Papers

We present several models of strategic choice concerning equilibrium reasoning and behaviour, as well as new applications to dynamic games. We propose concepts such as historical equilibrium, simple Nash equilibrium, cautious backward induction, and an approach inspired by how chess players reason in sequential games.

Artificial intelligence (AI) is increasingly embedded within scientific computing workflows that combine simulation, data processing, optimisation, visualisation and experimental or observational components. Learned models may serve as explicit workflow components, retain persistent state and, in adaptive settings, influence subsequent computation. Existing work has characterised scientific workflow management systems, dynamic and steered workflows, AI–HPC coupling motifs and the machine-learning lifecycle, although these areas are often discussed separately. This review brings them together from a systems perspective. We distinguish conventional scientific workflows, machine-learning pipelines, AI-coupled high-performance computing (HPC) workflows and broader automated research workflows, and propose a continuum describing the depth of AI participation from a computational stage to co-adaptive workflow control. The associated systems requirements are organised around five concerns: control and orchestration; compute and execution; data and model state; reproducibility and provenance; and governance and assurance. Representative systems and applications include AI-steered molecular simulation, drug and materials discovery, simulation–surrogate coupling and distributed self-driving laboratories. Workflow-level evaluation is considered in terms of scientific progress, execution cost, data movement, resource use, resilience and decision traceability. We conclude by identifying open problems in dynamic workflow representation, state-aware recovery, heterogeneous scheduling, interoperable data planes, model-mediated decision provenance and reproducible adaptive execution.

Most artificial neural systems are built to map given inputs to outputs. Adaptive agents face a prior problem: they must act without enough evidence, seek encounters with the world, and revise behavior when evidence appears. We propose another starting point for intelligent neural networks: proactive search without signals, curiosity at its most basic. We ask whether it can come from a minimal untrained circuit. The spiking unit studied here inverts its response to input: with no signal in its window it fires faster; once signals arrive it switches to a slower, inverted regime. Search needs three or more such oscillators in counter-phase, each reading the same input in a different time window. With no training, supervision, parameter tuning, or controller, the composite switches on its own between exploratory spiral search and exploitative tracking, finding both first-degree symmetry and second-degree groups. The switch comes from temporal disagreement between its fast and slow readings of the same signal. We view the circuit as evolutionarily trained: its abilities come from structure, not experience. Ablation over 63 configurations and 63,000 trials shows the switch needs both temporal staggering and counter-phase opposition, neither enough alone: the behavior is emergent, not programmed. The spiral persists at zero rotational diffusion, so it is structural, and degrades gently under perturbation. More oscillators improve spiral regularity but cut resource capture, so the smallest sufficient circuit wins. We propose that this principle underlies search in simple organisms, navigation and decisions in complex ones, and, being so simple and common, goes unnoticed unless you strip the logic bare. Eventually, networks of such proactive primitives may offer another foundation for AI architectures that explore our world rather than merely predict the next symbol in a sequence.

Accurate rare-event estimation can be computationally expensive. Classical adaptive importance sampling (IS) schemes often rely on restrictive proposal families and can struggle under multiple failure modes. We propose FAMIS, a flow-based multiple importance sampling (MIS) framework that learns a nonuniform mixture of normalizing flow proposals for rare event estimation. The method does not require presampled failure data or prior knowledge of the number, location, or geometry of the failure modes. Instead, it adaptively learns the mixture through sequential evaluations of the limit state function. To guide training toward the failure domain, FAMIS uses a smooth rare-event surrogate and a tempered target sequence. A defensive exploration mixture improves early-stage coverage, a Rao Blackwellized update adapts the mixture weights, and a Jensen-Shannon repulsion term promotes separation and diversity among the base components. The final failure probability is computed with a deterministic-mixture MIS estimator. Numerical experiments demonstrate that FAMIS accurately approximates quasi-optimal IS densities with fewer training samples and model evaluations, providing stable variance reduction across complex reliability problems.

