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arXiv2026

Functional Attentive Interpretable Regression

In function-on-function regression, the coefficient surface $β(s,t)$ may exhibit complex support structure---from localized patches to global patterns such as disconnected regions, bands, or rings---where effect similarity does not align with Euclidean proximity. Projection-based methods that rely on fixed basis expansions can obscure such structure, while direct smoothing approaches risk oversmoothing the surface and its boundaries. We propose Functional Attentive Interpretable Regression (FAIR), which represents $β(s,t)$ directly through coordinate features and uses self-attention to learn effect-adaptive neighborhoods, enabling information sharing at both local and global scales. A scalar compression network maps these learned representations to the coefficient surface. Sparsity and smoothness penalties applied over these neighborhoods promote localized support with coherent boundaries. We establish a sieve equivalence to tensor-product spline spaces and derive convergence rates. Simulations and applications to oceanographic and hydrological data demonstrate that FAIR recovers support geometry more accurately than existing methods while achieving superior prediction, particularly under sparse sampling.

stat.ML↗
arXiv2026

Efficient $C^1$ Bernstein Quasi-Trefftz Discretization for Heterogeneous High-Frequency Helmholtz Problems

We develop an efficient $C^1$ Bernstein quasi-Trefftz discretization for heterogeneous high-frequency Helmholtz problems on unstructured triangular meshes. The method first imposes strong $C^1$ continuity through Bernstein--Bézier smoothness relations on local macro-patches and then reduces the resulting conforming polynomial space by enforcing projected Helmholtz residual constraints. On two-triangle patches, this compresses the local dimension from quadratic growth in the polynomial degree to a trace-sized space of dimension $2p+1$ under the natural rank condition. Variable matrix-valued coefficients are handled through local polynomial projection, allowing coefficient-approximation effects to be separated from discretization error. A graph-residual formulation couples the reduced patch spaces and produces a sparse global system in compressed coordinates. The implementation combines explicit $C^1$ continuation, batched coefficient projection, batched residual construction, and stable local kernel extraction by QR factorization. Numerical experiments on heterogeneous unstructured meshes demonstrate high-order accuracy, roundoff-level $C^1$ conformity, robust high-frequency resolution, and substantial reductions in local and global computational cost. Turning-point and penetrable-scattering examples further illustrate the flexibility of the approach.

math.NA↗
arXiv2026

SAFEGuard: Detect Optimization-Based Jailbreak Attacks Through Harmful Semantic Analysis and Fluency Measurement

Despite the significant efforts devoted to aligning large language models (LLMs) with human values and ensuring safe deployment, recent work has revealed that LLMs remain vulnerable to adversarial jailbreak attacks that can bypass safety guardrails and elicit harmful responses. Many defense methods are proposed to detect jailbreaks but they are limited in their effectiveness to counter wide-range optimization-based jailbreak mechanisms that can yield highly fluency-optimized or harmful semantic obfuscated prompts. To tackle this challenge, we propose a unified detection framework SAFEGuard which incorporates a hybrid fluency measurement based on cross-layer distribution distance and perplexity, and the analysis of harmful semantics through gradient matching. Our method is grounded in a paramount observation: high fluency prompts maintain their malicious intention close to harmful prompts while harmful semantic obfuscated prompts often inject gibberish token sequences. Our evaluation demonstrates that SAFEGuard consistently outperforms state-of-the-art baselines and achieves significant improvement in accuracy across different optimization-based jailbreaks. This underscores the effectiveness of SAFEGuard against evolving jailbreak attacks.

cs.LG↗
arXiv2026

High-order smoothness and high-order collocation approximation for Volterra integral equation with multiscale and nonlinear exponent kernel

