Learning identifiable representations in deep generative models remains a fundamental challenge, particularly for sequential data with regime-switching dynamics. Existing approaches establish identifiability under restrictive assumptions, such as stationarity or limited emission models, and typically rely on variational autoencoder (VAE) estimators, which introduce approximation gaps that limit the recovery of the latent structure. In this work, we address both the theoretical and practical limitations of this setting. First, we establish identifiability of a broad class of recurrent nonlinear switching dynamical systems under flexible assumptions, significantly extending prior results. Second, we introduce $Ω$SDS, a flow-based estimator that enables exact likelihood optimization using expectation-maximisation. Through empirical validation on both synthetic and real-world data, our results demonstrate that $Ω$SDS achieves improved disentanglement compared to VAE-based estimators and more accurate forecasting of underlying dynamics.

When modeling class-imbalanced data, it is crucial to address the imbalance, as models trained on such data tend to be biased towards the majority classes. This problem is amplified under partial supervision, where pseudo-labels for unlabeled data are predicted based on imbalanced labeled data, propagating the bias. While recent semi-supervised models address class imbalance, they typically assume single-modal input data. However, with the growing availability of multimodal data, it is essential to leverage complementary modalities. In this article, we propose a multimodal deep generative model for semi-supervised learning under class imbalance. Our approach uses separate encoders for each modality, sharing latent variables across modalities, and simplifies joint posterior computation with a product-of-experts method. To further address class imbalance, we replace typical Gaussian distributions with Student's t-distributions for the prior, encoder, and decoder, better capturing the heavy-tailed latent distributions in imbalanced data. We derive a new objective function for training the proposed model on both labeled and unlabeled data using $γ$-power divergence. Empirical results on benchmark and real-world datasets demonstrate that our model outperforms baseline methods in generalization, achieving superior classification performance for partially labeled multimodal data with imbalanced class distributions.

Random directed acyclic graphs (DAGs) based on imposing an order on Erdős-Rényi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.

Large language models (LLMs) are now largely involved in software development workflows, and the code they generate routinely includes third-party library (TPL) imports annotated with specific version identifiers. These version choices can carry security and compatibility risks, yet they have not been systematically studied. We present the first large-scale measurement study of version-level risk in LLM-generated Python code, evaluating 10 LLMs on PinTrace, a curated benchmark of 1,000 Stack Overflow programming tasks. LLMs tend to specify version identifiers when directly prompted at 26.83%-95.18%, while down to 6.45%-59.19% in creating a manifest file directly. Among the specified versions, 36.70%-55.70% of tasks contain at least one known CVE, and 62.75%-74.51% of them carry Critical or High severity ratings. In 72.27%-91.37% of cases, the associated CVEs were publicly disclosed before the model's knowledge cutoff. The statistics show all models converge on the same small set of risky release versions, indicating a systemic bias rather than isolated model error. Static compatibility rates range from 19.70% to 63.20%, with installation failure as the dominant cause. The dynamic test cases confirm the pattern by 6.49%-48.62% pass rates. Further experiments confirm that these failures are attributable to version selection rather than code quality, and that externally anchored version constraints substantially reduce both vulnerability exposure and compatibility failures. Our findings reveal LLM version selection as a first-class, previously overlooked risk surface in LLM-based development. We disclosed these findings to the community of the evaluated models, and several confirmed the issue. All the code and dataset have been released for open science at https://github.com/dw763j/PinTrace.

Quantile regression is a fundamental tool for distributional learning but poses significant optimization challenges for deep models due to the non-smoothness of the pinball loss. We propose ConquerNet, a class of \textbf{con}volution-smoothed \textbf{qu}antil\textbf{e} \textbf{R}eLU neural \textbf{net}works, which yield smooth objectives while preserving the underlying quantile structure. We establish general nonasymptotic risk bounds for ConquerNet under mild conditions, providing minimax guarantees over Besov function classes. In numerical studies, we demonstrate that the proposed approach outperforms standard quantile neural networks at multiple quantile levels, showing improved estimation accuracy and training efficiency across the board, with particularly pronounced advantages at high and low quantiles.

