Papers

Machine unlearning aims to remove specified training data to satisfy privacy regulations such as GDPR. However, existing evaluations assume identical precision at unlearning and deployment, overlooking that production LLMs are deployed at low-bit precision. We show that INT4 quantization systematically restores forgotten content even when models pass compliance audits at bfloat16 (BF16), we term this the quantization recovery attack (QRA). We conduct the first systematic study of unlearning robustness under adapter-space INT4 quantization in the NF4+LoRA regime, evaluating seven methods on LLaMA-3-8B-Instruct across TOFU, MUSE-News, and WikiBio-WPU. INT8 is benign; INT4 induces recovery of up to 22x, worsening with dataset difficulty. We identify the FA-RA-Q-INT4 trilemma: no method simultaneously achieves strong forgetting, high utility, and quantization robustness. A dense Pareto sweep reveals a sharp phase transition once robustness is achieved, retaining accuracy collapses regardless of further tuning. To address this, we propose DURABLEUN-SAF (Sharpness-Aware Forgetting), a quantization-aware objective using Straight-Through Estimator gradients through INT4 rounding. DURABLEUN-SAF is the only method to achieve a stable empirical (0.047, {BF16, INT8, INT4})- durability certificate: Q-INT4= 0.043 +- 0.002, cert rate= 3/3, versus SalUn's cert rate= 1/3 at its own published hyperparameters. We call for Q-INT4 to be adopted as a standard evaluation metric alongside FA and RA.

We give new examples of graphs and trees with dominating set sequences that are not log-concave. These examples were generated by PatternBoost, a transformer-based reinforcement learning software developed by Charton-Ellenberg-Wagner-Williamson. We also show: for any positive integer $m$, there exists a tree whose dominating set sequence is not log-concave for at least $m$ indices by modifying a similar construction of Bautista-Ramos for the independent set sequence. We show that a large class of caterpillar graphs has log-concave dominating set sequences. A continuous analogue of the sequence is also log-concave for all graphs.

Kolmogorov-Arnold networks (KANs) offer a potent combination of accuracy and interpretability, thanks to their compositions of learnable univariate activation functions. However, the activations of well-fitting KANs tend to exhibit pathologically high-curvature oscillations, making them difficult to interpret, and standard regularization penalties do not prevent this. Here we derive a basis-agnostic curvature penalty and show that penalized models can maintain accuracy while achieving substantially smoother activations. Accounting for how function composition shapes curvature, we prove an upper bound on the full model's curvature relative to the curvature penalty, and use this to motivate richer forms of penalties. Scientific machine learning is increasingly bottlenecked by the trade-off between accuracy and interpretability. Results such as ours that improve interpretability without sacrificing accuracy will further strengthen KANs as a practical tool for both prediction and insight.

Pansharpening aims to generate high-resolution multispectral (HRMS) images by fusing low-resolution multispectral (LRMS) and high-resolution panchromatic (PAN) images. Although deep learning has advanced this field, mainstream frequency-based methods relying on standard scaled dot-product attention suffer from quadratic computational complexity and fail to exploit the inherent regional sparsity of remote sensing imagery. Furthermore, existing spatial enhancement strategies typically employ static convolution kernels, which struggle to adapt to the complex frequency and regional variations of PAN and MS images. To address these bottlenecks, we propose a Region-Aware Fusion (RAFNet) Network that synergistically models spatial and frequency information. Specifically, we design a Spatial Adaptive Refinement (SAR) module that leverages the discrete wavelet transform (DWT) for directional frequency separation and K-means clustering for regional partitioning, which enables the dynamic construction of region-specific adaptive convolution kernels, achieving spatially and frequency-adaptive feature enhancement. Moreover, we introduce a Clustered Frequency Aggregation (CFA) module based on a sparse attention mechanism guided by the semantic clusters, which executes a region-aware sparse attention strategy that drastically reduces computational redundancy while ensuring high-quality frequency feature extraction. In addition we integrated these modules into a progressive, multi-level spatial-frequency network architecture to facilitate robust interaction and accurate image reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that the proposed RAFNet significantly outperforms state-of-the-art pansharpening methods in both reduced- and full-resolution assessments. The code is available at https://github.com/PatrickNod/RAFNet.