We consider a Volterra integral equation with multiscale and nonlinear exponent kernel. We propose the high-order smoothing conditions, under which the initial singularity of the solutions can be eliminated up to any prescribed order. This indicates the application of the multiscale nature of the kernel on local modification of the solutions. Then a discontinuous high-order collocation method with arbitrary polynomial degree is developed and analyzed on uniform or graded meshes based on the solution regularity. This work serves as a comprehensive extension and complement to [Zheng, Qiu and Stynes, SIAM J. Numer. Anal., to appear] in both mathematical and numerical aspects.

math.NA↗
arXiv2026

Quantum Message Passing Convergence and Vanishing Block-Error Probability for Random LDPC Codes

Belief propagation with quantum messages (BPQM) is a quantum algorithm that decodes classical codes transmitted over classical--quantum channels. It realizes optimal decoding on tree factor graphs over pure-state classical-quantum channels. However, this tree-based analysis does not ensure vanishing block-error probability for LDPC Tanner graphs with cycles. In this work, we construct a two-stage BPQM decoder for random $q$-ary LDPC codes over symmetric $q$-ary pure-state channels, where $q$ is prime, and prove that its ensemble-average block-error probability vanishes as the blocklength $N$ tends to infinity. For regular ensembles with $d_v\geq3$, fidelity bounds yield double-exponential decay of the average symbol-error probability throughout the BPQM success region. We apply depth-$\ell$ BPQM to coordinates with tree neighbourhoods and treat the remaining coordinates as erasures. With a suitable $\ell=Θ(\log\log N)$, a noncommutative union bound controls the BPQM decoding errors, while the minimum-distance property guarantees erasure recovery. We also extend the analysis to finite-support irregular ensembles. These results are relevant to quantum algorithms based on Regev's reduction, where coherent decoding uncomputes a codeword register. Decoded quantum interferometry (DQI) uses a closely related Fourier-based framework that reduces sparse max-LINSAT optimization problems to LDPC decoding problems on pure-state channels. Our results justify the use of BPQM in the decoding step of DQI and of coding-theoretic algorithms based on Regev's reduction whenever the code is drawn from one of the random LDPC ensembles analyzed here and the induced memoryless symmetric pure-state channel lies in the BPQM success region.

quant-ph↗
arXiv2026

Selective Posterior Margin Regularization for Forward-Corrected Classification

Learning with class-conditional label noise often relies on a transition model from latent clean classes to observed annotations. Forward correction embeds this transition in the likelihood, yet finite-sample networks may still memorize corrupted labels. The corrected likelihood also induces a reverse posterior over the clean classes that could explain each annotation. When its leading class differs from the annotation, the model and transition matrix provide evidence against that annotation, but the leading alternatives can remain nearly tied. We introduce Selective Posterior Margin Regularization (SPMR), which preserves the Forward objective and converts this disagreement into a graded update on the clean classifier. SPMR selects the leading reverse-posterior class, scales a detached pairwise margin by the separation between the two leading posterior classes, and assigns correspondingly little influence to diffuse conflicts. The gap factorizes into transition- adjusted pairwise separation and the posterior mass carried by the leading pair. The active margin follows the locally minimum-norm logit direction that enlarges the selected pairwise margin. Across five known-transition benchmarks, SPMR improves full-length Forward by 2.5-7.0 percentage points and remains 0.7-2.5 percentage points above Forward with Mixup and early stopping. Matched interventions support distinct gains from the posterior-space coefficient, transition-adjusted target, and pairwise action. The same design transfers to estimated transitions, human annotations, architectural changes, and stronger Forward recipes. The formulation uses latent-class evidence already available inside Forward correction without promoting every posterior conflict to a corrected label.

cs.LG↗
arXiv2026

SLA-Safe Energy Control for AI-Native NG-RAN Using Stability-Aware Constrained PPO

