We study Nash equilibrium learning in partially observable Markov games (POMGs), a multi-agent reinforcement learning framework in which agents cannot fully observe the underlying state. Prior work in this setting relies on centralization or information sharing, and suffers from sample and computational complexity that scales exponentially in the number of players. We focus on a subclass of POMGs with independent state transitions, where agents remain coupled through their rewards, and assume that the underlying fully observed Markov game is a Markov potential game. For this class, we present an independent learning algorithm in which players, observing only their own actions and observations and without communication, jointly converge to an approximate Nash equilibrium. Due to partial observability, optimal policies may in general depend on the full action-observation history. Under a filter stability assumption, we show that policies based on finite history windows provide sufficient approximation guarantees. This enables us to approximate the POMG by a surrogate Markov game that is near-potential, leading to quasi-polynomial sample and computational complexity for independent Nash equilibrium learning in the underlying POMG.

Finite-sample analyses of deep Q-learning typically treat replayed data as independent, even though it is sampled from temporally dependent state-action trajectories. We study the Deep Q-networks (DQN) algorithm under explicit dependence by modelling the minibatches used for updating the network as $τ$-mixing. We show that this assumption holds under certain dependence conditions on the underlying trajectories and the mechanism used to sample minibatches. Building on this observation, we extend statistical analyses of DQN with fully connected ReLU architectures to dependent data. We formulate each update as a nonparametric regression problem with $τ$-mixing observations and derive finite-sample risk bounds under this dependence structure. Our results show that temporal dependence leads to a degradation in the statistical rate by inducing an additional dimensionality penalty in the rate exponent, reflecting the reduced effective sample size of $τ$-mixing data. Moreover, we derive the sample complexity of DQN under $tau$-mixing from these risk bounds. Finally, we empirically demonstrate on standard Gymnasium environments that the independence assumption is systematically violated and that replay sampling yields approximately exponentially decaying correlations, supporting our theoretical framework.

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models typically transition from an initial phase of generalization to memorizing the training set, existing theory assumes homogeneous data, leaving open how class imbalance and heterogeneity reshape these dynamics. In this work, we develop a high-dimensional analytical framework to study class-dependent learning in score-based diffusion models. Analyzing a random-features model trained on Gaussian mixtures, we derive the feature-covariance spectrum to characterize per-class generalization and memorization times. We reveal the explicit hierarchy governing these dynamics: class variance is the primary determinant of learning order-consistently favoring higher-variance classes-while centroid geometry plays a secondary role. Sampling imbalance acts as a modulator that can reverse this ordering and, under strong imbalance, forces minority classes to acquire distinct, delayed speciation times during backward diffusion. Together, these results suggest that diffusion models can memorize some classes while others remain insufficiently learned. We validate our theoretical predictions empirically using U-Net models trained on Fashion MNIST.

Evaluation protocols for learned intrinsic image decomposition on MPI Sintel have been inconsistent. Several prior works split the dataset by frames, which allows spatially similar frames of the same scene to appear in both train and test partitions. We quantify this leakage effect for the first time, across three architectures: a frame-level split inflates test R_PSNR by 1.6 to 2.0 dB (p less than 0.01 for all three, paired t-test across 3 seeds) relative to a scene-level split, confirming an architecture-independent protocol effect. A three-point gradient (random/temporal/scene) shows the gap is continuous, and under extended training the frame-level inflation exceeds 10 dB. We advocate scene-level splits as the community standard and provide reference numbers for six representative models under this protocol. As a case study within the corrected protocol, we present a physics-informed decomposition I = R composed with S + N with a source-separable three-way heteroscedastic uncertainty head. We empirically verify channel specialization: the non-Lambertian uncertainty channel shows r = 0.67 cross-correlation with non-Lambertian residual error, more than 4 times the texture channel's correlation. We further demonstrate downstream utility: filtering out the 75% highest-uncertainty pixels reduces reconstruction MSE by 77% on retained pixels, whereas random filtering produces no improvement. The specialization also holds on out-of-distribution real photographs. We report negative results for a more elaborate variant combining frequency decomposition, cross-task supervision, evidential learning, contrastive loss, and test-time adaptation. Our method reaches 15.98 plus or minus 0.41 dB R_PSNR, within 0.8 dB of a 5-member Deep Ensemble at one-fifth the cost, with the unique capability of source-separated uncertainty.

Large language models (LLMs) are reshaping how knowledge is produced, with increasing reliance on AI systems for generation, summarization, and reasoning. While prior work has studied cognitive offloading in humans and model collapse in recursive training, these effects are typically considered in isolation. We propose a unified perspective: humans and language models form a coupled dynamical system linked by a feedback loop of usage, generation, and retraining. We introduce a minimal model with three variables -- human cognition, data quality, and model capability -- and show that this feedback can give rise to distinct dynamical regimes. Our analysis identifies three regimes: co-evolutionary enhancement, fragile equilibrium, and degenerative convergence. Through a simple simulation, we demonstrate that increasing reliance on AI can induce a transition toward a low-diversity, suboptimal equilibrium. From an information-theoretic perspective, this transition corresponds to an emergent information bottleneck in the human-AI loop, where entropy reduction reflects loss of diversity and support under closed-loop feedback rather than beneficial compression. These results suggest that the trajectory of AI systems is shaped not only by model design, but by the dynamics of human-AI co-evolution.

