Science & Mathematics

Let $K\subset\mathbb{R}^d$ be a strictly convex body and let $Z\subset\mathbb{R}^d$ be a finite set of sites in general position. We consider the problem of calculating the volume $μ_d$ of $\bigcup_{z\in Z}(z-K)$. Let $V_z$ be the Voronoi cell of $z\in Z$ with respect to the convex distance function induced by $K$, and let $N$ be the nerve of the Voronoi cells. When $K$ is a ball, a classical result reduces the inclusion-exclusion formula to a sum over $N$: $μ_d(\bigcup_{z\in Z}(z-K))=\sum_{J\in N}(-1)^{|J|+1}μ_d(\bigcap_{z\in J}(z-K))$. When may the hypothesis that $K$ is a ball be dropped? We show that for $d\leq 2$ the reduced formula holds for every strictly convex $K$, while for each $d\geq 3$ there is a strictly convex $K$ for which it fails. For $x\in\mathbb{R}^d$, let $χ_x$ be the Euler characteristic of the subcomplex of $N$ induced by the sites lying in $K+x$. A sufficient condition for the reduced formula to hold is $χ_x\equiv 1$ on the union. When $d=3$ and $K$ is $C^4$, we show that $χ_x\equiv 1$ on the union for all $Z$ in general position if and only if $K$ is an ellipsoid. The proof relies on the Fubini-Pick affine invariant.

On-policy self-distillation (OPSD) supervises student-generated trajectories with a reference-conditioned version of the same base model. We ask whether every trajectory supplies distinct supervision that warrants its distillation cost. Gradient measurements on Qwen3-1.7B at initialization reveal that correct and incorrect responses have similar individual gradient magnitudes, but incorrect responses have approximately three times the coherent gradient share. Their estimated population-mean directions also largely overlap. A signal--noise model fitted at a small group size tracks alignment at larger group sizes without refitting. Motivated by these measurements, we introduce correctness-filtered OPSD (C-OPSD), which generates one response per problem and distills only a subset of incorrect responses. Removing unselected rows before both distillation forwards avoids their teacher/student forward and student backward work. Across Qwen3-1.7B, 4B, and 8B on AIME24, AIME25, and HMMT25, C-OPSD achieves on-par performance with full OPSD. In a measured micro-batch-size-four implementation, executed rows decrease by approximately 68%, and with retained rows packed into full micro-batches, training takes about 40% less time while rollout generation remains unchanged. Together, the measurements and training results connect outcome-conditioned supervision redundancy to more compute-efficient distillation.

Large language models are increasingly asked to shop on a user's behalf, which lets seller-controlled content such as badges, endorsements, and framing steer what they recommend. That poses the question at the core of generative engine optimization (GEO): not whether seller content shifts an agent's choice, but how much. The usual gauge of that influence, how often a cue wins the choice, has a blind spot: once a cue is strong enough to be picked almost every time, the choice rate can no longer show how much stronger one cue is than another. We introduce price-equivalent (PE) auditing, which removes this ceiling by pricing the cue in money. In a counterbalanced, position-controlled forced choice, we raise the cued product's price until it is chosen only half the time, and report that premium as the cue's price-equivalent: a formally defined, policy-conditioned parity threshold that makes very different cues comparable. Priced this way, cues that look equally strong at equal price differ by a wide margin, so choice-rate audits substantially under-resolve seller influence. We run the audit over 113,472 trials, seven models across families, and two product categories. To our knowledge, we also run the first price-equivalent audit of a decision-native model, Jev, which outputs a choice probability directly instead of generating text; strikingly, its profile is unlike any text model we tested, resisting most cues yet remaining susceptible to the strongest social-proof claims. We release the stimuli, logs, and code as a benchmark that reports each model's cue-price profile rather than a single score, giving developers and auditors a common, reproducible way to measure how content moves AI shopping agents.