One important AI-for-RAN use case is energy saving, in which radio resources and cell energy modes must be dynamically controlled without violating user quality-of-service (QoS) or service-level agreement (SLA) requirements. However, aggressive sleep-state or deactivation decisions may reduce energy consumption at the cost of throughput degradation, delay increase, SLA violations, and unstable mode switching, especially under time-varying and bursty traffic conditions. This paper proposes a stability-aware constrained reinforcement learning framework for SLA-safe energy control in 5G NG-RAN. The problem is formulated as a constrained Markov decision process in which an AI-native controller selects closed-loop energy-saving actions based on cell load, queue status, active-user information, current energy mode, and SLA-related indicators. The proposed framework uses constrained proximal policy optimization with adaptive Lagrangian penalties to account for throughput, delay, and SLA constraints. To improve operation under traffic distribution shift, the controller is trained using mixed nominal and stress traffic regimes, while a switching-stability penalty is introduced to reduce oscillatory transitions between active and low-power modes. Simulation results in a seven-cell NG-RAN environment show that the proposed controller reduces energy consumption by approximately 41.4% under nominal traffic, 10.5% under stress traffic, and 22.9% under unseen-stress traffic relative to the Always-On baseline. Under stress and unseen-stress traffic, the controller preserves zero SLA violation and zero throughput loss, indicating service-preserving operation under challenging conditions. The proposed method also reduces switching activity compared with basic threshold-based energy saving.

cs.NI↗
arXiv2026

Budgeted Task-Aware Acquisition of Dynamic Networks

Learning on dynamic graphs is difficult when changes in the underlying network are only partially observed. Acquiring current graph information incurs observation and computational costs, making complete updates impractical under limited resources. This paper focuses on budgeted task-aware acquisition on dynamic networks, where a model needs to decide which stale graph information to refresh for a downstream task. We propose Scout, a lightweight framework that learns the task value of querying each node from the maintained graph and observation history. Our evaluation covers one synthetic and four real-world dynamic networks, two downstream tasks, nine acquisition baselines, and several query budgets. Scout achieves the highest mean downstream performance in 19 of the 21 benchmark-budget settings. Task-utility supervision also outperforms structural-change supervision in 13 of the 16 real-world settings. On the same dynamic network, task-matched acquisition improves link-prediction AUC by 0.012-0.016 and node-classification accuracy by 0.064-0.09 over task-mismatched acquisition. These results show that useful graph observations depend on the downstream task and that limited observation budgets can be allocated more effectively by learning directly from downstream utility.

cs.LG↗
arXiv2026

Hierarchical Prompt Injector for Domain Generalization Segmentation

Domain Generalized Semantic Segmentation (DGSS) is a challenging task, as vision models often rely on low-level appearance cues that change across domains. In contrast, structural attributes exhibit cross-domain stability, motivating the use of structural priors for DGSS. Existing methods use prompt learning to transfer such priors into DGSS models, but typically encode each class as a single holistic prompt. Moreover, these methods apply prompts uniformly to all pixels, offering no mechanism to adapt when only a subset of object regions is visible due to viewpoint changes, occlusion, and environmental variation. We address this with \textbf{Spatial Hierarchical Prompts (SHP)} that enrich each class with region-level geometric anchors capturing structural appearance from distinct viewing angles, ensuring complementary coverage under arbitrary viewpoints. Additionally, we propose the \textbf{Hierarchical Prompt Injector (HPI)}, which enables spatially adaptive prompt injection in foundation models. HPI spatially grounds prompts by modeling their semantic relevance and spatial influence with visual features. Considering the difficulty of learning spatially and semantically aware prompt injection, we further introduce auxiliary supervision to align hierarchical prompts with their corresponding object regions. We achieve 70.62\% and 72.74\% mIoU on synthetic-to-real and real-to-real benchmarks, respectively. Code and checkpoints are released at https://github.com/MosukFate/HPI