Constructing minimum-volume prediction regions that satisfy conditional coverage is a fundamental challenge in multivariate regression. Standard approaches rely on explicitly estimating the full conditional density and subsequently thresholding it. This two-step plug-in process is notoriously difficult, sensitive to estimation errors, and computationally expensive. One would like to instead optimize the region directly. Formulating a direct solution is challenging, however, because it requires minimizing a volume objective that is coupled with the conditional quantiles of the model's own estimation error. In this work, we address this challenge. We introduce super-level-set regression (SLS), a novel mathematical framework that successfully resolves this implicit coupling, allowing us to directly parameterize and optimize the geometric boundaries of the target conditional level sets. By bypassing full distribution estimation and leveraging flexible volume-preserving frontier functions, our approach natively captures complex, multimodal, and disjoint conditional structures end-to-end. Ultimately, SLS offers a new perspective on multivariate conditional quantile regression, replacing the restrictive assumptions of density-first methods with a direct geometric optimization strategy.

Trimming suspicious calibration points is a common response to contamination in conformal prediction. Its effect on clean-target coverage, however, is governed by the retained law induced by trimming, not by the contamination level alone. We analyse fixed-threshold trimming as conditioning rather than purification. It replaces the contaminated calibration law with a retained law, reducing clean-target coverage to a one-dimensional score-CDF transfer problem with an exact finite-sample identity. A componentwise bound on the transfer gap gives a population-level diagnostic. This separates a clean-side covariance cost from a retained-contamination cost, governed by the dirty-to-clean retention ratio. Trimming helps when the anomaly score separates retention probabilities while remaining score-neutral on the clean population. Otherwise, it cannot substantially reduce contamination through the retained mixture coefficient. We also give finite-sample certificate templates that provide numerical guarantees under independent audit.

We propose a plug-and-play framework for speech enhancement and separation that augments predictive methods with a generative speech prior. Our approach, termed Stochastic Interpolant Prior for Speech (SIPS), builds on stochastic interpolants and leverages their flexibility to bridge predictive and generative modeling. Specifically, we decompose the interpolation dynamics into a task-specific drift and a stochastic denoising component, allowing a predictive estimate to be integrated directly into the generative sampling process. This results in a mathematically grounded framework for combining strong pretrained predictors with the expressive power of generative models. To this end, we train a score model using only clean speech, yielding a degradation-agnostic prior that can be reused across tasks. During inference, the predictor provides a deterministic drift that steers the sampling process toward a task-consistent estimate, while the score model preserves perceptual naturalness. Unlike prior hybrid approaches, which typically rely on architecture-specific conditioning and are tied to particular predictors or degradation settings, SIPS provides a unified framework that generalizes across predictors and additive degradation tasks. We demonstrate its effectiveness for both speech enhancement and speech separation using recent predictors such as SEMamba and FlexIO. The proposed method consistently improves perceptual quality, achieving gains up +1.0 NISQA for speech separation.

Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based diffusion models. For the probability flow ODE of a variance-preserving diffusion, Lipschitz regularity of the score induces a flow of bi-Lipschitz diffeomorphic transport maps. This ODE bridge allows us to analyze the distributional approximation power of bi-Lipschitz normalizing flows and, conversely, derive deterministic convergence guarantees for diffusion-based transport. Our key idea is to use the probability flow ODE to link regularity of the score to regularity of the induced transport maps. We verify score regularity for broad target densities, including compactly supported densities, Gaussian convolutions of compactly supported measures and finite Gaussian mixtures. We obtain a universal distributional approximation result: Gaussian pullbacks induced by bi-Lipschitz variance-preserving transport maps are $L^1$-dense among all probability densities. For Gaussian convolution targets, we further obtain convergence in Kullback-Leibler divergence without early stopping.

