Papers

We study the oracle complexity of computing a point with small fixed-point residual $\|T(x)-x\| \leq \epsilon$, for a general norm $\|\cdot\|$ and a self-map $T$ of a compact convex set. We study this problem in the setting where $T$ is nonexpansive with respect to the same norm $\|\cdot\|$ and accessed via an unbiased stochastic oracle with bounded variance $\sigma^2$. We provide an algorithm that solves such instances for any norm with a weak Rademacher type $q > 1$, with high probability. The algorithm is based on a recursive anchoring technique. For type-$2$ spaces, such as $\ell_p$-spaces for $p \in [2, \infty]$, our algorithm attains stochastic oracle complexity $\tilde O(\sigma^2 \epsilon^{-3} + \epsilon^{-1})$. We further prove a near-matching lower bound (i.e., matching up to poly-log factors) for such $\ell_{\infty}$-norm instances in high dimensions. Our lower bound holds against any randomized algorithm that succeeds with constant probability. It further extends to settings with “sparse” noise, where variance measured with respect to any $\ell_p$ norm is of the same order, ruling out the possibility of improving oracle complexity as a function of $\varepsilon$ by measuring variance in a non-matching $\ell_p$ norm.

Physical-layer authentication (PLA) in non-terrestrial networks (NTNs) is challenged by severe Doppler shifts, long delays, and fast channel variations, which cause distribution shifts and degrade conventional learning methods. Existing PLA schemes often rely on single features or generalize poorly to unseen environments. This paper proposes a secure adaptive framework for authentication in multi-zone networks (SAFA-MZ), a causal meta-learning framework for distributed PLA (DPLA) in NTNs. First, we design a multi-feature fingerprint that combines spatial, angular, combiner, subspace, and Doppler-delay features. The fingerprint is adaptive and distributed, as it fuses heterogeneous physical-layer features and measurements from multiple aerial nodes. Second, we formulate a structural causal model (SCM) to capture the relations among design choices, environmental factors, extracted features, and authentication outcomes. Third, we develop a model-agnostic meta-learning (MAML) strategy with invariant risk minimization (IRM) and causal consistency regularization for fast adaptation to unseen NTN environments with few labeled samples. Fourth, we propose a two-stage authentication scheme that performs local recognition and activates time-difference-of-arrival (TDOA) localization with a graph attention (GAT) network only when needed, which reduces backhaul overhead. Simulations show that SAFA-MZ achieves 92% accuracy and 96% AUC, outperforming centralized deep learning and single-feature baselines across diverse environments.

We perform field-level likelihood-free inference of the matter density parameter $\Omega_m$ from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer $\Omega_m$ from velocities alone with mean relative errors of approximately $18\%$ in-distribution and $\sim25\%$ OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful $\sigma_8$ predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer $\Omega_m$ with mean relative errors of about $10\%$ in-distribution and $10$–$17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of $\Omega_m$ information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.

Fairness auditing of text-to-image diffusion models often requires generating large numbers of images across sampling configurations, making comprehensive evaluation computationally expensive. We propose a causal-abstraction-based audit instrument for efficiently evaluating fairness under interventions on the classifier-free guidance scale. Given a fixed prompt and a target feature function, we represent the diffusion process as a low-level structural causal model and construct a corresponding high-level model over abstract denoising states. We characterize the projected causal structure, establish identifiability of the fairness-relevant interventional query, and provide sufficient conditions under which the high-level model preserves this query. A probabilistic transformer implements the high-level model as an amortized predictor of target-feature distributions across guidance scales. Experiments evaluate distributional fidelity, fairness-query accuracy, and computational efficiency. We present two auditing demonstrations: one using standard Stable Diffusion 1.5 and another using StayFair, a fairness-enhanced Stable Diffusion model, to examine their behavior across guidance scales.

