with logistic regression across 158 prespecified subgroups. The two primary models did not both satisfy the prespecified epsilon = 0.02 Rashomon-set tolerance: the logistic-regression AUC was 0.0488 below the best candidate-model AUC. The RF-LR discrimination gap is thus interpreted as disagreement between two specific models, not as a guaranteed lower bound on the full Rashomon set. Nine subgroups had discrimination gaps distinguishable from a prespecified clinical floor. The age >=80 and cardiac subgroup had the largest point estimate of V(S) (0.307), but was underpowered and did not meet the full high-priority decision rule. The univariate cardiac subgroup (V(S) = 0.193, 95% CI [0.163, 0.223]) was the only statistically distinguishable subgroup with adequate power. Post hoc analyses identified lactate as important for both models but did not establish a causal explanation for the disagreement. Four simulation studies quantified operating characteristics of the proposed procedures, including inflated small-sample detection rates and imperfect Wald-interval coverage. The framework offers a reproducible approach for ranking subgroup vulnerability to model disagreement while separating exploratory signals from adequately supported findings.

We study when logarithmic regret is attainable in structured adaptive linear-quadratic regulation. The state and input matrices depend affinely on a common unknown parameter. We consider neighborhoods of a known nominal model that is stabilizable and observable through the output associated with the state cost, with radii proportional to the inverse fourth root of the horizon. The key condition is controller identifiability, which requires the optimal gain derivative to vanish in every parameter direction that leaves the closed-loop dynamics unchanged under nominal optimal feedback. Under suitable regularity conditions on the noise density, this condition at the nominal parameter yields logarithmic local minimax regret when the gain derivative there is nonzero. Failure of the condition yields square-root local minimax regret. If the nominal gain derivative vanishes, local minimax regret remains bounded. We prove that controller identifiability is equivalent to the optimal gain remaining unchanged under sufficiently small invisible perturbations of the nominal model. Motivated by this invariance, we construct a certainty-equivalent policy that estimates only the visible parameter component and attains the logarithmic upper bound under controller identifiability. The policy requires neither the horizon nor the noise law, and its guarantee holds for independent, identically distributed noise with zero mean and finite positive definite covariance.

Dynamic layer skipping reduces LLM computation by allowing each token to execute only a subset of the model's layers. However, existing skippers rely on specialized generation loops and do not integrate with modern serving engines. As a result, fewer executed layers do not necessarily translate into lower serving latency: FlexiDepth skips 8 of Llama-3-8B's 32 layers on average, yet its standard generation loop decodes 14.6–21.0% more slowly than the base model. We present vSkipper, a virtualization layer that makes dynamic layer skippers pluggable in serving engines while preserving continuous batching, fixed-shape batches, paged KV caching, and captured decode graphs. At each routed layer, vSkipper groups tokens by the skipper's decision and uses routed execution only when predicted to be profitable. We implement vSkipper in SGLang and evaluate the released FlexiDepth checkpoint against upstream SGLang under identical prompts, arrivals, output lengths, and launch settings. At the knee of upstream's load curve, vSkipper reduces mean end-to-end latency by 36.8% on GSM8K and 13.6% on BBH. Under saturation, it increases request throughput by 11.3% and 7.4%. Serving adds no statistically resolved quality loss beyond the checkpoint's own. Across synthetic skip policies, two Qwen3 skippers, and three GPUs, we demonstrate reuse without workload-specific tuning. To our knowledge, vSkipper is the first system to realize serving-efficiency gains from per-token interior layer skipping within a modern LLM serving engine. The code is open-sourced as an SGLang fork at https://github.com/AKafakA/sglang-vskipper/tree/vskipper-ref

We view fairness as a property of distributional stability. Rather than assessing a predictor under a fixed data distribution, we study how its predictions change under perturbations that modify the composition of protected groups. A predictor is fair if it remains stable under such shifts. Under this perspective, several classical notions of fairness arise as stability with respect to specific perturbations, with the associated unfairness gap given by a Lipschitz constant of a prediction-rate functional. This formulation also yields guarantees that hold uniformly over a range of demographic compositions at test time, without requiring knowledge of the deployment distribution. It leads to a learning procedure based on convex combinations of reweighted predictors, formulated as a second-order cone program, for which we establish generalization bounds. Experiments on standard benchmarks illustrate the approach.

