pwc-archive/papers-with-abstracts huggingface dataset:
Learning and Generalization with Mixture Data
Authors: Harsh Vardhan, Avishek Ghosh, Arya Mazumdar
Date: 2025-04-29 00:00:00
Tasks: Domain Adaptation, Federated Learning, regression

In many, if not most, machine learning applications the training data is naturally heterogeneous (e.g. federated learning, adversarial attacks and domain adaptation in neural net training). Data heterogeneity is identified as one of the major challenges in modern day large-scale learning. A classical way to represent heterogeneous data is via a mixture model. In this paper, we study generalization performance and statistical rates when data is sampled from a mixture distribution. We first characterize the heterogeneity of the mixture in terms of the pairwise total variation distance of the sub-population distributions. Thereafter, as a central theme of this paper, we characterize the range where the mixture may be treated as a single (homogeneous) distribution for learning. In particular, we study the generalization performance under the classical PAC framework and the statistical error rates for parametric (linear regression, mixture of hyperplanes) as well as non-parametric (Lipschitz, convex and H\"older-smooth) regression problems. In order to do this, we obtain Rademacher complexity and (local) Gaussian complexity bounds with mixture data, and apply them to get the generalization and convergence rates respectively. We observe that as the (regression) function classes get more complex, the requirement on the pairwise total variation distance gets stringent, which matches our intuition. We also do a finer analysis for the case of mixed linear regression and provide a tight bound on the generalization error in terms of heterogeneity.
Sobolev norm inconsistency of kernel interpolation
Authors: Yunfei Yang
Date: 2025-04-29 00:00:00

We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis space. These lower bounds imply that kernel interpolation is always inconsistent, when the smoothness index of the norm is larger than a constant that depends only on the embedding index of the hypothesis space and the decay rate of the eigenvalues.
Deep learning with missing data
Authors: Tianyi Ma, Tengyao Wang, Richard J. Samworth
Date: 2025-04-21 00:00:00
Tasks: Deep Learning, Imputation

In the context of multivariate nonparametric regression with missing covariates, we propose Pattern Embedded Neural Networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural network trained on the imputed data, PENNs pass the vectors of observation indicators through a second neural network to provide a compact representation. The outputs are then combined in a third neural network to produce final predictions. Our main theoretical result exploits an assumption that the observation patterns can be partitioned into cells on which the Bayes regression function behaves similarly, and belongs to a compositional H\"older class. It provides a finite-sample excess risk bound that holds for an arbitrary missingness mechanism, and in combination with a complementary minimax lower bound, demonstrates that our PENN estimator attains in typical cases the minimax rate of convergence as if the cells of the partition were known in advance, up to a poly-logarithmic factor in the sample size. Numerical experiments on simulated, semi-synthetic and real data confirm that the PENN estimator consistently improves, often dramatically, on standard neural networks without pattern embedding. Code to reproduce our experiments, as well as a tutorial on how to apply our method, is publicly available.
Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions
Authors: Mickael Binois, Jeffrey Larson
Date: 2025-04-29 00:00:00
Tasks: Bayesian Optimization

We develop and analyze a method for stochastic simulation optimization relying on Gaussian process models within a trust-region framework. We are interested in the case when the variance of the objective function is large. We propose to rely on replication and local modeling to cope with this high-throughput regime, where the number of evaluations may become large to get accurate results while still keeping good performance. We propose several schemes to encourage replication, from the choice of the acquisition function to setup evaluation costs. Compared with existing methods, our results indicate good scaling, in terms of both accuracy (several orders of magnitude better than existing methods) and speed (taking into account evaluation costs).
Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow
Authors: Matthias Liero, Alexander Mielke, Oliver Tse, Jia-Jie Zhu
Date: 2025-04-29 00:00:00

This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of Gaussian measures. This invariance serves as the foundation for constructing a reduced gradient structure on the parameter space characterizing Gaussian densities. We derive explicit ordinary differential equations that govern the evolution of mean, covariance, and mass under the HK-Boltzmann gradient flow. The reduced structure retains the additive form of the HK metric, facilitating a comprehensive analysis of the dynamics involved. We explore the geodesic convexity of the reduced system, revealing that global convexity is confined to the pure transport scenario, while a variant of sublevel semi-convexity is observed in the general case. Furthermore, we demonstrate exponential convergence to equilibrium through Polyak-Lojasiewicz-type inequalities, applicable both globally and on sublevel sets. By monitoring the evolution of covariance eigenvalues, we refine the decay rates associated with convergence. Additionally, we extend our analysis to non-Gaussian targets exhibiting strong log-lambda-concavity, corroborating our theoretical results with numerical experiments that encompass a Gaussian-target gradient flow and a Bayesian logistic regression application.
Toward a digital twin of U.S. Congress
Authors: Hayden Helm, Tianyi Chen, Harvey McGuinness, Paige Lee, Brandon Duderstadt, Carey E. Priebe
Date: 2025-04-04 00:00:00
Tasks: Language Modeling, Language Modelling

