Numerical Analysis
Papers
Fresh from arXiv, typeset properly. Highlighted words trade on the market.
Saturday 10 October
We develop an adaptive Galerkin neural-network method for computing minimum-$L^2$-norm interior controls for wave equations with spatially varying coefficients. Within the Hilbert Uniqueness Method, adjoint waves are approximated directly in space-time by least-squares Galerkin projections onto trial spaces enriched by neural-network basis functions selected through residual-based training. Linear Galerkin solves determine the adjoint approximations, and a separate linear system reconstructs the control. The least-squares objective provides an indicator for adaptive enrichment and stopping; the experiments use a Ritz-based terminal-data version whose continuous-error interpretation additionally requires an eigenpair consistency estimate. The main difficulty is that adjoint errors perturb this reconstruction system. Assuming observability of the continuous equation, we derive sufficient stability conditions involving a worst-case factor $\sqrt{n}$ multiplying the maximal adjoint error, where $n$ is the number of retained terminal modes. A fully discrete error estimate separates terminal-space truncation, adjoint approximation, and assembly errors, yielding convergence to the minimum-norm control when the truncation error, the $\sqrt{n}$-weighted adjoint error, and the assembly errors tend to zero as $n$ grows. For spectral terminal bases, additional regularity and uniform contraction assumptions yield quantitative convergence rates and show that $O(\log n)$ accepted enrichment steps per mode suffice to balance the neural and truncation errors. Numerical experiments on a nonconvex Cassini oval, a square containing a low-speed lens, and a three-dimensional ball with a graded coefficient illustrate the method.
Artificial Intelligence
Running Fewer Loops Removes Refusal Behaviour in Recurrent-Depth Language Models
A recurrent-depth language model reuses one block of weights several times in a row. The number of repetitions, which we call loops, is chosen when the model runs, not when it is trained, and running fewer is cheaper and faster, so a deployment may choose to do it. Running fewer loops also makes these models less safe, and the loss of safety is larger than the loss of anything else we measured. We study four released Ouro checkpoints and Huginn-0125. At half of its trained depth, Ouro-1.4B-Thinking still solves 0.692 of the GSM8K maths problems, against 0.775 at full depth, keeping 89% of its accuracy. Over the same reduction, the rate at which it helps with harmful requests rises from 0.038 to 0.205, 5.3 times higher. The information is not lost: a linear classifier reads whether a request is harmful from the model's internal state after a single loop, with an ROC AUC of 0.967 against 0.986 at full depth. What the missing loops remove is the refusal that should follow. We measure the effect with four instruments, one generating no text at all, and reproduce it on a second model family. Removing a single direction from Ouro-1.4B's internal state at full depth drops its refusal rate on harmful prompts from 0.950 to 0.130, identifying what the shallow model is missing. Two run-time repairs do not help: the models' early-exit rules do not spend more loops on harmful requests, and choosing a depth per request does not recover the loss. Changing the training does. Standard safety training makes the shallow model safe only by refusing 0.865 of harmless requests, while training at randomly chosen depths reaches a separation of +0.399 between harmful and harmless refusal at one loop, against +0.118. On Huginn-0125 it keeps harmful help at or below 0.040 at every depth from 1 to 32 loops, where standard training reaches 0.194, and it costs no accuracy at full depth.
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Robotics
nanoflann: A Header-Only KD-Tree Library for Exact Nearest-Neighbor Search on Compile-Time Product Manifolds
Nearest-neighbor (NN) search underlies countless robotics algorithms, but many state spaces are not Euclidean: orientations live on $SO(2)$ or $SO(3)$ and poses on $SE(2)$ or $SE(3)$, and a Euclidean KD-tree on their raw coordinates returns wrong neighbors. We present a header-only, dependency-free C++ KD-tree library for exact NN search on user-defined product manifolds declared at compile time: the space is composed from base manifolds ($\mathbb{R}^n$, $SO(2)$, $SO(3)$, $S^n$; products $SE(2)$, $SE(3)$, tori) with a single type alias, and the library synthesizes a metric whose pruning is provably admissible, wrap-aware for circular coordinates and double-cover-aware for unit quaternions. Experiments confirm exactness (recall $1.0$ vs an exhaustive scan under the same product metric), where the Euclidean-on-raw shortcut collapses to recall $\approx 0.5^{m}$ for $m$ rotation blocks, with up to three orders of magnitude speedup over brute force. We further contribute an incremental, self-balancing single-tree index for points under heavy churn (e.g. sliding-window LiDAR maps) or $SE(3)$ trajectories: bounded memory and faster updates than prior work, with an optional asynchronous tail-latency-bounding mode. The implementation is open source: https://github.com/jlblancoc/nanoflann
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Networking
NAS Timers for Non-Terrestrial Networks: Current Standards and Directions
Response-supervision timers in the 5G Non-Access Stratum (NAS) bound the time allowed for signaling exchanges before retransmission or abnormal-case handling begins. In non-terrestrial networks, that interval can include satellite propagation, terrestrial transport, and processing by multiple core-network functions. Under current 3GPP specifications, the applicable timer value for satellite access is selected according to the satellite NG-RAN radio access technology (RAT) type. However, control paths within the same low Earth orbit (LEO) network can differ in propagation delay and processing load. This article reviews the relevant 3GPP timer semantics and traces the delay components covered by different timers through 5G registration. It organizes candidate refinements along two dimensions: configuration granularity and information scope. A registration case study illustrates the trade-off between avoiding premature timer expiry and recovering promptly from message loss. The article identifies the information and coordination that future specifications would need to address to support interoperable timer configuration.
