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arXiv2024

Convergence of a Ramshaw-Mesina Iteration

In 1991 Ramshaw and Mesina introduced a clever synthesis of penalty methods and artificial compression methods. Its form makes it an interesting option to replace the pressure update in the Uzawa iteration. The result, for the Stokes problem, is \begin{equation} \left\{ \begin{array} [c]{cc} Step\ 1: & -\triangle u^{n+1}+\nabla p^{n}=f(x),\ {\rm in}\ Ω,\ u^{n+1}|_{\partialΩ}=0,\\ Step\ 2: & p^{n+1}-p^{n}+β\nabla\cdot(u^{n+1}-u^{n})+α^{2}\nabla\cdot u^{n+1}=0. \end{array} \right. \end{equation} For saddle point problems, including Stokes, this iteration converges under a condition similar to the one required for Uzawa iteration.

math.NA↗

arXiv2026

A Simple Way of Getting Large Examples of Osborn Loops

Examples and counterexamples define the boundaries of mathematical propositions, test foundational conjectures, and resolve open structural problems in abstract algebra. In loop theory, an Osborn loop is a crucial generalization of a Moufang loop satisfying a specialized variable-sandwiching identity. While small finite non-associative examples are known, constructing large examples of proper Osborn loops (loops that are neither conjugacy closed nor Moufang) remains a computational bottleneck. In this paper, we establish an efficient framework for generating large proper Osborn loops by taking the direct product of non-associative conjugacy closed (CC) loops and Moufang loops. We outline the boundary constraints necessary to prevent structural collapse into sub-varieties and provide explicit examples up to order 2025 validated via the GAP package \texttt{LOOPS}.

math.RA↗

arXiv2026

SnapScope: A Platform for City-Scale Collection and Exploration of Public Snap Map Data

Snapchat's Snap Map is an ephemeral stream of geotagged public video and image stories, but the platform provides no documented API, no prior work describes a reproducible system for collecting this data at city scale, and no tool exists for managing and exploring the collected data interactively. We present SnapScope, an integrated platform that pairs a back-end collection pipeline with a web-based front end for scraper management, interactive data exploration, side-by-side neighborhood comparison, and data export. We deploy the platform over Riyadh, Saudi Arabia, collecting 515,364 unique public snaps across 23 days on a 1 km grid of 2,740 query points. A saturation probe over 21 consecutive runs shows that 94.8% of returned observations are duplicates of already-stored records. We provide a privacy-safe aggregate dataset under CC BY 4.0. The platform is city-agnostic and redeployable by substituting grid coordinates and boundary polygons.

cs.SI↗

arXiv2026

Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications

Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with permutation symmetries, as the most common kernels employed are better suited for vector inputs rather than unordered sets of items. Motivated by this issue, we turn to permutation invariant Bayesian Optimization for well placement in Carbon Capture and Storage projects. The high fidelity black box simulator is instructed to operate wells under group control, giving rise to permutation symmetries within injector and producer groups that cannot be exploited with standard GP kernels. In this work, our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations, and can be combined with standard kernels for additional vector-valued inputs. As a learned invariant baseline, we also consider a Deep Kernel Learning model (DKL-DS) using the Deep Sets architecture to learn a permutation-invariant embedding. We evaluate the proposed methodology across 8 use cases, comprising seven synthetic benchmarks and one realistic CCS case study (Johansen formation)

cs.LG↗

arXiv2026

Breaking Cycles for Scalable Fair Ordering in Blockchain Systems

In blockchain systems, transaction order directly determines financial outcomes: unfair ordering enables front-running and sandwich attacks that have extracted over \$686M from Ethereum users. Current fair-ordering protocols aggregate pairwise receive-order evidence from replicas. Under contention or adversarial manipulation, however, Condorcet cycles force them into global strongly connected component (SCC) condensation, causing delays, coarse batches, and scaling failures. We present FlashOrder, a deterministic fair-ordering engine that localizes cyclic ambiguity before it propagates across the batch. FlashOrder embeds pairwise preferences into one-dimensional canonical positions, clusters nearby transactions with a partition hypergraph, and performs hierarchical inter- and intra-cluster serialization, replacing batch-wide SCC condensation with localized sorting and aggregation. Evaluated against Themis (CCS '23) and Rashnu (VLDB '24) on a libhotstuff-based prototype, FlashOrder achieves up to 10.5$\times$ higher throughput than Themis and 4.8$\times$ higher than Rashnu, with the latency gap widening as network scales. In controlled adversarial simulation, it reduces maximum rank displacement by 88.7\%, and under Condorcet attacks it sustains 12.0$\times$ and 9.7$\times$ higher throughput than Themis and Rashnu on average. These results show that localizing cyclic ambiguity yields stronger fairness at substantially higher throughput.

