Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning mechanisms. In this work, we propose a novel analytical framework that recasts a multi-layer ReLU network into an equivalent single-layer linear model with input-dependent "effective weights". For any given input sample, the activation pattern of ReLU units creates a unique computational path, effectively zeroing out a subset of weights in the network. By composing the active weights across all layers, we can derive an effective weight matrix, $W_{\text{eff}}(x)$, that maps the input directly to the output for that specific sample. We posit that the evolution of these effective weights reveals fundamental principles of representation learning. Our work demonstrates that as training progresses, the effective weights corresponding to samples from the same class converge, while those from different classes diverge. By tracking the trajectories of these sample-wise effective weights, we provide a new lens through which to interpret the formation of class-specific decision boundaries and the emergence of semantic representations within the network.

Time series foundation models (TSFMs) have shown strong results on public benchmarks, prompting comparisons to a "BERT moment" for time series. Their effectiveness in industrial settings, however, remains uncertain. We examine why TSFMs often struggle to generalize and highlight spectral shift (a mismatch between the dominant frequency components in downstream tasks and those represented during pretraining) as a key factor. We present evidence from an industrial-scale player engagement prediction task in mobile gaming, where TSFMs underperform domain-adapted baselines. To isolate the mechanism, we design controlled synthetic experiments contrasting signals with seen versus unseen frequency bands, observing systematic degradation under spectral mismatch. These findings position frequency awareness as critical for robust TSFM deployment and motivate new pretraining and evaluation protocols that explicitly account for spectral diversity.

As machine learning (ML) is increasingly implemented in hardware to address real-time challenges in scientific applications, the development of advanced toolchains has significantly reduced the time required to iterate on various designs. These advancements have solved major obstacles, but also exposed new challenges. For example, processes that were not previously considered bottlenecks, such as hardware synthesis, are becoming limiting factors in the rapid iteration of designs. To mitigate these emerging constraints, multiple efforts have been undertaken to develop an ML-based surrogate model that estimates resource usage of ML accelerator architectures. We introduce wa-hls4ml, a benchmark for ML accelerator resource and latency estimation, and its corresponding initial dataset of over 680,000 fully connected and convolutional neural networks, all synthesized using hls4ml and targeting Xilinx FPGAs. The benchmark evaluates the performance of resource and latency predictors against several common ML model architectures, primarily originating from scientific domains, as exemplar models, and the average performance across a subset of the dataset. Additionally, we introduce GNN- and transformer-based surrogate models that predict latency and resources for ML accelerators. We present the architecture and performance of the models and find that the models generally predict latency and resources for the 75% percentile within several percent of the synthesized resources on the synthetic test dataset.

Department of Applied Mathematics Harbin Institute of T echnology, W eihai Weihai, China gaoxiang.zhao@stu.hit.edu.cn Abstract--Real-Time Auction (RT A) Interception aims to filter out invalid or irrelevant traffic to enhance the integrity and reliability of downstream data. However, two key challenges remain: (i) the need for accurate estimation of traffic quality together with sufficiently high confidence in the model's predictions--typically addressed through uncertainty modeling--and (ii) the efficiency bottlenecks that such uncertainty modeling introduces in real-time applications due to repeated inference. T o address these challenges, we propose DAUM, a joint modeling framework that integrates multi-objective learning with uncertainty modeling, yielding both traffic quality predictions and reliable confidence estimates. Building on DAUM, we further apply knowledge distillation to reduce the computational overhead of uncertainty modeling, while largely preserving predictive accuracy and retaining the benefits of uncertainty estimation. Experiments on the JD advertisement dataset demonstrate that DAUM consistently improves predictive performance, with the distilled model delivering a tenfold increase in inference speed. In online advertising, RT A mechanisms play a central role in determining which traffic are exposed to downstream systems. Since not all incoming traffic contributes equally to campaign performance, an effective interception process is needed to filter out unproductive requests while preserving those that align with predefined objectives. Achieving this goal is particularly challenging because it requires not only the accurate prediction of multiple user-behavior metrics but also dependable estimates of prediction confidence under highly dynamic conditions. A natural way to address these requirements is to combine multi-objective optimization with uncertainty modeling.

