Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called generalized Sinkhorn distance and the loss function is nonconvex and possibly unbounded. Such a distance allows to model uncertainty of distributions with different probability supports and divergence functions. For this class of regularized DRO problems, we derive a novel dual formulation taking the form of nested stochastic programming, where the dual variable depends on the data sample. To solve the dual problem, we provide theoretical evidence to design a nested stochastic gradient descent (SGD) algorithm, which leverages stochastic approximation to estimate the nested stochastic gradients. We study the convergence rate of nested SGD and establish polynomial iteration and sample complexities that are independent of the data size and parameter dimension, indicating its potential for solving large-scale DRO problems. We conduct numerical experiments to demonstrate the efficiency and robustness of the proposed algorithm.

In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong data-processing inequality. Here, we investigate quantum Doeblin coefficients as a generalization of the classical concept. In particular, we define various new quantum Doeblin coefficients, one of which has several desirable properties, including concatenation and multiplicativity, in addition to being efficiently computable. We also develop various interpretations of two of the quantum Doeblin coefficients, including representations as minimal singlet fractions, exclusion values, reverse max-mutual and oveloH informations, reverse robustnesses, and hypothesis testing reverse mutual and oveloH informations. Our interpretations of quantum Doeblin coefficients as either entanglement-assisted or unassisted exclusion values are particularly appealing, indicating that they are proportional to the best possible error probabilities one could achieve in state-exclusion tasks by making use of the channel. We also outline various applications of quantum Doeblin coefficients, ranging from limitations on quantum machine learning algorithms that use parameterized quantum circuits (noise-induced barren plateaus), on error mitigation protocols, on the sample complexity of noisy quantum hypothesis testing, on the fairness of noisy quantum models, and on mixing times of time-varying channels. All of these applications make use of the fact that quantum Doeblin coefficients appear in upper bounds on various trace-distance contraction coefficients of a channel. Furthermore, in all of these applications, our analysis using Doeblin coefficients provides improvements of various kinds over contributions from prior literature, both in terms of generality and being efficiently computable.

Understanding the nature of human sketches is challenging because of the wide variation in how they are created. Recognizing complex structural patterns improves both the accuracy in recognizing sketches and the fidelity of the generated sketches. In this work, we introduce ViSketch-GPT, a novel algorithm designed to address these challenges through a multi-scale context extraction approach. The model captures intricate details at multiple scales and combines them using an ensemble-like mechanism, where the extracted features work collaboratively to enhance the recognition and generation of key details crucial for classification and generation tasks. The effectiveness of ViSketch-GPT is validated through extensive experiments on the QuickDraw dataset. Our model establishes a new benchmark, significantly outperforming existing methods in both classification and generation tasks, with substantial improvements in accuracy and the fidelity of generated sketches. The proposed algorithm offers a robust framework for understanding complex structures by extracting features that collaborate to recognize intricate details, enhancing the understanding of structures like sketches and making it a versatile tool for various applications in computer vision and machine learning.

Diffusion-based generative models, such as Denoising Diffusion Probabilistic Models (DDPMs), have achieved remarkable success in image generation, but their step-by-step denoising process remains opaque, leaving critical aspects of the generation mechanism unexplained. To address this, we introduce \emph{Patronus}, an interpretable diffusion model inspired by ProtoPNet. Patronus integrates a prototypical network into DDPMs, enabling the extraction of prototypes and conditioning of the generation process on their prototype activation vector. This design enhances interpretability by showing the learned prototypes and how they influence the generation process. Additionally, the model supports downstream tasks like image manipulation, enabling more transparent and controlled modifications. Moreover, Patronus could reveal shortcut learning in the generation process by detecting unwanted correlations between learned prototypes. Notably, Patronus operates entirely without any annotations or text prompts. This work opens new avenues for understanding and controlling diffusion models through prototype-based interpretability. Our code is available at \href{https://github.com/nina-weng/patronus}{https://github.com/nina-weng/patronus}.

The growing trend of legal disputes over the unauthorized use of data in machine learning (ML) systems highlights the urgent need for reliable data-use auditing mechanisms to ensure accountability and transparency in ML. In this paper, we present the first proactive instance-level data-use auditing method designed to enable data owners to audit the use of their individual data instances in ML models, providing more fine-grained auditing results. Our approach integrates any black-box membership inference technique with a sequential hypothesis test, providing a quantifiable and tunable false-detection rate. We evaluate our method on three types of visual ML models: image classifiers, visual encoders, and Contrastive Image-Language Pretraining (CLIP) models. In additional, we apply our method to evaluate the performance of two state-of-the-art approximate unlearning methods. Our findings reveal that neither method successfully removes the influence of the unlearned data instances from image classifiers and CLIP models even if sacrificing model utility by $10.33\%$.