cs.DC↗

arXiv2026

Detecting Multiple Semantic Concerns in Tangled Code Commits

Code commits in a version control system (e.g., Git) should be atomic, i.e., focused on a single goal, such as adding a feature or fixing a bug. In practice, however, developers often bundle multiple concerns into tangled commits, obscuring intent and complicating maintenance. Recent studies have used Conventional Commits Specification (CCS) and Language Models (LMs) to capture commit intent, demonstrating that Small Language Models (SLMs) can approach the performance of Large Language Models (LLMs) while maintaining efficiency and privacy within local infrastructure. However, they do not address tangled commits involving multiple concerns, leaving the feasibility of using LMs for multi-concern detection unresolved. In this paper, we frame multi-concern detection in tangled commits as a multi-label classification problem and construct a controlled dataset of artificially tangled commits based on real-world data. We then present an empirical study using SLMs to detect multiple semantic concerns in tangled commits, examining the effects of fine-tuning, concern count, commit-message inclusion, and header-preserving truncation under practical token-budget limits. Our results show that a fine-tuned 27B-parameter SLM outperforms a state-of-the-art LLM across all concern counts. In particular, including commit messages improves detection accuracy by up to 31% (in terms of Hamming Loss) with negligible latency overhead, establishing them as important semantic cues.

cs.SE↗

arXiv2026

MultiSynt/MT: Trillion-Token Multi-Parallel Pre-Training Data Translated Across 36 Languages

Open web-scale pre-training corpora remain concentrated in English, limiting multilingual LLM development. We introduce MultiSynt/MT, an open synthetic parallel corpus with approximately 4.8 trillion target-language tokens across 36 languages, produced by translating 100 billion high-quality Nemotron-CC tokens with Tower+ and OPUS-MT/HPLT-MT systems. For many medium- and lower-resource European languages, this is the largest openly available pre-training resource. Across five high- and medium-resource languages, reference LLMs trained on MultiSynt/MT reach the final score of HPLT 2.0, a native-data baseline, using roughly 72% fewer pre-training tokens, and outperform it by approximately 15% relative at a matched 100B-token training budget. Our analyses also identify evaluation blind spots: standard multiple-choice benchmarks miss translation-quality differences that a fluency-sensitive LLM-as-judge protocol recovers on the trained LLMs without detecting a deficit relative to its native-data baseline, while Norwegian idiomatic and culturally grounded tasks remain better served by native data. We release the corpus, including row-aligned translations from multiple systems, to support controlled research on multilingual pre-training data and evaluation.

cs.CL↗

arXiv2026

OpenDiscoveryTrace: Process Traces for Evaluating AI Scientist Workflows

Existing benchmarks for autonomous AI scientists evaluate only final outputs---generated code, hypotheses, or papers---yet discard the reasoning process by which those outputs were obtained. This makes it impossible to audit scientific methodology, diagnose failure modes, or distinguish systematic reasoning from fortunate guessing. We present \textbf{OpenDiscoveryTrace}, a public dataset of 558 complete AI scientific agent trajectories that captures how models reason, not just what they produce. Each trajectory records a structured 9-field-per-step trace---including thoughts, tool calls, observations, errors, revision triggers, and self-reported confidence---as models execute 124 scientific tasks spanning drug discovery, materials science, genomics, and scientific literature analysis. The dataset covers seven models: three frontier models (GPT-5.4, Claude Opus 4.6, and Gemini 3.1 Pro; 124 trajectories each, fully balanced across domains and difficulty levels) and four open-weight models (Qwen2.5-7B, Mistral-7B-v0.3, Phi-3.5-mini, and Qwen2.5-1.5B; 30 each), plus 60 live-retrieval variant trajectories. Pilot analysis on 363 LLM-judged trajectories reveals that process traces expose behavioral differences invisible to output-only evaluation: all three frontier models achieve comparable success rates (84--89%), yet Claude Opus 4.6 produces 30$\times$ more errors than GPT-5.4 (2.5 vs. 0.08 per trajectory, $p < 0.0001$, Cliff's $δ= 0.613$), with qualitatively different error profiles---66.7% tool misuse for Claude versus 83.6% reasoning errors for GPT-5.4. We define five benchmark tasks with baselines from logistic regression, random forests, LSTMs, and Transformer models. The dataset, trace schema, agent harness, and benchmark definitions are publicly available under CC BY 4.0 to support research on process-level evaluation, scientific agent auditing, and AI governance.