This paper revisits Willis' elastodynamic homogenization (Mechanics of Materials, 41 (2009) 385-393) of periodic laminate composites and uses the equivalent inclusion-based method (EIM) to evaluate the unique effective constitutive properties with eigen-fields. The microstructure-specific Green's function is essential in Willis's exact homogenization method, which was derived from the corresponding periodic laminates. Our re-examination identifies several algebraic differences in the published formulae for the Floquet number and the related effective properties. In parallel, this paper simulates inhomogeneities with a comparison medium containing two eigen-fields, namely eigenstrain and eigen-momentum, to simulate stiffness and mass density mismatch, respectively. Therefore, the general Green's function can be directly used. The exact homogenization method with the updated specific Green's function is compared to the proposed EIM with eigen-fields homogenization scheme, and excellent agreement is obtained. The present paper provides a base to extend the homogenization framework to multi-dimensional Willis-type homogenization.

Proximity effects, in which one subsystem imprints its properties onto another, offer a route to controlling quantum matter. For localization, this raises the question of whether an extended system can be localized by its neighbor, and then delocalized again, in the regime of weak quasiperiodic disorder. Here, we demonstrate this behavior in a coupled Aubry–André ladder, where a staggered detuning applied to only one leg localizes the neighboring, undetuned leg through inter-leg hybridization, even before the detuned leg itself localizes. Upon further increasing the detuning, the undetuned leg undergoes re-entrant delocalization, while the detuned leg remains localized. Finite-size scaling supports the persistence of these regimes in the thermodynamic limit. On an IBM Quantum processor, we experimentally observe their dynamical signatures: strongly suppressed wave-packet spreading in the proximity-localized regime and its recovery upon re-entrant delocalization. Our results establish leg-selective detuning as a reversible control knob for localization and transport in coupled quantum systems.

Quantum transport simulations that combine density functional theory (DFT) with the nonequilibrium Green's function formalism (DFT-NEGF) are important to modern technology, yet their unfavorable scaling has long confined predictive simulations to small, idealized systems far below the ten-thousand-atom scale of realistic devices. Here, we introduce HamGNN-NEGF, a linear-scaling framework with DFT-level fidelity. An E(3)-equivariant graph neural network trained on conventional DFT Hamiltonians of small structures predicts Hamiltonians for large devices, avoiding costly DFT-NEGF training data. The predicted Hamiltonians are integrated with DFT-derived electrode self-energies, a nonorthogonal kernel polynomial method for Fermi-level determination, and a recursive Green's function algorithm, yielding a computational cost that scales linearly with device length at fixed cross section. Even for devices containing fewer than 500 atoms, HamGNN-NEGF achieves speedups exceeding three orders of magnitude over fully self-consistent DFT-NEGF, with the advantage increasing further with system size. Benchmarks on pristine Pt-Si-Pt, doped Pt-Si:P-Pt, and Pt-molecule-Pt junctions demonstrate meV-level Hamiltonian accuracy, faithful transmission spectra, and predictive simulations beyond 10,000 atoms. Eliminating transport self-consistency also enables hybrid functionals such as HSE06 without additional NEGF overhead, while a zero-bias Hamiltonian approximation extends the framework to finite-bias transport in weakly nonlinear regimes. HamGNN-NEGF thus bridges first-principles accuracy and device-scale simulation, providing a practical route toward predictive modeling of realistic nanoelectronic and quantum devices.