We present a simplified proof of the Erdős-Sós conjecture on trees in graphs, which is based on its recent resolution by GPT-6 Astra. At the same time, we also give another proof of the corresponding conjecture for antidirected trees in digraphs, posed by Addario-Berry, Havet, Linhares Sales, Reed, and Thomassé, and we simplify recent proofs of Kalai's conjecture for tight trees in hypergraphs. Our proof uses the language of random cyclic orderings in order to take advantage of symmetries that were obscured in the original argument, and we hope that the reader will find it intuitive. We also characterize the extremal examples for Kalai's conjecture, and we generalize it to the setting of so-called fully directed $r$-uniform hypergraphs, whose edges are ordered $r$-tuples.

A lattice Dirac operator designed to preserve exact chiral symmetry by weighting the derivative with a quenched random field—the chiral disordered fermions (\CDF) of [L.\ Jacobs, Phys.\ Rev.\ Lett.\ 51, 172 (1983)]—is reexamined with modern tools. We show that the disorder-averaged operator satisfies $\anticomm{\Deff}{\gfive}=0$ exactly, to all orders in disorder strength. Disorder lifts the doubler degeneracy, driving doublers off the real axis into a complex mass while the physical mode remains protected, but does so through non-Hermiticity rather than a Ginsparg–Wilson relation. Consequently the axial index vanishes in every formulation: the Hermitian trace $\Tr(\gfive D)$, the bi-orthogonal index for non-Hermitian operators, and the algebraic Riesz-projector index, including at exceptional points. The \CDF operator therefore cannot reproduce the axial anomaly: its failure is enforced by the exact chiral symmetry it preserves. We classify neighboring constructions by the Dirac channel carrying the lattice structure. Disorder in the $\g_\mu$ channel preserves chirality, realizes an Altland–Zirnbauer chiral class, and cannot carry an index; disorder in the $\mathbb{1}$ mass channel breaks chiral symmetry and yields Callan–Harvey/domain-wall physics. A one-parameter family interpolates between them, with the 1983 operator and Kaplan's domain wall as opposite limits, distinguished not by disorder itself but by the channel it occupies. This unifies lattice-QCD undoubling with the tenfold-way classification of disordered Dirac fermions and settles the disorder route to chiral lattice fermions.

Wildlife–vehicle collisions (WVCs) impose a large toll on U.S. highways, yet state crash databases often fail to record animal involvement, leaving agencies uncertain of the true missing count. This study evaluates whether existing crash records can identify individual WVCs and estimate overall unrecorded rates. We analyzed 4.9 million crash records from Colorado, Utah, Iowa, and Illinois (2007-2026). Each state's schema underwent a label-leakage screen to exclude explicit animal fields before harmonization into a shared vocabulary. Calibrated gradient-boosted classifiers were trained per state, interpreted using Shapley additive explanations, and evaluated for prevalence estimation via Adjusted Classify-and-Count and Maximum-Likelihood techniques across in-domain, cross-state, and synthetic reporting-gap scenarios. Detection performance depends heavily on record completeness rather than collision rarity. At ~4% prevalence, feature-rich Utah achieved an average precision of 0.88 versus 0.64 for feature-poor Colorado, and outperformed Iowa despite Iowa's 3x higher WVC rate. Within-state richness curves confirm feature depth drives accuracy. While classifiers ranked records accurately across states, probability calibration did not transfer directly. However, in-domain prevalence estimation recovered true collision rates within 0.001. This work shifts WVC analysis from spatial clustering to record-level detection and missing-data estimation using legacy datasets. Transportation agencies can retrospectively flag unrecorded WVCs, quantify total collision burden to support mitigation funding, and identify high-value reporting fields prior to revising crash-report manuals.

Background. Women who experience forced sexual violence face elevated risks of poor mental and physical health, but whether long-term health follows distinct trajectories and whether healthcare access and social support differentiate them remains unclear. Methods. We analyzed 1,848 women from the National Longitudinal Study of Adolescent to Adult Health (Add Health), followed from adolescence into adulthood. An identified Bayesian mixture model classified joint mental and physical health burden trajectories from six repeated indicators. Bayesian logistic models estimated associations of forced sexual experience, healthcare access, social support, and demographics with trajectory membership. Robustness was assessed across three mixture specifications and four- and five-class alternatives. Results. We retained three classes: low-burden/resilient (27.2% posterior mean weight), moderate/worsening burden (43.2%), and high chronic burden (29.7%). All specifications converged ($\hat{R}=1.00$) with well-separated classes; four- and five-class alternatives had convergence problems or an unstable additional class. Forced sexual experience was associated with higher posterior odds of high chronic burden (OR = 3.78, 95% credible interval [CrI] 2.84–5.04) and moderate/worsening burden (OR = 1.63, 95% CrI 1.26–2.12). Better healthcare access and greater social connectedness were independently associated with lower posterior odds of high chronic burden. \noindentConclusions. Long-term health after forced sexual experience follows heterogeneous trajectories. Healthcare access and social connectedness distinguish more favorable trajectories and represent modifiable targets for trauma-informed, longitudinal, survivor-centered care.