The rapid emergence of generative image models has led to the development of specialized watermarking techniques, particularly in-generation methods such as seed-based embedding. However, current evaluations in this area remain largely empirical, making them heavily reliant on the specific model architectures used for generation and inversion. This prevents any clear conclusion on the performance of any method, especially regarding security, for which a rigorous definition is lacking. Against this approach, we argue that the effectiveness of a watermarking scheme should be established purely through a thorough theoretical analysis. This is enabled by decoupling the model-dependent part from the actual decision mechanism of the watermarking system. Using this decoupling, we introduce a formal evaluation framework based on security, robustness, and fidelity. This allows precise comparisons between watermarking systems through a characteristic surface representing the trade-off between these three quantities, independent of any generative model. Based on this framework, we propose SSB, a novel watermarking method that generalizes previous seed-based methods by allowing to reach any security-robustness-fidelity regime on its characteristic surface. This work opens the door to the design of modern watermarking systems with theoretical guarantees that do not necessitate any costly empirical evaluations.

Most coding-agent benchmarks ask whether generated code behaves correctly. That remains essential, but repository-level engineering is increasingly agent-managed: one agent writes a repository, and later agents inspect, audit, or extend it as working context. In that setting, a generated repository is not only an answer to a task but also a communication artifact for future work. Even when strong agents nearly satisfy the visible behavioral objective, repositories can differ in how clearly they expose the intended behavior and design choices behind that behavior. We introduce BUILD-AND-FIND, a protocol for evaluating whether downstream agents can recover those intended choices from generated repositories, and how much inspection that recovery requires. For each task, a builder sees a hidden repository specification and creates a codebase; a finder sees only the codebase and a specification-traced multiple-choice question bank. The protocol separates behavioral correctness from artifact-side recovery and reports recovery accuracy, repeatability, implementation coverage, and inspection effort. Accuracy and stability act as gates: effort is interpreted only when recovery succeeds reliably. Among artifacts from which the same intent can be recovered, lower effort by the same finder suggests that the artifact makes that intent easier to locate. Question-only and spec-only controls quantify generic priors and specification access, while audits separate omitted claims from finder failures and check whether correct answers cite artifact evidence. In the released high-prior task pack, recovery accuracy is near saturation, so inspection effort and finder-specific effects provide the main panel-local comparison.

Implicit score matching provides a computationally efficient approach for training diffusion models and generating high-quality samples from complex distributions. In this work, we develop a score-matching framework for SU(N) lattice gauge theories, which can be extended to other Lie groups. We apply the method to SU(3) gauge configurations with the Wilson gauge action in two and four dimensions and assess the quality of the generated samples by comparison with Hybrid Monte Carlo (HMC) simulations. We show that the diffusion models can be successfully trained and applied for sampling the Wilson gauge action. For large values of inverse coupling, accurate reverse-time integration requires predictor-corrector schemes, for which we introduce a corrector based on Hamiltonian molecular dynamics. While the corrector significantly improves sampling quality, it also increases the computational cost. We outline several strategies for improving sampling efficiency.

Reinforcement learning (RL) with verifiable rewards has proven effective at post-training LLMs for coding, yet deploying separate task-specific specialists incurs costs that scale with the number of tasks, motivating a unified multi-task RL (MTRL) approach. However, existing MTRL methods treat all coding tasks uniformly, relying on fixed data curricula under a shared optimization strategy, ultimately limiting the effectiveness of multi-task training. To address these limitations, we propose ASTOR, a multi-tASk code reinforcement learning framework via uTility-driven coORdination. Centered on task utility, a signal capturing each task learning potential and cross-task synergy, ASTOR comprises two coupled modules: 1) Hierarchical Utility-Routed Data Scheduling module hierarchically allocates training budget and prioritizes informative prompts, steering training toward the most valuable data and 2) Adaptive Utility-Calibrated Policy Optimization module dynamically scales per-task KL regularization, matching update constraints to each tasks current training state. Experiments on two widely-used LLMs across four representative coding tasks demonstrate that ASTOR consistently improves a single model across all tasks, outperforming the best task-specific specialist by 9.0%-9.5% and surpassing the strongest MTRL baseline by 7.5%-12.8%.