Critical infrastructure location data is often incomplete and unevenly distributed globally, especially in developing regions. Earth observation foundation models are proposed as a new step in enabling us to more efficiently understand the natural and built environment, raising questions as to their effectiveness in performing challenging downstream tasks. Yet, foundation models remain largely untested for detecting and classifying the facility-scale critical infrastructure that underpins a range of important societal and economic functions. Subsequently, Infra-Bench CLS is introduced as a benchmark to test foundation models on 18,756 Sentinel-1 SAR and Sentinel-2 multispectral facility-scale critical infrastructure asset images covering seven continents and 13 infrastructure classes, with results reported for the 10 retained classes. Using linear probing and fine-tuning for two training dataset levels (1.0x and 0.3x), seven foundation models are evaluated (SatlasPretrain S2, SatlasPretrain S1, CROMA, Prithvi-EO-2.0, AlphaEarth Foundations, OlmoEarth v1.1-Base, and DINOv3 ViT-L/16). When comparing macro F1 scores to a ResNet-18 supervised baseline of 39.2 percent, the best foundation model achieved 57.9 percent, a 48 percent improvement. Top performing classes were airports (F1 85.3 percent), train stations (F1 82.1 percent), and data centers (F1 77.6 percent). By contrast, many of the power sector classes perform poorly (F1 27.5-46.2 percent). These findings suggest foundation models can enable superior critical infrastructure classification, but future work should evaluate performance on higher-resolution imagery, particularly for poorly performing sectors, such as power.

We establish nonasymptotic Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for deterministic matrix-weighted sums of multivariate Poisson martingale differences generated by uniformly ergodic Markov chains. Under an $L^{(2+\eta)p}$-moment condition, $\eta>0$, we obtain the explicit bound $$O\left(p^3\|A\|_4^2+pd^{1/4}\|A\|_2^{1/2}\|A\|_4^2\right),$$ where $A\in\mathbb{R}^n$ collects the moment sizes of the weighted increments. When these sizes are of order $n^{-1/2}$, the bound achieves the first optimal $O(n^{-1/2})$ rate for fixed $p$ and $d$. Consequently, we also obtain the first optimal $O(n^{-1/2})$ $W_p$ Gaussian approximation rate for multivariate additive functionals of uniformly ergodic Markov chains. Our analysis develops two techniques for addressing the interplay between higher-order Wasserstein distance and temporal dependence. First, building on the Ornstein–Uhlenbeck relative-score approach of Fang and Koike (2023), we formulate the bound in terms of antisymmetric Stein couplings while retaining the conditional tensor structure. Second, we develop a refresh-then-maximal coupling that combines an independent first-step resampling, which preserves the desired Stein identity, with a subsequent maximal coupling that provides effective control of the coupling increment. We apply these bounds to nonlinear Markovian stochastic approximation by decomposing normalized errors into matrix-weighted Poisson martingale sums and remainders. This yields the first sharp $W_p$ Gaussian approximation rates for both last iterates and Polyak–Ruppert averages. In particular, the optimized rates are $O(n^{-1/3})$ for polynomial-stepsize last iterates and $O(n^{-1/4})$ for Polyak–Ruppert averages, with an $O(n^{-1/2})$ rate for harmonic-stepsize last iterates under an additional spectral condition.

Soft Actor-Critic (SAC) represents a continuous policy as an unbounded Gaussian that is squashed by tanh. The Jacobian of that map is $\partial a/\partial u = 1-a^2$, which vanishes as $|a|\to 1$. A natural concern is that this throttle starves the actor of critic signal exactly where extreme actions (full brake, full throttle) are optimal. We test a minimal intervention that restores the missing signal: one extra term in the actor loss whose gradient on the pre-tanh mean is the detached action-gradient of $Q$, with no gain parameter. On a minimum-time double integrator whose optimum is bang-bang at the action bounds, vanilla SAC already reaches near-optimal return ($-31.6$ vs. a calibrated optimum of $-30.3$) across ten paired seeds. An ungated bypass does saturate the policy (99% of eval steps with $|a|\ge 0.9$) and collapses return to $-195.5$. A gated bypass that fires only on the flat shoulder $|a|\in[0.9,0.999]$ also fails, and does so without leaving a saturated policy. Warm-started MetaDrive fine-tuning shows the same pattern: the bypass does not improve return, and where collision rate falls it is typically traded for out-of-road departures. Auto-tuned entropy coefficient rises against the bypass, which is a push toward the tails. The Jacobian effect is real. Treating it as a bug to be undone is not free, and on the tasks studied here it is not helpful. Saturating a bound is not the same as solving a problem whose optimum lives on that bound.