Zavarzina asked whether every bijective non-contractive self-map of a precompact quasi-metric space is an isometry. We show that it need not be, even when the space is hereditarily precompact. On the integers, take the distance of an irrational rotation and add a fixed toll $c>0$ to every step from a nonnegative integer down to a smaller one. The resulting space, the toll spiral, is a hereditarily precompact quasi-metric space, and the shift $n\mapsto n+1$ is a bijective non-contractive map that is not an isometry. The construction works over any metric space $Y$: for every bijective isometry $\sigma$ of $Y$ and every point whose $\sigma$-orbit is aperiodic and totally bounded, adding the same toll along the orbit gives such a counterexample, for instance over the $p$-adic odometer. The conjugate of the toll spiral is not even precompact, so the hypothesis on the conjugate in Zavarzina's positive result cannot be dropped, even for bijections. The toll spiral is also not expand-contract plastic, since the inverse shift is a non-expansive bijection that is not an isometry. For an arbitrary bijective non-contractive map $F$, the distance from $F^kx$ to $F^ky$ has a limit as $k\to-\infty$; $F$ is an isometry for this limit, and the excess $D_0$ of the distance over it is the defect. On a hereditarily precompact space, we prove a monochromy theorem: if a pair $(a,b)$ has positive defect $\eta$, then there are natural numbers $t_1<t_2<\cdots$ such that either $D_0(a,F^{-\Delta}a)>\eta/4$ for every difference $\Delta=t_j-t_i$ with $i<j$, or $D_0(F^{-\Delta}b,b)>\eta/4$ for every such $\Delta$. Three boundary results delimit the remaining question; the open case, that of separated spaces compact in one of their topologies, has since been settled by the author (arXiv:2610.14301). The construction, in general and for the circle, is machine-checked in Lean 4 using Mathlib, with no unproved steps.

Estimating a ground-state energy and preparing a ground state both split into a front-end that supplies an approximate state $|\chi\rangle$ and a back-end that reads or refines it. We argue, and measure at every step, that the only thing crossing that split is the front-end's spectral weight distribution $p_n=|\langle E_n|\chi\rangle|^2$ over the eigenstates of the problem Hamiltonian $H_P$. Everything downstream is priced in it, so the front-end is a swappable module, and we swap it seven times without altering anything to its right. We call the arrangement WARP. Four back-ends spend that distribution. A readout (A) samples $g(t)=\langle\chi|e^{-iH_Pt}|\chi\rangle$ on the device and extracts true eigenvalues by classical signal processing, returning an energy below the variational bound of the state it was handed, from a signal $50\times$ shorter than a Fourier transform needs. Three routes spend the same account on a state instead. An adiabatic schedule (B) has a minimum gap set by the overlap; a discrete amplification (C) is cheaper in depth but must halt at an index the overlap fixes, so it needs a measured value and not a bound; a recursion (D) of depth $\mathcal{O}(3^m)$ raises the question of whether it can be run at all. The interactions are the substance. On stretched N$_2$ a sample-based diagonalisation reports a variational bound 79 mHa high, fifty times outside chemical accuracy; reading the state it has already prepared returns $E_0$ to $1.4\times10^{-6}$ Ha, three orders of magnitude inside it, and needs no new front-end and no new circuit. And because the weights price everything, they must be measurable when scarce, so we beat a weak reference against a strong one and recover overlaps four orders of magnitude below the shot-noise floor. We map the operating envelope throughout, and state the limitations.