In this paper we provide evidence that a virtual model of U.S. congresspersons based on a collection of language models satisfies the definition of a digital twin. In particular, we introduce and provide high-level descriptions of a daily-updated dataset that contains every Tweet from every U.S. congressperson during their respective terms. We demonstrate that a modern language model equipped with congressperson-specific subsets of this data are capable of producing Tweets that are largely indistinguishable from actual Tweets posted by their physical counterparts. We illustrate how generated Tweets can be used to predict roll-call vote behaviors and to quantify the likelihood of congresspersons crossing party lines, thereby assisting stakeholders in allocating resources and potentially impacting real-world legislative dynamics. We conclude with a discussion of the limitations and important extensions of our analysis.
Sparse mixed linear modeling with anchor-based guidance for high-entropy alloy discovery
Authors: Ryo Murakami, Seiji Miura, Akihiro Endo, Satoshi Minamoto
Date: 2025-04-29 00:00:00
Tasks: feature selection, Property Prediction

High-entropy alloys have attracted attention for their exceptional mechanical properties and thermal stability. However, the combinatorial explosion in the number of possible elemental compositions renders traditional trial-and-error experimental approaches highly inefficient for materials discovery. To solve this problem, machine learning techniques have been increasingly employed for property prediction and high-throughput screening. Nevertheless, highly accurate nonlinear models often suffer from a lack of interpretability, which is a major limitation. In this study, we focus on local data structures that emerge from the greedy search behavior inherent to experimental data acquisition. By introducing a linear and low-dimensional mixture regression model, we strike a balance between predictive performance and model interpretability. In addition, we develop an algorithm that simultaneously performs prediction and feature selection by considering multiple candidate descriptors. Through a case study on high-entropy alloys, this study introduces a method that combines anchor-guided clustering and sparse linear modeling to address biased data structures arising from greedy exploration in materials science.
Financial Data Analysis with Robust Federated Logistic Regression
Authors: Kun Yang, Nikhil Krishnan, Sanjeev R. Kulkarni
Date: 2025-04-28 00:00:00
Tasks: Federated Learning, Multi-class Classification, regression

In this study, we focus on the analysis of financial data in a federated setting, wherein data is distributed across multiple clients or locations, and the raw data never leaves the local devices. Our primary focus is not only on the development of efficient learning frameworks (for protecting user data privacy) in the field of federated learning but also on the importance of designing models that are easier to interpret. In addition, we care about the robustness of the framework to outliers. To achieve these goals, we propose a robust federated logistic regression-based framework that strives to strike a balance between these goals. To verify the feasibility of our proposed framework, we carefully evaluate its performance not only on independently identically distributed (IID) data but also on non-IID data, especially in scenarios involving outliers. Extensive numerical results collected from multiple public datasets demonstrate that our proposed method can achieve comparable performance to those of classical centralized algorithms, such as Logistical Regression, Decision Tree, and K-Nearest Neighbors, in both binary and multi-class classification tasks.
Coreset selection for the Sinkhorn divergence and generic smooth divergences
Authors: Alex Kokot, Alex Luedtke
Date: 2025-04-28 00:00:00

We introduce CO2, an efficient algorithm to produce convexly-weighted coresets with respect to generic smooth divergences. By employing a functional Taylor expansion, we show a local equivalence between sufficiently regular losses and their second order approximations, reducing the coreset selection problem to maximum mean discrepancy minimization. We apply CO2 to the Sinkhorn divergence, providing a novel sampling procedure that requires poly-logarithmically many data points to match the approximation guarantees of random sampling. To show this, we additionally verify several new regularity properties for entropically regularized optimal transport of independent interest. Our approach leads to a new perspective linking coreset selection and kernel quadrature to classical statistical methods such as moment and score matching. We showcase this method with a practical application of subsampling image data, and highlight key directions to explore for improved algorithmic efficiency and theoretical guarantees.
Causal Identification in Time Series Models
Authors: Erik Jahn, Karthik Karnik, Leonard J. Schulman
Date: 2025-04-28 00:00:00
Tasks: Causal Identification, Time Series

