Science & Mathematics

For large language models (LLMs) and multimodal large language models (MLLMs), model-reported self-confidence is often miscalibrated, yet it may still be useful for efficient evaluation. At the same time, LLM-as-a-judge offers a scalable alternative to direct human auditing, but its practical benefit depends on calibration quality and inference cost. This paper develops a unified statistical framework for both evaluation routes under alternative sampling strategies. For direct auditing, confidence-stratified sampling is used to recover population accuracy from partially verified outputs without requiring calibrated confidence. Finite-sample uncertainty is characterized, and the analysis shows how highly uneven confidence strata affect audit efficiency and label allocation. For judge-assisted evaluation, the judge is modeled through sensitivity and false-positive rate, yielding an error-corrected estimator with calibration uncertainty. The two routes are then compared through human-label and total-cost efficiency boundaries. Experiments on MMLU-Pro and MMMU-Pro show that miscalibrated self-confidence can still support statistically valid stratified auditing. Under highly imbalanced confidence distributions, proportional allocation substantially reduces estimation error relative to equal-per-stratum allocation. For judge-assisted evaluation, only a small subset of target--verifier pairs satisfies the idealized human-label efficiency condition, and automated inference costs can further limit potential savings. These findings clarify the statistical and economic conditions under which confidence-guided auditing and automated verification are useful.

Recently, there has been rise in multimodal vision-language models for computer-aided diagnosis (CAD), yet their application in breast diagnosis, particularly for predicting biopsy outcomes remains limited. This study presents a multimodal vision-language approach, incorporating Grad-CAM as an Explainable AI (XAI) technique, to predict benign tumors in patients recommended for biopsy, especially those classified as BI-RADS 4 and 5. A novel multimodal framework was devel- oped using Vision Transformer (ViT) for imaging feature extraction and DeBERTa-V3-Large for textual embeddings. The model was trained and evaluated on a comprehensive in-house dataset comprising 1,632 patients, each with four mammography views and a corresponding radiology report. The features of both modalities were extracted independently and fused by late fusion before classification. Grad-CAM was used to generate visual explanations highlighting key regions influencing model predictions. The proposed model demonstrated high sensitivity 90%, 95%, 99%, and 100% with corresponding specificities of 40%, 36%, 18%, and 11%, respectively. The best AUC achieved was 0.72 by multimodal approach on the test set, outperforming the image only (0.66) and text-only (0.68) baselines. The proposed multimodal architecture, enhanced with Grad-CAM, demonstrates a strong potential to identify benign tumors among high-risk patients, offering interpretable insights and thereby helping reduce unnecessary biopsies, patient anxiety, and healthcare costs.

Attention over tens of thousands of visual tokens dominates the inference of video diffusion transformers (DiTs). Existing methods reduce this cost through sparsity, low precision, or both, but use a single precision for all kept tiles. We observe that the output error introduced by approximation varies widely across tiles. Many tiles can be skipped with little error, others must be computed but gain little beyond low precision, and a few retain substantial error even at low precision. We present Triage, a training-free attention method that assigns each tile one of three approximation tiers: skipping it by replacing it with its block means, skimming it in NVFP4, or refining it with NVFP4 residual correction. A lightweight router predicts each tile's error under each tier from block statistics and moves a tile to a more accurate tier only when the predicted error reduction justifies the extra compute, with a single price setting this trade-off. A fused kernel executes all three tiers in a single pass on the FP4 tensor cores of RTX Blackwell GPUs. Across Wan2.2, HunyuanVideo, and LTX-2.5, Triage accelerates end-to-end generation by up to 2.32x over dense FlashAttention, and in each of five settings it runs faster than every baseline while reaching 0.3-3.0 dB higher PSNR than the highest-PSNR baseline.

