Computer Science & Mathematics

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.

Imagery captured by unmanned aerial vehicle (UAV) systems increasingly raises privacy concerns, as UAV aerial surveillance routinely captures sensitive objects such as pedestrians and vehicles alongside ordinary scene content. Existing privacy-preserving approaches typically employ class-agnostic saliency detection to indiscriminately obfuscate all visually salient regions, leading to unnecessary information loss and hindering downstream scene analysis. This paper proposes a category-selective encryption framework for privacy-preserving UAV surveillance. The core advance over prior class-agnostic approaches is semantic-level selectivity: the system first recognizes what is present in the scene via an 80-class detector, then encrypts only user-specified sensitive categories while leaving non-sensitive objects and background intact for downstream analytics. The framework supports two complementary encryption schemes: Thumbnail-Preserving Encryption (TPE), which applies adaptive pixelation with a learnable blend parameter and recovers content through a jointly trained Enhanced U-Net, and XOR stream cipher encryption, which offers parameter-free, mathematically exact reversibility. The architectural design, composite loss formulation, and joint training methodology are presented in detail, establishing a foundation for practical privacy-preserving UAV surveillance that balances protection strength and scene utility.

Simulation benchmarks are a useful way to measure progress in robotics; typically they provide success rate as the dominant measure of performance. However, success rate reports only whether a rollout completed the task, hiding by what margin it succeeded, how sensitive the success is to goal parameter changes, requirements it may have violated, and whether success persisted. Signal Temporal Logic (STL) provides a formal language for capturing specifications; it can be used to define requirements, and measure how close a robot behavior is to satisfying or violating them. Using STL monitors in a simulator, however, requires exposing simulator state and mapping it to specification-relevant signals. We present Specola, a tool for evaluating robot behaviors in simulation with respect to STL specifications. Specola provides an interface for writing specifications over simulator signals, and creates and manages the relevant monitors while a policy executes. We provide a Python API and command-line interface for integrating monitoring into existing policy execution loops. We provide an adapter interface for connecting new simulators, and provide adapters for nine simulation environments and benchmarks, including LIBERO, RoboCasa, Isaac Lab, and RoboDojo. We provide case studies that illustrate the nuanced evaluation that Specola enables. Code and adapters are available at https://github.com/specola-eval/specola.

Multi-objective reinforcement learning is a fundamental problem for modern AI, with applications spanning post-training, reasoning models, and robotic control. A central challenge is to learn policies that balance competing objectives, such as helpfulness versus honesty in safety and alignment, or speed versus energy in robotics. The optimal policy can vary sharply with objective-weighting combinations, and the extent of this variation depends crucially on the degree of conflict among objectives, making per-preference policy learning sample-inefficient. In this paper, we introduce objective-conflict coefficients and derive near-optimal regret bounds for online settings using this measure, thereby quantifying the impact of misalignment on learning efficiency. Then, we design routed ensemble policy learning, an algorithm that maintains a small set of basis policies and dynamically routes trajectories to the policy with the highest potential reward. Finally, we consider trajectory selection as another approach to mitigate objective conflict, and design a kernel surrogate trajectory attribution algorithm that estimates how feedback signals from a set of trajectories influence policy learning on other trajectories. The kernel can capture nonlinear interactions such as synergy and antagonism between trajectories. We evaluate our approach across diverse environments and benchmarks: routed ensembles improve average performance by 4.3% over baselines for online environments from Meta-World and MO-Gymnasium, and kernel surrogate attribution improves correlation with leave-one-out analysis over existing baselines by 50%. When applied to trajectory selection, kernel-based attribution yields a 27% improvement in reward over baseline attribution methods.

Multi-objective multi-agent reinforcement learning (MOMARL) addresses agent coordination and objective trade-offs simultaneously while optimising overall system performance. Existing work tends to treat multi-agent cooperation and multi-objective optimisation as largely independent components of a learning problem, which amounts to an exorbitant complexity except in trivial cases. We study here whether the structure provided by multiple objectives can itself be exploited to facilitate cooperation, rather than being treated as an additional optimisation challenge. We formulate MOMARL at both the team and individual levels and introduce objective-wise counterfactual credit assignment to evaluate each agent's contribution across the team objectives. We propose Meta-Gradient Informed Multi-Objective Multi-Agent Reinforcement Learning (MIRL), with static (MIRL-S) and dynamic (MIRL-D) variants. By incorporating meta-gradient information, MIRL enables agents to learn how to prioritise objectives individually while collectively optimising the system-level objective, allowing the multi-objective structure to directly guide cooperation. Experiments on a multi-objective multiple particle environment show that our methods improve Pareto-front quality over baselines, with the dynamic variant achieving the strongest performance.

Demand on blockchain-based marketplaces arrives in bursts and at a high rate. On these platforms the data are completely visible, which makes it feasible to compare the bursty demand against the usual load. The congestion manifests as an increased demand for gas, the primary resource a blockchain sells. Existing studies consider how to price the gas. The demand itself, and what it is made of during bursts, has not been measured. We measure it on Robinhood Chain, a layer-2 blockchain that quickly became a venue for trading tokenized equities and memecoins. We collected the data from every block of its first three active months and more than 50 million Uniswap swaps that occurred during bursty periods. We find that a burst trades about as many pools as a quiet period, mostly different ones, and trades them harder, on top of elevated demand that accumulated for hours. With the bursts aligned on their peaks, the median peak is 2.5 times the usual load. Both the rise and the fall of the demand are described by the sum of two exponential functions with different timescales, a slow one of hours and a fast one of minutes. Against a matched quiet period, a burst has 1.05 times the pools, 1.40 times the trades, and 1.21 times the senders. We use two models to explain the arrival of bursts: externally triggered cascades and self-excitation. The former fits the data relatively better. Inside a burst, the entry of each trader into a pool is followed for about 24 seconds by more entries than the existing traders predict. Whether this is because of imitation or because of a shared signal is left open.