Papers

Clinical data sources such as electronic health records and wearable sensors record patient status repeatedly over follow-up, often at irregular times and on different schedules for different measurements. These data create opportunities for continuously updated, individualized risk prediction. Existing approaches, however, often simplify the temporal structure for model fitting. We introduce Random Hazard Forests (RHF), a survival tree ensemble that estimates how a patient's hazard changes in continuous time as new measurements become available. The method formulates the estimation problem directly through a nonparametric hazard likelihood for predictable covariate processes. An efficient working model guides tree construction, after which flexible time-varying hazards are estimated for each terminal node. Given any predictable covariate path, each tree follows the path through its terminal nodes over time and assembles the corresponding node-level hazards into a trajectory. Averaging these trajectories across trees yields the pathwise hazard estimate. Because routing at each time uses only the covariate state available immediately beforehand, the construction accommodates internal longitudinal covariates without lookahead. Simulations and an intensive care application show that the forest accurately estimates changing risk under irregular and asynchronous covariate updates.

Multi-horizon rare-event forecasting is hard under long macroeconomic series' data constraints: labeled events are scarce, and standard uncertainty quantification assumes an exchangeability that autocorrelation violates. A controlled ablation shows an apparent rare-event threshold for Adaptive Conformal Inference instead reflects calibration-set size. Across 200 random calibration sets, support width of the nonconformity-score distribution explains up to 85% of coverage variance versus 2% for rare-event count; the same, not the same magnitude, replicates across synthetic conditions and five countries (five-country Spearman $\rho$ 0.45-0.66 vs. 0.02-0.23). A diversity-maximizing selector built on this is the only strategy tested that improves long-horizon coverage (67.8% to 81.4% at six months); Mondrian, shift-robust, and extreme-value alternatives fail to close it. Mondrian even worsens coverage under oracle labels. A compact proposition explains why: coverage deficit reflects how closely the calibration set's upper quantile reaches the test distribution's. Diversity is necessary, not sufficient. Demonstrated on a two-stage U.S. recession-forecasting framework with RegressorChain, whether six-month coverage reaches 90% under honest scoring remains open, a question this paper quantifies rather than resolves.

Functional decline in older adults is typically recognized only after falls or observable gait impairment, closing the window for prevention. We investigated whether temporal trajectories of routine biomarkers, already recorded but rarely analyzed longitudinally, can identify patients in the pre-clinical phase of mobility decline. Using the All of Us Research Program (N = 297,861; 11.1% cases), we derived trajectory features (slope, variability, delta, mean) for twelve biomarkers over a three-year pre-index window. LightGBM models incorporating trajectories significantly outperformed static laboratory summaries (AUROC 0.797 vs. 0.755; DeLong p < 0.001; AUPRC 0.380 vs. 0.304). A 1:1 age- and sex-matched analysis confirmed an independent trajectory signal (AUROC 0.727 vs. demographics-only 0.680). A horizon analysis demonstrated sustained prediction 3-12 months before decline onset (AUROC 0.768-0.740). Because the model uses only measurements already ordered in routine care, it supports passive, zero-burden EHR integration for early detection of pre-clinical functional decline.

Under mild assumptions, any quantum mechanical (QM) model or quantum field theory (QFT) admits a representation in terms of an ensemble of neural networks with countably many random parameters. We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width $N < \infty$. We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as reflection positivity or cluster decomposition. We present several complementary ways of understanding which features can and cannot be preserved at finite $N$, both in QM and in QFT.

World models built on the RSSM architecture, such as DreamerV3, keep a recurrent hidden state $h_t$ trained only to reduce prediction error. We show this state also tracks its own confusion, hiding in plain sight: nearly orthogonal to $h_t$'s directions of greatest variance, invisible to any variance-based method. It is functionally distinct from ensemble disagreement, which flags new inputs, and reconstruction error, which flags bad predictions right now. On a test holding prediction error fixed while confusion varies, a linear probe on $h_t$ finds the signal (AUROC 0.72, 5 runs), while an ensemble baseline scores below chance. A discounted count of recent high-error steps explains 80% of the probe's output ($R^2=0.80$). We confirm the signal is causally used, not merely present, by editing $h_t$ directly and watching behaviour change, including a check using real values from other trajectories instead of synthetic edits. Its geometry and closed form generalize across three control tasks; the decisive dissociation test itself holds cleanly on only one, and its practical use, deciding when to check reality instead of trusting imagination, generalizes to only two of the three tasks.