This paper proposes and analyzes a dual-measurement frequency-droop (DMFD) controller for meshed MVDC networks. Using only two local DC measurements, bus-voltage deviation and a filtered DC-port current or power deviation, the controller enables grid-forming operation at both AC and DC ports across the mesh. Although the DMFD regulates neither the DC voltage nor the DC current directly and acts only on the terminal frequency, it is shown that AC-side synchronization closes an effective DC droop at every synchronized terminal, so that the steady operating point of the mesh exists and is unique. Constant frequency deviations at a terminal and single-terminal islanding enter the same DC equations as equivalent current offsets, with the island frequency fixed by the island power balance, allowing node voltages and branch currents to be obtained from one linear system. The steady-state model yields design-use envelopes to map the droop ratios and the net DC-injection levels into bounds on DC-voltage deviation and terminal currents. A small-signal dynamic model is developed and used to generate eigenvalue loci and damping-ratio charts that guide controller-gain selection. Averaged EMT simulations on a four-terminal ring corroborate the analysis: in regimes where PLL-based grid-following control is known to lose damping, the DMFD controller maintains stable operation and follows the predicted steady-state characteristics.

Bus riders judge service by two failures: single trips that run late, and days on which the whole system misbehaves. We ask whether one unsupervised representation of raw GPS telemetry can serve both diagnoses on the NetMob 2026 Niterói bus dataset. An autoencoder compresses each trip into a 64-dimensional latent vector; the frozen encoder feeds supervised delay classifiers, and the reconstruction error serves as an anomaly score. Two findings are negative. First, the latent representation does not improve delay detection: gradient boosting on per-trip summary features reaches $0.846 \pm 0.013$ ROC-AUC against $0.838 \pm 0.016$ for the best latent setup, and the gap becomes significant once the preprocessing filters are relaxed. Second, two of the three external checks of the anomaly score were circular. Retraining without rainfall removes the rain association ($5.4\%$ against $5.0\%$ flagged, $p = 0.84$) and an apparent citywide disruption on 23 March. What survives is a day-level signal stable across three autoencoders (Spearman $ρ\geq 0.96$), driven mostly by day type, with degraded-telemetry days still separable within weekday and weekend strata. The alarm threshold limits detection more than the score does: a pooled percentile cut flags $5.7\%$ of trips on the worst degraded day, while re-scaling within each bus line flags $29.3\%$. The delay model rests almost entirely on one feature, no latent dimension is individually interpretable, and 22 chronic line-directions carry half of all delayed trips.

This paper investigates the proof-theoretic foundations of the principle of reiteration (R) in natural deduction, arguing that its legitimacy originates in the structural preservation of formulae within sequent calculus rather than in an independent logical rule. By examining singlesuccedent and multisuccedent sequent calculus, we demonstrate how logical operations transform principal formulae while preserving unaffected antecedent and succedent contexts. We subsequently analyse the schematic formulation of reiteration and compare natural deduction derivations with corresponding sequent calculus derivations. This comparison identifies two fundamental functions of reiteration, namely the reuse of previously employed formulae and the restoration of previously derived conclusions. We conclude that reiteration introduces no independent inferential content but explicitly represents the structural continuity of inferential dependencies already included into sequent calculus.

This work proposes a new Multi-Fidelity Particle Flow Filter (MFPFF) based on a linear control variate framework and multilevel Monte Carlo methods. Conventional particle filters often suffer from weight collapse and particle degeneracy in high-dimensional spaces. Particle flow filters address this by smoothly transporting prior particles toward the posterior distribution, thereby avoiding the need for resampling. This work constructs multi-fidelity particle flow filters by augmenting a small number of expensive high-fidelity particles (full-order model runs) with a large number of inexpensive low-resolution particles (reduced-order surrogates constructed via intrusive Galerkin projection). These surrogates act as control variates to enhance the statistical estimate of the full-order posterior, yielding enhanced analysis accuracy at comparable computational cost. The work focuses on two particle flows based on log homotopy, the stochastic Gromov flow and deterministic Exact flow. Numerical experiments with the Korteweg-De Vries (KdV) and Quasi-Geostrophic (QG) test problems demonstrate that the proposed MFPFF achieves accuracy comparable to high-fidelity simulations while significantly reducing computational expense.