Langevin sampling from distributions of the form $p(x) \propto \exp(-Ψ(x))$ faces two major challenges: (global) mode coverage and (local) mode exploration. The first challenge is particularly relevant for multi-modal distributions with disjoint modes, whereas the second arises when the potential $Ψ$ exhibits diverse and ill-conditioned local mode geometry. To address these challenges, a common approach is to precondition Langevin dynamics with problem-specific information, such as the sample covariance or the local curvature of $Ψ$. However, existing preconditioner choices inherently involve a trade-off between global mode coverage and local mode exploration, and no prior method resolves both simultaneously. To overcome this limitation, we propose the TIPreL, which introduces a time- and position-dependent preconditioner. This design effectively addresses both challenges mentioned above within a single framework. We establish convergence of the resulting dynamics in the Wasserstein-2 distance both in continuous time and for a tamed Euler discretization. In particular, our analysis extends the existing state of the art by proving convergence under time- and space-dependent diffusion coefficients, and only locally Lipschitz drifts, which has not been covered by prior work. Finally, we experimentally compare TIPreL with competing preconditioning schemes on a two-dimensional, severely ill-posed example and on a Bayesian logistic regression task in higher dimensions, confirming the efficiency of the proposed method.

Power-of-two (PoT) quantization significantly reduces the size of deep neural networks (DNNs) and replaces multiplications with bit-shift operations for inference. Prior work has shown that PoT-quantized DNNs can preserve accuracy for tasks such as image classification; however, their performance on resource-constrained edge devices remains insufficiently understood. While general-purpose edge CPUs and GPUs do not provide optimized backends for bit-shift operations, custom hardware accelerators can better exploit PoT quantization by implementing dedicated shift-based processing elements. However, deploying PoT-quantized models on such accelerators is challenging due to limited support in existing inference frameworks. In addition, the impact of different PoT quantization strategies on hardware design, performance, and energy efficiency during full inference has not been systematically explored. To address these challenges, we propose PoTAcc, an open-source end-to-end pipeline for accelerating and evaluating PoT-quantized DNNs on resource-constrained edge devices. PoTAcc enables seamless preparation and deployment of PoT-quantized models via TensorFlow Lite (TFLite) across heterogeneous platforms, including CPU-only systems and hybrid CPU-FPGA systems with custom accelerators. We design shift-based processing element (shift-PE) accelerators for three PoT quantization methods and implement them on two FPGA platforms. We evaluate accuracy, performance, energy efficiency, and resource utilization across a range of models, including CNNs and Transformer-based architectures. Results show that our CPU-accelerator design achieves up to 3.6x speedup and 78% energy reduction compared to CPU-only execution for PoT-quantized DNNs on PYNQ-Z2 and Kria boards. The code will be publicly released at https://github.com/gicLAB/PoTAcc

In routine care, individuals identified a priori as high-risk are usually tested for conditions more frequently. Protected attributes, such as sex or ethnicity may also determine testing frequency. Such heterogeneous detection rates across a population induce label error. This causes systematic model error for specific groups and biases performance metrics during validation. This paper proposes a method to correct for such bias in prediction models due to differential diagnostic delay. We use a causal inference framework to define our target estimand: an individual's diagnosis probability in a counterfactual scenario where their diagnosis rate matches that of a reference group. We model the longitudinal process as a hidden Markov model, in which confirmatory test results are emissions from a latent progressive disease stage. We validate our approach in simulated data and apply it to a case study of chronic kidney disease prediction using electronic health records. In simulations, our method reduces prediction bias and improves calibration-in-the-large, correcting the Observed:Expected ratio in the underdiagnosed group from 1.34 (standard deviation: 0.09) in a model developed without any correction for underdiagnosis bias to 1.02 (0.09). Violations of assumptions in the simulation affected the estimation of model parameters, but the proposed approach nonetheless remained better calibrated than the standard model. In the clinical case study, we identify diabetes as the main driver of observability, with an odds ratio of 10.36 (95% confidence interval, 9.80 - 11.02) in 6-month urine albumin-creatinine ratio testing rate. Using our approach to predict the counterfactual diagnostic rate in patients without diabetes, we improved the Observed:Expected ratio of a developed clinical prediction model from 1.55 (1.51 - 1.59) to 1.01 (0.98 - 1.04).