Delineating lung tumours on computed tomography (CT) takes a considerable share of the time spent on radiotherapy planning, and a contour proposed by a model can be refined interactively by the clinician. Promptable foundation models such as SAM 3 support this workflow by writing each correction into a session memory that conditions the remaining slices, while the model weights stay fixed. On 690 test cases from five public CT cohorts, fine-tuning SAM 3 on lung tumours raises the Dice obtained from a single point prompt from 0.298 to 0.757, and seven rounds of corrections raise it further to 0.765, but under memory conditioning alone the accuracy on slices the annotator has not touched stops improving after six rounds. We therefore treat each correction as a training signal and propose LeCor, which performs test-time training on a small set of case adapters that are reset for every case and meta-learned such that a single gradient step driven by a click improves the slices that were not clicked. On the 133 test cases that span at least eight slices, LeCor raises the Dice reached after seven correction rounds from 0.787 with the fine-tuned model to 0.827, reduces the number of cases that never reach a Dice of 0.80 from 47 to 27, and reaches in three correction rounds the accuracy that the fine-tuned model attains in seven.

In-vehicle assistants must translate natural-language requests into accurate vehicle function calls under strict memory and latency constraints, making small language models (SLMs) attractive for on-device deployment. For such models, a key design choice is how the available function surface is presented. Two approaches are to represent each function with a dedicated Functional Token (FT) or provide function schemas directly in the prompt. FTs enable compact inference but are restricted to functions learned during training, whereas Schema-in-Prompt (SIP) can generalize to unseen functions at the cost of longer prompts and higher inference overhead. We introduce a benchmark of 9,822 single-turn examples spanning 79 vehicle functions derived from Android Automotive, including held-out functions and requests requiring refusal. We compare both approaches under matched fine-tuning across four SLMs from 270M to 1.7B parameters. On functions seen during training, scaling provides limited benefit: the 270M model can match the 1.7B model, and the highest Seen accuracy in our main grid occurs at 0.6B. On held-out functions, FT achieves zero accuracy by construction, whereas SIP generalizes and improves substantially with scale. On out-of-scope requests, FT can invoke an unavailable function it was trained to emit, while SIP more reliably refuses based on the functions offered. This flexibility comes with a higher inference cost, chiefly the latency of processing the schema prompt. Our theoretical analysis formalizes why only SIP can predict functions withheld as training targets and why longer schema contexts increase inference cost. Overall, function-surface representation, rather than model scale alone, determines the capabilities and failure modes of SLM-based vehicle function calling.

Normalizing flow Boltzmann generators retain a tractable pushforward density, but training with forward KL depends on target samples that may be biased or omit modes. As a result, a flow can miss target mass while its observed importance weights give a high effective sample size. We introduce the log-ratio variation $\X_\omega$, the mean absolute pairwise difference of the target-to-pushforward log-density ratio under a weighting measure $\omega$, and use it to define KLXX, a new loss function. Two log-ratio variations are added to the forward KL (denoted by the two X's): one weighted by the target to improve accuracy, the other by a mixture of quench and temper samples with pushforward samples to search candidate modes. We derive the Fisher–Rao gradient flow of KLXX, where both variations contribute nonpositive dissipation, and a fixed-surrogate error bound for KLXX. We use KLXX in an adaptive-staging Boltzmann generator, with importance reweighting at every stage. We bound the sampling error of its inference scheme when the stage weights are essentially bounded, and prove it asymptotically unbiased in the sample size. In the numerical tests, KLXX improves mode coverage over forward KL. It also improves the generator's per-stage diagnostics against the loss that built the schedule. The observables the generator recovers are close to independent references. The log-ratio variations thus supply information that the forward KL loss usually omits.