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Computation and Language
PANINI-DR: Controlled Deep Research through Generative Semantic Workspaces
Deep research requires connecting multiple steps of search, reasoning, and computation, with intermediate findings guiding what to investigate next. As investigations grow, agents must maintain research state across model calls and check findings before errors propagate into subsequent work. We introduce PANINI-DR, a multi-agent harness that separates coordination of the overall investigation from the research and verification of individual subquestions. A shared workspace, built on the Generative Semantic Workspace representation, records subquestions, their dependencies, findings, and supporting evidence. Researchers investigate individual subquestions, while a separate verification agent checks proposed answers against those subquestions and their evidence. Verification feedback guides further investigation, and recorded findings inform subsequent assignments. We evaluate PANINI-DR on BrowseComp-Plus, FRAMES, and MoNaCo against seven state-of-the-art deep-research harnesses, all using a shared language-model backbone and frozen corpora. PANINI-DR achieves the strongest average performance across the three benchmarks. On BrowseComp-Plus, it achieves 73.3% accuracy, outperforming the next-best harness by 16.0 points. Its advantage is strongest on hard questions, where it answers nearly twice as many as the next-best harness. Ablations further show that structured planning and persistent state improve performance, as does checking each finding against its cited evidence before it is reused. Because a model can answer correctly from memory alone, we also analyze the evidence retained by each harness. PANINI-DR achieves the highest answer recoverability from saved evidence on all three benchmarks, while complementary claim-support audits show stronger evidence-backed answers. Accounting for this evidence changes how harnesses compare and further strengthens PANINI-DR's advantage.
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Machine Learning
Exploring Jailbreak Vulnerability Across Depth-Based Dynamic Inference in Large Language Models
Large Language Models (LLMs) have been shown to be computationally expensive and vulnerable to jailbreak attacks, in which adversarial prompts bypass safety alignment and induce harmful responses. To address this inefficiency, a range of techniques have been proposed to enable efficient LLM inference. Depth-based dynamic inference has demonstrated promising results by enabling outputs to be generated from intermediate layers. It offers the flexibility to adjust model behavior based on the available resource budget. However, how this flexibility affects the robustness of LLMs against jailbreak attacks remains unexplored. In this paper, we address this gap via a comprehensive investigation into the impact of depth-based dynamic inference on the robustness of LLMs against jailbreak attacks. Specifically, we make the following key observations: 1) Shallow exits are consistently more robust to jailbreak attacks than deeper ones; 2) Exit depth affects how easily the adversarial suffix can be optimized, with deeper exits reaching lower attack loss; and 3) Adversarial suffixes affect utility uniformly across exit depths. These insights can help design dynamic inference methodologies that are more robust to jailbreak attacks. Code is available at https://github.com/LassNajmuldeen/balcony-jailbreaking
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Hardware Architecture
MoSAIC: Learning DAG Scheduling Heuristics from Optimal Schedules through Motif-Aware Recovery and LLM-Guided Reasoning
Efficient task scheduling in heterogeneous computing systems remains a fundamental challenge in embedded and high-level synthesis flows. This paper presents MoSAIC (Motif-aware Scheduling with AI-driven Cognition), a learning-based framework that bridges the gap between exact and heuristic scheduling approaches for DAG-based applications. The system uses the reasoning capabilities of large language models (LLMs) to learn the relationships between DAG structures and scheduling priority functions. The framework first leverages the OR-Tools CP-SAT solver [4] to generate optimal schedules, which are then used to supervise the learning of compact priority-based scheduling functions through Bayesian Optimization. These learned heuristics capture relationships between scheduling decisions and structural graph features such as rank, depth, and fanout, enabling the construction of a reusable knowledge base across diverse DAG instances. Experimental results across synthetic graph families and real-world benchmarks, including PolyBench and MachSuite, show that the learned heuristics consistently improve over classical approaches such as HEFT [2], while maintaining low runtime overhead. The results indicate that combining optimal supervision with learning-based generalization provides a practical approach for scalable and adaptive task scheduling.