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications.

Instrumental variable (IV) and control function (CF) methods are powerful tools for causal effect estimation in the presence of unmeasured confounding, yet most existing approaches target only mean effects and/or demand substantial fitting and tuning effort. In this paper, we introduce a simple method, TabCF, for control function regression using tabular foundation models, which enables accurate, fast, identification-transparent, and tuning-light causal estimation of distributional quantities, such as interventional means and quantiles; we also propose a copula-based approximation for multivariate outcomes. TabCF performs favorably against representative methods across a broad range of small- to medium-sized synthetic and real data scenarios. The central message is two-fold: for practitioners, it highlights that TabCF is an effective tool for distributional causal inference; for researchers, it suggests that the proposed approach could be considered a strong baseline for future method development. Code is available at https://github.com/GepingChen/TabCF.

Adaptive prompt and program search makes LLM evaluation selection-sensitive. Once benchmark items are reused inside tuning, the observed winner's score need not estimate the fresh-data performance of the full tune-then-deploy procedure. We study inference for this procedure-level target under explicit tuning budgets. We propose SIREN, a selection-aware repeated-split reporting protocol that freezes the post-search shortlist, separates splitwise selection from held-out evaluation, and uses an item-level Gaussian multiplier bootstrap for uncertainty quantification. In a fixed-shortlist regime with smooth stabilized selection, the estimator admits a first-order item-level representation, and the bootstrap yields valid simultaneous inference on a finite budget grid. This supports confidence intervals for procedure-performance curves and pre-specified equal-budget and cross-budget comparisons. Controlled simulations and MMLU-Pro tuning experiments show that winner-based reporting can be optimistic and can change deployment conclusions, while SIREN remains close to the finite-sample reporting target.

Strichartz inequalities are a cornerstone of the modern theory of dispersive PDEs, but their extremizers are known explicitly only in a handful of sharp cases. The non-convexity of the underlying functional makes the problem hard, and to our knowledge no systematic numerical attack has been attempted. We propose a simple neural-network-based pipeline that searches for extremizers as critical points of the Strichartz ratio, and apply it in three settings. First, on the Schrödinger group we recover the Gaussian extremizers of Foschi and Hundertmark--Zharnitsky in dimensions $d=1,2$ to within $10^{-3}$ relative error, with no analytical prior. Second, on $59$ further admissible pairs in $d=1$ where the answer is conjectural, the method consistently finds Gaussians, supporting the conjecture that Gaussians are the universal extremizers in the admissible range. Third, on the critical Airy--Strichartz inequality at $γ=1/q$, where existence is open, the optimization does not converge to any $L^2$ profile: instead, the iterates organize themselves as mKdV breathers $B(0,\cdot;α,1,0,0)$ with growing internal frequency $α$, and the discovered ratio approaches the Frank--Sabin universal lower bound $\widetilde A_{q,r}$ from below with a power-law gap $\simα^{-0.9}$. We confirm the same picture with an independent Hermite-basis ansatz. We propose a precise conjecture: the supremum equals $\widetilde A_{q,r}$ and is approached, but not attained, along the breather family. The pipeline thus serves both as a validator on known cases and as a discovery tool when no extremizer exists.

Intense wildfire seasons require critical prioritization decisions to allocate scarce suppression resources over a dispersed geographical area. This paper develops a predictive and prescriptive approach to jointly optimize crew assignments and wildfire suppression. The problem features a discrete resource-allocation structure with endogenous wildfire demand and non-linear wildfire dynamics. We formulate an integer optimization model with crew assignments on a time-space-rest network, wildfire dynamics on a time-state network, and linking constraints between them. We develop a two-sided branch-and-price-and-cut algorithm based on: (i) a two-sided column generation scheme that generates fire suppression plans and crew routes iteratively; (ii) a new family of cuts exploiting the knapsack structure of the linking constraints; and (iii) novel branching rules to accommodate non-linear wildfire dynamics. We also propose a data-driven double machine learning approach to estimate wildfire spread as a function of covariate information and suppression efforts, mitigating observed confounding between historical crew assignments and wildfire growth. Extensive computational experiments show that the optimization algorithm scales to otherwise intractable real-world instances; and that the methodology can enhance suppression effectiveness in practice, resulting in significant reductions in area burned over a wildfire season and guiding resource sharing across wildfire jurisdictions.