cs.CV↗
arXiv2026

Tactile Search: Enhancing Targeting in 3D Space

Visual search is crucial in daily life, from scanning for relevant information to spotting signs of danger. When sensory channels are overloaded or degraded, cognitive tasks can be supported by crossmodal information representations through vibrotactile cues. We introduce Tactile Search, an approach that uses modulation of frequency and amplitude of vibrations to the hands, for guiding attention to the location of objects in 3D space. We evaluated this approach in a competitive VR game where participants searched for targets using both vision and touch. Across two studies -- an in-the-wild demonstration (n=55) and a controlled laboratory experiment (n=28) -- we found that vibrotactile feedback significantly improved performance and increased user confidence. In the combined haptic condition, performance did not differ across target heights. We further analyzed participants' subjective experiences and search strategies highlighting the benefits of the tactile cues. Our findings suggest that Tactile Search can enhance interaction and provide design considerations for integrating haptic search into interactive systems.

cs.HC↗
arXiv2026

Algorithmic List Decoding at Capacity and Optimal Proximity Gaps for Reed-Solomon Codes

We give a unified hidden-derivative framework for list decoding and mutual correlated agreement of ordinary Reed--Solomon codes over prime fields, on arbitrary prescribed evaluation sets. For every fixed slack $γ>0$, every sufficiently large block length $n$, every prime $q\ge n$, and every dimension $1\le k\le(1-γ)n$, a deterministic algorithm finds all codewords within relative distance $1-k/n-γ$ in $q^{O_γ(1)}$ time. The final list has size $n^{O_γ(1)}$, independently of $q$. Both statements extend to bounded-input-list recovery, with constants depending additionally on the input-list bound. For every fixed curve degree $\ell$, at most $n^{O_{γ,\ell}(1)}$ parameters on a curve $f_0+zf_1+\cdots+z^\ell f_\ell$ admit a nearby codeword whose exact agreement support is not a maximal jointly explained support of the coefficient words. For lines this gives MCA error $n^{O_γ(1)}/q$, with no proximity loss. The interpolation stage reparameterizes and optimizes the hidden-derivative construction of Brakensiek, Chen, Putterman, Zhang, and Zheng; differential root enumeration uses Kopparty's algorithm. We then prove that a specialization-safe differential equation has a cover by constant-dimensional varieties of polynomial cumulative degree, outside polynomially many parameter values. Intersecting these varieties with equations from the full agreement support yields both the field-size-independent list bound and exact-support MCA.

cs.IT↗
arXiv2026

Where Does the Sound Go? Tracing Acoustic Information Loss in Audio-Conditioned LLMs

Audio-conditioned language models often underuse acoustic cues such as prosody, emotion, and non-speech sounds, raising the question of whether ASR-supervised frontends discard this information before it reaches the LM. We test whether the frontend is responsible by comparing Whisper-Tiny and Whisper-Small with EnCodec, DAC-VAE, and WavTokenizer in a shared Qwen3.5-4B audio-LM pipeline on ASR, emotion recognition, and sound captioning. Encoder replacement alone does not resolve this underuse: Whisper variants remain strongest overall, including on emotion and environmental sound captioning. To localize the failure, we trace task-relevant information through the encoder, projector, LM layers, and LM head. Linear probes and geometric analyses show that discriminative acoustic structure remains recoverable at the final LM layer, even when MCQA accuracy trails probe accuracy by up to 83 points. Because the answer format and decoding procedure are controlled, this task-dependent gap points to content-specific readout failure rather than generic format bias. LogitLens analyses and a targeted LM head intervention support the conclusion that acoustic underuse is not explained solely by encoder-side information loss and that readout alignment can be a dominant bottleneck.