We consider the identification of memory and stochastic forcing in a one-dimensional generalized Langevin equation with state-dependent Brownian noise and optional additive symmetric $\alpha$-stable jumps. A finite-dimensional Markov embedding provides Kramers–Moyal conditional moment relations that separate memory drift, Brownian diffusion, and jump contributions. From increment ensembles conditioned on the observed velocity history, truncated statistics estimate the stable parameters, corrected second moments determine the Brownian amplitude, and first moments lead to a Volterra equation for the memory kernel, solved by RKHS regularization. We establish conditional finite-sample bounds for the moment estimators and a conditional $L^2$ error bound for kernel recovery with a data-selected regularization parameter. Numerical experiments examine Brownian and Brownian–Lévy models under different forces, memory kernels, observation lengths, measurement noise, and approximate history conditioning.

Let $q=3q_0^2$, where $q_0=3^s$ and $s\ge3$. We prove that a smooth, projective, geometrically irreducible curve over $\F_q$ with $q^3+1$ rational points and genus \[ \frac32q_0(q-1)(q+q_0+1) \] is $\F_q$-isomorphic to the Ree curve.

Voxel-based volumetric mapping is fundamental to 3D reconstruction, yet fixed-resolution grids remain inherently inefficient - wasting memory in uniform regions and losing detail in complex ones. Existing adaptive methods, such as MAP-ADAPT, partially address this by varying resolution based on geometry and user-defined semantic class lists, but these heuristics require expert tuning, lack generalization to unseen objects, and provide no explicit mechanism to control memory usage. We propose an adaptive framework that refines voxels based on semantic entropy, which captures label uncertainty, together with geometric curvature and texture richness as scene complexity cues, yielding principled resolution allocation without reliance on semantic taxonomies. To make the accuracy-memory trade-off explicit and user-controlled, we further introduce a reinforcement learning agent that learns voxel subdivision policies under a user-specified target memory budget, replacing hand-tuned thresholds with a single intuitive control parameter. The resulting multi-resolution TSDF achieves higher geometric accuracy, better semantic consistency, and improved memory-accuracy trade-offs compared to MAP-ADAPT and fixed-resolution baselines on both synthetic and real-world datasets. Our code and models are available at https://github.com/alpayozkan/UnRL.

Entanglement cost is the asymptotic rate of Bell pairs required to prepare a quantum state. Its regularized definition has made exact evaluation difficult, even for isotropic states (i.e., depolarized maximally entangled states). In this work, we determine the entanglement cost of every qubit isotropic state and, more generally, every two-qubit Bell-diagonal state. Our proof uses a family of suitably tuned qubit semigroups to transform a general log-Sobolev entropy bound into supporting lines of Wootters' function. A recent exact tensorization theorem of Dong et al. [arXiv:2606.17729] extends these bounds to arbitrarily many copies, yielding a general lower bound on entanglement cost. Matching this bound with the entanglement of formation also determines the exact cost for a broader class of two-qubit states. For qudit isotropic states, we derive another general lower bound from the full depolarizing $2\to 3$ norm. This bound substantially improves on the PPT-relative entropy of entanglement and nearly matches the entanglement of formation, leaving a gap of at most $2\%$ of $\log d$ that vanishes as $d$ grows. Finally, the exact qubit results and qudit bounds extend to the entanglement cost of preparing quantum depolarizing channels under both parallel and sequential strategies.

White men without an undergraduate degree receive the lowest average ratings among eight gender-race-education groups in controlled large-language-model evaluations of credit, hiring, and rental applications. We conduct full-factorial vignette experiments with 18 models from 12 developer groups, varying gender, race, age, citizenship, and education while holding stated financial or occupational circumstances constant within each setting. Each model evaluates all 32 profiles ten times per setting, yielding 17,280 ratings. Averaging over models, age, and citizenship, ratings for White men without degrees are the lowest among the eight groups, at 75.87 in credit, 92.71 in hiring, and 86.62 in rental housing on a 0-100 scale. Black women with degrees receive the highest average ratings, with corresponding gaps of 2.94, 3.66, and 3.56 points. Separate attribute effects favor women, Black applicants, and degree holders in all three settings. White men without degrees have the lowest or second-lowest mean in 46 of 54 model-scenario combinations (85.2%). This pattern connects to evidence of growing economic and health vulnerabilities among White men without degrees, highlighting a group whose disadvantages can be obscured by broad racial or gender categories.