Consider the following problem of learning an unknown linear order on $n$ items. In each round, the learner guesses a complete ordering of the items and receives either confirmation that the guess is correct or a counterexample: a pair of items in the wrong order. The goal is to identify the unknown order using as few queries as possible. We study this problem when up to $k$ of the returned counterexamples may be untruthful, where $k$ is not known in advance. We determine the optimal query complexity up to constant factors: \[ \Theta(n\log n + nk). \] Thus, while the noiseless complexity matches the classical complexity of sorting, each untruthful counterexample incurs an additional cost of order $n$. The upper bound is based on a geometric representation of permutations and Grünbaum's theorem, while the lower bound combines sorting arguments with a Condorcet-type construction. We also study the case where the target ranking has a low-dimensional geometric representation: each item is represented by a point in $\mathbb{R}^d$, and the ranking is obtained by projecting the points onto an unknown direction. For these classes we give an upper bound of $O(d^2\log n+dk)$ and a lower bound of $\Omega(d\log n+dk)$, leaving a factor of $d$ gap in the noiseless term.

Multimodal Large Language Models (MLLMs) are increasingly deployed in high-stakes domains where fairness is a critical safety requirement. In practice, these models are continually updated through continual learning (CL) to adapt to evolving tasks and data distributions. Prior work has shown that backdoor attacks can manipulate MLLM responses through hidden triggers, but naively implanted backdoors degrade as models undergo subsequent updates of CL. Although fairness has emerged as a central concern for MLLM deployment, whether backdoor-induced fairness violations can survive CL remains unexplored, leaving two critical questions unanswered: (1) whether a backdoor can reliably induce fairness violations in MLLMs, and (2) whether such fairness-targeted backdoors can persist through continual learning. We bridge this gap by proposing Persistent Fairness Backdoor Attack (PFBA) to inject persistent and group-specific discrimination into MLLMs. Specifically, PFBA achieves this through two novel mechanisms. The Latent Space Fairness Reinforcement reshapes the model's deep feature geometry by anchoring privileged-group representations to preserve utility while repelling and clustering targeted-group representations to sustain discrimination, and the Continual Learning Simulation iteratively optimizes the trigger against simulated parameter drift to ensure backdoor persistence across future updates. Extensive experiments demonstrate that PFBA induces severe fairness disparities that persist across continual learning rounds, evading standard backdoor defenses. The data and code are publicly available at https://github.com/lyygua/PFBA.

Deploying a safety layer for large language models on commodity hardware is constrained by the guards available to do it: current open guard models hold between 1 and 9 billion parameters, are oriented toward the graphics processing unit, and answer in seconds per request on a central processing unit. This paper presents a reproducible, license-aware knowledge-distillation recipe addressing that constraint. A strong open guard labels a corpus of roughly 97,000 prompts, drawn from 24 public datasets, into seven safety categories aligned to a public hazard taxonomy, and a fleet of small students spanning lexical, shallow, encoder and generative architectures is trained to reproduce that signal. The corpus is partitioned at the license boundary, so that a deployable and a research model differ only in their training data and the cost of that restriction becomes measurable. Every model is scored against an independent gold benchmark of 6,361 rows over four slices, labeled apart from the teacher and including a slice of harmless prompts that makes over-defense measurable. The distilled students match the teachers on adversarial text within overlapping confidence intervals and reduce false alarms on harmless prompts, the smallest generative student reaching 3.8% against 4.8% for the 8-billion-parameter teacher, while the encoder classifies in roughly 24 ms per request on CPU. Per-class rebalancing is the only decisive ingredient of the recipe. No superiority over the distilled guards is claimed; on the clean reference slice they remain ahead.