Training high-quality diffusion models is computationally expensive, and inference-time guidance often adds further sampling cost. In this work, we introduce Swift, a simple yet effective self-guided training method that uses a frozen weak denoiser to improve a stronger model without adding inference overhead. For each noisy input, Swift extrapolates the clean regression target away from the weak denoiser's prediction, amplifying components that remain underfit. The weak guide can be an early training checkpoint, requires no backpropagation during main-model training, and is discarded afterward. The resulting model retains the original sampler and supports both conditional and unconditional generation without label dropout or an unconditional branch. We explain this mechanism through a spectral analysis of finite-time population gradient flow in an RKHS. With an early-stopped weak guide, we prove that a nonempty range of extrapolation strengths yields strictly lower posterior-mean error than matched standard training, despite shifting the regression target away from the posterior mean. Experiments on CIFAR-10 and ImageNet-256 demonstrate improvements across model scales and representations. In one ImageNet-256 configuration, Swift surpasses the baseline's best FID using roughly half the total training compute, including guide preparation and training overhead. On RAEv2, it achieves FID 1.15 without inference-time guidance and 0.99 with guidance. These results establish target extrapolation as an effective approach to weak-to-strong diffusion training with efficient single-model inference.

Whether a language model "knows what it knows" matters for trustworthy deployment and for deciding when it should abstain. Prior work usually measures this through one channel: verbalized confidence, a linear probe on hidden states, or agreement among sampled answers (semantic entropy), and often treats these as interchangeable. We compare all three in a pre-registered audit of five Qwen2.5 models (0.5B-7B, including a base/instruct pair at 7B) on factual retrieval (PopQA, SimpleQA) and multi-step reasoning (GSM8K, MATH). First, probes trained on prefill states to predict whether sampled answers will disagree become informative earlier for retrieval (about 7% of layer depth on average) than for reasoning (about 28%). The pre-registered five-layer test supported this only marginally; a finer 21-layer follow-up, designed after those results, supports it more clearly. In most retrieval cells, however, a prompt-only TF-IDF classifier matches the probe, so the early signal may reflect surface features of the question. Second, verbalized confidence is unstable: slightly different prompt templates yield scores that barely correlate. Third, Expected Calibration Error is misleading: verbal confidence looks well calibrated because it clusters near the base rate while discriminating poorly, whereas sampling agreement has worse ECE but about twice the resolution. Of five pre-registered hypotheses, two were falsified, one was partly supported, one was not supported, and one could not be tested because the base model's verbal confidence was degenerate.

Generator--critic trading systems pair an LLM-based trader that makes trading decisions with a red team agent that evaluates these decisions and provides feedback for revision. However, improving individual trading decisions does not ensure that both agents learn from experience and improve together over time. This raises an important question: how can the trader and red-Team select useful experience and learn from each other's evolving behavior? On one hand, experience that benefits decisions under one market condition may become ineffective or harmful under another. On the other hand, trading outcomes reflect both agents' actions, making it difficult to derive appropriate experience for each role. In this work, we propose ACE-Trader, an adversarial co-evolution trading framework. Specifically, we first develop separate context-dependent memory selectors that learn to identify useful experience for the current trading decision. Both selectors receive shared feedback from net-return differences between complete memory-assisted and memory-free trading pipelines, with online updates emphasizing recent outcomes. We further design a co-evolution mechanism that links role-specific memories through shared trading records. We use these records to evaluate the Red-Team's risk assessments and the effects of the Trader's revisions against realized market outcomes, then derive experience for their respective memories. By linking this experience to the corresponding records, we enable the Trader to improve its proposals based on prior critiques and the Red-Team to adjust its review focus as the Trader's behavior changes. Experiments on U.S. stock trading show that ACE-Trader outperforms all 22 active baselines in cumulative return and achieves the highest Sharpe ratio and lowest maximum drawdown across both active methods and passive benchmarks.

Open-vocabulary human-object interaction detectors describe interactions in free text, and this creates a problem for evaluation. Category scoring rejects valid paraphrases, while semantic similarity scoring can reward predictions that name the wrong action or reverse the roles of the participants. We present a diagnostic protocol that holds every prediction fixed and scores it under five views, namely official category evaluation, an identity control, lexical normalization, graded semantic credit, and strict propositional equivalence. Comparing these views separates the effect of the matching engine from the effect of semantic credit. The protocol pairs controlled transformations that preserve or break meaning with a blinded audit of natural predictions, and we derive consistency checks that link mean credit, invalid acceptance, and transformation counts. Applied to six systems on HICO-DET, the views disagree on which system leads. GEN-VLKT leads under official evaluation, SL-HOI leads under SHOE, and GEN-VLKT leads again under strict equivalence. Semantic gains range from 1.6 to 20.3 mAP, and AgentHOI keeps less than half of its gain once equivalence is enforced. We recommend that semantic scores be reported together with relational validity and paired uncertainty, so that recovered credit is not read as better interaction understanding.