Adversarial training is effective on balanced datasets, but its robustness degrades under longtailed class distributions, where tail classes suffer high robust error and unstable decision boundaries. We propose Manifold-Constrained Adversarial Training (MCAT), a unified framework that enforces the semantic validity of adversarial examples by penalizing deviations from class-conditional manifolds in feature space, while promoting balanced geometric separation across classes via an ETF-inspired regularization. We provide theoretical results that link geometric separation to lower bounds on adversarially robust margins, and show that manifold-constrained adversarial risk upperbounds robust risk on high-density semantic regions. Extensive experiments on standard longtailed benchmarks demonstrate consistent improvements in overall, balanced, and tail-class adversarial robustness.

Pearl's causal hierarchy shows that observational, interventional, and counterfactual queries are qualitatively distinct. We ask a quantitative version of this question: how many additional bits are needed to specify higher-rung causal answers once lower-rung answers are known? We formalize this via query-class description length, the Kolmogorov complexity of the answers a structural causal model (SCM) gives to a class of queries, with system size given. Our main construction gives acyclic SCMs on $n$ binary variables whose common observational distribution has constant description length, while single-variable intervention answers can require $\Theta(n^2)$ additional bits. For SCMs with independent noises, fixed finite gate-schema and noise libraries, and at most $d$ parents per variable, a degree-sensitive upper bound gives an observational-interventional gap of at most $O(nd\log(en/d)+n\log n)$. This makes the quadratic construction order-optimal in the dense regime and a rooted-tree construction order-optimal for bounded indegree. The quadratic separation persists under $\varepsilon$-accurate total-variation descriptions for every fixed $\varepsilon<1/4$. At the next rung, even knowing every hard-intervention distribution can leave a $\Theta(n)$ counterfactual description gap; a masked-parity construction extends this to $\Theta(n^2)$. These separation rates hold in the worst case and with high probability under uniform hidden parameters. A general ambiguity-to-bits theorem and Shannon analogue, together with explicit encodings, show that the gaps in our constructions equal the logarithm of residual higher-rung ambiguity up to lower-order terms.

In this paper, we present our system for SemEval-2026 Task 6 (CLARITY) on response clarity and evasion detection in question-answer pairs from U.S. presidential interviews, comparing fine-tuned encoders with prompt-based LLMs. Our LLM ensemble achieves 80 macro-F1 on the 3-class Task 1 (9th/41) and 59 on the 9-class Task 2 (3rd/33). Across 8 transformer encoders optimized through a four-stage pipeline, partial encoder layer unfreezing outperforms full fine-tuning by a wide margin. Combining English and multilingual encoders further improves ensemble performance over either family alone, despite multilingual models being individually weaker. Prompt-based LLMs, without any task-specific parameter updates, outperform fine-tuned encoders, particularly on minority classes; among open-weight LLMs, parameter count does not predict performance. Enriched input, concatenating the full interviewer turn, improves LLM performance but not that of encoders, an effect that persists with Longformer's extended context window, suggesting the divergence is not attributable to sequence-length capacity alone in our settings. The Clear Reply/Ambivalent boundary remains the dominant failure mode, mirroring the disagreement among human annotators. Our code, prompts, model configurations, and results are publicly available.

We propose HeroCrystal, a novel privacy-preserving framework for multi-camera domain-adaptive object detection, addressing challenges such as data privacy, class imbalance, and heterogeneous architectures. Our framework consists of three key stages. In the Generated Stage, we introduce a one-shot, target-aware diffusion-based generation module that learns visual style from a single target-domain image while leveraging prompt-based control to synthesize specific object instances. Unlike conventional style transfer-based methods that require large target datasets and ignore semantic-level discrepancies, our approach enables privacy-preserving augmentation to reduce ethical concerns, and introduces controllable rare object generation to mitigate long-tailed category degradation. In the Federated Stage, we employ probabilistic Faster R-CNN on the client side to improve localization accuracy, and a dynamic model contrastive strategy to suppress domain-specific bias. The server side performs model fusion across heterogeneous architectures without accessing raw data. Finally, in the Distilled Stage, we propose an inconsistent categories integration algorithm to resolve label inconsistency and architecture heterogeneity across clients. Extensive experiments on multiple cross-domain detection benchmarks demonstrate that our method outperforms existing multi-source domain adaptation and federated learning baselines under multi-class, privacy-preserving settings. Our method improves mAP by +2.1% over prior privacy-preserving approaches and achieves a new state-of-the-art mAP of 33.4%, highlighting the effectiveness of HeroCrystal in enabling practical multi-camera AI surveillance systems. The source code is publicly available at https://github.com/ccuvislab/HeroCrystal.