Fisher width measures the Gaussian width of a probe set after deformation by the local Fisher geometry. We study its evolution along learning trajectories and ask when training loss can serve as an effective coordinate for this quantity. We first derive an exact trace–shape factorization and a deterministic stability bound for fixed compact probes. In a population Gaussian-teacher logistic model, the teacher-aligned state is extremal on every loss level below $\log 2$: it has minimal parameter norm and maximizes both Fisher trace and Euclidean-ball Fisher width. We then show that population gradient flow asymptotically selects this branch, with explicit rates for the aligned and orthogonal coordinates. This yields, for $d\geq2$, \[ \frac{w_F(B_2^d;\theta(t))} {\sqrt{L(\theta(t))}} \longrightarrow \frac{\sqrt6}{\pi}\mathbb E[\chi_{d-1}]. \] Controlled full-Fisher experiments support the matched-loss branch and the population predictions. In a nonlinear MLP with a diagonal model-Fisher approximation, GD and SGD remain close at matched loss, whereas Adam follows a substantially displaced branch; the fixed probes tested retain highly similar temporal shapes. These results support a branchwise, rather than universal, loss parametrization of Fisher width.

Modern machine learning compilers select tensor memory layouts to minimize execution cost under hardware constraints. Layout selection is global: an operator may be fastest under one layout while its consumers prefer another, and aligning these preferences requires explicit layout conversions that can hurt model performance. Despite its practical importance, layout selection lacks a formal basis, so current compilers rely on ad-hoc heuristics. This paper presents the first formal study of layout selection in machine learning compilers. We formulate the problem as combinatorial optimization over dataflow graphs, minimizing the sum of operator execution costs and the per-tensor cost of these conversions. Our theoretical analysis shows that optimal layout selection is computationally hard, even for programs containing only matrix multiplications over two-dimensional tensors. We design an optimal polynomial-time algorithm for dataflow graphs of bounded treewidth. For general instances, we give a weighted MaxSAT encoding that an off-the-shelf solver can optimize. The formulation unifies several existing layout optimization strategies, including XLA's layout assignment, partition dimension selection in systolic array compilers, and layout planning in mobile GPU optimizers. We implement the formalization in a production compiler for an AI accelerator and measure the execution time of the compiled models under greedy heuristics, the compiler's rule-based strategy, and an optimal solver. Simple heuristics degrade execution time by up to $5\times$ on some workloads. Where the compiler's cost model is accurate, the solver matches or beats the rule-based strategy. On workloads with complex data movement it falls behind, and since the solver minimizes the stated objective exactly, that gap isolates cost-model error from search quality, showing where compiler effort actually pays off.

Heterogeneous multi-robot service systems must assign requests to compatible robots, construct feasible schedules, and adapt as new tasks arrive online. Historical data can help anticipate future demand, but relying too heavily on inaccurate predictions can degrade performance under distribution shifts. We develop a prediction-aware adaptive rollout framework for heterogeneous multi-robot task assignment with scheduled and real-time requests. The problem is formulated as a finite-horizon stochastic dynamic program incorporating robot-task compatibility, ordered service requirements, routing constraints, service windows, and end-of-horizon return requirements. The proposed policy evaluates current assignments using sampled future request scenarios while restricting immediate commitments to requests already observed. To enable online use, the framework combines pruned candidate controls, wait actions, and an interaction-aware base policy for efficient future-cost estimation. Robustness to forecast error is provided by adaptively reweighting predicted requests based on recent prediction mismatch and selectively re-optimizing assigned but unstarted requests. We also introduce a historical-data-driven procedure for selecting the heterogeneous fleet composition before deployment. In a case study using real nursing-task requests from hospital inpatient floors, the proposed approach achieves near-complete service and reduces serviced-request wait times relative to reactive, token-passing, prediction-positioning, and myopic greedy baselines, with the largest improvements in tail-delay metrics.

Complex-valued arrays arise in signal processing, where scientific interpretation depends on retaining amplitude and phase information. Existing covariance estimation methods either ignore the multiway organization of such data or rely on real-domain embeddings that do not directly exploit their complex structure. We develop sparse separable factor analysis (SSFA), a latent factor model for complex-valued arrays with a separable covariance structure across modes. Each mode-specific covariance matrix is modeled through a low-rank Hermitian factor structure and a diagonal residual covariance matrix. To obtain interpretable estimates, we impose elementwise lasso penalties on the complex loading matrices and estimate the SSFA parameters using a mode-wise parameter-expanded expectation-maximization procedure. The resulting loading updates admit closed-form complex soft-thresholding solutions, which shrink the modulus of each loading while preserving its phase. A separate balancing step resolves the scale nonidentifiability of the separable covariance structure. Simulation studies show that SSFA improves covariance estimation relative to vectorization-based methods, including complex principal component analysis. We apply SSFA to local field potential recordings from mice, where we compare separability structures induced by different groupings of brain region, frequency, and time and perform model-based imputation of recordings missing because of electrode misplacement.