In this paper, we analyze the applicability of the Causal Identification algorithm to causal time series graphs with latent confounders. Since these graphs extend over infinitely many time steps, deciding whether causal effects across arbitrary time intervals are identifiable appears to require computation on graph segments of unbounded size. Even for deciding the identifiability of intervention effects on variables that are close in time, no bound is known on how many time steps in the past need to be considered. We give a first bound of this kind that only depends on the number of variables per time step and the maximum time lag of any direct or latent causal effect. More generally, we show that applying the Causal Identification algorithm to a constant-size segment of the time series graph is sufficient to decide identifiability of causal effects, even across unbounded time intervals.
Emergence and scaling laws in SGD learning of shallow neural networks
Authors: Yunwei Ren, Eshaan Nichani, Denny Wu, Jason D. Lee
Date: 2025-04-28 00:00:00

We study the complexity of online stochastic gradient descent (SGD) for learning a two-layer neural network with $P$ neurons on isotropic Gaussian data: $f_*(\boldsymbol{x}) = \sum_{p=1}^P a_p\cdot \sigma(\langle\boldsymbol{x},\boldsymbol{v}_p^*\rangle)$, $\boldsymbol{x} \sim \mathcal{N}(0,\boldsymbol{I}_d)$, where the activation $\sigma:\mathbb{R}\to\mathbb{R}$ is an even function with information exponent $k_*>2$ (defined as the lowest degree in the Hermite expansion), $\{\boldsymbol{v}^*_p\}_{p\in[P]}\subset \mathbb{R}^d$ are orthonormal signal directions, and the non-negative second-layer coefficients satisfy $\sum_{p} a_p^2=1$. We focus on the challenging ``extensive-width'' regime $P\gg 1$ and permit diverging condition number in the second-layer, covering as a special case the power-law scaling $a_p\asymp p^{-\beta}$ where $\beta\in\mathbb{R}_{\ge 0}$. We provide a precise analysis of SGD dynamics for the training of a student two-layer network to minimize the mean squared error (MSE) objective, and explicitly identify sharp transition times to recover each signal direction. In the power-law setting, we characterize scaling law exponents for the MSE loss with respect to the number of training samples and SGD steps, as well as the number of parameters in the student neural network. Our analysis entails that while the learning of individual teacher neurons exhibits abrupt transitions, the juxtaposition of $P\gg 1$ emergent learning curves at different timescales leads to a smooth scaling law in the cumulative objective.
A comparison of generative deep learning methods for multivariate angular simulation
Authors: Jakob Benjamin Wessel, Callum J. R. Murphy-Barltrop, Emma S. Simpson
Date: 2025-04-28 00:00:00
Tasks: Deep Learning

With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the benefit of simplicity, and work reasonably well in low dimensions, but as the number of variables increases, they can lack the required flexibility and scalability. Classical parametric models for angular variables, such as the von Mises-Fisher (vMF) distribution, provide an alternative. Exploiting mixtures of vMF distributions increases their flexibility, but there are cases where even this is not sufficient to capture the intricate features that can arise in data. Owing to their flexibility, generative deep learning methods are able to capture complex data structures; they therefore have the potential to be useful in the simulation of angular variables. In this paper, we explore a range of deep learning approaches for this task, including generative adversarial networks, normalizing flows and flow matching. We assess their performance via a range of metrics and make comparisons to the more classical approach of using a mixture of vMF distributions. The methods are also applied to a metocean data set, demonstrating their applicability to real-world, complex data structures.
On Stopping Times of Power-one Sequential Tests: Tight Lower and Upper Bounds
Authors: Shubhada Agrawal, Aaditya Ramdas
Date: 2025-04-28 00:00:00

We prove two lower bounds for stopping times of sequential tests between general composite nulls and alternatives. The first lower bound is for the setting where the type-1 error level $\alpha$ approaches zero, and equals $\log(1/\alpha)$ divided by a certain infimum KL divergence, termed $\operatorname{KL_{inf}}$. The second lower bound applies to the setting where $\alpha$ is fixed and $\operatorname{KL_{inf}}$ approaches 0 (meaning that the null and alternative sets are not separated) and equals $c \operatorname{KL_{inf}}^{-1} \log \log \operatorname{KL_{inf}}^{-1}$ for a universal constant $c > 0$. We also provide a sufficient condition for matching the upper bounds and show that this condition is met in several special cases. Given past work, these upper and lower bounds are unsurprising in their form; our main contribution is the generality in which they hold, for example, not requiring reference measures or compactness of the classes.
Toward a Harmonized Approach -- Requirement-based Structuring of a Safety Assurance Argumentation for Automated Vehicles
Authors: Marvin Loba, Nayel Fabian Salem, Marcus Nolte, Andreas Dotzler, Dieter Ludwig, Markus Maurer
Date: 2025-05-06 00:00:00