cs.SD↗
arXiv2026

Ulam Rank Aggregation Is Hard to Approximate for Four Rankings

We study the approximability of rank aggregation under the Ulam metric. In the \emph{Ulam median} problem, the goal is to find a ranking (permutation) minimizing the sum of its Ulam distances to the input rankings, while in the \emph{Ulam center} problem, the objective is to minimize the maximum such distance. We prove that, for every $0<\varepsilon< 1/34$, it is $\mathrm{NP}$-hard to approximate either Ulam median or Ulam center within a factor of $35/34-\varepsilon$, even when the input consists of only four rankings. We further show that unless P = NP, neither problem admits a polynomial-time additive approximation scheme. Prior to our work, only the exact versions of both problems were known to be $\mathrm{NP}$-hard, and that too only when the number of input rankings is unbounded [Fischer et al., ESA'25 and Bachmaier et al., J. of Discrete Algorithms'15]. Furthermore, our inapproximability results are optimal in terms of the number of input rankings since for three inputs it is already known to be polynomial-time solvable [Chakraborty, Das, Krauthgamer, SODA'21]. En route, we introduce a new general framework for reducing Boolean constraint satisfaction problems (CSP) to the Ulam median with only four inputs. As a specific instantiation of the reduction framework, we obtain our hardness-of-approximation results. The corresponding hardness for the Ulam center follows from a reduction from the Ulam median.

cs.CC↗
arXiv2026

FACT: A Forensic Agent with Compiled Tool-Use Trajectories for AI-Generated Image Detection

AI-generated image detection is increasingly open-world: new image generators produce highly realistic images that make visual artifacts harder to identify. Existing detectors usually rely on a fixed set of forensic cues, so a detector that works well for one generator family may fail on another. We introduce FACT (Forensic Agent with Compiled Tool-use Trajectories), which learns an image-conditioned tool-use policy for forensic analysis. Instead of applying a fixed detector, FACT decides which forensic tools to call, interprets the returned evidence, and stops when sufficient evidence has been collected. FACT follows an Evolve--Distill--Refine pipeline: it evolves an execution-verified forensic skill, compiles the skill into action--observation tool-use trajectories, distills them into a compact agent, and refines the policy with cost-aware GRPO. Across two internal and four public benchmarks, FACT achieves the best performance among all compared methods, including on recent unseen generators, deepfakes, and manipulated images.

cs.CV↗
arXiv2026

A budget-dependent crossover between coverage- and response-based training-set selection for machine-learned interatomic potentials

Selecting compact training sets for machine-learned interatomic potentials requires deciding whether to preserve structural diversity or target configurations on which models disagree. The better choice can depend on how much data is retained, making a comparison at one training-set size insufficient. Here we link selection criteria to prediction accuracy through a budget-resolved comparison of retrained MACE models on GAP-20 Carbon and pooled revised MD17. Structural coverage is compared with a response-guided selector that targets disagreement between a coverage-trained model and a full-data reference. This retrospective response witness tests the value of model disagreement for compressing an already labelled pool. At 5\%, coverage gives smaller absolute deviations from the full-data error than random sampling across four force endpoints in both datasets. The witness has larger deviations than coverage at 1\% and 5\%, but the ordering reverses at 20\%. At 20\%, witness-selected models also lower direct held-out force errors by 0.46--5.89\% relative to coverage, with all eight paired training-seed intervals favouring the witness. Six errors fall below the full-data reference. Mean force-error reductions are 0.164--0.167~meV~$\textÅ^{-1}$, with larger gains for tail and masked endpoints. Complementary analyses show that learned similarity preserves the coverage ranking, while selecting by frozen-model error gives higher error than embedding coverage. These findings establish retained-data budget as a deciding variable in atomistic training-set selection and provide a direct test of when response-guided compression improves on structural coverage.

cs.LG↗
arXiv2026

Correct Tests Are Not Enough: Measuring and Training Oracle Conversion in Specification-Based Test Generation