Achieving strong performance with graph neural networks (GNNs) typically requires training and hyperparameter tuning for each dataset, incurring repeated costs and effort. Graph in-context learning (ICL) avoids this by using a single pretrained model to predict unknown node labels directly from labeled context nodes. Existing approaches, however, rely on dense attention across nodes, making inference increasingly expensive as graphs grow. In this work, we present Ephris, a new graph in-context learner built on sparse message passing, scaling linearly with the number of node-feature entries and graph edges. Ephris is pretrained entirely on synthetic graphs generated from structural causal models with diverse graph structures and relational dynamics, exposing the model to varied dependencies among topology, features, and labels. We evaluate Ephris on 51 node-classification datasets against 15 extensively tuned GNNs and existing graph ICL methods under both high- and low-label train/validation/test splits. Across both settings, Ephris ranks first on all four aggregate measures: Elo, improvability, average rank, and accuracy. Its inference cost remains comparable to training a single GNN once, while being over 10 times faster than previous graph ICL models. Together, these results advance the performance-runtime Pareto frontier, demonstrating that strong graph ICL does not require dense attention. Code and model weights are available at https://github.com/nums-ai/ephris.

Evolutionary program search driven by large language models (LLMs) has produced record-breaking constructions for open problems in combinatorics and beyond. We apply this approach to the longstanding problem of improving the best-known bounds for binary linear codes. Building on the EvoTune evolutionary framework and the ShinkaEvolve codebase, we introduce LinCodeEvolve, which evolves code-construction programs against an exact minimum-distance evaluator. A strategy loop combines diversity-driven search and expert supervision: when progress plateaus, new strategies are used to redirect the search. LinCodeEvolve discovers seven record-breaking codes, $[172,21,66]$, $[173,20,68]$, $[176,21,68]$, $[181,21,70]$, $[184,21,72]$, $[189,22,72]$ and $[200,21,77]$, six of which have concise quasi-cyclic descriptions. With standard code modification techniques, they improve $22$ entries of the tables. Every code is verified by exhaustive enumeration. These results suggest that LLM-guided search can help find improved codes and complement existing methods in coding theory.

Vision-language models (VLMs) increasingly operate in embodied and spatially grounded settings, where accurate understanding of depth, viewpoint, and three-dimensional relations is essential. However, improving spatial reasoning typically relies on ground-truth answers, answer-derived rewards, or other forms of task-specific supervision. We introduce Spatial-OPSD, a label-free self-improvement framework that instead exploits spatial structure naturally available from perception and reconstruction tools. During training, a privileged teacher receives automatically obtainable spatial priors, such as depth, reconstructed 3D relations, and camera geometry, while the student observes only the original visual-language input. On trajectories sampled by the student itself, the teacher provides dense token-level supervision, allowing the student to internalize spatial knowledge without ground-truth answer labels or privileged information at inference time. To extend this supervision beyond a single round, we adopt a round-wise recursive training scheme: the teacher remains frozen within each round to provide a stable learning target, and the improved student initializes both teacher and student in the next round, where privileged spatial priors re-establish an informative teacher–student asymmetry. This enables repeated self-improvement while avoiding a rapidly moving teacher during optimization. Across four VLM families, a single round of Spatial-OPSD consistently improves the five-benchmark average, while three rounds further push a strong spatially specialized model to the open-source frontier, achieving the highest average among the open models and the best results on three of five spatial reasoning benchmarks. Our code is available at https://github.com/vermouth599/Spatial-OPSD.