Despite increasing testing operation on public roads, media reports on incidents show that safety issues remain to this day. One major cause factoring into this circumstance is high development uncertainty that manufacturers face when deploying these systems in an open context. In particular, one challenge is establishing a valid argument at design time that the vehicle will exhibit reasonable residual risk when operating in its intended operational design domain. Regulations, such as the European Implementing Regulation 2022/1426, require manufacturers to provide a safety assurance argumentation for SAE-Level-4 automated vehicles. While there is extensive literature on assurance cases for safety-critical systems, the domain of automated driving lacks explicit requirements regarding the creation of safety assurance argumentations. In this paper, we aim to narrow this gap by elaborating a requirement-based approach. We derive structural requirements for an argumentation from literature and supplement these with requirements derived from stakeholder concerns. We implement the requirements, yielding a proposal for an overall argumentation structure. The resulting "safety arguments" argue over four topic complexes: The developed product, the underlying process including its conformance/compliance to standards/laws, as well as the argumentations' context and soundness. Finally, we instantiate this structure with respect to domain-specific needs and principles.
Optimal Droop Control Strategy for Coordinated Voltage Regulation and Power Sharing in Hybrid AC-MTDC Systems
Authors: Hongjin Du, Tuanku Badzlin Hashfi, Rashmi Prasad, Pedro P. Vergara, Peter Palensky, Aleksandra Lekić
Date: 2025-05-06 00:00:00

With the growing integration of modular multilevel converters (MMCs) in Multi-Terminal Direct Current (MTDC) transmission systems, there is an increasing need for control strategies that ensure both economic efficiency and robust dynamic performance. This paper presents an enhanced Optimal Power Flow (OPF) framework for hybrid AC-MTDC systems, integrating a novel droop control strategy that coordinates DC voltage and AC frequency regulation. By embedding frequency control loops into the MMCs, the method enables system-wide coordination, enhancing power sharing and improving system resilience under disturbances. The proposed strategy dynamically adjusts converter operating points to minimize generation costs and DC voltage deviations, thus balancing economic objectives with system stability. A modified Nordic test system integrated with a four-terminal MTDC grid is used to validate the approach. Optimization is performed using Julia, while the system's dynamic performance is evaluated through electromagnetic transient simulations with the EMTP software. Case studies across multiple scenarios demonstrate that the proposed method consistently achieves lower generation costs than active power control and adaptive droop control strategy while maintaining stable control characteristics. The results highlight the method's capability to deliver cost-effective operation without compromising performance, offering a promising solution for the coordinated control of future hybrid AC-DC transmission networks.
Attention Mechanism, Max-Affine Partition, and Universal Approximation
Authors: Hude Liu, Jerry Yao-Chieh Hu, Zhao Song, Han Liu
Date: 2025-04-28 00:00:00

We establish the universal approximation capability of single-layer, single-head self- and cross-attention mechanisms with minimal attached structures. Our key insight is to interpret single-head attention as an input domain-partition mechanism that assigns distinct values to subregions. This allows us to engineer the attention weights such that this assignment imitates the target function. Building on this, we prove that a single self-attention layer, preceded by sum-of-linear transformations, is capable of approximating any continuous function on a compact domain under the $L_\infty$-norm. Furthermore, we extend this construction to approximate any Lebesgue integrable function under $L_p$-norm for $1\leq p <\infty$. Lastly, we also extend our techniques and show that, for the first time, single-head cross-attention achieves the same universal approximation guarantees.
Contextures: The Mechanism of Representation Learning
Authors: Runtian Zhai
Date: 2025-04-28 00:00:00
Tasks: Representation Learning, Self-Supervised Learning

This dissertation establishes the contexture theory to mathematically characterize the mechanism of representation learning, or pretraining. Despite the remarkable empirical success of foundation models, it is not very clear what representations they learn, and why these representations are useful for various downstream tasks. A scientific understanding of representation learning is critical, especially at this point when scaling up the model size is producing diminishing returns, and designing new pretraining methods is imperative for further progress. Prior work treated different representation learning methods quite differently, whereas the contexture theory provides a unified framework for analyzing these methods. The central argument is that a representation is learned from the association between the input X and a context variable A. We prove that if an encoder captures the maximum information of this association, in which case we say that the encoder learns the contexture, then it will be optimal on the class of tasks that are compatible with the context. We also show that a context is the most useful when the association between X and A is neither too strong nor too weak. The important implication of the contexture theory is that increasing the model size alone will achieve diminishing returns, and further advancements require better contexts. We demonstrate that many pretraining objectives can learn the contexture, including supervised learning, self-supervised learning, generative models, etc. Then, we introduce two general objectives -- SVME and KISE, for learning the contexture. We also show how to mix multiple contexts together, an effortless way to create better contexts from existing ones. Then, we prove statistical learning bounds for representation learning. Finally, we discuss the effect of the data distribution shift from pretraining to the downstream task.