Can an agent learn a numerical search strategy through executable practice and then transfer that strategy as text? We study low-budget black-box optimization, where unaided language models remain well below strong classical optimizers. During development, an agent repeatedly writes and evaluates optimizer programs. It then distills the resulting program and practice record once into a 197-word primary Harness A, which is frozen before evaluation. Harness A reduces Gemini Flash regret by 48% in an independent $N=30$ study ($p<.001$), enters the GP-BO performance range on the practice family, and lowers mean regret on all three held-out BBOB landscapes. The same text improves every tested Gemini executor and transfers to Claude Sonnet, reducing regret by 43% and 49% ($p\leq.005$). An independent end-to-end replication produces Harness B, a different program and text at the same performance tier. The same framework also attains the lowest regret on a sealed YouTube reward-tuning production benchmark. Executable practice is thus a viable way to discover a search policy, and language a portable medium for deploying it.

Online gradient descent is usually studied through external regret, where the learner competes with fixed alternatives. Recent work shows that first-order methods control richer action-dependent deviations. We ask for a geometric characterization of the deviations with respect to which online gradient descent, mirror descent, and follow-the-regularized-leader (FTRL) achieve no regret. We identify exactness as the common principle. Exactness means that the relevant displacement field is generated by a scalar potential, or equivalently that the associated one-form is exact in the geometry used by the algorithm. This geometry depends on the algorithm. For gradient descent it is Euclidean geometry, for mirror descent it is the geometry induced by the regularizer, and for FTRL it is the cumulative dual state. Under mild regularity conditions, exactness yields sublinear regret, while nonzero circulation provides the complementary obstruction and leads to linear regret. This gives a unified geometric framework for understanding the deviation classes controlled by these algorithms and reveals that different first-order methods can control genuinely different classes of deviations. These deviation classes have direct consequences for learning, particularly in games. We study the equilibrium notions induced by exact-form deviations and introduce conservative correlated equilibrium, reflecting both the conservative geometry of the underlying displacement fields and the restricted family of deviations available to the players. We characterize its relation to correlated equilibrium, determine when the resulting equilibrium notions coincide and when they separate, and show how these relationships depend on the geometry and the learning algorithm. Overall, this work gives a unified geometric account of what first-order online learning algorithms are no-regret with respect to, beyond fixed comparators.

Quantum state tomography is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become computationally prohibitive as the system size increases due to the exponential growth of the density matrix, describing a quantum state, with the number of qubits. We propose a low-rank tensor-network framework for mixed-state quantum state tomography based on a block tensor train (Block-TT) factorization. Specifically, the density matrix is represented as the contraction of a Block-TT with its Hermitian transpose, yielding a TT analogue of the Burer-Monteiro factorization. This parameterization guarantees Hermiticity and positive semidefiniteness by construction while compressing the number of optimization variables from exponential to linear in the number of qubits. Building on this representation, we develop single-site and two-site density matrix renormalization group (DMRG) algorithms for estimating quantum states from compressed measurements. The resulting methods operate directly on the compressed parameterization, support adaptive rank refinement, and exploit efficient tensor-network contractions for expectation-value evaluation. The framework is applicable to a broad class of low-rank quantum states, including pure states, nearly pure states, and ground states that admit accurate tensor-network approximations. Numerical experiments demonstrate accurate state reconstruction from limited measurements together with substantial reductions in memory requirements and computational cost compared with conventional low-rank tomography methods.

Sea-ice stage of development (SoD) describes the age and associated thickness of sea ice and provides important information for navigation, and operational ice monitoring. SoD labels are obtained from operational ice charts, where trained analysts interpret satellite observations and assign standardized stage codes to regions with similar ice conditions. These codes often represent ranges of compatible ice thicknesses rather than exact physical values. Deep-learning methods can automate SoD mapping and commonly adopt operational ice charts as reference labels for training. These annotations are not exact, however; this is because chart interpretation relies on analyst judgement and on the observations available at the time, so different ice services may assign different SoD labels to the same conditions. We term this variation across independently produced expert annotations multi-annotator label uncertainty; collapsing the annotations into a single deterministic target discards this variation. A second source of uncertainty originates in the learned model itself. In this paper, we quantify both sources: annotation uncertainty from disagreement among independent ice-service charts and model uncertainty from the learned predictive models. We then evaluate their relationship by testing whether model uncertainty is higher where ice services disagree. We observe that supervision incorporating information from multiple annotators can improve this correspondence, with soft supervision achieving the highest overall correlation of 0.256. The relationship becomes substantially stronger near the ice edge, where model predictive uncertainty closely tracks multi-annotator disagreement, reaching a correlation of 0.704 within 0–10 km. Among the uncertainty-estimation approaches, Monte Carlo dropout provides the best-calibrated confidence estimates, with an expected calibration error of 0.050.