Language model (LM)-based agents have demonstrated promising capabilities in automating complex tasks from natural language instructions, yet they continue to struggle with long-horizon planning and reasoning. To address this, we propose an enhanced multi-agent framework that decomposes automation into three roles: a planner for high-level decision-making, an actor for task execution, and a memory manager for contextual reasoning. While this modular decomposition aligns with established design patterns, our core contribution lies in a systematic compute-allocation analysis, revealing that planning is the dominant factor influencing task performance. Execution and memory management require significantly less compute and model capacity to achieve competitive results. Building on these insights, we introduce a planner-centric reinforcement learning approach, which exclusively optimizes the planner using trajectory-level rewards from a VLM-as-judge, while freezing the other components. Extensive experiments on benchmarks spanning web navigation, OS control, and tool use demonstrate that concentrating model capacity and learning on high-level planning yields robust and compute-efficient improvements in long-horizon agent automation. Our code is publicly released.

Feature attribution is central to diagnosing and trusting deep neural networks, and Integrated Gradients (IG) is widely used due to its axiomatic properties. However, IG can yield unreliable explanations when the integration path between a baseline and the input passes through regions with noisy gradients. While Guided Integrated Gradients reduces this sensitivity by adaptively updating low-gradient-magnitude features, input-space guidance still produces intermediate inputs that deviate from the data manifold. To address this limitation, we propose Manifold-Aligned Guided Integrated Gradients (MA-GIG), which constructs attribution paths in the latent space of a pre-trained variational autoencoder. By decoding intermediate latent states, MA-GIG biases the path toward the learned generative manifold and reduces exposure to implausible input-space regions. Through qualitative and quantitative evaluations, we demonstrate that MA-GIG produces faithful explanations by aggregating gradients on path features proximal to the input. Consequently, our method reduces off-manifold noise and outperforms prior path-based attribution methods across multiple datasets and classifiers. Our code is available at https://github.com/leekwoon/ma-gig/.

Conventional federated learning assumes that greater learner participation improves training performance, by leveraging abundant, independently generated local data. However, in federated reinforcement learning (FRL) for unmanned aerial vehicle (UAV) teams in hazardous environments where experience generation is severely constrained by safety considerations, energy limitations, and mission duration, this assumption may break. This work introduces Experience-Constrained Hierarchical Federated Reinforcement Learning (EC-HFRL), a framework in which clusters act as federated learning agents, while multiple intra-cluster learners represent parallel learning resources that reuse a shared experience pool. We show that increasing participation does not necessarily improve learning performance. Instead, learning performance is strongly associated with experience reuse strategy and the dominance of key analytically identified gradient transition experiences within a cluster. In particular, minibatch size primarily determines effective replay exposure, while higher intra-cluster participation increases reuse level. Empirical results demonstrate that the performance regimes are strongly associated with the structure of the learning signal, rather than federated aggregation effects, clarifying the limited and secondary role of learner participation in experience-constrained FRL.