Ensuring the safety of reasoning large language models (LLMs) across languages is essential for their reliable deployment. However, when exposed to jailbreak attacks in non-high-resource languages, these models may generate unsafe responses even when their reasoning traces identify safety risks. To address this issue, we propose aligning cross-lingual thoughts and responses (ACTR), a framework that improves multilingual safety alignment by strengthening the use of existing safety reasoning. Specifically, we first present the think gap score (TGS) to compare the normalized contributions of reasoning traces to attention outputs during response generation across languages, and use reasoning- trace substitution to measure the cross-lingual safety gap. Next, using a corpus of jailbreak queries, we assess neuron importance through changes in response representations caused by neuron masking and compare the high-importance neuron sets obtained with reasoning enabled and disabled to identify safety think neurons that support the use of safety reasoning. Finally, we devise neuron-selective consistency optimization (NSCO), which uses a frozen judge model to reward agreement between the safety categories of reasoning traces and responses while updating only the parameters associated with the selected neurons, requiring no human-annotated responses or preference data. Across two reasoning models, ACTR achieves lower average attack success rates than the evaluated state-of-the-art methods on AdvBench-X and MultiJail, with safety gains extending to unseen languages, while preserving or improving average performance on multilingual knowledge and mathematical reasoning tasks and limiting false refusals of benign requests. Warning: this paper contains examples with unsafe content.

Multimodal GUI agents have achieved impressive results on general software benchmarks, yet their ability to operate professional scientific software remains largely unexplored. In materials science, sparse domain-specific web data, specialized interfaces, and tacit workflow conventions create blind spots that general-purpose pretraining cannot readily bridge. We present MatToolBench, the first real-environment benchmark for evaluating multimodal GUI agents on professional materials science software, comprising 204 tasks across 10 tools in three modalities: GUI operation, OriginPro scripting, and code-based database queries, all executed inside a Windows 11 VM. Each task is decomposed into fine-grained sub-criteria by domain experts, enabling interpretable partial-credit scoring; the GUI component of our multi-level evaluation pipeline achieves an average F1 of 0.98. For OriginPro figure-generation tasks, we further conduct a human-LLM agreement study to validate the use of a multimodal judge for secondary aesthetic assessment. Our experiments show that strong performance on general benchmarks does not transfer to professional scientific workflows, and that this gap is not a visual-grounding problem alone: failures arise from domain-specific operational knowledge, sparse pretraining coverage of scientific software, weak cross-tool artifact handoff, and critical states exposed only visually. Even the best model reaches only 25% success rate on GUI tasks and 45% on code tasks. MatToolBench therefore serves as a challenging diagnostic benchmark and real-environment testbed for data-scarce, knowledge-intensive scientific workflows.

Omnimodal large language models (Omni-LLMs) encode audio and visual streams into temporally interleaved token sequences for multimodal reasoning. However, processing long audio-visual token sequences incurs substantial prefill costs. Existing compression methods have made progress, but often overlook temporal changes in audio-visual semantic relevance. Motivated by temporal variation and local continuity, we propose OmniRoute, a training-free, two-stage compression framework. First, Temporal Evidence-Guided Budgeting (TEGB) derives chunk-wise modality preferences and initial leading-modality budgets from semantic relevance and local content variation. Second, Budget-Constrained Semantic Compression (BCSC) compresses the leading modality and then calibrates the follower's retention target using the actual retained fraction. For video, it combines spatiotemporal grouping with query-guided selection; for audio, it selects tokens based on encoder attention and query relevance, then merges residual tokens into context anchors under visual guidance. Experiments on four representative benchmarks demonstrate a better trade-off between inference efficiency and performance than competitive baselines. The code and interface will be released to facilitate further research.

This paper investigates spatial productivity convergence across Chinese provinces during structural transformation, examining how a shift in auonomous demand composition reshaped regional productivity dynamics. Using Panel Structural Vector Autoregressive modelling and province level data from 2001 to 2021, we analyse eastern, central, ad western regions across two sub-periods through the augmented Kaldor-Verdoorn law. A post-2011 spatial reversal emerges: inland regions exhibit stronger Verdoorn coefficients, while fiscal multipliers converge across coastal and inland areas, validating China's redistributive fiscal policies in narrowing regional productivity gaps. The Kaldor-Verdoorn coefficient remains robust throughout, while export effects on productivity collapse and government expenditure effects strenghten.