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Artificial Intelligence
SocraticRepair: Planning-Guided Socratic Tutoring for Program Debugging and Misconception Repair
Large language models are increasingly used in computer science education. However, the teaching abilities of even the most powerful LLMs are limited: they tend to reveal the solution prematurely and may lose focus on the learner's current debugging objective. To address this, we introduce SocraticRepair, a planning-guided Socratic tutoring framework for program debugging and miscon- ception repair that adapts prior planning-guided tutoring work (Li et al., 2026b). The framework is instantiated in the Python programming domain by fine-tuning Qwen2.5-Coder-7B-Instruct on synthetic multi-turn tutoring dialogues constructed from four preprocessed programming datasets. The system is evaluated using a predefined set of independent metrics and benchmarked against a general-purpose LLM. The experiments show that SocraticRepair achieves higher scores on stepwise scaffolding and question quality while also substantially reducing premature solution disclosure. The results also identify reliable pedagogical plan generation as an important remaining challenge.
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Computation and Language
Do LLMs differentiate linguistic traits internally?: A layer-wise analysis
Large language models often produce judgments that resemble human responses, but it remains unclear whether they internally capture linguistic nuances such as conventional versus idiomatic meaning. A layer-wise representational analysis was conducted on two equal-sized pre-trained models, Llama-3.2-1B and Gemma-3-1B-PT, to examine whether and where these models differentiate linguistic traits from input. The analysis combined layer-wise probing with geometric distance measures, using the top embedding dimensions ranked by principal component loadings for each layer. The results show that even with equal capacity, models organize linguistic information in fundamentally different ways, suggesting the need to analyze internal representational geometry, examining not just behavioral outputs but semantic space alignment when evaluating how closely human and model language interpretation correspond.
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Cryptography and Security
On the Effectiveness of NetFlow-Based Deanonymization of Tor Onion Services (Extended Version)
In the context of Tor, deanonymization attacks via traffic correlation have long been studied for both clients and onion services. Complementing prior investigations that utilize fine-grained flow metadata such as packet sizes and timings, we study a relatively less explored yet easier-to-obtain adversarial capability: deanonymization using only coarse NetFlow-style telemetry, such as one-minute, 1-out-of-1,000 sampled packet counts. We first revisit active NetFlow-based traffic analysis attacks against Tor onion services and show, through large-scale experiments with live Tor data, that coarse telemetry is sufficient to deanonymize a targeted onion service when the adversary can induce discernible traffic patterns through controlled downloads. We then introduce a stronger active attack based on controlled introduction requests, which removes application-specific assumptions and gives adversaries more flexibility while achieving comparable success rates. Finally, we present a passive deanonymization attack that sends zero traffic to target onion services. The attack exploits Tor's puzzle-based DoS defense as a side channel: public puzzle difficulty reveals service-load changes that can be semantically matched against NetFlow traces. Our findings show that coarse network telemetry poses a practical deanonymization threat to onion services today and call for proactive mitigations and a redesign of the globally visible defense signals that may leak service-load information.
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Hardware Architecture
Programmable Data Layouts via On-The-Fly Data Transformation
The performance of modern computing systems is heavily bottlenecked by the widening gap between processing throughput and main memory latency, a problem exacerbated when an application's logical data access patterns misalign with the physical layout of data in memory. To address this, we propose a hardware-software co-design framework comprising the Data Transformation Language (DTL) and the Data Transformation Unit (DTU). DTL allows programmers to concisely express complex data layout reorganizations, which the compiler translates into efficient hardware routing configurations. The DTU, a hardware engine logically situated between the Last-Level Cache (LLC) and main memory, transparently evaluates these configurations on-the-fly to gather scattered data elements into dense, logically contiguous cache lines. By converting explicit layout transformations into virtual views, this approach eliminates the need for explicit data materialization in software. We evaluate the DTU within a quad-core RISC-V SoC using FireSim, demonstrating substantial improvements in execution speed and memory efficiency.