Dendritic silhouettes are cheap. Pond ice neurons, diffusion-limited aggregates, wiring-minimizing arbors, and biological neurons can share a branching statistic because they share a growth instability, not because they are functionally similar. We take that observation as a modeling constraint. The ice neuron only structurally resembles a biological neuron. A biological neuron carries an internal state and a field that it helps generate, letting geometry, dynamics, and field co-sculpt one another. In our construction, the ice neuron is the zero-gain limit of an interfacial system in which a FitzHugh–Nagumo state lives on the moving front and writes back into the field that drives it, with dimensionless gain $\gamma$. At $\gamma=0$, morphology and internal dynamics decouple into a Mullins–Sekerka growth band and a damped oscillator. Finite $\gamma$ deforms the spectrum, shifts the selected instability, and opens an oscillatory region below the isolated Hopf threshold. On a dendrite grown at $\gamma=0$ and then frozen, field closure increases distal persistence without changing the geometry; its first-order effect remains positive across repeated realizations of the same growth rule and localizes to a small set of non-cable field shortcuts. Nonlinear dynamics remain finite beyond the linear instability: below threshold, closure is almost the transmission; at spike amplitude, it is a correction to a regenerative cable event. A dendritic tree therefore is not intrinsically a structural spandrel. Shape alone is morphology without an internal state or a source term. That is the dendritic silhouette of the ice neuron. Excitability adds an active cable. Field closure is the biophysical mélange in which the neuron helps write the field that acts back on it, sculpting its dynamics and, during growth, its structure. That is a biological neuron.

Event contracts reach economic finality through different institutional paths. Polymarket distinguishes oracle adjudication, adapter consumption, Conditional Tokens payout recording, technical redeemability, and optional holder redemption. Kalshi distinguishes venue determination, public finalization, lifecycle messages, and exact REST settlement fields. Resolved, settled, and finalized do not themselves define comparable endpoints. We define a mechanism-aware comparison certificate using functional roles rather than common labels. A scalar cross-venue duration is admissible only when payoff semantics, endpoint functions, calendar support, censoring, observation grades, and dependence units are jointly aligned. We separate exact paired, interval-qualified paired, and standardized unpaired estimands. Polymarket evidence contains 108,638 exact-linked conditions, 99,283 protocol payout records, 92,158 observed redemptions of any amount, and 91,817 observed positive-payout redemptions. Kalshi evidence contains 152,694 ordinary markets reconstructed as at risk at the enrollment boundary and 7,611,594 exact MVE market objects. Exact public endpoints cover 71,657 ordinary markets and 7,357,576 MVE objects. Exact determination-to-endpoint pairs total 70,979 for ordinary markets and 126,806 for MVE. These are Kalshi-native finality results, not Polymarket-Kalshi estimates. REST endpoint completeness can be high when exact lifecycle paths are sparse, and transport gaps can preserve two exact clocks while preventing claims about intermediate revisions. Current MVE timer fields do not identify historical version-consistent timer rules, and public finalization does not identify member cash. Cross-venue numerical comparison remains blocked until Paper 7.3 supplies blind first/stable decidability clocks and a semantic/calendar registry establishes genuinely comparable events and endpoints.

Valid Model Context Protocol (MCP) messages do not guarantee that an agent framework preserves the distinctions downstream software needs. We present a differential testing method that follows a fixed tool result through each framework's public interfaces and checks explicit consumer requirements. Applied to 18 designed fixtures in four pinned Python integrations, the method identifies 13 unique fixture-task divergences involving structured values, declared errors, and rich content. Google ADK satisfies every primary contract in its observed path; the other integrations show interface-specific changes or an execution failure. Whether a change matters depends on the consumer: treating absent optional fields as equivalent to null explains most of OpenAI's strict rich-content failures. In an exploratory replay, parsing JSON text recovers more structured values but also returns incorrect values and values for fields absent at the source. Documented settings help in conflicting-output stress cases without restoring a separate structured slot. Fault challenges expose an oracle weakness and test its repair on fresh cases. The study provides reproducible, interface-specific evidence from controlled cases, not production failure rates or model-behavior measurements. Its practical implication is that post-wire regression tests need to specify both the information required and how the consumer reads it.