We infer the initial condition for the Balitsky-Kovchegov (BK) evolution equation at next-to-leading order accuracy from HERA proton structure function data. A simultaneous description of both the total cross section and charm production measurements is obtained. We then show that inclusive hadron production in deep inelastic scattering can provide complementary constraints on the non-perturbative initial condition of the BK equation. As a more differential observable, it serves as a sensitive probe of gluon saturation phenomena. We demonstrate this by calculating predictions for the nuclear modification factor in hadron production in photon-nucleus scattering at leading order in the dipole picture. We find that saturation effects lead to significant nuclear suppression at small $x_\mathrm{Bj}$.

Disconnected diagrams remain a major challenge for precision lattice QCD calculations because of their large statistical fluctuations. We investigate a subtraction method based on a domain decomposition of the Dirac operator, yielding a biased but substantially less noisy estimator. Applying the method to charmonium disconnected correlators computed using distillation, we achieve a variance reduction of about three orders of magnitude at only twice the computational cost, providing a practical alternative to completely neglecting disconnected contributions.

Non-rigid partial-to-full shape correspondence from sparse anchors requires identifying the corresponding region on the full surface and recovering dense correspondences between the partial shape and that region. We present NHO, which combines sparse anchors with the intrinsic geometry of the partial shape to learn a neural Hamiltonian operator whose localized eigenspace encodes both the region support and intrinsic coordinates for dense correspondence. NHO parameterizes the Hamiltonian potential as an intrinsic neural field and optimizes it using anchor evidence together with spectral and geometric constraints. To resolve the spatial ambiguity left by sparse anchors, we introduce reciprocal refinement between operator estimation and correspondence recovery. At each round, the current eigenspace provides spectral coordinates and restricts matching to its induced support, while geometrically reliable correspondences provide additional evidence for updating the potential. After refinement, aggregated eigenfunction energy yields the final localization, and the recovered map initializes dense correspondence refinement. Experiments demonstrate competitive accuracy on both tasks and robustness to uniform scaling and rotation.

We propose a new spiking neural network (SNN) design to process static images and event streams using time-to-first-spike (TTFS) latencies. Our key research question is which architectural choices best accommodate local and online learning in multi-layer convolutional SNNs. This question is addressed via an original framework combining residual-like connections with multi-depth feature aggregation and consensus. The full SNN pipeline features an early-vision front end, to convert raw visual data into sparse spike latencies, a four-layer convolutional backbone trained layerwise with unsupervised spike-timing-dependent plasticity (STDP), a deterministic Multi-Depth Temporal Fusion (MDTF) and a final classifier trained with reward-modulated spike-timing-dependent plasticity (R-STDP). Rather than replacing early features in deeper layers, the proposed MDTF preserves early temporal evidence, adding sparse residual events from intermediate layers, and incorporating deeper features only when they agree in time with earlier representations. The resulting architecture is experimentally validated across MNIST, Fashion-MNIST, CIFAR-10, and N-MNIST, delivering strong classification performance under a fully local learning regime. Selective multi-depth fusion significantly outperforms traditional STDP/R-STDP baselines on higher-variability visual tasks (achieving +18.2 pp on Fashion-MNIST and +29.2 pp on CIFAR-10). Furthermore, activity-budget analyses show that the network retains high accuracy even when removing a large fraction of late or weak spike events, confirming its high data efficiency and reduced event-processing requirements. The codebase is publicly available at github.com/aidinattar/multi-depth-temporal-fusion-snn.