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Information Theory · Cross-listed from physics.app-ph
Directivity Estimates and Tolerance Tradeoffs in the Presence of Random Perturbations
The practicality of realizing high-directivity sources is studied using a generalized sensitivity metrics. These measures are based on the error model adopted in previous studies on array tolerance, but account for heterogeneous array characteristics in an arbitrary source-expansion basis, making it applicable to the study of continuous sources, ideal uncoupled arrays, and heterogeneous arrays with mutual coupling. The formulation provides the ensemble average of realized directivity under the selected error model, making it a fast predictor of anticipated directivity reduction due to source perturbation. The data required to compute these predictions are straightforward to obtain via simulation or measurement, with a significant simplification when the system can be approximated as lossless. The directivity and the proposed tolerance measures allow for the formulation of optimization problems illustrating the tradeoff between these measures. Several examples demonstrate these tradeoffs, special cases, comparison to previous estimates of maximum directivity, and the accuracy of sensitivity as a predictor of statistical performance over large ensembles of design realizations.
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Artificial Intelligence
Continuous Risk-Based Scheduling for Food Safety Inspection: Integrating Historical Decay with Event-Driven Consumer Review Signals
Batch risk-based inspection scheduling struggles to detect a critical failure class: food facilities with recent clean inspections that subsequently develop severe violations. Traditional systems recompute risk on fixed planning cycles using static historical data, leaving blind spots between inspection cycles. To address this, we introduce the Continuous Inspection Risk (CIR) system, an event-driven scheduling pipeline that re-ranks the inspection queue dynamically as new data arrives. CIR combines a decay-weighted historical score with a stream of real-time consumer reviews triaged by a language-model classifier. A key structural contribution is our temporal partition rule, which strictly excludes reviews predating the most recent inspection to prevent superseded signals from skewing current risk. Evaluating CIR on 9,505 routine inspections in Santa Clara County, California (2024-2026), we show that history-based scoring alone reduces mean time-to-detection of major violations by 69 days (20.9%) under a 30% inspection budget, but fails to anticipate severe vermin-related closures (0/8 detected). Incorporating post-inspection review signals drastically improves performance, predicting 7 of 8 vermin closures with an average lead time of 117 days-firing on the exact day of review publication in four instances. Introducing a review corroboration rule improves precision from 0.70 to 0.78 without loss of recall. Finally, we analyze critical implementation challenges, documenting a data-hygiene pitfall (stale review leakage across inspection boundaries) and an evaluation limitation involving unobserved facility self-remediation. This work provides the first case-level evaluation of event-driven inspection triggering using open data and provides a reproducible benchmark for review-augmented public health systems
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Databases
Join Order Enumeration and Optimization for Double-Star and Helix Join Graphs
Join ordering is classic problem in data management. We highlight the connection between structure-specific dynamic programming algorithms and the mathematical enumeration of the possible merge trees from a join graph. We present two case studies, on double-star and helix shaped join graphs, that we believe carry useful techniques for a toolbox of building structure-specific join optimizers. For the double-star case, we show how the enumeration leads directly to a significantly improved search algorithm, whereas for the helix case we show that a algorithm derived from the mathematical enumeration is not necessarily better than structure-agnostic algorithms.
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Computation and Language
SAFE-KV: Causal Suffix Repair for Behavior-Preserving Non-Prefix KV Cache Reuse in RAG
Retrieval-augmented generation (RAG) reuses the same documents across many requests, making non-prefix KV-cache reuse attractive. Yet a cached document state is not reusable text: it is a context-conditioned causal state whose keys and values depend on the prefix, position, and preceding documents under which it was computed. We formulate non-prefix KV reuse as a behavior-preservation problem with full prefill on the exact prompt as the reference, and introduce SAFE-KV, which repairs a composed cache by re-encoding the causal suffix from a selected start document. On Qwen2.5-7B-Instruct, prefix-conditioned composition preserves only 47.2% of HotpotQA-500 and 37.8% of 2Wiki-500 full-prefill answers; SAFE-KV with risk-guided K2 selection restores 99.8%/98.4% (donor-copy protocol) and 100.0%/98.4% with actual suffix forwarding. Document-only and fixed-window repairs recover far less, because the document states after the repaired region keep histories that omit it. Reuse without repair is exact up to four documents and degrades at sixteen, where suffix repair recovers 98-100%. Faithful repair re-encodes most of the context, so in a single-request L40S study SAFE-KV's operating rule serves every workload by full prefill. SAFE-KV thus establishes the causal-state contract for non-prefix reuse and a validated repair mechanism that meets it.