Deep reinforcement learning (DRL) has delivered strong results in domains such as Atari and Go, but it still suffers from high sample cost and weak transfer beyond the training setting. A common response is to reuse information from previously trained models through transfer, distillation, ensemble methods, or federated training instead of learning each target task from random initialization. The literature on these mechanisms is fragmented, and published comparisons are hard to interpret because tasks, baselines, and compute budgets differ. This paper presents a PRISMA-guided systematic review of empirical studies on pretrained knowledge reuse in DRL. Starting from 589 records retrieved from IEEE Xplore, the ACM Digital Library, and citation tracing, we screened 570 unique records and assessed 89 full texts. After applying the final eligibility criteria, 15 empirical studies remained in the main synthesis. We analyzed them qualitatively across three factors: source-target similarity, diversity among reused models, and the fairness of comparisons against from-scratch baselines. Three patterns recur across the surviving corpus. First, positive results are concentrated in settings where source and target tasks share substantial structure or where the method includes an explicit gating or alignment mechanism. Second, evidence for ensembles and federated aggregation is promising but sparse and mostly limited to narrow settings. Third, compute-matched comparisons are rare, which weakens claims about efficiency gains over stronger single-agent baselines. The paper contributes a narrower and internally consistent review scope, a study-level synthesis of empirical evidence, and a provisional independence spectrum that should be treated as a hypothesis for future benchmarking rather than a validated metric.

Accurate prediction of physician referral links is essential for optimizing care coordination and reducing fragmentation in healthcare delivery. However, existing computational methods, ranging from triadic closure heuristics to graph neural networks, fail to capture the intrinsic properties of physician referral networks, including sparsity, disassortative degree mixing, and hub-dominated topology. Here, we propose H3, a healthcare three-hop index that addresses these limitations by modeling indirect referral pathways through intermediate physicians, with degree-based normalization and a redundancy penalty to mitigate hub-mediated noise. Using Medicare Physician Shared Patient Patterns data, we evaluate H3 under two complementary prediction regimes: within-period prediction, which assesses recovery of contemporaneous referral links under sparse conditions, and cross-period prediction, which tests robustness to temporal shift as referral windows expand. Across both regimes, H3 consistently outperforms classical heuristics and deep learning-based baselines. Unlike black-box neural network approaches, H3 produces fully decomposable predictions traceable to specific intermediary physicians, offering a transparent and deployable solution for referral network completion.

Self-attention in Transformers is typically implemented as $\mathrm{softmax}(QK^\top/\sqrt{d})V$, where $Q=XW_Q$, $K=XW_K$, and $V=XW_V$ are learned linear projections of the input $X$. We ask whether these learned projections are necessary, or whether they can be replaced by a simpler similarity-based diffusion operator. We introduce Gaussian Kernel Attention (GKA), a drop-in replacement for dot-product attention that computes token affinities directly using a Gaussian radial basis function (RBF) kernel applied to per-head token features. Each head learns only a bandwidth parameter $\sigma_h$, while a single output projection $W_O$ preserves compatibility with the standard Transformer interface. GKA can be interpreted as normalized kernel regression over tokens, linking modern Transformer architectures to classical non-local filtering and kernel smoothing methods. We evaluate GKA in both vision and language modeling settings. For autoregressive language modeling within the nanochat framework, we implement causal masking and sliding-window constraints by masking and renormalizing the Gaussian kernel. At depth 20, a GKA model with $0.42\times$ the parameters and $0.49\times$ the total training FLOPs of a standard attention baseline trains stably, exhibits a near-zero train-validation gap, and demonstrates competitive behavior on standard benchmarks, albeit with higher bits-per-byte (BPB) at this compute scale. Overall, GKA provides a minimal, interpretable attention mechanism with an explicit locality scale, offering a dimension in the accuracy-efficiency trade-off for Transformer design.

Personalized federated learning (pFL) aims to adapt models to client specific data distributions, yet it often fails to reliably preserve personalized information. Local training is hindered by high variance gradients induced by limited and heterogeneous client data, while aggregation further distorts client specific optimization directions. To address these challenges, we propose pFLAlign, a gradient alignment framework to maintain client specific information during both local training and aggregation. pFLAlign consists of two complementary mechanisms: one adapts local gradient directions to reduce variance during client side optimization, and the other mitigates aggregation induced distortion by realigning the global model with each client's personalized direction. Theoretically, we derive pFLAlign from a PAC Bayesian analysis, which reveals how personalized gradient alignment preserves client specific information. Our experiments and ablation studies show that pFLAlign consistently improves personalization performance and training stability, achieving state of the art results.