Generating tests from a natural-language specification requires both an input that exposes faulty behavior and a correct expected output. These requirements need not improve together: a model can increase test correctness by choosing easier inputs, or discover useful inputs whose expected outputs it cannot predict. We study this interaction through executable reward decomposition and suite-level oracle-conversion measurement. Our generator jointly emits five input--output tests in one response. During training, audited reference programs provide correctness feedback, while a fixed bank of faulty programs provides two utility signals: potential input kill and effective kill after checking the generated output. An additive GRPO objective preserves both signals without requiring execution at inference time. On an audited TC-Bench split with 506 training and 142 evaluation tasks, three independently trained Qwen3.5-9B runs at step 75 increase full-test correctness from 28.59\% to 42.54\%, input kill from 24.06\% to 25.27\%, and effective full kill from 12.23\% to 14.15\%. Matched 50-step ablations reveal a trade-off: removing kill rewards yields higher correctness and slightly higher full kill, but lowers input kill to 21.60\%. A fixed-input source--oracle crossover on 64 training-pool tasks attributes the principal NoKill-to-FullKill difference to harder input selection rather than worse output prediction on identical inputs. These results identify oracle conversion as a measurable bottleneck and show the benefits and limits of preserving input-utility feedback in joint test generation.

cs.SE↗
arXiv2026

Grounded and Faithful P&ID Reasoning: Constraining Vision-Language Models with Recovered Evidence Graphs

Piping and Instrumentation Diagrams (P&IDs) are the authoritative maps of process plants: isolation, maintenance, and HAZOP decisions depend on what connects to what. Vision-language models describe these sheets fluently, yet they often invent or miss process connections---and an invented or missed link can reverse an isolation or reachability call, so a plant decision cannot trust a fluent answer that was never checked against the linework. We instead recover an explicit graph of the drawing---its symbols, the process connections between them, and the tags that name them---and then require the model to answer only by querying that graph through seven read-only operators, so a topology claim is returned only when it cites the query results that support it. On TopoPID-VQA, a new suite of 3000 topology questions over these sheets, Graph-Grounded Harness (Ours) raises exact match accuracy from 36.7--41.3% under image-only prompting to 74.3--76.0% for Qwen3-VL-4B, Qwen3-VL-8B, and Gemma-4-E4B. It does so on an imperfect substrate: on Digitize-PID dataset the recovered graph scores F1 0.742 on exact process connections, and 0.801 once symbols and tags are pooled in. The residual errors track that gap---grounding pays off where the recovered graph is right, and perception error still breaks topology questions where it is not.

cs.LG↗
arXiv2026

Broken on Arrival: Silently Defective LLM Artifacts in Public Model Registries and How to Catch Them

Developers increasingly run large language models locally by pulling quantized GGUF artifacts from public registries, yet nothing in the distribution pipeline functionally tests these conversions before they reach users. We executed 327 quantized code-capable model artifacts: 305 from the official Ollama library, spanning 15 model lines at every eligible quantization level at or under 8 GB, and 22 from the most-downloaded community repositories on HuggingFace. Each ran a 15-task smoke suite calibrated so that healthy artifacts pass while a known-broken one fails; suspects then faced full 164-task evaluation, a second inference backend, an independent distributor's conversion of the same model and quantization as referee, and, for community files, re-testing under the artifact's own template. The official library carries five silently defective artifacts, a batch of four Qwen2.5-Coder-3B conversions and one phi3.5-mini conversion, that solve zero of 164 tasks and zero of the smoke suite on both backends while independent conversions of the same models work: 1.6% of official artifacts, 2 of 29 model-and-size conversion groups. The adjudication chain cleared small-model artifacts that a naive threshold would condemn as broken when they are merely collapsed by extreme quantization, and it exposed two older community conversions that degrade badly on CUDA yet pass on Metal: not defective files but backend-dependent failures, a third phenomenon no registry currently tests for. Two confirmed defects produce output whose surface statistics sit inside the healthy range, invisible to any low-noise heuristic short of execution. We release the audit dataset, the quantcheck acceptance-testing tool, and disclosure reports for every confirmed defect (https://github.com/aditi-p31/quantcheck), and argue that model registries need the acceptance gate that package registries already run.

cs.SE↗