Many real-world optimization problems consist of multiple tightly coupled subproblems whose solutions must be coordinated to achieve high overall performance. However, existing large language model driven automated heuristic design approaches are limited to single-problem settings. In this paper, we propose CoupleEvo. CoupleEvo proposes three evolutionary coordination strategies to evolve heuristics for coupled optimization problems: the sequential strategy evolves heuristics for one subproblem after the other; the iterative strategy alternates the evolution of heuristics for different subproblems over successive generations; and the integrated strategy evolves heuristics for all problems simultaneously. The approach is evaluated on two representative coupled optimization problems. Experimental results show that decomposition-based strategies (sequential and iterative) provide more stable convergence and higher solution quality, while the integrated evolution strategy suffers from increased search complexity and variability. These findings highlight the importance of coordinating evolutionary search across interdependent subproblems and demonstrate the potential of LLM-driven heuristic design for complex coupled optimization problems. The code is available: https://github.com/tb-git-kit-research/CoupleEvo.

Continuous post-deployment compliance audits, mandated by emerging regulations such as the EU AI Act and Digital Services Act, create a class of strategic gaming distinct from the one-shot input/output gaming studied in prior work. Regulated systems can delay outcome reporting, drift their reports within plausible noise envelopes, exploit longitudinal sample attrition, and cherry-pick among ambiguous metric definitions. We formalize continuous auditing as a $T$-round Stackelberg game between an auditor that commits to a temporal policy and an adaptive auditee, and identify a structural feature of any noise-aware static-auditor design: a cover regime in which coverage gaps and granularity gaps cannot be closed simultaneously. We make this formal as Observation 1 and show that two minimal extension policies, each derived from the observation, close the regime along orthogonal axes: a sample-size-aware static rule (Periodic-with-floor) closes the granularity-failure case, while a history-conditioned suspicion-escalation policy closes the coverage-failure case for the naive Drift strategy -- and neither closes both, exactly as the observation predicts; an audit-aware OffAuditDrift strategy that exploits Stackelberg commitment defeats both. To support empirical study we contribute a non-additive harm decomposition (welfare loss $W$, coverage loss $C$) that exposes how attrition shifts harm from the regulator-accountable surface to a regulator-invisible one; an initial library of five auditee strategies (Delay, Drift, Cherry-pick, Attrition, OffAuditDrift) and five auditor policies, calibrated to summary statistics from published audits of the DSA Transparency Database; and a reproducible simulator with a small, extensible Python interface.

Large language models (LLMs) have shown promise for event log analysis, but their high computational requirements, reliance on cloud infrastructure, and security concerns limit practical deployment. In addition, most existing approaches focus only on the identification of the problem and do not provide actionable remediation. Small language models (SLMs) present a light-weight alternative that can be fine-tuned for a specific purpose and hosted locally. This paper investigates whether SLMs, when fine-tuned for a specific task, can serve as a practical alternative for event log analysis while also generating solutions. We first create a large-scale synthetic Windows event log dataset that contains remediation actions using a high-performing LLM. We then fine-tune multiple SLMs and LLMs using the LoRA parameter-efficient fine-tuning technique and evaluate their performance by comparing with expert assessment. The results show that the dataset accurately reflects real-world scenarios and that fine-tuned SLMs consistently outperform LLMs in identifying issues and providing relevant remediation, while requiring fewer computational resources.

Online-safety regulation under the UK Online Safety Act and the EU Digital Services Act increasingly treats scalar metrics as compliance evidence. Once announced, such a metric also becomes an optimization target: a strategic platform can improve its score by routing recommendations through semantically equivalent content variants, without reducing true harm. We ask when such an audit metric can still certify a genuine reduction in harm. The protocol is modeled as a published transformation graph whose connected components form semantic classes, and the metric itself is treated as a security object. Three results follow. First, any metric that scores variants directly is manipulable as soon as two equivalent variants in a harmful class disagree in score. Second, the semantic-envelope lift, which assigns each variant the maximum score in its class, is the unique pointwise minimum among conservative classwise-constant repairs. Third, a class-stratified certificate, $H^\star(x) \le (1/\hatα) M_{\mathrm{Env}(m)}(x) + \barη$, holds for every platform strategy, with $\barη$ absorbing annotation and protocol error. We check the claims at three levels: exhaustive enumeration on a finite-state grid of mixed strategies, an SMT encoding in Z3 cross-replayed in cvc5, and a bounded single-player MDP encoded in PRISM-games. The fragile metric fails manipulation invariance and cannot support the same useful predeclared class-coverage certificate; under the envelope-level certificate, it produces large violations at every tested instance, with a large mean gaming gap across random catalogs at a fixed audit budget. The semantic-envelope metric exhibits no such violation in the tested instances.

Large language models (LLMs) are increasingly deployed in teams, yet existing coordination approaches often occupy two extremes. Highly structured methods rely on fixed roles, pipelines, or task decompositions assigned a priori. In contrast, fully unstructured teams enable adaptability and exploration but suffer from inefficiencies such as error propagation, inter-agent conflicts, and wasted resources (measured in time, tokens, or file operations). We introduce Language Agent Teams for Task Evolution (LATTE), a framework for coordinating LLM teams inspired by distributed systems, where processors must operate under partial observability and communication constraints. In LATTE, a team of agents collaboratively construct and maintain a shared, evolving coordination graph which encodes sub-task dependencies, individual agent assignment, and the current state of sub-task progress. This protocol maintains consistency while empowering agents to dynamically allocate work, adapt coordination, and discover new tasks. Across multiple collaborative tasks and a variety of base models, we demonstrate how LATTE reduces token usage, wall-clock time, communication, and coordination failures (e.g. file conflicts and redundant outputs) while matching or exceeding the accuracy of standard designs including MetaGPT, decentralized teams, top-down Leader-Worker hierarchies, and static decompositions.

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.