KV-cache compression is often justified by attention maps with a few large weights. This is incomplete: large weights may not contain most of the mass, omitted values can cancel, and preserving the attention output may not preserve the task. We separate these questions. Global score gaps – not threshold counts – determine how many tokens are needed to retain a target mass. For a realized row, the weighted sum of omitted values is the exact missing statistic. A controlled retrieval–aggregation model explains when truncation helps and when it hurts. These results motivate CertKV, a training-free compressor that reserves one tail-summary slot per head and allocates the rest by value dispersion. Under matched budgets, CertKV is top-two in seven of nine LongBench-v2 settings, remains in the leading compressed tier on 128K RULER, and realizes a ten-fold cache budget in a packed Llama prototype. Compressibility depends on the mass, values, future queries, and task – not on a sparse-looking map alone.

Federated Continual Learning (FCL) is fundamental to real-world distributed learning systems, requiring models to adapt to sequential, non-IID data across clients while mitigating catastrophic forgetting and client drift. Existing approaches formulate continual learning (CL) as a sequence of per-task optimization problems, applied locally at each client and coupled through aggregation, using heuristic mechanisms such as replay, regularization, or projection-based constraints. However, forgetting in FCL is inherently a long-term, distributed phenomenon, arising from the interaction of temporal task evolution and cross-client heterogeneity, which is not explicitly regulated. In this work, we cast FCL as a stochastic control problem and propose Federated Queue-regulated Continual Learning (FedQCL), a framework based on Lyapunov drift-plus-penalty (DPP) optimization. FedQCL introduces virtual queues to track the accumulation of forgetting across tasks and clients, enabling explicit control of the stability-plasticity trade-off. By optimizing a DPP objective, the method jointly improves current-task performance while the queue-based formulation provides an interpretable and tunable mechanism to balance adaptation and retention through a single parameter, without requiring gradient projection or additional communication overhead. Empirical evaluations on standard benchmarks, including Split-CIFAR-10, Split-CIFAR-100, and Split-TinyImageNet, demonstrate that FedQCL outperforms state-of-the-art baselines with respect to accuracy while significantly reducing forgetting under heterogeneous data distributions.

Machine learning has had a positive impact on the sports industry, with one of its most promising applications being the prediction of athlete performance and injury risk. Recent advances have employed state-of-the-art models to improve prediction accuracy, yet progress remains limited by data availability and the reliance on subjective observations or expert assessments. To address these limitations, researchers in sports such as soccer, basketball, and wrestling have begun integrating heterogeneous data sources, such as wearable device readings, with traditional subjective assessments. However, similar multimodal approaches remain underexplored in tennis. In this work, we propose a multimodal weighted ensemble learning framework, Predictive Athlete Readiness for Tennis (PART), to monitor athlete wellness and estimate near-term injury risk in tennis players. PART processes a wide range of inputs, including physiological metrics, training and match data, sleep information from wearable devices, self-reported questionnaires, vertical jump assessments, and motion analysis from match-play videos. From these modalities, specialized machine learning and deep learning models independently extract four athlete-specific characteristics: overall wellness, injury risk, physical capability, and playing style. To overcome the complexity of combining these diverse modalities, PART employs a supervised weighted ensemble integration strategy, assigning adaptive weights to each predictive model based on its reliability. Evaluation of multimodal data collected from nine collegiate tennis players demonstrates that PART achieves strong performance in monitoring athlete wellness and estimating near-term injury susceptibility. Beyond collegiate athletes, the framework also shows promise for recreational tennis players, offering personalized insights to mitigate injury risk and optimize performance.