Persistent external memory enables LLM agents to maintain context across sessions, yet its security properties remain formally uncharacterized. We formalize memory poisoning attacks on retrieval-augmented agents as a Stackelberg game with a unified evaluation framework spanning three attack classes with escalating access assumptions. Correcting an evaluation protocol inconsistency in the triggered-query specification of Chen et al. (2024), we show faithful evaluation increases measured attack success by $4\times$ (ASR-R: $0.25 \to 1.00$). Our primary contribution is MEMSAD (Semantic Anomaly Detection), a calibration-based defense grounded in a gradient coupling theorem: under encoder regularity, the anomaly score gradient and the retrieval objective gradient are provably identical, so any continuous perturbation that reduces detection risk necessarily degrades retrieval rank. This coupling yields a certified detection radius guaranteeing correct classification regardless of adversary strategy. We prove minimax optimality via Le Cam's method, showing any threshold detector requires $Ω(1/ρ^2)$ calibration samples and MEMSAD achieves this up to $\log(1/δ)$ factors. We further derive online regret bounds for rolling calibration at rate $O(σ^{2/3}Δ^{1/3})$, and formally characterize a discrete synonym-invariance loophole that marks the boundary of what continuous-space defenses can guarantee. Experiments on a $3 \times 5$ attack-defense matrix with bootstrap confidence intervals, Bonferroni-corrected hypothesis tests, and Clopper-Pearson validation ($n=1{,}000$) confirm: composite defenses achieve TPR $= 1.00$, FPR $= 0.00$ across all attacks, while synonym substitution evades detection at $Δ$ ASR-R $\approx 0$, exposing a gap existing embedding-based defenses cannot close.

Agentic AI systems, specifically LLM-driven agents that plan, invoke tools, maintain persistent memory, and delegate tasks to peer agents via protocols such as MCP and A2A, introduce a threat surface that differs materially from standalone model inference. Agents accumulate sensitive context, hold credentials, and operate across pipelines no single party fully controls, enabling prompt injection, context exfiltration, credential theft, and inter-agent message poisoning. Current defenses operate entirely within the software stack and can be silently bypassed by a sufficiently privileged adversary such as a compromised cloud operator. Confidential computing (CC) offers a hardware-rooted alternative: Trusted Execution Environments (TEEs) isolate agent code and data from privileged system software, while remote attestation enables verifiable trust across distributed deployments. This survey synthesizes the design space in four parts: (i) a unified taxonomy of six TEE platforms (Intel SGX, Intel TDX, AMD SEV-SNP, ARM TrustZone, ARM CCA, and NVIDIA H100 CC) covering deployment roles and performance tradeoffs; (ii) an agent-centric threat model spanning perception, planning, memory, action, and coordination layers mapped to nine security goals; (iii) a comparative survey of CC-based defenses distinguishing findings that transfer from single-call inference versus what requires new agentic designs; and (iv) six open challenges including compound attestation for multi-hop agent chains and GPU-TEE performance at LLM scale. While several hardware trust primitives appear mature enough for targeted deployments, no broadly established end-to-end framework yet binds them into a coherent security substrate for production agentic AI.