Robust chemodynamic mapping of the Milky Way requires accounting for the selection function of the survey used, the probability that a given star is included in the final catalog as a function of its observable properties. We derive the empirical selection function of the SDSS-V Galactic Genesis survey, the largest Milky Way Mapper program targeting red giant stars for Galactic structure studies. Treating the Galactic Genesis sample as a subsample of its 2MASS parent catalog, we model the selection function as a function of sky position, apparent H magnitude, and G-H color using a Bayesian binomial estimator, computing both a mean and maximum a posteriori (MAP) version. The resulting selection function reflects the survey's targeting strategy and observing history, including the transition from the pencil-beam SDSS-IV footprint to the fuller sky coverage of SDSS-V and the prioritization of the Magellanic Clouds. Using this selection function with the FIRE-2 Milky Way-mass simulations, we construct mock Galactic Genesis catalogs built on existing mock Gaia DR3 catalogs, injecting realistic photometric noise and applying the selection function via a per-star Bernoulli accept-reject procedure. We demonstrate the mock catalogs' utility with an example application to azimuthal metallicity variations in the disk. Furthermore, we release a Python package allowing users to recompute the selection function for their own samples and science cases. The package, selection function and mock catalogs will be updated and made available as the survey continues, extending the tools needed to reach the full scientific potential of SDSS-V Galactic Genesis.

Transformer-based language models exhibit an astonishing capacity to generalize to longer and more difficult problem instances than those seen in training. However, theoretical understanding of this phenomenon still lags behind. Unlike most machine learning models, the generalisation abilities of transformers inherently require considering two axes. On one hand, one must examine in-distribution statistical generalisation, which concerns the ability of a model to broaden a function from training samples to novel samples of the same distribution. On the other hand, given the sequential nature of language data, one must also consider length generalisation, which reflects whether a model trained on inputs of a given length can extrapolate to longer ones.These two notions have mostly been studied separately, leaving open how they interact. In this work, we give a joint treatment of both axes for fixed-precision transformers. We give generalisation guarantees in terms of the parameter sizes of the involved models, as well as the quantization space and the alphabet size that supply the sequences. Finally, we illustrate how the requirements in the sample count and training length trade off. In particular, we find that increasing training length can be exponentially more efficient than increasing the sample size. Experiments support predictions of the theory.

Reinforcement learning with verifiable rewards trains on cheap checks, such as unit tests, that a policy can learn to game, while a stronger check is too expensive to run on every rollout. We study how to spend a limited strong-verifier budget in GRPO, separating which weakly passing rollouts to audit from what reward a caught hack receives. At a fixed policy state with centered advantages, the expected update depends on a design only through each rollout's marginal audit probability and correction; reflecting a caught hack's reward about the failure reward negates the advantages of an all-hack group; and auditing whole groups with the fewest weak passes first (low-pass budgeted audits, LB) minimizes the advantage mass left on hacks among pass-count designs with a fixed correction when a label's value falls with the pass count. We tested this analysis in actual LLM training: from each run's starting state, the sign of this mass on a frozen panel predicted whether hacking would be suppressed in 33 of 39 runs, including 13 of 16 preregistered ones. In LeetCode (Wong et al., 2026) and Countdown-Code (Khalifa et al., 2026), LB drives hacking to near zero, while random audits with the same penalty and budget do not and use more labels. We also find that the randomness of the update affects training: in Countdown-Code, two unbiased corrections, per-item reward-level IPW and a group-level advantage correction, bring hacking down too but end 6.1-11.8 and 8.0-11.5 points lower in held-out accuracy than LB at the same budget. A full audit, which the group-level correction reproduces in expectation, stays within about two points of LB in three seeds, while LB uses 28% of its labels, and allocating the same correction by pass count recovers most of the loss (one seed). Training outcomes thus depend not only on the expected update but also on the randomness of its estimate.

Data distributions often possess one or more symmetries: for example, all orientations of any specific dog are included in the distribution of all possible dog pictures. Despite the omnipresence of such symmetries, modern generative modeling approaches may fail to incorporate or learn them, which can lead to lower sample efficiency and poorer generalization. To what extent do diffusion models fail to learn data distribution symmetries, and what sources of symmetry breaking are most responsible? Here, we answer this question in the theoretically tractable setting of linear diffusion models. We show that of three potential sources of symmetry breaking---a non-symmetric initial weight matrix, a noisy learning target, and finite-sample noise---target noise produces the most robust symmetry breaking, since it persists even in the sample-rich regime. Using local laws from random matrix theory, we derive formulas for average symmetry error in fairly general cases involving symmetry within a subspace and show that smaller symmetries are harder to learn.