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Machine Learning
DeltaNet-PC: Test-Time Memory Without Backpropagation Through Time
Test-time memorization of sequential information is a foundational capability for any intelligent system that needs to rapidly store and retrieve data, as demonstrated by the attention mechanism in large language models. However, Transformers and linear attention variants are trained via backpropagation through time (BPTT), which has drawbacks such as its enormous memory requirements. Predictive coding (PC), an algorithm that optimizes a prediction-error energy function with local updates, offers a compelling solution but still lacks test-time memory for sequential data. We develop a solution to this problem by treating the per-step memory update $\Delta S_t$ as a latent variable, as opposed to a slow weight to be learned. By taking the log probability of a standard PC-based probabilistic model, we derive a PC-native solution for verbatim sequence memory, and relate our update rule to common choices in the linear attention literature (e.g., DeltaNet). We present an extensive set of empirical tests to probe our system's properties, including its scaling capacity, memory footprint, and ability to infer a context from evidence (e.g., bank (river) vs. bank (money)). We show how DeltaNet-PC can be used for storing single sequences of data, multiple sequences of data, and key-value associative memory pairs with perfect recall accuracy.
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Information Theory
Effective DoF Collapse in Sparse Near-Field Beamforming: A Block-Rank-1 Mechanism
Sparse near-field arrays phase-cohere $M$ widely separated sub-arrays of $N$ elements and underpin distributed MIMO, satellite formations, and integrated sensing and communication. We show that their interference suppression over a protected region is set by coherence within a single sub-array rather than by the span of the formation: the effective rank of the region covariance can collapse from $MN$ to $M$. Two independent arguments establish this. For canonical line and disk regions each diagonal covariance block is exactly a classical concentration operator, which supplies sharp per-block rank thresholds and makes fewer than one spatial degree of freedom per sub-array a conservative design rule; an orthogonal decomposition with eigenvalue interlacing gives a nonasymptotic sufficient condition that assumes nothing about the coupling between platforms. The consequences are covariance-side and beamformer-independent: the unloaded Capon functional upper-bounds worst-case signal-to-interference ratio, while its regularized counterpart scales very differently for angularly separated and for in-cone targets. An eight-satellite LEO study validates the theory, including realized worst-case SIR.
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Machine Learning
Game-Theoretic Reinforcement Learning based Topology-Agnostic Defense for Virtual Power Plants
The rapid proliferation of distributed energy resources (DERs) aggregated by virtual power plants (VPPs) elevates cybersecurity risk by expanding the attack surface. A coordinated cyberattack has the potential to disrupt distribution-system, bulk-system, and market operations. Existing cyberphysical defense strategies largely assume access to grid network models and operating conditions, which may not be available to third-party aggregators. This paper proposes a novel hybrid, perturbation-based cyber-physical defense for VPP-operated DERs that blends game-theoretic planning with model-free reinforcement learning (RL) under a Bayesian belief-update framework. Topology agnosticism is defined from the VPP information and implementation perspective: the VPP does not require access to the feeder topology, line parameters, switching configuration, or full system state. This work advances the state of the art through three contributions: (1) a multi-output Gaussian process with Hamiltonian Monte Carlo for discrete attacker-type inference, probability of detection, and confidence of detection for modeling the belief distribution; (2) moment-matched Gaussian propagation of posterior beliefs across episodes; and (3) an RL policy that adaptively integrates Stackelberg leader (VPP) actions with exploration. Furthermore, we establish equilibrium existence and derive an episode-level closed-loop utility bound connecting attacker-belief uncertainty with GT-RL action alignment. Evaluations on IEEE 13- and 123-Bus feeders with DER portfolios demonstrate effective detection under attacker-model uncertainty and evaluated feeder re-configuration conditions, while requiring no explicit feeder-topology knowledge. Overall, the results indicate that combining bi-level game-theoretic planning, nonparametric Bayesian inference, and adaptive RL is a promising direction for VPP cybersecurity.
