Science & Mathematics

Comparative judgement uses pairwise comparisons to rank items, but recovering accurate rankings from a limited number of judgements depends on both the inference method and the pairs selected. We developed a Bayesian Bradley-Terry model (BBTM) that uses Polya-Gamma data augmentation for efficient Gibbs sampling and quantifies uncertainty in latent abilities and ranks. We propose three active learning strategies based on the knowledge gradient (KG) principle. We define our acquisition functions using Kendall's tau distance, posterior rank entropy, and posterior separation. Approximate one-step updates to posterior moments reduce the computational cost of evaluating candidate pairs. We also introduce Posterior Separation Reliability (PSR), which measures the spread of posterior mean abilities relative to posterior uncertainty. It provides an internal indicator of ranking reliability without requiring a reference ranking. In synthetic experiments covering different item counts, comparison budgets, and noise levels, BBTM generally recovers ranking more accurately than preference-based Bayesian comparative judgement (PBCJ). At low to moderate noise levels, the pairwise entropy pair selection strategy performs best in ranking recovery. However, at the highest noise levels, the KG strategy based on posterior separation produces better point rankings. PSR increases alongside improvements in ranking accuracy as comparisons accumulate. Robustness experiments identify the proportion of informative outcomes needed to meet specified accuracy targets within a fixed comparison budget. In a moderate noise setting, replacing 30\% of outcomes with random choices has little effect on ranking performance. These findings demonstrate the value of Bayesian inference and active learning pair selection for recovering ranks from limited, noisy paired comparisons.

In this paper, we study the inconsistency of matrices in multicriteria group decision making under the assumption of uncertainty in their entries. The study binds together an $n$-dimensional probabilistic product measure $P$ and the Koczkodaj indicator $K_{n}$ of order $n$ used in pairwise comparisons. In the case of $n$ greater than 3, it starts with a new definition of $K_{n}$ based on the Steiner triple system of order $n$. It is of interest that the new indicator requires only $O \left( n ^{2} \right)$ evaluations, while the old one $O \left( n ^{3} \right)$. Our study results in analytic formulae for the probabilities of events $K_{n} \leq \varepsilon$ corresponding to uniform, exponential, and normal distribution functions, whenever the remainder of $n$ divided by 6 equals 1 or 3. For the remaining values of $n$, we present analytic formulae for their strict bounds. The formulae lead to much more efficient algorithms when compared with Monte Carlo simulations. This unexpected feature is illustrated by a few numerical experiments.

We are the first to give a certified rule for whether unseen data belong in a pretrained model's context or its weights, built on an exact law for their information value. That value, the code length saved on held-out queries, equals in expectation the bits stored about the query, plus a prior repair, minus a decoding loss, for any model, architecture, dataset and task. The law's ceilings certify the choice from one measurement, and an anytime-valid test makes it from held-out queries, with error controlled whenever it stops. Every certificate the ceilings issue on a trained transformer, TabPFN, an occupancy network and a stereo network is correct. The test picks TabPFN over XGBoost and a trained surrogate over an in-context learner on airfoil pressure, calls the better of GPT-2's cache and fine-tune in 61,948 of 64,000 query streams over 32 comparisons, and errs in at most 3.3% of null streams. The law also diagnoses when learning in context helps and when it does not. Deleting part of a context is held-out validation of that part in any model, and adding parts one at a time traces the learning curve in context: one patch that sees a shape feature cuts an occupancy network's code length there a hundredfold, while eight that miss it nearly double it, and one camera that sees the surface beats four in a stereo network. Ranked by this label-free valuation, a kriging learner's three best support cars beat four drawn at random, and on a yes-or-no claim the valuation recovers a published evidence adjudicator, with AUROC 0.91.

The continued demand for smaller, faster, and more energy-efficient technologies has driven condensed-matter research towards materials combining multiple responses within a single phase. Particularly interesting examples are multiferroic materials featuring cross-couplings between order parameters. Ni3TeO6 is a prominent member of this material class, exhibiting a hysteresis-free transition under magnetic field which simultaneously affects the magnetic structure, electric polarization, and phonon frequencies. Here, we uncover the microscopic origin of this multiferroic transition using a combination of neutron scattering techniques. We establish the presence of a finite Dzyaloshinskii-Moriya exchange term giving rise to non-reciprocal, chiral spin waves which soften in magnetic field. Their condensation alters the magnetic structure which controls the electric polarization and drives an ionic displacement, thereby coupling the magnetic, electric, and lattice degrees of freedom. Our study demonstrates that neutron scattering is a powerful technique to elucidate microscopic interactions in multiferroic materials, informing the design of next-generation electronic devices.