We study statistical estimation on implicit weighted similarity graphs presented as node-arrival streams. Previous work~\cite{LZ26b} obtained constant-pass, sublinear-space algorithms for several basic statistics of such graphs, including the diversity index $\mathsf{DI}=\sum_i d_i^{-1}$ and the degree moments $M_p=\sum_i d_i^p$ for $p>0$, together with their associated sampling problems $L_{\mathsf{DI}}$ and $L_{M_p}$. We settle three questions left unresolved by the previous work. First, we show that any two-pass streaming algorithm that $1.1$-approximates $\mathsf{DI}$ requires $\Omega(n)$ bits of space; combined with the three-pass $\tilde{O}(\sqrt n)$-space algorithm of~\cite{LZ26b}, this establishes a sharp transition between two and three passes for $\mathsf{DI}$. Second and third, for every fixed $c>0$ we give a three-pass $n^{-c}$-perfect $L_{\mathsf{DI}}$-sampler using $O_c(\sqrt n\log n)$ words and a two-pass $n^{-c}$-perfect $L_{M_p}$-sampler using $O_{p,c}(n^{1-1/(p+1)}\log n)$ words. Matching lower bounds up to polylogarithmic factors show that both the number of passes and the polynomial dependence on $n$ are optimal.

Large language model (LLM) judges are often used as rewards to train policies on objectives that deterministic verifiers cannot capture. However, these rewards are often collapsed to pass/fail ({0, 1}), which reports the verdict but not how well a response met each criterion. We model each pass/fail verdict as a score on an unreported scale, compared with one cutoff. A stretch of that scale moves every score proportionally toward or away from the cutoff, but never across it, so no verdict changes. A policy is therefore free to apply any stretch without changing anything the panel reports. Under a joint-Gaussian model, a third grade adds a second threshold and removes this affine stretch ambiguity. On MATH and SciBench outputs from one seven-criterion judge, all 14 constructed criterionwise stretches were invisible after binarization but visible with three grades. At $n=1{,}024$, a test given both population laws had at least 96.5% power at a $1.5\times$ stress. Retaining grades closes one blind spot created by binarization, but verdicts alone remain insufficient as some changes are still indistinguishable from genuine improvement. These include arbitrary within-grade changes and fixed-covariance, loading-aligned mean shifts – the signature of a sycophancy-shaped lift the panel reads as competence. The shared-factor reference approximation fit MATH and SciBench but not HealthBench, delineating its empirical scope. We recommend keeping at least three grades (for example, asking the judge whether each criterion is fully, partially, or not met and rewarding {0, 0.5, 1}), and externally validating gains along the remaining direction, which no finer scale removes.

Invoices are commercial documents that contain various pieces of information, including the purchased items, time, and total money. Making the extraction of important information crucial. The stored information serves different purposes. Korean language is the native language of about 80 million people, playing an important role in not only South and North Korea but also in many other countries such as Vietnam, Philippine where a large number of Korean companies are located. In this context, to automatically extract proper information from the invoices with Korean language, we propose an efficient Optical Character Recognition (OCR) model in which a deep learning model is combined with some image preprocessing techniques. The proposed OCR model is assessed in a rich set of collected invoices showing that 87% F1-score can be achieved with negligible time processing.

Asthma deterioration forecasting must remain reli- able when patient populations, sensor ecosystems, and available modalities change across cohorts. Existing models commonly optimize within-cohort discrimination and may produce poorly calibrated probabilities after transfer. We present CALIBRA, a calibration-first multimodal temporal framework for short- horizon risk prediction with incomplete data. Dedicated recurrent encoders process environmental, pulmonary, symptom, medication, wearable, and context streams; a reliability-conditioned gate suppresses stale or absent modalities, while gradient-reversal training discourages avoidable cohort signatures. A shrinkage- based hierarchical logistic layer calibrates probabilities using a patient-disjoint target subset, and split conformal prediction provides abstention-capable prediction sets. To avoid fabricating clinical evidence, we evaluate the complete implementation on a documented three-cohort semi-synthetic benchmark with controlled distribution shift, informative missingness, and sealed target patients. Across five configured seeds, CALIBRA achieved mean target-test AUPRC 0.224 versus 0.240 for the strongest non-ablation comparator, TemporalTransformer; mean AUROC was 0.717, and Brier score was 0.098. Experiments additionally assess complete-modality failures, calibration, conformal coverage, decision curves, subgroup behavior, ablations, runtime, and parameter count. The results verify the method and reproducible pipeline under controlled shift, but do not establish clinical effectiveness. External validation on harmonized real asthma. Overall this artifact provides evidence for carefully governed real-cohort validation.