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Computation and Language · Cross-listed from eess.AS
Word-Aligned Prosody Reflects Speaker Differences More Than Depression or PTSD Severity
Word-aligned prosody is increasingly used to detect depression and posttraumatic stress disorder (PTSD), yet the stability and clinical relevance of these measurements remain unclear. We examine stability at two levels. At the word level, we ask whether a speaker produces the same word in a similar speaker-specific way across different utterance contexts. At the speaker level, we ask whether averaging prosody across many words produces consistent speaker scores across separate recordings. Drawing on principles of psychological measurement, we compare these representations in four corpora spanning acted, spontaneous, and clinical speech. Word-specific deviations show little cross-context recurrence (0.01-0.16), whereas speaker summaries are highly consistent, reaching 0.997 in ESD, 0.73-0.90 in MSP-Podcast, and 0.84-0.996 in DAIC-WOZ and PTSD-STOP. Despite this consistency, associations with depression or PTSD severity do not exceed 0.15; equivalence tests exclude effects of 0.30 in all analyses and 0.20 in DAIC-WOZ, while within-person associations with daily PTSD symptoms are near zero ($|\rho|\leq0.04$). Thus, aggregation yields stable speaker-level prosodic measures, but these measures do not detectably track depression or PTSD severity in the studied corpora. Code is available at https://github.com/jen900704/word-aligned-prosody.
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Computation and Language
UDHRBench: Benchmarking Human Rights in Large Language Models
Large language models are increasingly deployed in contexts requiring adherence to ethical and legal norms, yet their alignment with internationally recognized human rights standards remains underexplored. We introduce UDHRBench, a large-scale benchmark for operationalising the evaluation of large language model compliance with the Universal Declaration of Human Rights. The dataset comprises 1,124 human rights confronting questions covering all 30 articles and 4,496 responses from four large language models (ChatGPT, Grok, Gemini, and Fanar), manually annotated by experts for alignment, with high inter-annotator agreement ($\kappa = 0.801$). Our analysis reveals systematic and non-trivial misalignments, showing that violations typically arise through seemingly rational reasoning: appeals to efficiency, risk management, or scientific neutrality, rather than explicit rejection of rights. We further propose an LLM-as-a-Judge framework for automated evaluation using zero-shot and few-shot prompting, achieving 89.8% weighted F1-score in detecting human-rights misalignment, alongside a novel Alignment Leniency Score that quantifies how judge models resolve ambiguous cases. The dataset, annotations, and code will be released as open-source resources (https://sina.birzeit.edu/UDHRBench).
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Machine Learning
Only What You've Signed up For: Secure Workflows with Constrained Diffusion Agents
As agentic AI systems take on increasingly complex and consequential tasks, securing them against prompt injection becomes critical. Existing defenses often rely on detecting or reasoning about injected malicious instructions and can therefore remain vulnerable to adaptive attacks that optimize the injection itself. Diffusion language models (dLLMs), an emerging framework for language generation, offer a new opportunity for security enforcement: by iteratively refining their sequence wide predictions, they enable broader-scope constraint enforcement throughout generation. This paper introduces Policy-Constrained Diffusion Agents (CoDA), a framework that enforces task dependent security policies directly within the denoising process of diffusion language models. At each denoising step, CoDA projects token distributions onto a policy-compliant set, maintaining constraint satisfaction throughout generation. We evaluate CoDA across state-of-the-art diffusion language model families under both static and adaptive prompt-injection attacks. Results demonstrate substantial reductions in attack success rate with competitive task utility and practical inference overhead.
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Machine Learning · Cross-listed from physics.flu-dyn
Physics Foundation Models for Efficient Control of Fluid Flows
We investigate whether a physics foundation model (PFM) pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control. We construct a PFM-based controller by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations and train the policy using proximal policy optimization (PPO). We evaluate the approach on HydroGym's two-dimensional Kolmogorov-flow environment using vorticity observations at \(64\times64\) and \(128\times128\) resolutions and Reynolds numbers \(\mathrm{Re}=100\) and \(200\). Across these settings, we compare the frozen PFM controller against a baseline MLP policy trained with the same PPO framework. The PFM controller achieves consistently higher reward while requiring smaller executed action magnitudes over training, indicating improved control performance with reduced control effort. These results provide initial evidence that representations learned through self-supervised next-frame prediction can be transferred directly to closed-loop fluid flow control. Project page: https://mahindrautela.github.io/morph.