In network traffic, legitimate behaviours and attack techniques evolve jointly - the phenomenon known as 'concept drift' [1]. Every detector is thereby left obsolete between two updates, and always one step behind adversaries. In this work, we propose to move the point of intervention from the model, repaired after the drift, to the feature space, selected before learning. We therefore introduce t-robustness, a stability score defined for each feature independently of any detection model, comparable across an entire feature space. It combines the step-by-step distance between successive statistical states of a feature, and its cumulative divergence from its initial state, so that a slow monotonic drift cannot pass for stability. The candidates are drawn from abnormal network connectivity patterns left by scans, DoS and communications between endpoints, read through graph community metrics and spectral metrics. The evaluation is performed on the UGR16 dataset, across three learning scenarios and a control scenario, as well as without model update, and demonstrate that t-robust feature spaces sustain detection where the baselines collapse: retained expectancy at the last test interval reaches 0.6025, against 0.5230 for graph community features and 0.3831 for the base NetFlow features.

Minimum-norm confidence envelope strategies offer a nonparametric approach to constructing nonasymptotic, simultaneous confidence regions for band-limited functions, exploiting the theory of Reproducing Kernel Hilbert Spaces (RKHS). While the finite-sample coverage guarantees of these envelopes have been established, their consistency has not been analyzed so far. In this paper, we study this construction, here termed the Minimum-Norm Confidence Envelope (MiNCE) framework, and establish the strong uniform consistency of the resulting bands, both for noise-free and noisy observation models, under mild assumptions on the measurement noises. We further extend this formulation to the frequency domain, deriving nonasymptotic, simultaneous, strongly uniformly consistent confidence bands for the smoothed spectra. Numerical experiments in nonparametric regression and spectral estimation empirically confirm our theoretical results, illustrating the contraction of the confidence envelopes toward the target function as the sample size increases.

Weak Sparse Identification of Nonlinear Dynamics (WSINDy) provides a noise-robust approach for learning dynamical systems from data without requiring numerical differentiation. However, for high-dimensional systems, tensor-product libraries of candidate functions grow exponentially with the state dimension, making standard WSINDy expensive in both computation and memory. The Multidimensional Approximation of Nonlinear Dynamics (MANDy) addresses this scaling through a tensor-train (TT) representation of the candidate library, but does not provide a mechanism for sparse model selection. Here, we combine these approaches to develop TT-WSINDy, which performs the weak-form transformation, regression, and sparsification in TT format. We show that the TT formulation recovers the corresponding WSINDy regression problem and derive polynomial time and memory complexity bounds for the tensor-train sparsification procedure. Numerical experiments demonstrate robustness to measurement noise and computational savings for high-dimensional systems.

Leave-One-Subject-Out (LOSO) evaluation estimates generalisation performance for subject-based classification but makes Neural Architecture Search (NAS) computationally expensive because a fully nested implementation requires N independent architecture searches and, assuming approximately linear training cost, scales as O(N^2). We propose a leakage-free, block-based approach that shares NAS runs across subjects. On the BioVid Heat Pain dataset, our approach increased the mean accuracy from 82.79% to 83.39% while reducing the number of parameters by up to 99.2%.

Real-world datasets often exhibit evolving distributions, known as concept drift. Ignoring drift degrades predictive performance, while reliance on fixed hyperparameters further limits model adaptability under changing conditions. Adaptive learning addresses this challenge by continuously updating models online, allowing them to incrementally adjust and remain effective as data distributions evolve. This paper presents the Stream Cruise Control Method (SCCM), a comprehensive framework for drift detection and adaptation in online regression. SCCM enables automated adaptation through early-response, pre-update drift detection, drift magnitude quantification, KPI-window-based thresholding for local false-alarm mitigation, dynamic hyperparameter tuning, and model recalibration. SCCM also adopts an in-memory design for real-time adaptability, unlike purely reactive methods that typically activate adaptation only after performance degradation is observed. By using dynamic thresholding and remaining agnostic to data distributions, SCCM supports KPI-based monitoring across varying data streams, including high-dimensional and large-scale settings. SCCM is integrated with four online regression models and evaluated on 18 synthetic datasets covering abrupt, incremental, and alternating gradual drift, together with eight real-world datasets. The evaluation uses both R2 and MSE and compares against eight detector–adaptation baselines. Results show improved predictive performance and effective drift handling across the evaluated online regression settings.