Understanding the thickness dependence of the excess energy of thin films and identifying the deviation from the scaling law that holds for thicker films are crucial for predicting the formation of two-dimensional (2D) materials derived from nonlayered structures, commonly referred to as non-van der Waals (non-vdW) 2D materials. Here, we analytically study the excess energy of thin films as a function of the number of layers $N$, assuming pair potentials. We show that the $1/N$ scaling law of the excess energy breaks down in the monolayer limit when the interatomic interactions are long-ranged. The analytical results are confirmed by numerical simulations using the Lennard-Jones and Morse potentials. The present work suggests that non-vdW 2D structures can be formed by pair potentials alone.

Among existing embedding compression approaches, low-rank factorization provides a simple and mathematically principled solution by approximating the embedding matrix with a reduced-rank decomposition. However, its practical effectiveness is often limited, as the resulting linear bottleneck constrains representational capacity. To overcome these limitations, we propose an enhanced factorization scheme that increases expressive power by introducing learnable non-linear projections within the compressed embedding layer. Our method is inspired by the Kolmogorov Arnold Networks (KAN) paradigm, which replaces fixed linear transformations with learnable univariate functions. Despite promising results in other domains, applications of KANs in NLP remain scarce and have so far been largely limited to final or task specific layers, rather than core representational components such as embedding layers. We evaluate the proposed approach by integrating the compressed embedding layer into the Skip-gram framework and comparing it against a standard low-rank baseline under matched parameter budgets on the Word Analogy and Semantic Similarity benchmarks. We further introduce an effective initialization strategy from a pre-trained, uncompressed embedding layer. The behavior of the model is analyzed both immediately after initialization and after a brief post-initialization refinement phase, considering training with the standard Skip-gram objective as well as variants augmented with distillation from the original embedding layer. Overall, our results show that augmenting low-rank factorization with learnable non-linear projections effectively mitigates the limitations of linear bottlenecks, yielding more faithful compressed embeddings under fixed dimensionality and suggesting a promising direction for embedding layer compression beyond purely linear methods.

Understanding generalization of randomized learning algorithms remains a central challenge. Mutual-information and total-variation bounds provide complementary ways to quantify data--hypothesis dependence, but they can behave quite differently in high-dimensional regimes. We study a one-parameter family of dependence measures, the vector-valued $L_p$-norm correlation $V_α$, and derive generalization bounds whose dependence terms interpolate between total variation (TV) at $α=1$ and variance and $χ^2$ related behavior at $α=2$. For $α>2$, the Hölder-conjugate loss moment is below two, yielding heavy-tailed specializations that can remain finite even when the loss variance is infinite. A particularly interpretable specialization occurs at $α=2$, where the bound can be expressed in terms of the variability of the algorithm's output density across datasets, $\int \sqrt{\mathrm{Var}_S[p(w\mid S)]}~ dw$. We show that the entire $V_α$ family is invariant under smooth bijective reparameterizations of the hypothesis space. We also introduce an adaptive density stability (ADS) condition that implies explicit control of $V_2$, and we verify it for Gibbs-type posteriors under bounded losses (yielding rates that depend on the inverse temperature and sample size). To address scaling, we extend the framework to a conditional formulation using supersamples, analogous in spirit to conditional mutual information (CMI), and discuss evaluations in the output space as a practical surrogate for estimating dependence. Simulations on Bayesian linear regression illustrate how tuning $α$ can change the tightness of the resulting bounds across regimes. Additional supersample experiments on noisy MNIST and on a pretrained ResNet-50 for CIFAR-10 show similar behavior of the projected loss-space bounds beyond the original clean-MNIST setting.