cs.AI↗

arXiv2026

Benchmark Contamination: A Taxonomy Organized by Defeated Mitigation

A benchmark score is a joint property of the model, the evaluation harness, the elicitation budget, the sampled population, and contamination status. Leaderboards publish the model and the score, so capability and leakage stay observationally equivalent. Existing taxonomies classify contamination for automated detection, not the question a reporter faces at publication: given the mitigations already applied, which validity threats remain open? We introduce a taxonomy organized by the mitigation each type defeats -- direct, derivative, temporal, distributional, and acquired -- spanning training-time and evaluation-time leakage. Holding out a private test set closes the first alone. The fifth is acquired during the evaluation itself; because it is a property of one run, it must be recorded with the reported score rather than with the benchmark release. We operationalize it as a four-field disclosure protocol in which "unknown" is a valid entry, released under CC BY 4.0 with a JSON Schema, a validator, and worked examples. Two coders external to the design team applied a pre-registered instrument to 41 documents. Per-variable linear-weighted $κ$ runs from 0.00 to 0.35 (median 0.21) over 29 main-pass documents against a single-coder test-retest ceiling of 0.84, collapsing under the class skew the registration anticipated; pooling raises it to 0.46 through chance correction rather than better agreement. Two variables fall below the prevalence-robust threshold registered in advance: strata reporting and the acquired type introduced here. Disagreement concentrates on when a variable applies rather than on what a document states. Elicitation budgets are reported in 13% of documents, and no document addresses all five types. The contribution is the taxonomy, the score-side artifact that follows from it, and a pre-registered measurement of instrument reliability and current disclosure.

cs.CR↗

arXiv2026

AgentDrift: A Step-Labeled Benchmark of Injection-Hijacked LLM Agent Trajectories

LLM agents complete tasks by issuing sequences of tool calls, and every observation they read is a channel through which an indirect prompt injection can enter. A successful injection has a characteristic shape when the trajectory is read in order: a benign prefix gives way to actions that serve the attacker rather than the user. Existing benchmarks measure whether such attacks succeed against live agents, and existing guard models judge a trace as a whole; no public corpus labels, step by step, where an injection enters a trajectory and which steps it corrupts. We present AgentDrift, a benchmark of 12,536 synthetic tool-call trajectories over five agent domains in which every one of the 71,024 steps carries one of four labels: benign, injection point, hijacked, or failed injection. The corpus contains 4,000 benign, 5,536 attacked, 1,500 failed-attack, and 1,500 hard-negative trajectories; attacked trajectories follow three compliance patterns whose label strings obey a stated regular grammar. Failed attacks carry an injection the agent resisted, and hard negatives carry legitimate content that resembles an attack, so a detector must separate attempt from success and deviation from novelty. Trajectories were generated by a single open model under category-specific protocols, enforced by a closed-vocabulary structural validator, screened by an LLM judge, and audited by hand on 1,200 trajectories; we show that the LLM judge was itself fooled by the hard negatives. A surface-feature logistic regression recovers only 55.4% of attacks (F1 0.647), including only 8.2% of partial hijacks and 23.1% of delayed executions, so nearly half of the attacks require modeling the behavioral sequence. We measure template concentration, attack-goal-family collapse, and world-identity leakage in the generated data, and release the corpus with its documentation under CC BY 4.0.

cs.CR↗

arXiv2026

Open-Set Vessel Re-Identification from Underwater Ship-Radiated Noise with a Raw-Waveform Selective-Kernel Acoustic Neural Network (SKANN) and a Cross-Passage Evaluation Protocol