One aim of neural network field theory is to put a quantum or effective field theory on a computer, with the network ensemble itself as the theory. We ask how far that aim can be pushed for a function class regular enough to be computed with. Our main result is a no-go theorem with assumptions that hold for standard network architectures. We use it to separate four versions of neural network field theory, according to whether the defining object is the finite width ensemble or its infinite width limit, and whether the target we want to compute is a quantum or an effective field theory. Neither finite width interpretation is straightforwardly consistent. For finite width ensembles with finite variance at each point, the QFT interpretation fails reflection positivity, while the EFT interpretation establishes no scale separation by which the positivity violation can be placed outside its domain of validity. Of the two limit versions, one can be simulated in full and the other only in part, as only its smeared correlators are computable with a controlled error. As such, at the level of a controlled numerical computation, the QFT and EFT versions cannot be distinguished. One dimension escapes the obstruction, yet reflection positivity is shown to still fail there at every finite width for the cosine network. Two escapes from the theorem remain, giving up either finite variance at a point or exact rotation invariance, and we discuss both of these possibilities.

The rapid advancement of large language models (LLMs) has led to increasing interest in their application to scientific domains such as chemistry. However, existing chemistry benchmarks often provide only a narrow view of model capability, focusing on limited task sets while overlooking robustness to variations in problem formulation and chemical representation. As a result, reported performance may overestimate a model's true ability to reason consistently across realistic settings. To address this challenge, we introduce ChemDIRT (Diversified Instruction, Representation, and Task Benchmark), a comprehensive evaluation framework designed to assess the robustness of chemical reasoning in LLMs. ChemDIRT systematically measures model performance across variations in instructions and molecular representations while spanning eight categories of chemistry tasks. By evaluating both accuracy and consistency under these controlled perturbations, ChemDIRT provides a more reliable assessment of model reasoning capabilities than conventional single-format benchmarks. We benchmark a diverse set of open- and closed-source LLMs, revealing substantial prompt sensitivity, representation dependence, and uneven performance across task families.

A verification substrate is more credible when exposing errors in its own claims, not just model outputs. GBI-DCSE v3 falsified an architectural claim: the reported Fisher value epsilon ~ 0.066 satisfies the kappa^2 <= 10^4 budget only on the slice [epsilon, 3, 4, 5], while the full box [epsilon, 20]^4 requires epsilon ~ 0.326472. This erratum highlights whether an enterprise verification architecture can isolate interface failure, task competence, policy admissibility, and control integrity while keeping claims auditable. BoundaryBench v0.1 established the baseline: Qwen3-4B-Instruct-2507 completed 768 frozen executions, but 0% cleared the contract (369 failed parsing, 399 failed validation), limiting downstream selectivity metrics. This companion study evaluates three successive improvements. First, BeTaL-GBI v0.2 applies Benchmark Tuning with an LLM-in-the-loop over 2,218,750,380 grid points, separating format admission from conditional performance (rho_adm = N_admitted/N; rho_task = N_verified/N_admitted). Following schema repair, a model-free feedback search achieves a 2.87% mean held-out target gap, outperforming non-feedback baselines (13.61%, 11.46%). Second, GBI v2 swaps static keys for a reference-independent witness state W and policy P. Across 512 synthetic tasks, a 16-gate policy detects all 116 injected severe contradictions and accepts all 99 clean records (broad denominator: 4.27%). Hallucinator and evidence-forger surrogates are blocked with zero silent promotions. Third, GBI-DCSE v3 maps 99 claims to machine-readable evidence: 95 of 96 testable claims pass, with 148 standalone checks executed without failure. The harness exercises signed ledgers, PBFT quorums, and enclave forgery across 62 configurations. Under synthetic conditions, GBI-DCSE is a selective, policy-versioned, self-auditing test and routing substrate.

Cardiac auscultation remains the most cost-effective screening procedure for cardiovascular diseases, and requires listening at the four main auscultation spots. Despite this, automatic heart sound analysis algorithms mostly classify patients using a single heart sound (single-channel), or, when using more than one (multi-channel), analyze each channel individually. To our knowledge, no prior work classifies patients through the synchronous analysis of multi-channel heart sounds, following the procedure used by physicians. This motivates us to study whether synchronous multi-channel analysis outperforms single-channel approaches, and whether it holds an advantage over asynchronous multi-channel methods that analyze channels one by one, potentially by capturing inter-channel interference phenomena. To answer these questions, we introduce a selection algorithm that identifies optimal heart sound segments from each of the four auscultation spots, which are then fed into a multi-input CNN that classifies patients by analyzing the four selected sounds simultaneously. Our synchronous approach, combining the proposed selection algorithm with a multi-input CNN, achieves a superior overall accuracy of 96.5%, a 9.1% gain over the best-performing single-channel and asynchronous multi-channel methods. The benefit of the proposed segment selection strategy over random selection is confirmed by a paired statistical significance test ($p = 0.003$). These results were obtained on 735 patients from the CirCor DigiScope dataset with complete recordings from all four spots, and their scope and generalizability are discussed in light of this and other methodological considerations.