Rubrics are widely used to evaluate open-ended question answering by breaking overall quality into explicit criteria. These explicit criteria make rubrics a rich source of learning guidance, yet their potential for guiding the training process has been largely overlooked. Existing methods use rubrics mainly as direct feedback signals, without explicitly modeling the capabilities behind their criteria. This leaves their capability structure largely unused in guiding the training process. We introduce Rubric-Structured Reinforcement Learning (RSRL), an RL framework that unlocks the full potential of rubrics by exploiting their structure throughout the training process, rather than treating them simply as direct reward signals. At its core, RSRL builds on three key designs: (1) Rubric-to-Capability Structuring first recovers the capability structure hidden in rubric criteria, (2) Self-Sufficient Capability Learning then uses this structure to bootstrap underdeveloped capabilities into effective learning, (3) Capability-Residual Credit Routing finally preserves capability-specific gains during optimization. Experiments show that RSRL consistently improves both overall performance and underdeveloped capabilities, boosting downstream scientific question-answering performance by up to 7.43 over the initial policy and 7.60 over non-rubric structured RL baselines, showing that reinforcement learning can substantially benefit from the capability structure encoded in rubrics.

Multi-agent systems driven by large language models (LLMs) rely on structured communication topologies to facilitate information exchange and collaborative reasoning. However, effectively scheduling these topologies to dynamically determine who talks to whom and when to communicate remains a fundamental challenge in balancing collective reasoning performance against exponential token overhead. Existing topology scheduling approaches either enforce static communication graphs that cannot adapt to dynamic problem-solving states, or overlook agent role complementarity while failing to explicitly incorporate the synthesized graph structure into team-level decision evaluation. To tackle these limitations, we propose ACTS, a role-aware adaptive communication topology scheduling framework for efficient LLM multi-agent collaboration. Orchestrated within a Centralized Training with Decentralized Execution (CTDE) paradigm, ACTS introduces a novel dual-attention mechanism. Specifically, a Role-conditioned Relational Attention module dynamically selects variable-cardinality interaction partners based on agent roles and evolving execution states, while a Topological Attention Mixer explicitly embeds the directed communication topology into team value decomposition for precise credit assignment. Comprehensive evaluations across 9 challenging benchmarks covering code generation, multi-step reasoning, general knowledge, and competitive mathematics demonstrate that ACTS consistently outperforms state-of-the-art baselines, boosting average accuracy by up to 6.19 percentage points while reducing token consumption by over 15%. The project website is available at https://acts-mas.github.io/ACTS/.

Multi-agent systems (MAS) can complete a task despite local execution errors that are corrected, bypassed, or carried forward without individually determining its outcome. We call these implicit failures (IFs) and study them as signals for process observability beyond final task outcome. Across 1,828 traces from nine MAS-benchmark configurations, IFs occur in 54.3% of successful and 75.2% of failed traces. We develop taxonomies of error types and subsequent absorption mechanisms, supported by human and cross-model annotation audits. Counterfactual replay further probes how repairing an IF changes the final outcome. To examine the practical value of IFs, we evaluate IF-based best-of-N trace selection against existing process reward models, and introduce a novel RL algorithm, IF-GRPO, that uses IF costs to refine preferences among successful trajectories in GRPO. Experiments show that IF-GRPO exhibits some gains in accuracy and process metrics. Importantly, it exposes trade-offs between task performance, IF count and cost, and token-normalized IF density. Overall, our results show that IFs provide complementary process observability into how MAS reach their outcomes, including error recovery, propagation, and IF-based process differences that final task success alone does not expose.

Histopathology is central to cancer diagnosis, but morphology in Hematoxylin and Eosin (HE)-stained images does not directly reveal the molecular states that characterize disease heterogeneity and inform tumor characterization, prognostic assessment, and biomarker discovery. Spatial Transcriptomics (ST) measures spatially resolved gene expression, providing molecular information within tissue architecture, yet differences in assay coverage and spot informativeness make paired HE--ST observations unequally reliable for representation learning. We propose Reliability-Guided Spatial Transcriptomics (REST) supervision with Biological Program Bank (BPB), a program-structured and reliability-guided ST-supervised training framework for predicting molecular information from H\&E images. REST constructs BPB from curated signature, pathway, and cell-type gene sets to provide a shared structure for ST encoding, reliability estimation, and molecular reconstruction. Guided by BPB, Spot-Reliability Contrastive Alignment (SRCA) measures the reliability of each spot from assay-level program coverage and spot-level activity dispersion, and reweights HE--ST alignment accordingly. Biology-Informed Program Reconstruction (BIPR) further uses learnable program queries to reconstruct member-gene expression from histological morphology. REST's training corpus comprised 209 samples (407,475 spots across 16 organs); evaluation used 70 disjoint samples (230,056 spots across eight organs) for gene-expression, pathway-activity, and cell-signature prediction. REST achieved the highest Macro correlation among state-of-the-art ST-supervised training methods and outperformed existing pathology foundation models. Code is available at https://github.com/lanfz2000/REST.