Kullback-Leibler (KL) regularization is widely used in offline decision-making and offers several benefits, motivating recent work on the sample complexity of offline learning with respect to KL-regularized performance metrics. Nevertheless, the exact sample complexity of KL-regularized offline learning remains largely from fully characterized. In this paper, we study this question in the setting of multi-armed bandits (MABs). We provide a sharp analysis of KL-PCB (Zhao et al., 2026), showing that it achieves a sample complexity of $\tilde{O}(\eta SAC^{\pi^*}/\epsilon)$ under large regularization $\eta = \tilde{O}(\epsilon^{-1})$, and a sample complexity of $\tilde{\Omega}(SAC^{\pi^*}/\epsilon^2)$ under small regularization $\eta = \tilde{\Omega}(\epsilon^{-1})$, where $\eta$ is the regularization parameter, $S$ is the number of contexts, $A$ is the number of arms, $C^{\pi^*}$ policy coverage coefficient at the optimal policy $\pi^*$, $\epsilon$ is the desired sub-optimality, and $\tilde{O}$ and $\tilde{\Omega}$ hide all poly-logarithmic factors. We further provide a pair of sharper sample complexity lower bounds, which matches the upper bounds over the entire range of regularization strengths. Overall, our results provide a nearly complete characterization of offline multi-armed bandits with KL regularization.

AC optimal power flow (ACOPF) is foundational yet computationally expensive in power grid operations, driving learning-based surrogates for large-scale grid analysis. These surrogates, however, often fail to generalize across network topologies, a critical gap for deployment on grids not seen during training and for routine operational what-if studies. We introduce LUMINA-Bench, a comprehensive benchmark suite for ACOPF surrogate learning covering multi-topology pretraining, transfer, and adaptation. The benchmark evaluates homogeneous and heterogeneous architectures under single- and multi-topology learning settings using unified metrics that capture both predictive accuracy and physics-informed constraint violations. We additionally compare constraint-aware training objectives, including MSE, augmented Lagrangian, and violation-based Lagrangian losses, to characterize accuracy-robustness trade-offs across settings. Data processing, training, and evaluation frameworks are open-sourced as the LUMINA suite to support reproducibility and accelerate future research on feasibility-aware OPF surrogates.

We introduce PF-AGD, the first parameter-free, deterministic, accelerated first-order method to achieve $O(\epsilon^{-5/3}\log(1/\epsilon))$ oracle complexity bound when minimizing sufficiently smooth, non-convex functions; this is the best-known bound for first-order methods on smooth non-convex objectives. Unlike existing methods possessing this rate that require a priori knowledge of smoothness constants, we use an adaptive backtracking scheme and a gradient-based restart mechanism to estimate local curvature. This yields a practical algorithm that matches best-known theoretical rates. Empirically, PF-AGD outperforms the practical variant of AGD-Until-Guilty (Carmon et al., 2017), as well as other parameter-free variants, and is a viable alternative to nonlinear conjugate gradient methods.

Ultrasound foundation models have achieved strong performance on structured prediction tasks but remain exclusively vision-based, limiting zero-shot and few-shot transfer to novel tasks where task-specific annotation is scarce. We address this gap with EchoCare-CLIP, a CLIP-style dual-encoder contrastive framework that aligns ultrasound images with clinical text in a shared embedding space. We curate a multi-organ corpus of over 16K image-text pairs spanning breast, liver, lung, and thyroid, with over 78% of captions derived from expert-annotated reports, and complement the remainder with a three-tier template-based and LLM-based caption generation pipeline. We evaluate model configurations spanning two text encoder families (CLIP, BioClinicalBERT) and two caption strategies (template-based, LLM-generated) against OpenAI CLIP and BiomedCLIP baselines. Our trained models consistently improve cross-modal alignment over baselines, with the best configuration achieving a paired alignment score of 0.682. However, stronger alignment does not guarantee better downstream performance: CLIP-based variants with partial fine-tuning achieve the strongest zero-shot classification on external held-out datasets (0.709 on BUSI; 0.626 on AULI), while full end-to-end fine-tuning degrades transfer due to overfitting. On linear probing and few-shot adaptation, model rankings are dataset-dependent, reflecting a trade-off between domain adaptation and representational generalizability. We further show that template-based captions match or outperform LLM-generated captions, suggesting lexical diversity is not a proxy for caption quality. Taken together, our results demonstrate that ultrasound vision-language alignment is achievable from public data alone, but robust clinical transfer requires careful balancing of domain adaptation, encoder capacity, and caption supervision quality.