While agentic reinforcement learning (RL) has emerged as a promising paradigm for training small language models (SLMs), existing frameworks are predominantly tool-centric and struggle with data-centric environments. Specifically, applying tool-centric frameworks to stateful tasks like SQL debugging introduces severe spatial inefficiencies since proper environment isolation typically requires a separate database container per rollout. Naively reusing databases without tracking evolving states across multi-turn interactions causes trajectory contamination and cross-trajectory interference, which severely destabilizes policy updates. To overcome these bottlenecks, we introduce BIRD-RL, a novel four-stage agentic RL curriculum that alternately enhances foundational agent reasoning and trajectory-adaptive on-policy exploration to circumvent the instability inherently associated with direct end-to-end learning. Crucially, to support this curriculum, BIRD-RL is driven by a Trajectory-scoped Persistent Execution Infrastructure, which enables safe database replica reuse while preserving trajectory isolation. This design improves spatial RL efficiency by 12.8x, successfully enabling scalable agentic RL for complex data-centric tasks without needs of Kubernettes. Empirical evaluations on the BIRD-CRITIC-SQLite benchmark demonstrate that our 7B and 14B models achieve Success Rates of 44.40% and 48.00%, respectively, showing competitive performance against strong proprietary model-based agents such as Claude-Opus-4.6 Agent (48.20%). Furthermore, BIRD-RL successfully trains unified SLMs capable of both advanced SQL debugging and generation, highlighting its broader potential for multi-objective optimization across heterogeneous, real-world data-centric tasks.

Recent advances in multi-turn reinforcement learning (RL) have substantially improved the performance of LLM agents on complex, long-horizon interactive tasks. However, despite progress in fine-grained credit assignment, policy optimization still applies these learning signals through response-specific probability ratios. Different textual responses can induce the same executable effect, yet credit differences arising from subsequent outcomes remain tied to their individual textual realizations. We identify this mismatch as credit-update misalignment. Our analysis reveals that credit-text pairing directly shapes policy-update directions, even when the policy context and executable effect are held fixed. Motivated by this finding, we propose Effect-Marginal Policy Optimization (EMPO), which aligns policy optimization with execution-level equivalence through an effect-level surrogate that couples updates across alternative textual realizations. EMPO preserves the original credit signals, integrates with both trajectory-level and step-level credit estimators, and requires no additional critics or rollouts. Experiments on ALFWorld, WebShop, and Sokoban show that EMPO outperforms strong baselines in both task performance and learning efficiency.

Understanding a one-to-one tutoring video requires more than recognizing its events. A model must connect a visible teacher intervention to the learner response it elicits and to the follow-up adjusted to that response. Existing video and educational-dialogue benchmarks typically emphasize event recognition, temporal reasoning, social-state inference, or transcript-based interaction, but rarely diagnose this action-response-adjustment relation. We introduce VIRA-Bench, a focused diagnostic benchmark for short-horizon pedagogical contingency in one-to-one online tutoring. VIRA-Bench contains 1,005 tutoring clips and 1,322 multiple-choice questions with researcher evidence audit and expert verification, organized into Observable Evidence Grounding (OEG), Interaction Contingency Reasoning (ICR), and Support-Response Modeling (SRM). Across 11 models, the best reaches 61.3%, well below the 91.0% human reference on a stratified subset, and ICR generally has the lowest layer accuracy among leading models. Under controlled input manipulations, removing video most strongly degrades OEG, whereas disrupting temporal order most strongly degrades ICR. Free-response, Stem+Options, and synchronized-shuffle controls show that response format, static question cues, and video-ASR mismatch do not explain these layer-specific patterns. The results identify distinct behavioral evidence dependencies without claiming an internal architectural mechanism. VIRA-Bench provides a focused evaluation resource for multimodal dialogue grounding, pedagogical discourse, and temporal reasoning in online tutoring.

For every prime power $q>19683$, we settle the Cheng--Murray deep-hole problem for full-length Reed--Solomon codes in every dimension $2\le k\le q-2$, with the characteristic-two cases stated explicitly. For odd $q$, the deep holes are precisely the words of degree $k$. For even $q$ and $k\ge3$, the same conclusion holds except for an additional family when $k=q-3$. In even characteristic and dimension two, every deep hole has a unique expression $a h(X)+bX+c$, where $a\ne0$ and $h$ is a normalized $o$-polynomial. The proof combines quadratic quotient algebras, graph-theoretic weighted independent-set inequalities, and planar arc completion. We also obtain normal rational curve rigidity in the corresponding nonexceptional dimensions, the projective Reed--Solomon covering radii, and distinct-coordinate solvability and remainder criteria.