Vision-Language Models are increasingly used in autonomous-driving systems, yet their ability to recover dynamic physical state from visual input remains insufficiently characterized. We study velocity understanding as a controlled diagnostic across three tasks: surrounding-agent speed, current ego speed, and short-horizon future ego-speed proposal. On nuScenes, we evaluate open-weight general-purpose and PhysicalAI VLMs, together with the driving-oriented Alpamayo-1.5 Vision-Language-Action model, using multiple input and output formulations. We combine verbal evaluation with temporal perturbations, counterfactual ego-speed hints and linear probes of hidden representations. The tasks exhibit distinct failure modes. Surrounding-agent speed is weakly encoded in an agent-specific form, whereas current ego speed is often internally accessible but poorly verbalized: continuous probes achieve 4.7-5.8 km/h MAE compared with 10.2-16.8 km/h MAE for verbal outputs. Multiple frames provide inconsistent verbal gains to single frame inputs, and frame order is rarely exploited. Under non-optimized QLoRA, task-specific adaptation improves both task-relevant latent speed representations and verbal readout, but continuous surrounding-agent speed estimation remains weak, while most future-speed gains survive frame shuffling, indicating limited temporal grounding. Driving specialized Alpamayo-1.5 shows stronger latent representations for surrounding-agent and future ego speed, while current ego-speed decodability is comparable and substantial probe-verbal gaps remain. Thus, driving specialization can strengthen motion representations but does not guarantee stronger encoding across both scene and ego states or reliable readout. The results show that plausible planning outputs do not necessarily imply reliable recovery or temporal grounding of the underlying dynamic state.

Software developers often struggle to identify all locations that their changes affect, and incomplete changes frequently result from these omissions. To mitigate this problem, several approaches have been proposed to recommend additional locations that should be modified together with a developer's current change. A large class of these techniques mines co-change rules from repository revision histories, but because they rely solely on which elements have been modified together, they cannot recommend elements that have rarely co-changed, and they disregard the textual information that accompanies commits. A second class of techniques does exploit textual information, but it derives it from the source code or from a change request rather than from commit history, and it does not use the developer's current change as its input. To address these limitations, we propose GitCF, a change recommendation method that compares a developer's current change with past changes in the revision history and recommends additional change locations by combining two sources of similarity: the set of modified elements and the textual content of commits, including commit messages, code diffs, and linked issue descriptions. We evaluate GitCF on 543 incomplete changes from 17 open-source projects, where an incomplete change denotes a commit in which an omitted modification is supplied in a later commit, comparing it against three co-change-rule-based techniques. GitCF outperforms the strongest baseline on all five metrics (MAP, Recall@10, Recall@20, Hit@10, and Hit@20); in particular, it raises Hit@10 from 0.322 to 0.403, and the improvement in average precision is statistically significant.

Explicit intermediate reasoning gives large language models (LLMs) a stronger problem-solving mode. We study learning from this think-mode advantage via on-policy distillation (OPD). OPD preserves student-generated trajectories and provides dense token-level teacher targets at student-visited prefixes. Privileged reasoning is used during distillation rather than student inference. Uniform ThinkOPD, a natural think-enabled OPD baseline, conditions a fixed teacher on one shared think trace and uniformly distills every sibling student response. Although its prefixes are on-policy, the trace need not follow a route compatible with every complete response: the same privileged trace can induce different teacher-student discrepancies even when responses reach the same outcome. We summarize this interaction with trace-response divergence (TRD) and introduce ThinkOPD, which routes supervision at the response level by combining group-relative reward gain with a TRD-based compatibility proxy. Final response weights are normalized within each rollout group. Across mathematical reasoning and code generation, ThinkOPD outperforms Uniform ThinkOPD in both same-model settings and both cross-model teacher-student pairs, and it exceeds representative rationale and self-distillation baselines in a controlled comparison. Controlled interventions show that outcome benefit and the TRD-based proxy provide complementary routing signals in this setting. Think-enabled OPD provides a controlled setting for studying how teacher advantage becomes transferable along student responses.