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Numerical Analysis
Interpolation in path-connected metric spaces using splines on embedded graphs
We study a local graph-based interpolation framework for data defined on graph vertices embedded in a metric space. The resulting interpolants are constructed from variational graph splines defined on small neighborhoods, yielding continuous-domain extensions of the graph data. We analyze their behavior through energy estimates, Lipschitz continuity, and stability properties, and compare them with $k$-Nearest Neighbor ($k$NN) interpolation as a natural baseline due to its simplicity and widespread use. Numerical experiments on the manifold of symmetric positive definite matrices illustrate the relative performance of the proposed local interpolation schemes and $k$NN interpolation across varying levels of smoothness and noise.
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Machine Learning
LexiCan: Lexicographic Canonicalization of Point Clouds for Machine Learning Applications
Canonicalization resolves the rotational and permutation ambiguity of 3D point clouds by selecting a unique orbit representative, maintaining their geometric information while allowing standard architectures, such as Transformers, to operate on them. Existing canonicalizations, however, exhibit discontinuity jumps on molecular configurations and non-trivial invariance errors in popular molecular datasets, which lead to ambiguity in their representation. To bridge this gap, we introduce LexiCan, a canonicalization that is provably invariant under either $O(3)$ or $SO(3)$, empirically invariant to rotations to within $\sim 10^{-6}$ angstroms on the QM9 and QM-sym molecular datasets, and mitigates discontinuity jumps on QM-sym, while running orders of magnitude faster than an existing canonicalization. Finally, non-invariant models perform better on QM9 property prediction and ModelNet40 shape classification with LexiCan than with that canonicalization.
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Computer Vision
ExeWorldBench: Benchmarking Code-Based Executable 3D World Modeling
Coding agents are increasingly evolving beyond reproducing what a world looks like toward constructing executable worlds that capture how a world works. This shift calls for executable world modeling, which integrates two core capabilities: world understanding, reasoning about the underlying structural, mechanical, and causal principles of a world, and executable realization, translating that understanding into a code-based system whose behavior emerges from physical interactions. However, existing benchmarks provide only fragmented evaluations centered on physical reasoning, visual fidelity, or behavioral correctness, leaving the integration of these capabilities insufficiently assessed. To bridge this gap, we introduce ExeWorldBench, to our knowledge the first benchmark to comprehensively evaluate world understanding and executable realization through code-based 3D world construction. ExeWorldBench comprises three progressively challenging tasks: Mechanism Executability, which evaluates the realization of individual mechanisms from visual observations; Compositional Executability, which extends to multi-stage systems with spatial, mechanical, and causal dependencies; and Intent-Driven Executable World Synthesis, which requires constructing executable worlds from high-level goals and physical requirements. Extensive experiments on frontier models reveal substantial limitations in executable world modeling, offering insights into the development of more physically grounded and causally coherent world construction systems.
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Computation and Language
Active Learning for Finding a Needle in a Haystack
Training a classifier to find a rare class of documents, such as hate speech directed at a particular religious group, requires labelled examples that are expensive to obtain when the class makes up only a small fraction of a corpus. Active learning reduces this cost, but it must start from an initial labelled set that contains examples of the target class. Random sampling cannot supply these at reasonable cost, so they must be selected in some other way, such as keyword search, and any such selection biases the initial set towards part of the target class. We evaluate whether active learning can correct this bias. On AG News and Measuring Hate Speech, at a prevalence of around 1%, we compare random sampling with eight active learning strategies, starting from initial sets that cover or omit known subgroups of the target class, and measure recall on the omitted subgroups as well as F1. On AG News, almost every strategy recovers the omitted subgroup. On Measuring Hate Speech, uncertainty-based strategies recover less of the omitted subgroups than random sampling, whereas discriminative active learning recovers 55% of them without a significant loss of F1. Aggregate metrics conceal these differences.
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Computer Vision
TRIG: Toward Measuring Texture Realism in Image Generation
This paper studies the backbone used by metrics for evaluating the quality of generated images. Although generative models have advanced rapidly, some outputs still exhibit unrealistic texture characteristics, and these differences are difficult to measure. Widely used evaluation metrics provide limited insight into texture realism, since they often rely on a backbone trained for another objective, such as image classification or image-text alignment. Such objectives typically encourage invariance to low-level variations that carry texture, so the resulting features primarily encode semantic and global structure. As a result, texture-specific discrepancies may not be explicitly captured. We propose TRIG, a metric directed at the texture realism of generated images. Its backbone is instead the discriminator of a generative adversarial network pre-trained on a texture dataset, which provides a learned prior for the local statistics of natural textures. A plausibility head is fine-tuned to identify local texture degradations, while preserving natural defocus and sensor noise as positive cases. On the features of this backbone, we compute a standard distributional distance between a reference set of real images and a set of generated ones. We apply TRIG to several generative models and observe closer agreement with human realness ratings than baseline metrics.
