Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled with indicator variables for identifying the support of the continuous variables. In this paper we investigate compact extended formulations for such problems through perspective reformulation techniques. In contrast to the majority of previous work that relies on support function arguments and disjunctive programming techniques to provide convex hull results, we propose a constructive approach that exploits a hidden conic structure induced by perspective functions. To this end, we first establish a convex hull result for a general conic mixed-binary set in which each conic constraint involves a linear function of independent continuous variables and a set of binary variables. We then demonstrate that extended representations of sets associated with epigraphs of rank-one convex functions over constraints modeling indicator relations naturally admit such a conic representation. This enables us to systematically give perspective formulations for the convex hull descriptions of these sets with nonlinear separable or non-separable objective functions, sign constraints on continuous variables, and combinatorial constraints on indicator variables. We illustrate the efficacy of our results on sparse nonnegative logistic regression problems.

In a high-dimensional regression framework, we study consequences of the naive two-step procedure where first the dimension of the input variables is reduced and second, the reduced input variables are used to predict the output variable with kernel regression. In order to analyze the resulting regression errors, a novel stability result for kernel regression with respect to the Wasserstein distance is derived. This allows us to bound errors that occur when perturbed input data is used to fit the regression function. We apply the general stability result to principal component analysis (PCA). Exploiting known estimates from the literature on both principal component analysis and kernel regression, we deduce convergence rates for the two-step procedure. The latter turns out to be particularly useful in a semi-supervised setting.

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve various downstream analyses and achieve state-of-the-art performance in many applications. Despite the empirical effectiveness, most existing methods lack theoretical understanding under a general nonlinear setting. To fill this gap, we develop a statistical framework on a low-dimension product manifold to model the data augmentation transformation. Under this framework, we introduce a new representation learning method called augmentation invariant manifold learning and design a computationally efficient algorithm by reformulating it as a stochastic optimization problem. Compared with existing self-supervised methods, the new method simultaneously exploits the manifold's geometric structure and invariant property of augmented data and has an explicit theoretical guarantee. Our theoretical investigation characterizes the role of data augmentation in the proposed method and reveals why and how the data representation learned from augmented data can improve the $k$-nearest neighbor classifier in the downstream analysis, showing that a more complex data augmentation leads to more improvement in downstream analysis. Finally, numerical experiments on simulated and real datasets are presented to demonstrate the merit of the proposed method.

Normalized-Cut (N-Cut) is a famous model of spectral clustering. The traditional N-Cut solvers are two-stage: 1) calculating the continuous spectral embedding of normalized Laplacian matrix; 2) discretization via $K$-means or spectral rotation. However, this paradigm brings two vital problems: 1) two-stage methods solve a relaxed version of the original problem, so they cannot obtain good solutions for the original N-Cut problem; 2) solving the relaxed problem requires eigenvalue decomposition, which has $\mathcal{O}(n^3)$ time complexity ($n$ is the number of nodes). To address the problems, we propose a novel N-Cut solver designed based on the famous coordinate descent method. Since the vanilla coordinate descent method also has $\mathcal{O}(n^3)$ time complexity, we design various accelerating strategies to reduce the time complexity to $\mathcal{O}(|E|)$ ($|E|$ is the number of edges). To avoid reliance on random initialization which brings uncertainties to clustering, we propose an efficient initialization method that gives deterministic outputs. Extensive experiments on several benchmark datasets demonstrate that the proposed solver can obtain larger objective values of N-Cut, meanwhile achieving better clustering performance compared to traditional solvers.

Identifying cerebral cortex layers is crucial for comparative studies of the cytoarchitecture aiming at providing insights into the relations between brain structure and function across species. The absence of extensive annotated datasets typically limits the adoption of machine learning approaches, leading to the manual delineation of cortical layers by neuroanatomists. We introduce a self-supervised approach to detect layers in 2D Nissl-stained histological slices of the cerebral cortex. It starts with the segmentation of individual cells and the creation of an attributed cell-graph. A self-supervised graph convolutional network generates cell embeddings that encode morphological and structural traits of the cellular environment and are exploited by a community detection algorithm for the final layering. Our method, the first self-supervised of its kind with no spatial transcriptomics data involved, holds the potential to accelerate cytoarchitecture analyses, sidestepping annotation needs and advancing cross-species investigation.