Can Large Language Models (AI agents) aggregate dispersed private information through trading and reason about the knowledge of others by observing price movements? We conduct a controlled experiment where AI agents trade in a prediction market after receiving private signals, measuring information aggregation by the log error of the last price. We find that although the median market is effective at aggregating information in the easy information structures, increasing the complexity has a significant and negative impact, suggesting that AI agents may suffer from similar limitations as humans when reasoning about others. Consistent with our theoretical predictions, information aggregation remains unaffected by allowing cheap talk communication, changing the duration of the market or initial price, and strategic prompting, thus demonstrating that prediction markets are robust. We establish that "smarter" AI agents perform better at aggregation and they are more profitable. Surprisingly, giving them feedback about past performance has no impact on aggregation.

Automated single-cell annotation is difficult when the most abundant genes are not the most discriminative ones, or when a target state is poorly covered by a fixed reference atlas. GPTCelltype-style one-shot prompting allows large language models (LLMs) to produce plausible labels from generic expression signals, while reference-based annotators can force unfamiliar states into the nearest known category. We propose MAT-Cell, a prompt-driven framework for batch-level single-cell annotation that separates evidence grounding from label decision. MAT-Cell first uses Reverse Verification Query (RVQ) to combine tissue context, observed differentially expressed genes, and LLM-elicited biological priors into structured candidate-specific premises. Verifier agents then convert these premises into explicit premise-to-claim reasoning trees, and bounded multi-round debate compares,challenges, and revises the resulting claims before consensus or final adjudication.The returned Syllogistic Derivation Tree (SDT) provides an auditable debate trace rather than a formal proof of the annotation. In open-candidate benchmarks across five datasets, a locally deployed Qwen3-30B model with MAT-Cell achieves 75.5% average accuracy, compared with 64.2% for the strongest evaluated CoT baseline and 51.9% for the strongest evaluated scPilot variant. In oracle-candidate bench-marks across three species,MAT-Cell remains competitive across backbones, and local inference substantially reduces monetary cost for batch annotation. Code is available at: https://anonymous.4open.science/r/MATCell-4067

Formal model evaluation methods typically certify that a model satisfies a prescribed target key performance indicator (KPI) level. However, in many applications, the relevant target KPI level may not be known a priori, and the user may instead wish to compare candidate models by analyzing the full trade-offs between performance and reliability achievable at test time by the models. This task, requiring the reliable estimate of the test-time KPI distributions, is made more complicated by the fact that the same data must often be used both to pre-select a subset of candidate models and to estimate their KPI distributions, causing a potential post-selection bias. In this work, we introduce post-selection distributional model evaluation (PS-DME), a general framework for statistically valid distributional model assessment after arbitrary data-dependent model pre-selection. Building on e-values, PS-DME controls post-selection false coverage rate (FCR) for the distributional KPI estimates and we establish explicit conditions under which it is provably more sample efficient than a baseline method based on sample splitting. Experiments on synthetic data, text-to-SQL decoding with large language models, and telecom network performance evaluation demonstrate that PS-DME enables reliable comparison of candidate configurations across a range of reliability levels, supporting the statistically reliable exploration of performance--reliability trade-offs.

Diabetic foot ulcers (DFUs) are a severe complication of diabetes associated with significant morbidity, amputation risk, and healthcare burden. Developing effective continuous monitoring frameworks requires first establishing reliable baseline models of normal foot biomechanics. This paper presents a feasibility study of an anomaly detection framework applied to time-series data from wearable foot sensors, specifically NTC thin-film thermocouples for temperature and FlexiForce A401 pressure sensors for plantar load monitoring. Data were collected from healthy adult subjects across 312 capture sessions on an instrumented pathway, generating 93,790 valid multi-sensor readings spanning September 2023 to June 2024. Two unsupervised algorithms, Isolation Forest and K-Nearest Neighbors using Local Outlier Factor (KNN/LOF), were applied to detect statistical deviations in foot temperature and pressure signals. Results show that Isolation Forest is more sensitive to subtle, distributed anomalies, while KNN/LOF identifies concentrated extreme deviations but flags a higher proportion of sessions not corroborated by Isolation Forest. Since no clinical ground truth is available, this difference is interpreted as lower specificity under the shared 5 percent contamination assumption rather than a confirmed false-positive rate. A mild positive correlation (0.41-0.48) between pressure and temperature features supports the case for combined multi-modal monitoring. These findings establish a validated baseline analytical pipeline and provide a methodological foundation for future clinical validation studies involving diabetic patients, where the relationship between detected anomalies and DFU-related pathophysiology can be directly assessed.