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Computation and Language
Sanzaru: Benchmarking Protocol Formation under Epistemic & Communication Asymmetry
A language model's ability to solve a task individually does not ensure that a team can solve it under unequal access to information and communication. SANZARU examines this gap through cooperative bomb-defusal puzzles adapted from BOMBANANA! (Lefto Studio, 2026). Task information and action authority are divided among three agents: one cannot hear, another cannot speak, and the third cannot see. The benchmark contains 120 puzzle instances across seven families, each targeting a distinct coordination ability. Across 1512 episodes, 7 models achieve an overall success rate of 49%, ranging from 20% to 86% under the evaluated configurations. Teams develop or adopt diverse communication protocols, from simple gesture codes to Morse and encodings of entire manuals. Yet trace analysis attributes about 60% of 771 team losses to communication, and agents attempt to use channels unavailable to their teammates despite explicit role instructions. Together, task outcomes and interaction traces enable evaluation of both collaborative performance and perspective taking throughout cooperation. The benchmark is available at https://github.com/markli404/sanzaru-benchmark.
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Machine Learning
Beyond Adjacent Layers: Graph-Guided Layer Fusion for Compressing Large Language Models
Existing depth-compression methods for large language models (LLMs) score layers individually or group only adjacent or contiguous layers, implicitly assuming that functional redundancy is local. We test this assumption by computing full pairwise Centered Kernel Alignment (CKA) similarity matrices for thirteen LLMs from six architecture families (1.6B-14B parameters). Non-adjacent layers have 3.6-15.9x more high-similarity pairs than adjacent ones, a structure that prior similarity-based layer merging has not systematically exploited. We propose Fusion via Community Mining (FCM), which builds the full L x L similarity graph, uses spectral community detection to find clusters of functionally equivalent layers, keeps the highest-Block-Influence layer in each cluster, and applies LoRA recovery; a pre-specified rule computed only on calibration data chooses between cosine and CKA similarity. At 2x compression, FCM lowers mean perplexity below ShortGPT on twelve of thirteen models, significantly on ten (Welch's t-test with Holm-Bonferroni correction; up to 50% on Qwen3-4B), with Mistral-7B the only loss (+13.4%). Against FlattenGPT, SWM, and DeltaLLM under matched calibration and recovery, FCM gives the best perplexity on ten of thirteen models (mean rank 1.15), and it also outperforms MKA on three anchor models. FCM matches or exceeds ShortGPT on 15 of 20 zero-shot reasoning cells and also improves MMLU, LAMBADA, HumanEval pass@1, and free-form generation quality. The 2x-compressed Qwen2.5-7B has 46% fewer parameters, 42% lower peak VRAM, and 84% higher decode throughput on a single A100. Spectral grouping outperforms Fisher contiguous segmentation by 41% and uniform partitioning by 51%, and FCM's advantage grows beyond a 2x crossover up to 3x and persists at the 14B scale. Code: https://github.com/Usama1002/fcm-layer-fusion
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Computation and Language
Learning Proposition-Level Links from Sentence-Level Supervision for Neuro-Symbolic NLI
We study neuro-symbolic natural language inference (NLI) with independently translated propositional representations of the premise and hypothesis. Before symbolic reasoning, the system must infer semantic links between their proposition-level units (atoms). Existing systems based on Abstract Meaning Representation (AMR) and Boolean satisfiability (SAT) identify these links using fixed embedding-based source selection and pretrained sentence-level NLI models not trained for atom-level linking. We introduce a trainable atom linker that jointly predicts link existence, source selection, and relation type. Without atom-pair training annotations, we treat cross-formula link structures as latent and train the linker from sentence-level NLI labels, keeping the translator and SAT reasoner fixed. We evaluate on the full public test splits of Stanford Natural Language Inference (SNLI) and Sentences Involving Compositional Knowledge (SICK), and the matched and mismatched validation splits of Multi-Genre Natural Language Inference (MNLI). Our system improves accuracy by 11.40-27.09 percentage points over a baseline applying sentence-trained NLI models unchanged to atom pairs within the same SAT pipeline. It also improves over the prior fixed-linker AMR-to-SAT system by 8.14-26.32 percentage points on SNLI and both MNLI splits, with a smaller gain on SICK.