We present a framework SCStory for online story discovery, that helps people digest rapidly published news article streams in real-time without human annotations. To organize news article streams into stories, existing approaches directly encode the articles and cluster them based on representation similarity. However, these methods yield noisy and inaccurate story discovery results because the generic article embeddings do not effectively reflect the story-indicative semantics in an article and cannot adapt to the rapidly evolving news article streams. SCStory employs self-supervised and continual learning with a novel idea of story-indicative adaptive modeling of news article streams. With a lightweight hierarchical embedding module that first learns sentence representations and then article representations, SCStory identifies story-relevant information of news articles and uses them to discover stories. The embedding module is continuously updated to adapt to evolving news streams with a contrastive learning objective, backed up by two unique techniques, confidence-aware memory replay and prioritized-augmentation, employed for label absence and data scarcity problems. Thorough experiments on real and the latest news data sets demonstrate that SCStory outperforms existing state-of-the-art algorithms for unsupervised online story discovery.

Organic chemistry is undergoing a major paradigm shift, moving from a labor-intensive approach to a new era dominated by automation and artificial intelligence (AI). This transformative shift is being driven by technological advances, the ever-increasing demand for greater research efficiency and accuracy, and the burgeoning growth of interdisciplinary research. AI models, supported by computational power and algorithms, are drastically reshaping synthetic planning and introducing groundbreaking ways to tackle complex molecular synthesis. In addition, autonomous robotic systems are rapidly accelerating the pace of discovery by performing tedious tasks with unprecedented speed and precision. This article examines the multiple opportunities and challenges presented by this paradigm shift and explores its far-reaching implications. It provides valuable insights into the future trajectory of organic chemistry research, which is increasingly defined by the synergistic interaction of automation and AI.

Continual learning (CL) aims to acquire new knowledge while preserving information from previous experiences without forgetting. Though buffer-based methods (i.e., retaining samples from previous tasks) have achieved acceptable performance, determining how to allocate the buffer remains a critical challenge. Most recent research focuses on refining these methods but often fails to sufficiently consider the varying influence of samples on the learning process, and frequently overlooks the complexity of the classes/concepts being learned. Generally, these methods do not directly take into account the contribution of individual classes. However, our investigation indicates that more challenging classes necessitate preserving a larger number of samples compared to less challenging ones. To address this issue, we propose a novel method and policy named 'Class-Adaptive Sampling Policy' (CASP), which dynamically allocates storage space within the buffer. By utilizing concepts of class contribution and difficulty, CASP adaptively manages buffer space, allowing certain classes to occupy a larger portion of the buffer while reducing storage for others. This approach significantly improves the efficiency of knowledge retention and utilization. CASP provides a versatile solution to boost the performance and efficiency of CL. It meets the demand for dynamic buffer allocation, accommodating the varying contributions of different classes and their learning complexities over time.

We propose ProtoArgNet, a novel interpretable deep neural architecture for image classification in the spirit of prototypical-part-learning as found, e.g. in ProtoPNet. While earlier approaches associate every class with multiple prototypical-parts, ProtoArgNet uses super-prototypes that combine prototypical-parts into single prototypical class representations. Furthermore, while earlier approaches use interpretable classification layers, e.g. logistic regression in ProtoPNet, ProtoArgNet improves accuracy with multi-layer perceptrons while relying upon an interpretable reading thereof based on a form of argumentation. ProtoArgNet is customisable to user cognitive requirements by a process of sparsification of the multi-layer perceptron/argumentation component. Also, as opposed to other prototypical-part-learning approaches, ProtoArgNet can recognise spatial relations between different prototypical-parts that are from different regions in images, similar to how CNNs capture relations between patterns recognized in earlier layers.

There have been significant advancements made by large language models (LLMs) in various aspects of our daily lives. LLMs serve as a transformative force in natural language processing, finding applications in text generation, translation, sentiment analysis, and question-answering. The accomplishments of LLMs have led to a substantial increase in research efforts in this domain. One specific two-layer regression problem has been well-studied in prior works, where the first layer is activated by a ReLU unit, and the second layer is activated by a softmax unit. While previous works provide a solid analysis of building a two-layer regression, there is still a gap in the analysis of constructing regression problems with more than two layers. In this paper, we take a crucial step toward addressing this problem: we provide an analysis of a two-layer regression problem. In contrast to previous works, our first layer is activated by a softmax unit. This sets the stage for future analyses of creating more activation functions based on the softmax function. Rearranging the softmax function leads to significantly different analyses. Our main results involve analyzing the convergence properties of an approximate Newton method used to minimize the regularized training loss. We prove that the loss function for the Hessian matrix is positive definite and Lipschitz continuous under certain assumptions. This enables us to establish local convergence guarantees for the proposed training algorithm. Specifically, with an appropriate initialization and after $O(\log(1/\epsilon))$ iterations, our algorithm can find an $\epsilon$-approximate minimizer of the training loss with high probability. Each iteration requires approximately $O(\mathrm{nnz}(C) + d^\omega)$ time, where $d$ is the model size, $C$ is the input matrix, and $\omega < 2.374$ is the matrix multiplication exponent.