Just as Socrates recognized the limits of his own knowledge, Retrieval-Augmented Language Models (RALMs) should learn to abstain when the retrieved evidence cannot support a reliable response. Existing approaches largely rely on monolithic LLMs to handle heterogeneous retrieval failures in a single step, resulting in limited abstention performance and high computational costs. We instead decompose retrieval failures into two distinct states: (i) the unanswerable state, where the required evidence is absent, and (ii) the distracted state, where relevant evidence is mixed with conflicting, negated, or adversarial information. Based on this decomposition, we introduce a lightweight module (Sieve) that screens retrieved document sets for distracting evidence before invoking a costly LLM (Sage) for grounded generation and abstention. Evaluated across both general and high-stakes expert domains, our Sieve and Sage framework preemptively detects distracting noise, improving system accuracy by up to 69.4 percentage points and Macro-F1 by 55.2 percentage points compared to one-stage baselines. Furthermore, it achieves up to a 1.99x speedup, establishing a highly efficient and reliable abstention pipeline for RALM with abstention.

Sampling many responses and keeping one that passes a verifier lets large language models solve problems beyond their single-response ability, but this search must be paid again for every query, while many deployments answer with a single response. Post-training on verified responses can transfer the benefit of search into the model. With a fixed budget, selecting by correctness alone spends slots on problems the model already answers correctly, leaving fewer to correct its failures. To address this imbalance, we propose GapFT, which trains on the gap between Pass@K and Pass@1: problems that the source model fails with one response but solves within K samples. GapFT keeps the objective and training budget fixed and changes only which verified responses enter training; an exact decomposition splits the resulting Pass@1 change into corrected failures and regressions on problems the source model already solved. On LogiQA 2.0 and ReClor with three model families, GapFT is above budget-matched uniform rejection-sampling fine-tuning (RFT) in every setting, with a positive pooled effect, and on Llama-3.1-8B and Mistral-7B it recovers about two thirds to four fifths of the gain of fine-tuning on the entire verified pool with 11-34% of its problems. Further analyses reveal that the gain comes from failures that the first few search samples recover, while failures found only by deeper search displace replay and add no net gain, that filling the same budget with gold-labeled failures search cannot reach lowers accuracy, and that the gain is bounded by how many transferable failures search exposes.

Industrial predictive maintenance increasingly depends on learning from equipment spread across sites whose sensor data cannot easily be pooled. Federated averaging (FedAvg) solves this with a central aggregation server; gossip learning removes the server, but its behaviour for recurrent failure-detection models has not been measured under controlled conditions. We compare synchronous ring gossip with FedAvg, isolated local training and a centralized reference for a stacked LSTM that detects imminent failure on the NASA C-MAPSS turbofan benchmark. All methods share one open implementation, architecture, initialization, optimizer, data split and training budget, and the primary endpoint uses one terminal window per test engine to avoid the statistical dependence of overlapping windows. On FD001 (five seeds), gossip reached a terminal-window F1 of 89.6 +/- 1.3%, compared with 89.9 +/- 1.1% for FedAvg, 83.6 +/- 6.7% for local training and 93.5 +/- 2.1% for centralized training, while transmitting the same payload as FedAvg without a coordinator. Node models agreed closely but not exactly (1.8% pairwise decision disagreement versus 5.6% without communication). Across FD002-FD004, peer communication improved terminal-window F1 over local training by 13-28 points; gossip matched FedAvg on FD003 and FD004 but was 4.3 points lower on the multi-condition FD002 subset. Simulated message loss, node failure and server outage changed neither method appreciably, whereas larger rings degraded gossip faster. Ring gossip is therefore a practical serverless alternative when data heterogeneity is moderate, and faster-mixing topologies become important as heterogeneity grows.