AI systems increasingly search among candidate answers and deploy the highest-scoring one. Increasing search changes which errors matter, so a precise evaluation at one computation budget can leave another budget unresolved. We connect this information gap to the cost of closing it. For independent best-of-n search, aggregate reliability measurements identify deployment only through the directions they observe; we derive an exact ambiguity frontier when only small search widths are audited. Retaining candidate ranks and truth labels enables a constructive alternative: one audit can estimate reliability across all widths up to N. With known score percentiles, the minimax worst-coordinate mean squared error scales as (1 + log N)/T + N/M, capped at a constant, for expected budgets of T truth labels and M candidate observations. Matching lower bounds allow adaptive label acquisition, establishing that the distinct label and candidate costs are intrinsic to this experiment. An explicit design attains this order; a complementary record-based procedure supplies simultaneous guarantees without a known score distribution. Retrospective mathematical-reasoning and code-generation analyses show why search-dependent validation matters. In held-out CodeRM pools, a shared audit reduces the 95th-percentile maximum error across 100 widths by 58% and 40% relative to uniform labeling. These results turn structural ambiguity into a quantitative prescription for reusable validation.

Recent works have highlighted the expressive limitations of embedding based retrieval models through both theoretical analyses and challenging benchmarks such as LIMIT. While multi-vector embeddings consistently outperform single-vector embeddings, the precise representational gap between them remains poorly understood. In this work, following Jayaram's work, we provide the first explicit family of query and document sets, together with their relevance matrices, for which single-vector embeddings that rank all relevant documents above irrelevant ones require exponential size, whereas polynomial-size multi-vector embeddings suffice. Our result establishes an exponential separation between the expressive power of single-vector and multi-vector embeddings for the task of ranking of documents as opposed to approximating numerical scores as in the work of Jayaram. Motivated by our theoretical construction, we introduce ANDOR, a new retrieval benchmark that naturally instantiates these hard examples. We show that state-of-the-art single-vector embedding models perform poorly on ANDOR in the zero-shot setting and exhibit only marginal improvements after fine-tuning, highlighting the inherent difficulty of the benchmark compared to prior work. In contrast, multi-vector models consistently outperform their single-vector counterparts and improve substantially with fine-tuning, closely aligning with our theoretical predictions.

While machine learning models have demonstrated strong performance in many domains, these models have shown profound vulnerabilities when they are exposed to adversarial threats. While adversarial attacks fall into various categories, the most prominent category in research studies is evasion. In evasion attacks, the adversary generates perturbed versions of samples, which might not be observable by human eyes. These samples generally fool the machine learning models with high confidence. This phenomenon poses a significant security violation against machine learning models. In this paper, we investigate the certified and empirical robustness of various Kolmogorov-Arnold network architectures against strong evasion attacks. At first, we provide the mathematical foundations for randomized smoothing and interval bound propagation, and report the $\ell_2$-certified robustness of the models under randomized smoothing. After that, we systematically evaluate the robustness of various defended and undefended KAN models under FGSM, PGD, and C&W attacks in order to find out the optimal defense strategies and architectures.

Physical Cell Identity (PCI) assignment is essential for interference management in dense 5G networks. As cellular networks scale, PCI reuse becomes unavoidable, which may cause collisions, confusions, and multiple forms of modular interference. Jointly mitigating these effects gives rise to a large-scale, multi-objective combinatorial optimization problem that is difficult to solve efficiently at practical network scales. In this work, we propose a congruence decomposition framework with neural block solvers for large-scale PCI assignment. The proposed decomposition exploits the arithmetic structure of PCI values to decouple multiple modular interference objectives into a collection of blockwise Min-$k$-Partition subproblems, followed by a graph coloring procedure to resolve PCI conflicts. For the resulting NP-hard Min-$k$-Partition subproblems, we develop neural block solvers by parameterizing their relaxed quadratic formulations with graph neural networks, enabling efficient optimization at large scales. Discrete assignments are recovered through conditional expectation rounding with theoretical guarantees. Experiments on synthetic cellular graphs and real-world 5G networks show that the proposed method consistently outperforms existing modular-interference-aware baselines in modular interference reduction, conflict elimination, and computational efficiency.

