Gaussian processes are now commonly used in dimensionality reduction approaches tailored to neuroscience, especially to describe changes in high-dimensional neural activity over time. As recording capabilities expand to include neuronal populations across multiple brain areas, cortical layers, and cell types, interest in extending Gaussian process factor models to characterize multi-population interactions has grown. However, the cubic runtime scaling of current methods with the length of experimental trials and the number of recorded populations (groups) precludes their application to large-scale multi-population recordings. Here, we improve this scaling from cubic to linear in both trial length and group number. We present two approximate approaches to fitting multi-group Gaussian process factor models based on (1) inducing variables and (2) the frequency domain. Empirically, both methods achieved orders of magnitude speed-up with minimal impact on statistical performance, in simulation and on neural recordings of hundreds of neurons across three brain areas. The frequency domain approach, in particular, consistently provided the greatest runtime benefits with the fewest trade-offs in statistical performance. We further characterize the estimation biases introduced by the frequency domain approach and demonstrate effective strategies to mitigate them. This work enables a powerful class of analysis techniques to keep pace with the growing scale of multi-population recordings, opening new avenues for exploring brain function.

We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with mini-batching, both using constant step sizes. Our analysis derives convergence rates for both algorithms under classical a priori assumptions on the smoothness of the target function. These assumptions are expressed in terms of the integral operator associated with the tangent kernel, as well as through a bound on the effective dimension. Additionally, we establish stopping times that yield minimax-optimal convergence rates within the classical reproducing kernel Hilbert space (RKHS) framework. These results demonstrate the efficacy of GD and SGD in achieving optimal rates for nonlinear inverse problems in random design.

Imperceptible adversarial attacks have recently attracted increasing research interests. Existing methods typically incorporate external modules or loss terms other than a simple $l_p$-norm into the attack process to achieve imperceptibility, while we argue that such additional designs may not be necessary. In this paper, we rethink the essence of imperceptible attacks and propose two simple yet effective strategies to unleash the potential of PGD, the common and classical attack, for imperceptibility from an optimization perspective. Specifically, the Dynamic Step Size is introduced to find the optimal solution with minimal attack cost towards the decision boundary of the attacked model, and the Adaptive Early Stop strategy is adopted to reduce the redundant strength of adversarial perturbations to the minimum level. The proposed PGD-Imperceptible (PGD-Imp) attack achieves state-of-the-art results in imperceptible adversarial attacks for both untargeted and targeted scenarios. When performing untargeted attacks against ResNet-50, PGD-Imp attains 100$\%$ (+0.3$\%$) ASR, 0.89 (-1.76) $l_2$ distance, and 52.93 (+9.2) PSNR with 57s (-371s) running time, significantly outperforming existing methods.

The relationship between conditional expected returns, conditional risk, and asset characteristics has been a central topic in financial economics for decades. Yet, inference in this domain remains constrained by the unbalanced and high-dimensional nature of real-world data. In this paper, we address these challenges by introducing a nonparametric, kernelbased framework for the joint estimation of conditional mean and covariance matrices, providing a powerful and tractable solution to the econometric inference problem highlighted by Cochrane (2011). Our framework is specifically designed to deliver positive semidefinite covariance matrices across any state and for cross sections of varying sizes, filling a significant gap in the literature.

Bayesian Optimization (BO) is a popular approach to optimizing expensive-to-evaluate black-box functions. Despite the success of BO, its performance may decrease exponentially as the dimensionality increases. A common framework to tackle this problem is to assume that the objective function depends on a limited set of features that lie on a low-dimensional manifold embedded in the high-dimensional ambient space. The latent space can be linear or more generally nonlinear. To learn feature mapping, existing works usually use an encode-decoder framework which is either computationally expensive or susceptible to overfittting when the labeled data is limited. This paper proposes a new approach for BO in high dimensions by exploiting a new representation of the objective function. Our approach combines a random linear projection to reduce the dimensionality, with a representation learning of the nonlinear manifold. When the geometry of the latent manifold is available, a solution to exploit this geometry is proposed for representation learning. In contrast, we use a neural network. To mitigate overfitting by using the neural network, we train the feature mapping in a geometry-aware semi-supervised manner. Our approach enables efficient optimizing of BO's acquisition function in the low-dimensional space, with the advantage of projecting back to the original high-dimensional space compared to existing works in the same setting. Finally, we show empirically that our algorithm outperforms other high-dimensional BO baselines in various synthetic functions and real applications.

Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation of formulas for mathematical constants because each such formula must be correct for infinite digits of precision, with "near-true" formulas providing no insight toward the correct ones. Consequently, formula discovery lacks a clear distance metric needed to guide automated discovery in this realm. In this work, we propose a systematic methodology for categorization, characterization, and pattern identification of such formulas. The key to our methodology is introducing metrics based on the convergence dynamics of the formulas, rather than on the numerical value of the formula. These metrics enable the first automated clustering of mathematical formulas. We demonstrate this methodology on Polynomial Continued Fraction formulas, which are ubiquitous in their intrinsic connections to mathematical constants, and generalize many mathematical functions and structures. We test our methodology on a set of 1,768,900 such formulas, identifying many known formulas for mathematical constants, and discover previously unknown formulas for $\pi$, $\ln(2)$, Gauss', and Lemniscate's constants. The uncovered patterns enable a direct generalization of individual formulas to infinite families, unveiling rich mathematical structures. This success paves the way towards a generative model that creates formulas fulfilling specified mathematical properties, accelerating the rate of discovery of useful formulas.

In real-world applications, as data availability increases, obtaining labeled data for machine learning (ML) projects remains challenging due to the high costs and intensive efforts required for data annotation. Many ML projects, particularly those focused on multi-label classification, also grapple with data imbalance issues, where certain classes may lack sufficient data to train effective classifiers. This study introduces and examines a novel oversampling method for multi-label text classification, designed to address performance challenges associated with data imbalance. The proposed method identifies potential new samples from unlabeled data by leveraging similarity measures between instances. By iteratively searching the unlabeled dataset, the method locates instances similar to those in underrepresented classes and evaluates their contribution to classifier performance enhancement. Instances that demonstrate performance improvement are then added to the labeled dataset. Experimental results indicate that the proposed approach effectively enhances classifier performance post-oversampling.

Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method in 2D and 3D that addresses this challenge and efficiently handles meshes with intricate structures. Additionally, we present an algorithm that adapts the mesh resolution to local geometry in 2D for efficient representation. We demonstrate the effectiveness of our approach on 2D point cloud and 3D multi-view reconstruction tasks. Visit our project page (https://sonsang.github.io/dmesh2-project) for source code and supplementary material.

It is clinically crucial and potentially very beneficial to be able to analyze and model directly the spatial distributions of cells in histopathology whole slide images (WSI). However, most existing WSI datasets lack cell-level annotations, owing to the extremely high cost over giga-pixel images. Thus, it remains an open question whether deep learning models can directly and effectively analyze WSIs from the semantic aspect of cell distributions. In this work, we construct a large-scale WSI dataset with more than 5 billion cell-level annotations, termed WSI-Cell5B, and a novel hierarchical Cell Cloud Transformer (CCFormer) to tackle these challenges. WSI-Cell5B is based on 6,998 WSIs of 11 cancers from The Cancer Genome Atlas Program, and all WSIs are annotated per cell by coordinates and types. To the best of our knowledge, WSI-Cell5B is the first WSI-level large-scale dataset integrating cell-level annotations. On the other hand, CCFormer formulates the collection of cells in each WSI as a cell cloud and models cell spatial distribution. Specifically, Neighboring Information Embedding (NIE) is proposed to characterize the distribution of cells within the neighborhood of each cell, and a novel Hierarchical Spatial Perception (HSP) module is proposed to learn the spatial relationship among cells in a bottom-up manner. The clinical analysis indicates that WSI-Cell5B can be used to design clinical evaluation metrics based on counting cells that effectively assess the survival risk of patients. Extensive experiments on survival prediction and cancer staging show that learning from cell spatial distribution alone can already achieve state-of-the-art (SOTA) performance, i.e., CCFormer strongly outperforms other competing methods.

In recent years, the application of deep networks has revolutionized the field of machine learning, particularly in tasks involving complex data such as images and natural language. These models, typically trained using stochastic gradient descent, have demonstrated remarkable performance on various benchmarks, raising questions about the underlying mechanisms that contribute to their success. Despite their practical efficacy, the theoretical understanding of these models remains relatively limited, creating a pressing need for deeper insights into their generalization abilities. The classical theory shows that the latter is a consequence of regularization, which is the way to impose a priori knowledge into the model and to favour "simple" solutions. While usually regularization is achieved either by choosing simple models or explicitly adding a penalty term to the empirical risk during training, this is not the case for deep neural networks, which are trained simply by minimizing the empirical risk. A new perspective has then emerged in the recent literature, which relates regularization directly to the optimization procedure (gradient based methods). The main idea is to show that the training dynamics themselves exhibit self regularizing properties, by inducing an implicit regularization (bias) which prefers generalizing solutions (see [Vardi, 2023] for an extended review of the importance of implicit bias in machine learning). In this context, a common approach is to study simplified models that approximate the networks used in practice. Analyzing the implicit bias of optimization algorithms for such networks is facilitated but still might give some insights on the good performance of neural networks in various scenarios.