Multimodal multi-label emotion recognition is important for affect-aware systems, but models trained with complete text, visual, and acoustic streams often degrade sharply when some streams are unavailable at deployment. We address this train-test gap by learning a compact representation that preserves emotion-specific evidence from any available subset of modalities. We propose the Multi-modal Emotion Recognition Perceiver (MERP), which maps the joint sequence into a fixed-size latent bank, thereby keeping repeated reasoning independent of raw input length; it extracts label-specific evidence before and after latent reasoning and aligns the two levels through reconstruction. MERP further uses positive and negative class prototypes, a noise-gated feature enhancer with frequency-shaped perturbations during training, and confidence-aware class-wise fusion to strengthen separability, reduce sensitivity to missing inputs, and combine complementary predictors. Under 20 percent test-time random modality drop, MERP achieves micro-F1 scores of 0.563 on CMU-MOSEI and 0.780 on M3ED, exceeding the strongest evaluated baselines by 0.004 and 0.005, respectively; in the severe CMU-MOSEI audio-only setting, it retains 0.473 micro-F1 versus 0.022 for LDDU. These results show that fixed latent reasoning provides a practical, testable route to robust multimodal emotion recognition without requiring missing-modality examples during training. Code is available at https://github.com/Creative-zcx/MERP.

A question about a whole-slide image rarely names every morphological finding needed to answer it. Question-guided patch selection can therefore overlook supporting morphology, while slide-level compression can dilute focal evidence. Inspired by how pathologists combine broad slide review, question-directed examination, and integration of their findings, we introduce BEYONDPATH, a Preserve-Focus-Fuse framework for whole-slide image question answering. Preserve learns a question-agnostic Morphology Bank through answer supervision across multiple questions about each training slide. Focus retrieves questionspecific evidence from all foreground patches, including regions outside the Bank. Fuse integrates the preserved morphology at the retrieved evidence positions through Morphology-on-Visual-Evidence Fusion, producing a fixed 96-token visual prefix. On WSI-Bench, BEYONDPATH achieves an Avg-9 of 0.769 and leads all eight reported report-generation metrics using the same checkpoint. It also achieves 0.639 zero-shot overall accuracy on SlideBench-BCNB. Controlled ablations show complementary benefits from morphology preservation and question-directed retrieval, and support cross-question supervision and fusion at the evidence positions. These results support looking beyond the question's explicit cues: preserving broader slide morphology while retaining the ability to seek evidence for each question.

Visual grounding (VG) in visual question answering (VQA) is a fundamental capability of Vision-Language Models (VLMs), enabling the detection of the most relevant region in an image to answer the question. This reflects the model's capability of multimodal comprehension, which is crucial when interacting with visually impaired people (VIP). Indeed, visual grounding, when applied to assistive scenarios, is not merely a technical feature, but rather a trust and safety requirement. In this work, we study visual grounding in VLMs for visually impaired people. To this end, we assess open-source VLMs on visual grounding using the VizWiz-VQA-Grounding dataset and challenge, which contains real-life images taken by VIP. We propose VG-SHAP, which extends an existing explainability framework to provide visual grounding explanations, allowing the evaluation of black-box VLMs. Our results on the VizWiz-VQA-Grounding challenge show that despite generating correct answers, VLMs struggle to ground in the proper region in the image. However, these results are constrained by the quality of the segmentation model of our explainability framework and further research is necessary.

Pinching antenna systems (PASS) provide flexible transmitter-side radiation reconfiguration for high-frequency wireless communications. This paper applies PASS to non-orthogonal multiple access (NOMA) covert communication networks, where activated pinching antennas (PAs) transmit superimposed signals to a pair of users stochastically distributed within a rectangle. Two passive wardens respectively monitor the downlink transmissions intended for two users. More specifically, we derive the closed-form detection error probability (DEP) expressions for two wardens under bounded noise uncertainty. Then we analytically determine the optimal detection thresholds and minimum DEPs in the worst-case covert detection scenarios. The covert transmission rates of two users are further characterized by taking into consideration ideal successive interference cancellation and non-ideal successive interference cancellation at near user and intra-NOMA interference at far user. Numerical results are presented to confirm that: 1) PASS-NOMA is capable of providing higher covert rates relative to conventional orthogonal multiple access OMA schemes; 2) As the number of activated PAs begun to increase, the near user has ability to obtain a larger covert rate gain than far user; and 3) The DEP of PASS-NOMA networks is larger than that of both PASS-OMA and traditional antenna based NOMA in specific output power regions.