Witsenhausen's counterexample has resisted a closed form solution for decades. However, it has remained unknown whether a mathematically tractable representation exists or not. In this paper, we solve this open problem, showing that the optimal policies are either linear or not tame and characterizing the exact regions where the two properties hold. Moreover, in the linear optimal region, we give an essentially unique closed form solution for the optimal policy, and show that no optimal first-stage policy is definable in any $o$-minimal expansion of the ordered real field in the nonlinear optimal region.

Financial communication connects numerical accounts of economic activity with explanations of performance, responsibility and future expectations. Arabic financial natural language processing offers methods for studying these connections across corporate reports, market disclosures, journalism and banking interactions. Its contribution to digital humanities depends on retaining the relationship between a computational representation and the document from which it was made. This chapter follows that relationship from source collection and Arabic text processing to the analysis of vocabulary, evaluation, entities, causal attribution and multilingual reporting. It then examines what financial summaries and retrieval-grounded answers preserve or lose, and how dialectal intent detection changes the perspective from institutions speaking to institutions listening. Published Arabic resources are discussed in relation to the questions they were designed to answer, with a distinction between financial pretraining corpora, annotated datasets and evaluation benchmarks. A running constructed example connects the methodological discussion without presenting illustrative analysis as empirical findings. The chapter argues for an account of Arabic financial NLP in which linguistic context, documentary provenance and interpretive judgement remain part of the evidence throughout the analytical process.

Direct Preference Optimization (DPO) learns from pairwise preferences through a logistic objective whose score-difference parameterization follows the Bradley--Terry model. We study how failure of this modeling assumption limits DPO, distinguishing structural misspecification from limited model capacity and finite-sample estimation. Our main contribution is a characterization of structural approximation error through the triangle-curl of the preference log-odds, which vanishes exactly when preferences admit a Bradley--Terry representation. We upper bound the achievable excess logistic risk by a score-class approximation term and a triangle-curl term, and establish a lower bound proportional to triangle-curl under additional boundedness assumptions. For ReLU score models, including clipped models, we derive explicit approximation rates showing that increasing capacity can eliminate the score-approximation term while leaving the structural obstruction unchanged. We further establish finite-sample bounds for clipped empirical risk minimizers that separate network approximation, structural misspecification, and estimation error. We place these results within a surrogate-risk framework by identifying contextual preference accuracy (CPA) as a natural measure of agreement between preference judgments and changes in pairwise probability ratios relative to the reference policy. Standard logistic consistency and calibration results connect DPO's objective to this policy property and transfer our excess-risk upper bounds to CPA, without treating CPA as a complete measure of generated-response quality.

Large language model agents are often deployed in environments where new knowledge, tools, and workflows keep arriving. Such an agent is therefore expected to adapt continually, learning new tasks as they arrive without forgetting earlier ones. This resembles the continual learning problem, but at a pace that conventional gradient updates cannot sustain. Nonparametric self-evolving agents are a natural alternative: they adapt by rewriting their own harness, such as prompts, memory, and skills, from task feedback while the model weights stay frozen. We study whether such agents are effective continual learners across four drifting task streams that shift in topic, workflow, or domain (built from BIRD, BFCL, and ScienceWorld). Evaluating three representative methods spanning experience retrieval and self-modification (ReasoningBank, GEPA, and Meta-Harness), we find that although self-evolution improves aggregate performance on most streams, higher plasticity consistently comes at the cost of stability. Specifically, self-modifying methods apply global edits to a shared prompt or workspace, interfering with unseen tasks and overwriting earlier knowledge as the stream shifts. Conversely, similarity-based memory retrieval localizes updates across distant domains, but still retrieves foreign memories on unseen tasks and suffers from retrieval collision when similar queries require conflicting workflows. These findings show that current self-evolving agents remain incomplete continual learners.