While accurate measurement of socioeconomic indicators remains challenging in data-scarce regions, which limits policy interventions and resource allocation, high-resolution geospatial data is widely available and can contain information on various livability statistics. We investigate which physical features are encoded within foundation model embeddings, such as AlphaEarth, AnySat, and TerraMind, and provide a systematic framework for identifying the most predictive geospatial indicators. By analyzing how different types of geospatial data influence urban livability predictions, our approach enables researchers to prioritize the most informative features for their specific applications. Additionally, we demonstrate how to leverage foundation model embeddings to enhance prediction performance for these outcomes. This work contributes a principled methodology for extracting actionable information from satellite imagery while accounting for complex spatial dependencies, with applications in predicting urban livability in regions with limited observation data.

Enterprises managing large X.509 certificate inventories face a prioritization problem: deterministic analysis tools that precisely identify standards violations are indispensable for remediation, but applying them exhaustively across millions of certificates is operationally impractical. We present X-amine509, a two-stage triage system that uses machine learning to rapidly rank certificates by predicted risk and route only the highest-risk items to full deterministic analysis. Certificate risk is quantified as a composite score derived from 177 defect checks grounded in CA/Browser Forum Baseline Requirements, NIST IR 8547/SP 800-57, and cryptographic strength criteria, weighted by security severity across four tiers ranging from cryptographic breaks to minor compliance deviations. We collected 1,027,714 X.509 certificates from Fortune 500, .gov, and .edu domains and scored each using this rubric. On a held-out test set of 201,976 certificates, our best model (Extra Trees) achieves $R^2$ of 0.993 with MAE of 2.26, while Decision Tree scores $R^2$ of 0.986 at 3.7 million certificates per second on a single machine. Ranking quality confirms the triage value: aggregate NDCG exceeds 0.997, and severity-tier classification reports 99.76% accuracy with 98.90% recall on critical-tier defects. Thirteen months later, we retrieved another 571,374 certificates to test our models' durability over time, and the Extra Trees and Decision Tree models maintain MAE below 6.8, $R^2$ of at least 0.915, aggregate NDCG above 0.988, severity-tier accuracy of at least 99.52%, and critical-tier recall of at least 97.03%. Feature importance analysis identifies validity period, Extended Key Usage configuration, negative serial number encoding, and self-signed status as the strongest risk predictors, providing coarse interpretability at the triage stage.

Brain-age prediction models are commonly evaluated by predictive accuracy, yet accurate predictions alone do not establish that a model relies on reproducible or neurobiologically supported mechanisms. Post-hoc explanation methods can expose these mechanisms, but existing workflows typically stop at diagnosis or require correction targets to be specified before model analysis. We propose XAI-Refine, an automated explanation-knowledge loop for brain-age prediction from resting-state functional connectivity. At each iteration, XAI-Refine consolidates complementary post-hoc analyses across repeated training runs into reliable, structured model explanations. It converts each reliable explanation into a neutral neurobiological question, retrieves and verifies relevant literature, and compiles the verified evidence into an admissible set in the same typed explanation space. The target for refinement is defined as the minimal projection of the current model explanation onto the admissible set induced by applicable verified knowledge. This revised explanation is then translated into a differentiable constraint while preserving the originating model variable, measurement operator, and applicable scope. Candidate updates are promoted only when multi-seed validation confirms target-directed explanatory movement, predictive performance remains within a prespecified guardrail, and non-target explanatory drift remains bounded. Experiments on functional-connectivity-based brain-age prediction evaluate predictive performance, explanation reliability, literature alignment, and target-specific model revision, illustrating a structured route from post-hoc analysis to evidence-guided model refinement.