A Markov chain is a widely used stochastic process modelling random events over time. These models are built on subsets of the entire dataset, referred to as states, which are considered to be homogeneous regarding transition probabilities. However, the creation of these states is often disregarded or based on prior assumption, potentially violating the homogeneity requirement and thus decreasing the validity and predictive power of the model. In order to fill this gap, this paper combines supervised feature selection with unsupervised learning techniques for data-driven state construction. Density-based clustering, spectral clustering, and Kohonen self-organizing maps are examined for their ability to identify latent groups without prior assumptions. The contribution of this study is twofold. First, the paper presents a methodological framework for state construction incorporating suitable unsupervised learning techniques, with appropriate measures both for classification performance and Markov model accuracy. Secondly, the framework is tested on an application, resulting in a comparative analysis showing that spectral clustering and Kohonen self-organizing maps are best at capturing inherent structure. These results serve as a cornerstone in providing theoretical and methodological guidance for improving state definition in applied Markov modelling.

A quantitative equational theory $U$ reasons about terms that agree up to a numerical error. It presents a free algebra $T_UA$ over a metric space $A$ of generators, the terms of the syntax at the least distance the axioms derive, and that metric is its semantic content. We give a functorial invariant of it, the persistent magnitude homology of $T_UA$: a barcode where the module is tame, finite linear algebra where $T_UA$ is finite, Lipschitz in each degree. Magnitude homology is graded by length and knows nothing of persistence, its persistent refinement nothing of where its bars begin and end, yet the two are one construction: filtering the length nerve by sublevel sets of the length yields the persistence module, and the associated graded of that filtration is the magnitude complex. A long exact sequence exchanges them, and each side gains what it lacked. Magnitude homology locates the critical values of the barcode, so a graded computation lists the lengths at which an endpoint can occur, and the barcode acquires a stability estimate of $(n+1)\delta$ in degree $n$ under a perturbation of size $\delta$, and a computed perturbation shows that the factor cannot be dropped. An inclusion of theories induces a morphism of the presenting monads and, where the induced map is bijective and shortens no distance by more than $\delta$, a comparison of barcodes under the same bound, so a barcode movement measures the metric-semantic strength of the added axioms. Four examples are computed, one in every degree.

Cloud environments built on Amazon Web Services face a structural security vulnerability: once a credential passes authentication, the resulting session is often treated as trusted for its entire duration. This assumption fails when credentials are stolen. We introduce the Explainable Adaptive Zero Trust Framework (EAZTF), a cloud-native security layer that continuously reevaluates the legitimacy of API actions throughout a session. EAZTF combines Isolation Forest and XGBoost to evaluate eight CloudTrail and IAM-derived behavioral features in real time and produce a Trust Risk Score (TRS) that determines whether a session continues, requires step-up MFA, or is restricted. Each decision is accompanied by a SHAP or LIME explanation, providing human-readable audit records for security analysis and compliance. The framework is also evaluated against four adversarial evasion strategies: credential theft, behavioral mimicry, API rate evasion, and privilege escalation. Experiments on an 8,500-record synthetic CloudTrail dataset show that Isolation Forest achieves 94.4% precision, 91.2% recall, and an F1 score of 0.928. Across the four adversarial scenarios, the mean detection rate is 91.0%, with behavioral mimicry being the most difficult at 83.9%. SHAP analysis identifies IP reputation, login-time deviation, and API call velocity as the three dominant features. A structured NIST SP 800-207 self-assessment gives EAZTF a mean compliance score of 93%, compared with 38% for a traditional perimeter baseline. Mean time to detect decreases from hours to under one minute. Because the evaluation uses synthetic data, these results should be interpreted as indicative rather than validated production performance.