Underwater acoustic target recognition has converged on closed-set classification by vessel type, a task that does not answer whether a monitoring system has heard this hull before. We formalise open-set, cross-passage vessel re-identification on public hydrophone data and specify a protocol that removes the two easiest routes to a high score: hull-disjoint splits keyed to MMSI/IMO, galleries and queries from disjoint passages of each hull, source-pure galleries, and an audio-adjudicated transit-deduplication gate. We describe SKANN, a raw-waveform encoder whose front end is a four-scale bank of learned filters fused by selective-kernel attention, trained with an angular-margin objective and an augmentation regime that perturbs recording chain, ambient noise and multipath while preserving the narrowband lines that carry identity. On a 40-hull IARA gallery (96 queries, 98 passage candidates), cross-passage rank-1 is 0.25 for the embedding and 0.26 for an automated narrowband-tonal comparator; the two are statistically indistinguishable at the top of the ranking, the embedding orders the rest of the list more reliably (AUC 0.82 vs 0.76), and their score fusion reaches rank-1 0.35 -- the only contrast that attains nominal significance, presented as evidence of partial complementarity, not as a recommendation. Transit deduplication alone removes a 16-21 point apparent rank-1 advantage, larger than any between-method difference. Two further findings delimit what public data can support: ShipsEar cannot separate hull identity from recording channel under an identity protocol, and cross-network fine-tuning helps vessels seen during fine-tuning but is a null result on unseen ones. The results support analyst triage over a ranked shortlist, not identification. Checkpoint, validation embeddings, transit map and per-query outputs are released under CC-BY-4.0 (doi:10.5281/zenodo.22160138).

eess.AS↗

arXiv2025

Security Science (SecSci), Basic Concepts and Mathematical Foundations

This textbook compiles the lecture notes from security courses taught at Oxford in the 2000s, at Royal Holloway in the 2010s, and currently in Hawaii. The early chapters are suitable for a first course in security. The middle chapters have been used in advanced courses. Towards the end there are also some research problems.

cs.CR↗

arXiv2026

Fully Distributed GNE Algorithms for Multi-Robot Placement without Consensus on Multipliers

Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.

cs.LG↗

arXiv2026

Input-to-State Stability Framework for Fully Distributed Primal-Dual Dynamics for Quadratic GNEPs Without Multiplier Consensus

Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.

math.OC↗

arXiv2026

TSExplorer: An interactive data annotation and exploration tool for time-series data

We present TSExplorer, a cross-platform tool for interactive annotation and exploration of time-series data. The tool enables users to inspect high-dimensional datasets through multiple complementary 2D visualizations derived from high-dimensional feature representations. TSExplorer is designed as a general-purpose research tool supporting a wide range of workflows, including exploratory data analysis, annotation of unlabeled or partially-labeled datasets, comparison of feature representations, and post-hoc inspection and refinement of existing labels with interactive visual feedback.

cs.HC↗

arXiv2026

Towards a universal language of concepts: A survey

Humans can learn and generalize novel concepts from sparse data because they express knowledge in rich structural formats. In this paper, we propose that programs are a strong candidate for universal representation of concepts. We review computational models of concept learning that use programs as their concept representation and evaluate their contribution toward a universal representational language.

cs.AI↗

arXiv2026

Hardware Trojan Threats to Multi-Chiplet Photonic Neural Network Accelerators

Multi-chiplet photonic neural network accelerators (MCPNAs) combine photonic computation, photonic communica-tion, and heterogeneous chiplet integration to enable scalable and energy-efficient AI acceleration. However, their distributed archi-tecture and reliance on third-party chiplets introduce significant hardware security risks. This paper examines Hardware Trojan (HT) threats to MCPNAs across three dimensions: confidentiality, integrity, and availability.

cs.AR↗

arXiv2026

VIBE: Video Instruction-aligned Background music gEneration

Current video-to-music (V2M) models lack semantic control and fail to penalize instruction violations, largely due to their reliance on reconstruction objectives and the representational bottleneck of static cross-modal conditioning in Diffusion Autoregressive (DAR) architectures. To resolve this, we introduce VIBE, a novel text-and-video-to-music (T+V2M) generation model that leverages: (1) Conditioning Connection, a depth-wise cross-layer conditioning mechanism that dynamically bridges the planning and diffusion refinement heads and (2) a comprehensive reward modeling taxonomy, optimizing for both hard, verifiable constraints (e.g., tempo, key) and soft, subjective qualities (e.g., musicality, multimodal alignment) with a structured 5-stage training curriculum. Upon evaluation using audio-visual alignment, instruction following, and audio quality metrics, along with a subjective human evaluation study, we observe that VIBE demonstrates enhanced controllability and instruction adherence while performing comparably to most evaluated baselines on generation fidelity and multimodal alignment.

cs.SD↗