Federated learning (FL) across multiple HPC facilities faces stochastic admission delays from batch schedulers that dominate wall-clock time. Synchronous FL suffers from severe stragglers, while asynchronous FL accumulates stale updates when queues spike. We propose FedQueue, a queue-aware FL protocol that incorporates scheduler delays directly into training and aggregation, which (i) predicts per-facility queue delays online to budget local work, (ii) applies cutoff-based admission that buffers late arrivals to bound staleness, and (iii) performs staleness-aware aggregation to stabilize heterogeneous local workloads. We prove the convergence for non-convex objectives at rate $\mathcal{O}(1/\sqrt{R})$ under bounded staleness, and show that the admission controls yield bounded staleness with high probability under queue-prediction error. Real-world cross-facility deployment of FedQueue shows 20.5% improvement over baseline algorithms. Controlled queue simulations demonstrate robust improvement over the baselines; in particular, up to 60% reduction in time to reach a target accuracy level under high queue variance and non-IID partitions.

Softmax routing approaches hard top-1 routing as the temperature tends to zero, but the limiting passage is singular at router ties. This paper develops a boundary-layer calculus for this soft-to-hard limit in population squared-loss mixture-of-experts regression. For a router with logits $a_k(x;\phi)$, the relevant local quantity is the top-two margin $\Delta(x;\phi)$, and the relevant global quantity is the boundary mass $\mathbb{P}(\Delta(X;\phi)\le w)$. Under smoothness and transversality assumptions, coarea and tubular-neighborhood estimates show how this mass scales with the slab width; in the binary case the leading coefficient is an explicit surface integral over the routing interface. These geometric estimates give quantitative bounds between the soft objective $L_\tau$ and the hard objective $L_0$, including an $O(\tau^\alpha)$ uniform comparison under a margin-tail condition, and yield $\Gamma$-convergence of the soft objectives on compact parameter spaces. The main conclusion is that the zero-temperature approximation is controlled by the probability carried by an $O(\tau)$ neighborhood of the routing interfaces, not by temperature alone. After isolating this boundary-layer part of the problem, we record a conditional landscape-transfer theorem from hard to small-temperature soft routing and a reduced two-expert Gaussian calculation illustrating local symmetry breaking. Synthetic diagnostics are included only as controlled checks of the boundary-layer predictions.

Human evaluation remains the primary standard for assessing modern AI systems, yet annotator disagreement, bias, and variability make system rankings fragile under standard majority vote aggregation. Majority vote discards annotator reliability and item-level ambiguity, often yielding unstable comparisons across annotator subsets. We introduce STABLEVAL, a disagreement-aware evaluation framework that models latent item correctness and annotator-specific confusion patterns to produce posterior expected item credit and calibrated agent-level scores. Unlike label-denoising approaches such as Dawid-Skene, STABLEVAL is explicitly designed for stable and uncertainty-aware system evaluation rather than hard label recovery. We formalize ranking stability as a first-class evaluation objective and analyze how aggregation methods preserve or distort underlying annotator behavior. Across controlled synthetic experiments and multiple real-world human-annotated benchmarks, majority vote exhibits increasing score error and ranking instability under annotator heterogeneity and adversarial noise, while STABLEVAL yields more stable and statistically grounded system rankings. These results demonstrate that modeling disagreement is essential for robust and reproducible AI evaluation.

Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood; (ii) available generalization bounds deteriorate as the number of negative samples increases, contradicting the empirical benefits of large negative sets; and (iii) the retrieval performance of CRL has received limited theoretical attention. In this paper, we develop a unified statistical learning theory for CRL. For downstream tasks, we evaluate retrieval quality using an AUC-type population criterion and show that the contrastive loss is statistically consistent with optimal ranking. We further establish a calibration-style inequality that quantitatively relates excess contrastive risk to excess retrieval suboptimality. For upstream training, we study both supervised and self-supervised contrastive objectives and derive generalization bounds of order $O(1/m + 1/\sqrt{n})$ and $O(1/\sqrt{m} + 1/\sqrt{n})$, respectively, where $m$ denotes the number of negative samples and $n$ the number of anchor points. These bounds not only explain the empirical advantages of large negative sets but also reveal an explicit trade-off between $m$ and $n$. Extensive experiments on large-scale vision–language models corroborate our theoretical predictions.

This paper develops the angular and static-channel component of Geometric and Spectral Alignment for residual Jacobian chains. Starting from Cartan-coordinate rigidity and fitted effective-rank windows, we study how dominant singular subspaces are transported across adjacent layers and how the resulting finite matrices can be displayed in physical channel coordinates. The main results are deterministic, margin-verified results. We bound the error between full interface transport and its dominant-window truncation, add fitted-tail errors so that empirical spectra can be certified against the Gibbs–Cartan tail model, and distinguish source-mode incidence from fully physical input-output channel incidence. Given row groups and active supports, the Physical Alignment Matrix decomposes orthogonally as core plus overlap plus noise. Active-column gaps, pairwise overlap margins, and noise bounds combine into a static certificate radius under which the full transport and the truncated transport induce the same active supports, pairwise incidence graph, SRS sets, hub columns, and core/overlap/noise masks. The finer SC/SA/ST labels of the Invariant Channel Mapping require additional row-energy and profile-correlation margins, stated as explicit perturbation tests. The empirical section reports the matrices and block-energy heatmaps that measure these certificate quantities across CNNs, language models, and vision/diffusion backbones. The figures are interpreted as finite-dimensional measurements; complete membership in the Physical GSA certificate domain requires checking the numerical margin protocol stated in Section 10.

Federated learning (FL) is vulnerable to poisoning attacks, where malicious clients upload manipulated updates to degrade the performance of the global model. Although detection methods can identify and remove malicious clients, the model remains affected. Retraining from scratch is effective but costly, and existing unlearning methods remain unsatisfactory in both effectiveness and efficiency. We propose Federated Adversarial Unlearning (FAUN), a lightweight framework that retains only a short window of malicious clients' updates and employs adversarial optimization on a proxy dataset to derive updates that eliminate malicious directions. Applying these updates for a few unlearning rounds, followed by benign fine-tuning, enables fast removal of malicious effects and stable recovery. Experiments on three canonical datasets show that FAUN achieves recovery comparable to retraining while requiring far fewer rounds and reduces attack success rates to near zero, confirming FAUN successfully eliminates the contributions of unlearned clients.

The nonuniform and growing impact of adversarial noise across the layers of deep neural networks has been used in the literature, without a formal mathematical justification, to detect adversarial inputs and improve robustness. In this work, we study this phenomenon in detail and present a formal adversarial noise amplification theorem. We specify a set of sufficient conditions under which the adversarial noise amplification is mathematically guaranteed. Based on theoretical observations, we propose a novel training methodology with a custom spectral loss function and a specific architectural design to enhance the amplification signal for detecting adversarial data. Finally, we introduce a new, lightweight detection mechanism that leverages the enhanced amplification signal and operates entirely at inference time. To validate our approach, we demonstrate the detector's efficacy against both state-of-the-art attacks and a purpose-built adaptive attack, confirming that enhanced amplification can serve as a robust and reliable signal for adversarial defense.