Discrete black-box optimization is often addressed using approaches such as Sequential Model-Based Optimization (SMBO), which aims to improve sample efficiency by fitting surrogate models that approximate a costly objective function over a discrete search space. In many real-world problems, the set of feasible inputs is often given by logical constraints known in advance. However, existing surrogate modeling techniques generally fail to capture the symbolic rules governing feasibility in discrete input spaces. In this paper, we propose a surrogate modeling approach based on tensor decomposition that captures the structure of discrete search spaces while directly integrating feasibility information. To implement this approach, we formulate surrogate model training as a constrained polynomial optimization problem and solve a relaxed formulation using a differentiable penalty term derived from T-norms. Our experiments on both synthetic and real-world benchmarks, including a pressure vessel design task, demonstrate that the proposed method improves sample efficiency by effectively guiding the search away from infeasible regions.

Divergence-based regularization and Sharpness-Aware Minimization (SAM) are two prominent approaches for improving generalization in deep learning, both motivated by robustness to perturbations. However, their relationship has remained largely unexplored. Building on classical second-order expansions of $f$-divergences, we show that the two methods are locally consistent under parameter-space perturbations: both induce curvature-sensitive penalties, with divergence regularization yielding a Fisher-weighted quadratic form and SAM penalizing sharpness through the dominant Hessian eigenvalue. For negative log-likelihood objectives with exponential-family output distributions, this correspondence becomes especially transparent, since the Fisher and Gauss-Newton matrices coincide. We further show that the same local geometric perspective extends to input-space perturbations, where divergence-based regularization is defined through transformations of the input. In this setting, the regularizer induces a pullback quadratic form on the input space, providing a more general perturbation framework than standard SAM while preserving the same local sensitivity interpretation. To validate the analysis empirically, we use the asymmetric $\alpha$-skew Jensen-Shannon divergence (JSD) family as a controlled testbed. Its local curvature coefficient scales as $\alpha(1-\alpha)$ and is maximized at the symmetric point $\alpha=\tfrac12$, which recovers the standard JSD. Loss-landscape visualizations in the input-perturbation regime show that stronger induced curvature penalization is associated with flatter local minima. Experiments on four benchmark datasets further demonstrate that both accuracy and negative log-likelihood are consistently best near this regime of maximal curvature penalization.

Fully homomorphic encryption (FHE) enables inference on private data without revealing it to the server, but evaluating an entire input under FHE is expensive. We study selective homomorphic inference, where only a sensitive region of interest (ROI) is encrypted, and computations independent of that region are performed in plaintext. Selective evaluation produces the same output as full FHE on the same model, without retraining. Its efficiency depends on how quickly encrypted dependencies spread through the network. For small encrypted ROIs, locality-preserving architectures can achieve order-of-magnitude homomorphic-evaluation speedups, whereas architectures with early global mixing provide essentially no speedup. These results identify locality as the key architectural property governing the benefit of selective homomorphic inference.

This article introduces PeriodicCALM, an effective real-time anomaly detection framework designed for cyclostationary data streams. While classical cyclostationary processes feature periodically time-varying statistical properties, real-world signals often contain recurring impulsive components that conceal abnormal behavior. Existing real-time methods for struggle with these dynamics, frequently misinterpreting phase-dependent variability as non-cyclic anomalies and causing excessive false alarms. To address this, PeriodicCALM incorporates cycle-dependent variability to systematically ignore regular cyclic impulses while accurately isolating genuine anomalies. Operating in real time with continuous retraining capabilities, the method adapts dynamically to evolving signal characteristics. Comparative evaluations against the baseline CALM framework using simulated data demonstrate significant improvements in detection accuracy and training efficiency, alongside a reduction in prediction latency. Furthermore, the practical utility of PeriodicCALM is validated on real-world vibration signals collected from a compressor monitoring system.