Sampling from unnormalized distributions over large discrete state spaces becomes difficult when a multimodal target is far from a tractable reference. We introduce Iterative Exact Discrete Guidance (IEDG), a population-exact, trajectory-wise guidance framework for unnormalized discrete targets. Rather than learn the full reference-to-target correction in one step, IEDG introduces a global Boltzmann tilt along an annealing trajectory. Each stage learns a stage-local posterior correction for an incremental Boltzmann tilt of the current source, while the resulting corrections are accumulated relative to a fixed analytic posterior. At the population optimum, exact stage posteriors recover the correct reverse dynamics, whose exact simulation reproduces the target distribution. IEDG chooses stage increments by relative effective sample size (rESS), which controls Rényi-2 displacement and locally adapts the step size to the thermodynamic geometry of the annealing path. Our stagewise total-variation analysis shows that limited overlap amplifies Bregman fitting error by $1/\sqrt{\mathrm{rESS}}$, while posterior, simulation, and truncation errors enter additively. IEDG improves all distribution-level errors over the neural baselines on ordered, exactly enumerated Ising $4\times4$, while substantially reducing one-shot errors on Ising/Potts $16\times16$ across thermodynamic regimes and attaining the best neural-sampler result on several reported local-statistic and phase-coverage metrics. On Max-Cut, its best-of-512 and average-sample ratios exceed all the baselines. Code and artifacts are available at https://github.com/StillFantasy123/iterative-exact-discrete-guidance.

Video Large Language Models (VideoLLMs) have achieved strong video understanding capabilities but incur substantial inference overhead due to the large number of visual tokens. Existing VideoLLM token compression methods largely rely on selection-independent scoring, overlooking cross-frame complementarity and consequently retaining redundant evidence across frames. Instead, we view video token selection as a progressive evidence accumulation process. It aims to retain visual evidence that is individually informative and collectively complementary under a limited token budget. Building on this insight, we introduce GleanVID, a training-free inference acceleration framework for VideoLLMs. Specifically, GleanVID first allocates the global token budget across frames according to temporal novelty and then selects tokens by jointly considering local representativeness and subspace complementarity, thereby preserving richer and less redundant visual evidence. Extensive experiments across diverse VideoLLMs and benchmarks demonstrate that GleanVID consistently achieves state-of-the-art performance. Notably, with only 25% of visual tokens, GleanVID preserves 98.6% of Qwen3-VL's original performance while reducing its prefill latency by 44.7%. On LLaVA-OV-7B, GleanVID at a 25% retention ratio even slightly surpasses the original model.

Self-Distillation Fine-Tuning (SDFT) enables a language model to act as its own teacher: by conditioning on a demonstration, the model produces an implicit reward via pointwise mutual information, which guides on-policy learning without external supervision. However, SDFT operates at training time: it requires gradient updates and access to expert demonstrations, making it inapplicable at inference. We propose test-time self-distillation, a decoding-time method that extracts a steering signal from the self-distillation framework without any parameter updates, reward models, or training data. Our key insight is that counterfactual contexts, i.e. fixed textual templates that hypothetically prime the model for excellent versus poor reasoning, can substitute for the demonstration. The log-odds ratio of a candidate answer under these two counterfactual conditions defines a new reward signal. We derive the optimal KL-regularized policy under this reward, which takes the form of a Gibbs reweighting of the base distribution. Crucially, this reweighting is global: it cannot be decomposed into independent per-token operations without ignoring future trajectory quality. We therefore approximate the target distribution via beam search. Experiments on mathematical reasoning (MATH500), code generation (HumanEval), and graduate-level science QA (GPQA) across multiple model scales show that test-time self-distillation improves over standard sampling, low temperature, beam search and power sampling baselines on average, demonstrating that the self-distillation principle can be operationalized at inference time.