In this study, we propose extension of fuzzy c-means (FCM) clustering in multi-view environments. First, we introduce an exponential multi-view FCM (E-MVFCM). E-MVFCM is a centralized MVC with consideration to heat-kernel coefficients (H-KC) and weight factors. Secondly, we propose an exponential bi-level multi-view fuzzy c-means clustering (EB-MVFCM). Different to E-MVFCM, EB-MVFCM does automatic computation of feature and weight factors simultaneously. Like E-MVFCM, EB-MVFCM present explicit forms of the H-KC to simplify the generation of the heat-kernel $\mathcal{K}(t)$ in powers of the proper time $t$ during the clustering process. All the features used in this study, including tools and functions of proposed algorithms will be made available at https://www.github.com/KristinaP09/EB-MVFCM.

Policy gradient methods are one of the most successful methods for solving challenging reinforcement learning problems. However, despite their empirical successes, many SOTA policy gradient algorithms for discounted problems deviate from the theoretical policy gradient theorem due to the existence of a distribution mismatch. In this work, we analyze the impact of this mismatch on the policy gradient methods. Specifically, we first show that in the case of tabular parameterizations, the methods under the mismatch remain globally optimal. Then, we extend this analysis to more general parameterizations by leveraging the theory of biased stochastic gradient descent. Our findings offer new insights into the robustness of policy gradient methods as well as the gap between theoretical foundations and practical implementations.

A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition allows for a quantification of the strength of alignment of each point to a cluster, with these cluster alignment strengths leading naturally to a model selection criterion which renders the proposed approach fully automatable. The algorithm is simple to implement and computationally efficient, and produces clustering solutions of extremely high quality in comparison with relevant benchmarks from the literature. R code to implement the approach is available from https://github.com/DavidHofmeyr/ I. Introduction Clustering, or cluster analysis, is the task of partitioning a set of data into groups, or clusters, which are seen to be relatively more homogeneous than the data as a whole. Clustering is one of the fundamental data analytic tasks, and forms an integral component of exploratory data analysis. Clustering is also of arguably increasing relevance, as data are increasingly being collected/generated from automated processes, where typically very little prior knowledge is available, making exploratory methods a necessity. In the classical clustering problem there is no explicit information about how the data should be grouped, and various interpretations of how clusters of points may be defined have led to the development of a very large number of methods for identifying them. Almost universally, however, clusters are determined from the geometric properties of the data, with pairs of points which are near to one another typically being seen as likely to be in the same cluster and pairs which are distant more likely to be in different clusters.

We show that the behavior of stochastic gradient descent is related to Bayesian statistics by showing that SGD is effectively diffusion on a fractal landscape, where the fractal dimension can be accounted for in a purely Bayesian way. By doing this we show that SGD can be regarded as a modified Bayesian sampler which accounts for accessibility constraints induced by the fractal structure of the loss landscape. We verify our results experimentally by examining the diffusion of weights during training. These results offer insight into the factors which determine the learning process, and seemingly answer the question of how SGD and purely Bayesian sampling are related.

In the context of fact-checking, claims are often repeated across various platforms and in different languages, which can benefit from a process that reduces this redundancy. While retrieving previously fact-checked claims has been investigated as a solution, the growing number of unverified claims and expanding size of fact-checked databases calls for alternative, more efficient solutions. A promising solution is to group claims that discuss the same underlying facts into clusters to improve claim retrieval and validation. However, research on claim clustering is hindered by the lack of suitable datasets. To bridge this gap, we introduce \textit{MultiClaimNet}, a collection of three multilingual claim cluster datasets containing claims in 86 languages across diverse topics. Claim clusters are formed automatically from claim-matching pairs with limited manual intervention. We leverage two existing claim-matching datasets to form the smaller datasets within \textit{MultiClaimNet}. To build the larger dataset, we propose and validate an approach involving retrieval of approximate nearest neighbors to form candidate claim pairs and an automated annotation of claim similarity using large language models. This larger dataset contains 85.3K fact-checked claims written in 78 languages. We further conduct extensive experiments using various clustering techniques and sentence embedding models to establish baseline performance. Our datasets and findings provide a strong foundation for scalable claim clustering, contributing to efficient fact-checking pipelines.