In recent years, Electroencephalographic analysis has gained prominence in stress research when combined with AI and Machine Learning models for validation. In this study, a lightweight dynamic brain connectivity framework based on Time Varying Directed Transfer Function is proposed, where TV DTF features were validated through ML based stress classification. TV DTF estimates the directional information flow between brain regions across distinct EEG frequency bands, thereby capturing temporal and causal influences that are often overlooked by static functional connectivity measures. EEG recordings from the 32 channel SAM 40 dataset were employed, focusing on mental arithmetic task trials. The dynamic EEG-based TV-DTF features were validated through ML classifiers such as Support Vector Machine, Random Forest, Gradient Boosting, Adaptive Boosting, and Extreme Gradient Boosting. Experimental results show that alpha-TV-DTF provided the strongest discriminative power, with SVM achieving 89.73% accuracy in 3-class classification and with XGBoost achieving 93.69% accuracy in 2 class classification. Relative to absolute power and phase locking based functional connectivity features, alpha TV DTF and beta TV DTF achieved higher performance across the ML models, highlighting the advantages of dynamic over static measures. Feature importance analysis further highlighted dominant long-range frontal parietal and frontal occipital informational influences, emphasizing the regulatory role of frontal regions under stress. These findings validate the lightweight TV-DTF as a robust framework, revealing spatiotemporal brain dynamics and directional influences across different stress levels.

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at the finest relevant scales, leading to a high-dimensional state space. In this work, we propose an approach to learn stochastic multiscale models in the form of stochastic differential equations directly from observational data. Drawing inspiration from physics-based multiscale modeling approaches, we resolve the macroscale state on a coarse mesh while introducing a microscale latent state to explicitly model unresolved dynamics. We learn the parameters of the multiscale model using a simulator-free amortized variational inference method with a Product of Experts likelihood that enforces scale separation. We present detailed numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy compared to under-resolved direct numerical simulation and closure-type models at equivalent resolution, as well as reduced-order modeling approaches.

Ordinal categorical data are routinely encountered in a wide range of practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the cumulative probabilities of the response with a set of covariates through a parsimonious linear predictor, shared across response categories. When the number of observations grows, standard sampling algorithms for Bayesian inference scale poorly, making posterior computation increasingly challenging in large datasets. In this article, we propose three scalable algorithms for approximating the posterior distribution of the regression coefficients in cumulative probit models relying on Variational Bayes and Expectation Propagation. We compare the proposed approaches with inference based on Markov Chain Monte Carlo, demonstrating superior computational performance and remarkable accuracy; finally, we illustrate the utility of the proposed algorithms on a challenging case study to investigate the structure of a criminal network.

In this paper we propose a sequential minimax optimization (SMO) method for solving a class of constrained bilevel optimization problems in which the lower-level part is a possibly nonsmooth convex optimization problem, while the upper-level part is a possibly nonconvex optimization problem. Specifically, SMO applies a first-order method to solve a sequence of minimax subproblems, which are obtained by employing a hybrid of modified augmented Lagrangian and penalty schemes on the bilevel optimization problems. Under suitable assumptions, we establish an operation complexity of $O(\varepsilon^{-7}\log\varepsilon^{-1})$ and $O(\varepsilon^{-6}\log\varepsilon^{-1})$, measured in terms of fundamental operations, for SMO in finding an $\varepsilon$-KKT solution of the bilevel optimization problems with merely convex and strongly convex lower-level objective functions, respectively. The latter result improves the previous best-known operation complexity by a factor of $\varepsilon^{-1}$. Preliminary numerical results demonstrate significantly superior computational performance compared to the recently developed first-order penalty method.

The ability to reason lies at the core of artificial intelligence (AI), and challenging problems usually call for deeper and longer reasoning to tackle. A crucial question about AI reasoning is whether models can extrapolate learned reasoning patterns to solve harder tasks with longer chain-of-thought (CoT). In this work, we present a theoretical analysis of transformers learning on synthetic state-tracking tasks with gradient descent. We mathematically prove how the algebraic structure of state-tracking problems governs the degree of extrapolation of the learned CoT. Specifically, our theory characterizes the length generalization of transformers through the mechanism of attention concentration, linking the retrieval robustness of the attention layer to the state-tracking task structure of long-context reasoning. Moreover, for transformers with limited reasoning length, we prove that a recursive self-training scheme can progressively extend the range of solvable problem lengths. To our knowledge, we provide the first optimization guarantee that constant-depth transformers provably learn $\mathsf{NC}^1$-complete problems with CoT, significantly going beyond prior art confined in $\mathsf{TC}^0$, unless the widely held conjecture $\mathsf{TC}^0 \neq \mathsf{NC}^1$ fails. Finally, we present a broad set of experiments supporting our theoretical results, confirming the length generalization behaviors and the mechanism of attention concentration.

Linear regression is frequently applied in a variety of domains. In order to improve the efficiency of these methods, various methods have been developed that compute summaries or \emph{sketches} of the datasets. Certain domains, however, contain sensitive data which necessitates that the application of these statistical methods does not reveal private information. Differentially private (DP) linear regression methods have been developed for mitigating this problem. These techniques typically involve estimating a noisy version of the parameter vector. Instead, we propose releasing private sketches of the datasets. We present differentially private sketches for the problems of least squares regression, as well as least absolute deviations regression. The availability of these private sketches facilitates the application of commonly available solvers for regression, without the risk of privacy leakage.