Clinical trial prescreening requires distinguishing unmet conditions from insufficient evidence in patient records. Given patient records, criterion questions, and predefined answer options, we retrospectively compared JEV, a non-generative decision model returning native option probabilities, with schema-constrained Qwen Flash across 2,048 test patient-condition pairs from TrialGPT and question-answer datasets derived from MIMIC-III and MIMIC-IV, all evaluated under strict Zero Data Retention (ZDR) policies to ensure clinical data privacy. Both models assessed conditions individually or in batches sharing the same patient context, with performance measured against reference labels. In batch mode, JEV and Qwen achieved similar macro-F1 scores on TrialGPT (0.652 vs. 0.660) and MIMIC-IV (0.807 vs. 0.814), whereas JEV substantially outperformed Qwen on MIMIC-III (0.768 vs. 0.534; $Δ$ = +0.234, 95% CI: 0.187-0.281). This advantage largely reflected higher recall for conditions labeled as having insufficient information (56.3% vs. 9.9%). Across all three datasets, JEV also had lower observed median job latency (1.18-1.40 vs. 2.80-8.90 s) and 53%-74% lower estimated cost per condition. These findings position JEV as an initial assessment component that provides criterion-level judgments and flags potential information gaps for review. JEV's observed errors in interpreting clinical evidence underscore the need to verify its outputs against patient records before they inform eligibility decisions.

High-resolution video matting requires preserving fine details, such as hair strands and soft transparency, while maintaining consistency across frames. Memory-based methods achieve strong matting quality by matching current-frame features with information stored from earlier frames, but this process becomes increasingly costly as resolution grows. We present MatAnyone-E, an efficient extension of MatAnyone 2 that focuses computation where it is most needed. Our approach first performs low-resolution propagation to identify uncertain regions that require closer inspection and the memory candidates most relevant to them. It then performs high-resolution matching only for these regions using the selected memory, while reusing low-resolution matching results elsewhere. This strategy reduces both the number of locations requiring detailed matching and the amount of memory searched, while preserving the information needed to produce a complete matte. We further reduce the cost of generating high-resolution mattes with a lightweight decoder designed around measured runtime bottlenecks and trained to reproduce the original decoder's representations. Experiments show that MatAnyone-E maintains matting quality comparable to MatAnyone 2 while achieving an estimated 7.4x inference speedup and reducing peak GPU memory usage to 7.6% of the usage of MatAnyone 2 at 4K. With compilation-enabled inference on a single NVIDIA H200 GPU, it reaches 73.07 FPS at 1080p and 28.62 FPS at 4K.

The gap between AI capability deployment and safety assurance is structural and cannot be closed through internal evaluations alone. Analyzing documented harms (2017-2026) across the human lifespan reveals that disparate incidents --- from voice assistants endangering children to AI companions implicated in adolescent suicide and automated care denials for the elderly --- reflect a single failure: evaluating systems against an implicit adult user model. We introduce five developmental moderators structured into a Lifespan Vulnerability Matrix across six life stages. The matrix reveals a nonmonotonic risk distribution: vulnerability peaks at both ends of the lifespan, governance coverage is asymmetrical, and authority to convert model errors into real-world impact is scrutinized least. We then propose a set of lifespan design principles generalizing existing child-protective instruments, and an institution-agnostic, three-tier external evaluation framework --- comprising automated simulation, expert red teaming, and post-deployment monitoring --- indexed directly to matrix risk cells.

Web-connected sensing applications continuously generate multivariate time series with evolving behavioral categories, making Time Series Class-Incremental Learning (TSCIL) essential for adapting to new classes without forgetting previously acquired knowledge. However, preserving diverse and evolving class distributions under strict privacy and memory constraints remains a fundamental challenge. Existing approaches often face a trade-off between retaining sufficient historical knowledge for accurate recognition and minimizing the memory required for continual adaptation. To address these limitations, we propose TRACE, a memory-efficient, replay-free framework that preserves class-specific knowledge through generative modeling rather than sample rehearsal. TRACE employs a compact, frozen temporal-spectral representation and lightweight class-specific autoencoders to capture complex intra-class variations. By independently preserving each class model, TRACE avoids recursive generation and catastrophic forgetting, while enabling direct classification through reconstruction-based scoring without retaining historical samples or large statistical matrices. Extensive experiments across five TSCIL benchmarks demonstrate that TRACE achieves competitive classification accuracy while reducing mean retained memory by approximately 98.26% compared with TS-ACL, the strongest evaluated analytical baseline, and achieving an approximately 33.43% relative improvement in accuracy on GrabMyo.