Let A be a nonempty compact subset of the plane and let A (r) be its parallel set at distance r. We prove that the number of holes of A (r) the number of bounded components of its complement, which is its rst Betti number satises $\infty$ r 0 $\beta$1(A (r) ) dr $\le$ 4050 (diam A) 4 r -3 0 for every r0 > 0, the integrand vanishing for r $\ge$ diam A/ $\sqrt$ 3. The proof rests on Fu's theorem that the critical values of the distance function of a planar compact set form a set of vanishing half-dimensional Hausdor measure, on two lemmas of Rataj, Spodarev and Meschenmoser, and on a square-root summability estimate for the gaps of the critical-value set, of which we give a complete proof. We show by an explicit family of curves two combs facing each other that no analogous bound can hold at a xed radius: a connected curve of bounded length, diameter, oscillation count, parallel-set area and parallel-set perimeter can have arbitrarily many holes at one radius, so the integrated estimate cannot be replaced by a xed-radius bound in terms of these coarse geometric quantities. We also bound the hole count uniformly in the radius by the number of components of local maxima of the distance function, and record a bound on the boundary length of a parallel set by its area. The results supply the deterministic input for limit theorems on the persistent homology of the Wiener sausage.

Explainable Artificial Intelligence (XAI) solutions are essential for building trust in AI technologies and their integration in real manufacturing lines. However, most existing methods are tailored to technical experts, limiting their accessibility to diverse user groups such as blue-collar workers in manufacturing lines who use AI for quality control. In this work, we introduce an XAI interface for object detection in industrial manufacturing based on a fine-tuned vision-language model, designed to generate intuitive explanations for non-expert users. We benchmark existing vision-language models and demonstrate that out-of-the-box models often fall short in delivering clear, context-relevant explanations for non-expert users. To address this, we fine-tune a vision-language model and integrate it into our interface, enabling contextualized, accessible explanations for non-expert users. We demonstrate improvements in explanation clarity, instruction adherence, image groundedness, and contextual awareness over GPT 4o-mini on proprietary and public robotics dataset. This approach advances the accessibility and usability of AI explanations, making them more intuitive and applicable in manufacturing domain.

Boltzmann counting possesses an exact scale invariance from which the specific entropy emerges without asymptotic approximation. Under thermodynamic replication, this invariance exposes the Gibbs excess at the multinomial level. Its resolution reveals a state-dependent scale structure whose additive refinement generates a continuum reference measure, giving a combinatorial origin to the reference structure of continuous statistical mechanics. The resulting entropy is relative to this measure, and for an ideal gas the scales acquire operational meaning through reversible work.

Video watermarking underpins copyright protection and provenance for generated media, yet almost every video is compressed by a codec before it is stored or shared. A codec discards precisely the perceptually redundant components that most watermarks rely on, so the payload is often lost even when the marked video looked flawless beforehand. Existing methods leave this path open, since they treat compression as one entry in a generic list of distortions, while a real codec is not differentiable and cannot enter gradient-based training. We present COVER, the first learned video watermark built around codec compression as its design target, which survives that compression by embedding the payload in the latent space of a frozen generative video autoencoder and recovering it by re-encoding the received video into that same latent space. To make codec robustness trainable, we build a differentiable codec surrogate bank that simulates the dominant degradation modes of practical compression, and we train the embedder and the latent decoder through three shared recovery paths under a fidelity objective that constrains the residual in the pixel and frequency domains. Across four codecs at 12 settings, COVER attains 93.72% average bit accuracy, ranks first on 11 of the 12, improves the strongest prior method by 2.68 points, and lifts the worst operating point from 68.90% to 73.72% while each marked video stays visually close to the source clip that produced it.

Inspired by the flight and song of birds, we propose an approach that enables cooperating agents to effectively identify obstacles in their environment by having a stationary source agent emit a frequency-modulated chirp while one or more listener agents observe the direct and reflected signals while in motion. We present a novel mapping approach that exploits the “frequency gap” between direct and reflected chirp signals to define candidate reflection ellipses, which are then fed into a 2D accumulation filter to identify locations with the highest density of potential reflections. We demonstrate this work first with simulation results derived from an efficient, bespoke audio simulator, examining the effect of obstacle count, sampling rate, and path curvature on the ability to accurately identify environmental obstacles for a one-listener scenario. We then examine different cooperative motion strategies for two-listener configurations. Finally, we validate the real-world viability of this approach through field experiments in an outdoor park setting to demonstrate the ability to identify frequency gaps using off-the-shelf hardware. Our results provide a foundation for a low-cost approach to environmental mapping in swarm robotic systems.