Decision trees are prized for their interpretability and strong performance on tabular data, but popular greedy top-down induction algorithms can yield suboptimal and unnecessarily complex structures. Optimal decision tree methods address this through global optimization, yet remain restricted to axis-aligned threshold splits, which limit the expressivity of each node and often force deep, complex trees to capture non-linear feature effects. Shape Generalized Trees (SGTs) generalize threshold splits to learnable univariate shape functions, improving expressivity and enabling more compact trees. However, existing SGT induction algorithms are greedy and offer no optimality guarantees. In this work, we introduce Literati, the first algorithm for optimal SGT induction. We propose a novel AND/OR graph formulation of the problem that jointly optimizes tree structure and shape function complexity. To solve this AND/OR graph, we develop an AO*-based algorithm with two enhancements that improve anytime performance while preserving optimality: a secondary heuristic for OR-node selection and a round-robin policy for AND-node exploration. Across 24 real-world datasets, Literati achieves higher training and test accuracy than state-of-the-art tree approaches.

The fixed-charge network flow problem (FCNFP) couples continuous flow allocation with discrete arc-activation decisions, making it a canonical but computationally challenging model for a variety of network design and resource allocation problems. Exact mixed-integer linear programming formulations capture the fixed-charge structure faithfully, but often become difficult to solve on large networks. We propose a scalable continuous-optimization algorithm for large-scale single-commodity FCNFP based on an iteratively reweighted least-squares (IRLS) framework. The method replaces the discontinuous fixed-charge and linear arc cost objective with a smooth nonconvex Lasry–Lions surrogate and solves a sequence of weighted quadratic flow subproblems. Each subproblem is solved by a warm-started dual semismooth Newton method whose Newton systems have weighted graph-Laplacian structure, enabling the use of modern Laplacian solvers. To further improve the discovered arc supports of the challenging underlying combinatorial problem, we also develop an algorithmic variant that incorporates objective-driven perturbation restarts and an anchor-union restricted search that jointly leverages supports discovered by IRLS and by complementary FCNFP heuristics. Computational experiments on 410 benchmark, synthetic, and large-scale instances show that our method obtains the best objective quality among the evaluated scalable FCNFP algorithms, with a mean gap of $1.316\%$ to a time-limited MILP reference and a win-or-tie rate of $90.0\%$ among the non-MILP methods. The results indicate that combining smooth continuous optimization with support-level search is an effective strategy for producing high-quality feasible solutions to large-scale FCNFP.

Decays of beauty and charm hadrons provide sensitive probes of physics beyond the standard model, including decays with invisible particles, in which part of the final state leaves no reconstructed detector signature. The large heavy-flavour data samples recorded by the LHCb experiment at the CERN LHC, together with its precise tracking, displaced vertex reconstruction, and particle identification, make it particularly well suited to learning a map of reconstructed heavy-hadron decay environments directly from data. We propose to bring recent advances in jet flavour tagging at ATLAS and CMS to significantly improve on the performance of the current LHCb taggers and extend them to the reconstruction of heavy-flavour decays with several invisible particles in the final state. To achieve this, we introduce a self-supervised transformer architecture that learns the decay maps without flavour or exclusive-decay labels by inferring masked particle identification information and completing jets from which constituents have been removed. Across five classification tasks in simulated LHCb Open Data, the self-supervised model outperforms an otherwise identical transformer with random weights, and performs comparably to a fully supervised transformer. We achieve a tagging power of about 10%. In addition, removing constituents from reconstructed exclusive decays also systematically increases the model anomaly score relative to random removals from the same heavy hadrons. We confirm this behaviour directly in 2017 LHCb proton-proton collision Open Data: the score increases for all eight studied heavy-flavour channels, and the signal region response exceeds that in the adjacent sidebands. These studies provide a proof of principle that mapping heavy-flavour decay environments through jets can transform flavour tagging in LHCb and extend the discovery reach for incomplete or otherwise unusual decays.

We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tensor networks (FCTNs) with nuclear-norm-regularized bond corrections. Each bond matrix is parameterized as a baseline all-ones matrix plus a low-rank correction $C_{ij} = U_{ij}V_{ij}^\top$, and the nuclear norm of the correction implemented via the variational Frobenius norm penalty on the factors drives unnecessary bonds to zero. We prove that under faithfulness, positivity, and a no-implicit-rerouting assumption on the local tensor architecture, every optimal FCTN with zero reconstruction error $\varepsilon = 0$ has effective graph exactly equal to the moral graph. For the approximate regime ($\varepsilon > 0$), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter $\beta$. The effective graph is read directly from the optimized bond matrices.