Natural language autoencoders translate a language model's internal activations into readable explanations. Explaining every token position is costly. Which positions should an auditor inspect to understand a potential threat? We study this question across $4.7$ million explanations on prompt injection and concealment. We compare signals from model computation with a ranker trained only on chat structure. Chat structure usually selects more relevant explanations than the computational signals, without requiring a model forward pass for position selection. On three of four datasets, explaining just $5\%$ of positions retains nearly all of the success rate from explaining every position, where success means obtaining an explanation about the threat. The benefit varies with the audit task. We also show that pretrained verbalizers recover words that models have learned to conceal through fine-tuning, without additional verbalizer training. These results identify where auditors can concentrate explanation generation and show that useful explanations can extend beyond the model a verbalizer was trained to describe.

Extreme-mass-ratio inspirals (EMRIs) offer a powerful probe of additional fundamental fields through their cumulative influence on gravitational-wave phases. However, modeling vector radiation from generic Kerr orbits requires the evolution of the Carter constant, which cannot be determined from energy and angular-momentum balance alone. Here we derive the orbit-averaged electromagnetic Carter-constant flux for eccentric and inclined, nonresonant Kerr geodesics, including sections at infinity and event horizon. Combining the gravitational and electromagnetic energy and angular-momentum fluxes, we construct generic adiabatic inspirals using a four-dimensional Chebyshev interpolation mathod. We incorporate the relativistic trajectories into the state of the art of FastEMRIWaveform package and perform Bayesian inference of vector charge carried by secondaries. Our analysis reveals substantial correlations between the charge and intrinsic source parameters, with vector charge constraints exhibiting a nonmonotonic dependence on orbital inclination. These results establish a framework for investigating additional vector-radiation channels in generic EMRIs and their implications for tests of gravity with future space-based gravitational wave observations.

Precipitation nowcasting demands accurate short-term forecasts under strong spatiotemporal variability. Diffusion models are well suited to modeling complex precipitation distributions, yet existing approaches often introduce increasingly specialized designs, leaving the capability of a standard diffusion architecture underexplored. We show that a standard Diffusion Transformer already provides a simple and scalable foundation for precipitation nowcasting, with domain-specific requirements accommodated naturally within its design space. Based on this principle, we develop NowcastDiT and instantiate this flexibility through two complementary adaptations: a dynamics-aware noise prior for temporally coherent forecasts, and end-to-end reinforcement learning with timestep-aware rewards for meteorological skill. Experiments on SEVIR and MRMS benchmarks show that NowcastDiT achieves state-of-the-art performance in both perceptual quality and meteorological skill. These results suggest that standard DiT can serve as an effective foundation for precipitation nowcasting.

High-resolution dynamic functional connectivity (DFC) can reveal rapidly evolving brain-network interactions, but short temporal windows yield noisy, often low-rank covariance estimates. Graph-Variate Dynamic (GVD) connectivity addresses this by modulating fast instantaneous interactions with stable trial-level support. This suppresses spurious fluctuations and emphasizes persistent, informative connections. We show that the Hadamard construction lifts low-rank instantaneous connectivity from the positive-semidefinite to the positive-definite cone, keeping high-resolution trajectories on the SPD manifold without ridge regularisation or post-hoc projection. We introduce GVD-CFM, a class-conditional generative model for high-resolution dynamic connectivity. Each trial is represented as SPD GVD matrices on a product Riemannian manifold, then mapped through a global log-Euclidean diffeomorphism and an invertible temporal DCT basis. A Transformer-based conditional flow models all spectral modes jointly and generates the full trajectory non-autoregressively in Euclidean coordinates while preserving exact correspondence with valid SPD sequences. Retaining the full DCT basis also enables decoding on denser temporal grids without retraining. Across multiple EEG motor-imagery datasets, GVD-CFM delivers the strongest overall results for held-out distributional fidelity, temporal-dynamics preservation, and synthetic-to-real classification. It also remains computationally efficient relative to strong raw-signal and direct GVD-space generative baselines. GVD-CFM therefore provides a practical framework for realistic, temporally coherent, high-resolution brain-network generation with preserved manifold structure and resolution-flexible decoding from a single trained model.