Quantification, estimating class prevalences in bags of unlabeled instances is vital in domains where aggregate statistics are more important than individual instance labels, such as biosignal monitoring, fall detection, and activity recognition. We investigate this issue in the challenging setting of imbalanced time series data and develop CC-GMNet-TS, a class-conditioned Gaussian mixture quantifier that combines a Transformer-based feature extractor with per-class latent mixtures. Unlike previous mixture-based quantifiers, which use a single Gaussian mixture shared by all classes, CC-GMNet-TS assigns each class its own compact mixture in a bounded latent space and scores segment embeddings against these class-specific components to create bag-level representations that emphasize rare but informative patterns. Bags are constructed from labeled pools using the Artificial Prevalence Protocol (APP) and prior shift bag sampling (PShift) to cover a wide range of class prevalence scenarios, and the model is trained end-to-end with a quantification-oriented loss. Experiments on three benchmarks: EMG Data for Gestures, SmartFallMM, and UCI-HAR show that CC-GMNet-TS achieves lower error across the three benchmarks compared to traditional aggregators and recent deep quantifiers, while ablations confirm the contributions of both the Transformer backbone and class-conditioned mixtures during PShift.

Gaussian distributions are used to model uncertainty in signals and states, and Gaussian mixtures are often used when the underlying distribution is multimodal. Unlike a single Gaussian, a Gaussian mixture generally has no closed-form expression for differential entropy and therefore requires numerical approximation. We propose a Gauss–Hermite quadrature method for evaluating Gaussian mixture differential entropy. The quadrature order controls the numerical resolution of the approximation. The method is evaluated on one- and two-dimensional Gaussian mixture benchmarks against Taylor approximations, analytic entropy bounds, and numerical integration references. For repeated optimization over continuous actions, we also propose a Hermite polynomial surrogate in action space. In a radar pointing benchmark, its second-order form achieves substantially lower surrogate error and optimizer regret than a second-order Taylor surrogate based on local derivatives at the nominal action, while both methods use nine direct objective evaluations per replanning step. The Hermite surrogate also improves pointing performance in the tested benchmark.

We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For a partition $\mathcal O$, the Gibbs kernel $G_{\mathcal O}$ resamples within the current block from the stationary conditional distribution; when this update is tractable, composing or mixing it with a baseline kernel $P$ can accelerate convergence. We select $\mathcal O$ by rounding the bottom nonconstant eigenfunctions of $P^2$, or the algebraically smallest eigenfunctions of $P$ for additive mixtures, using weighted $k$-means. For $F(\mathcal O)=\|G_{\mathcal O}P-\Pi\|_{F,\pi}^2$, we derive exact trace and normalized-cut representations and show that $F$ equals the Pearson $\chi^2$-mutual information between the initial block label and the state after one transition, giving this matrix objective a natural probabilistic interpretation. In the two-block case, a threshold sweep exactly solves the associated one-dimensional weighted two-means rounding problem. For general $k \geq 2$, weighted $k$-means rounds the bottom $(k-1)$-dimensional embedding, after which candidates are rescored by $F$; the rounding distortion is a distance between subspaces that yields spectral approximation bounds. We extend the framework to additive mixtures, finite-horizon objectives, and discounted infinite-horizon objectives. In contrast to classical normalized spectral clustering, which uses top nonconstant modes to find low-flow persistent clusters, our method uses bottom modes to favor large normalized cross-block flow and rapid loss of block-label information. Experiments on a controlled-spectrum graph, a mean-field Ising model, and Bayesian variable selection show notable per-iteration improvements in convergence and statistical estimation.

We demonstrate that structured distortion of training data - which we term complexity induction - can induce compositional generalization in a standard CNN classifier without architectural modification. Using synthetic images of colored geometric shapes, we encode classes as flat string labels (e.g., "red-circle") with no explicit attribute decomposition, and exclude certain color-shape combinations from training entirely. We apply two distortion methods derived from Jaccard string similarity between class names: mixed labels (soft target distributions encoding inter-class overlap) and expanded dataset (false training samples with structurally motivated incorrect labels). Both methods induce the ability to predict unseen class combinations, and act at different levels: mixed labels activate the classifier for unseen combinations by exploiting the CNN's natural embedding structure, while expanded training improves the embedding factorization itself. A control with random (unstructured) false labels confirms that the effect depends on the structure of the distortion, not on noise per se. These results suggest that structured complication of training signals can influence both the internal organization of learned representations and their compositional interpretation - a principle that may underlie the role of natural language in cognitive development.