State-of-the-art cloud-native applications require intelligent schedulers that can effectively balance system stability, resource utilisation, and associated costs. While Kubernetes provides feasibility-based placement by default, recent research efforts have explored the use of reinforcement learning (RL) for more intelligent scheduling decisions. However, current RL-based schedulers have three major limitations. First, most of these schedulers use monolithic centralised agents, which are non-scalable for large heterogeneous clusters. Second, the ones that use multi-objective reward functions assume simple, static, linear combinations of the objectives. Third, no previous work has produced a stress-aware scheduler that can react adaptively to dynamic conditions. To address these gaps in current research, we propose the Adaptive Graph-enhanced Multi-Agent Reinforcement Learning Dynamic Kubernetes Scheduler (AGMARL-DKS). AGMARL-DKS addresses these gaps by introducing three major innovations. First, we construct a scalable solution by treating the scheduling challenge as a cooperative multi-agent problem, where every cluster node operates as an agent, employing centralised training methods before decentralised execution. Second, to be context-aware and yet decentralised, we use a Graph Neural Network (GNN) to build a state representation of the global cluster context at each agent. This represents an improvement over methods that rely solely on local observations. Finally, to make trade-offs between these objectives, we use a stress-aware lexicographical ordering policy instead of a simple, static linear weighting of these objectives. The evaluations in Google Kubernetes Engine (GKE) reveal that AGMARL-DKS significantly outperforms the default scheduler in terms of fault tolerance, utilisation, and cost, especially in scheduling batch and mission-critical workloads.

Repeated AI assistance can improve immediate task performance while reducing the skill available for future independent work. We develop a mathematical framework for this long-run tradeoff. The model tracks two state variables: a latent human skill level governing expected independent performance, and a delegation level representing the learner's evolving tendency to rely on AI. Skill changes through error-driven learning under practice and decay under delegation; delegation responds to observed performance, increasing when AI-assisted work appears to outperform independent work. We analyze the resulting dynamics and contrast them with fixed delegation. With fixed delegation, skill follows a one-dimensional learning-decay process with a single stable equilibrium. With adaptive delegation, the coupled system has two attracting equilibria separated by the stable manifold of an interior saddle. The existence and geometry of this separatrix require a global phase-plane analysis of the coupled dynamics. The system is path-dependent: small differences in initial skill or reliance can lead to different long-run outcomes. We use this characterization to show that AI assistance can improve short-run performance while producing worse long-run performance than a no-AI baseline. Increasing AI capability can enlarge the basin of attraction of the low-skill equilibrium, making delegation appear beneficial for longer while increasing the risk of eventual skill loss. The qualitative picture is observed to persist across alternative specifications. Together, these results show that the risk is not AI assistance itself, but the coupling between performance-driven reliance and use-dependent skill change.

Grokking, the abrupt transition from memorization to generalisation after extended training, suggests the presence of competing solution basins with distinct statistical properties. We study this phenomenon through the lens of Singular Learning Theory (SLT), a Bayesian framework that characterizes the geometry of the loss landscape. The key measure is the local learning coefficient (LLC) which quantifies the local degeneracy of the loss surface. SLT links lower-LLC basins to higher posterior mass concentration and lower expected generalisation error. Leveraging SLT, we develop a basin-selection perspective on grokking in quadratic networks: LLC ranks competing near-zero-loss basins by statistical preference, while the training-time transition between them is governed by optimisation dynamics. In this view, grokking corresponds to a transition from a higher-LLC (memorising) basin to a lower-LLC (generalising) basin that dominates the posterior. To support this, we derive analytic formulas for the LLC in shallow quadratic networks under both lazy and feature learning regimes. Empirically, we demonstrate that LLC trajectories estimated from training data track the onset of generalisation and provide an informative probe of the optimisation path.