Deep residual architectures are modeled as products of near-identity Jacobians. This paper proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors, emphasizing a normalized top-radial Cartan coordinate and fitted power-law chart. Full-rank factors are mapped from $\mathrm{GL}(d)$ to the positive cone by $A\mapsto A^\top A$, then to ordered eigenvalue data. Under Frobenius normalization, exact power-law spectra form a trace-normalized Cartan orbit. This orbit is a Gibbs family on ranks, a Fisher information line, and a Bures–Wasserstein curve with line element $d/4$ times Fisher information. The main rigidity theorem is a slack-aware margin inequality: interface radial amplitude, non-backtracking slack, and signed residual variation control displacement of the fitted Cartan coordinate. In the exact-chart zero-slack case, a depth-$L$ budget gives exponent drift of order $(\log M)/L$; generally, slack and residual increments augment the bound. We separate scalar top-radial from full-Cartan spectral control, which also needs Bures/Hellinger residual variation. We prove approximate-power-law and metric-chart versions, converse lower bounds, Fisher–KL/Bures action estimates, and near-identity expansions for normalized residual chains. Near-identity results verify transport budgets; chart quality remains measurable. Effective rank is a spectral-energy quantile, giving finite-width power-law tail bounds and robust rank-window transition estimates. Empirical static-weight exponent profiles serve as diagnostics; full verification also requires interface budgets, slacks, and residuals for the same operator chain.

Pretraining optimizers are tuned to produce the strongest possible base model, on the assumption that a stronger starting point yields a stronger model after subsequent changes like post-training and quantization. This overlooks the geometry of the base model which controls how much of the base model's capabilities survive subsequent parameter updates. We study three pretraining optimization approaches that bias optimization toward flatter minima: Sharpness-Aware Minimization (SAM), large learning rates, and shortened learning rate annealing periods. Across model sizes ranging from 20M to 150M parameters, we find that these interventions consistently improve downstream performance after post-training on five common datasets with up to 80% less forgetting. These principles hold at scale: a short SAM mid-training phase applied to an existing OLMo-2-1B checkpoint reduces forgetting by 31% after MetaMath post-training and by 40% after 4-bit quantization.

Large language models (LLMs) are increasingly used for title-abstract screening in systematic reviews, but their decisions lack calibrated uncertainty. We show that an auxiliary BERT+GCN classifier supplies a structured uncertainty signal that improves LLM screening efficiency, and we identify the prompt-delivery strategy that maximises the benefit-to-cost ratio. We evaluate five LLM prompt-delivery conditions on eight drug-class datasets from the Cohen (2006) benchmark using 3 seeds x 5-fold stratified cross-validation (600 fold-level results). A BERT+GCN model trained per fold classifies each test paper as INCLUDE, EXCLUDE, or MAYBE via two spectral tests (algebraic radical and categorical paradox). Conditions vary information content (none / label / full scores), selectivity (all papers vs. MAYBE only), and timing (proactive vs. reactive two-pass). A cross-model pilot against gpt-4.1-mini on three datasets tests cross-generation transfer. Three findings: (i) Full-context delivery yields significant gains in F1 (+0.011, paired Wilcoxon p=0.008) and WSS@95 (+0.050, p=0.039) at a 1.28x token-cost premium, while preserving recall. (ii) MAYBE-only routing is Pareto-optimal: highest mean recall (0.92) and AUC-ROC (0.54) at only 1.05x baseline cost – one sixth of full-context overhead. (iii) The two-pass design escalates 22.2% +/- 8.8% of records yet never revises its decision (0% flip rate across all datasets and folds), giving decisive evidence that current instruction-tuned LLMs cannot self-triage. The cross-model pilot shows an identical +0.8% recall uplift for both LLM generations. A per-paper ablation across 20,796 observations shows the dual paradox test reduces empirically to a one-line logit-gap criterion. We release the full pipeline; the 600-run experiment replays in under one hour from cached LLM responses.

Cloud services experience frequent incidents that require rapid diagnosis and resolution. Troubleshooting guides help engineers respond consistently, but creating them manually is labor-intensive, resulting in incomplete coverage and outdated documentation. We present FixItFlow, an automated system that generates troubleshooting guides from historical incident data using large language models. The system extracts diagnostic patterns from engineer actions, synthesizes structured guides with verified commands, and enforces strict validation to prevent fabricated content. In our evaluation with 26 engineers, generated guides achieved 61.5% positive ratings for clarity and demonstrated a 2.3x reduction in mitigation time for incidents with associated guides. These results indicate that automated guide generation can improve incident response while reducing documentation burden on engineering teams.