A long standing goal in neuroscience has been to elucidate the functional organization of the brain. Within higher visual cortex, functional accounts have remained relatively coarse, focusing on regions of interest (ROIs) and taking the form of selectivity for broad categories such as faces, places, bodies, food, or words. Because the identification of such ROIs has typically relied on manually assembled stimulus sets consisting of isolated objects in non-ecological contexts, exploring functional organization without robust a priori hypotheses has been challenging. To overcome these limitations, we introduce a data-driven approach in which we synthesize images predicted to activate a given brain region using paired natural images and fMRI recordings, bypassing the need for category-specific stimuli. Our approach - Brain Diffusion for Visual Exploration ("BrainDiVE") - builds on recent generative methods by combining large-scale diffusion models with brain-guided image synthesis. Validating our method, we demonstrate the ability to synthesize preferred images with appropriate semantic specificity for well-characterized category-selective ROIs. We then show that BrainDiVE can characterize differences between ROIs selective for the same high-level category. Finally we identify novel functional subdivisions within these ROIs, validated with behavioral data. These results advance our understanding of the fine-grained functional organization of human visual cortex, and provide well-specified constraints for further examination of cortical organization using hypothesis-driven methods.

Stochastic gradient descent (SGD) algorithm is the method of choice in many1 machine learning tasks thanks to its scalability and efficiency in dealing with2 large-scale problems. In this paper, we focus on the shuffling version of SGD3 which matches the mainstream practical heuristics. We show the convergence4 to a global solution of shuffling SGD for a class of non-convex functions un-5 der over-parameterized settings. Our analysis employs more relaxed non-convex6 assumptions than previous literature. Nevertheless, we maintain the desired compu-7 tational complexity as shuffling SGD has achieved in the general convex setting.8 1 Introduction9 In the last decade, neural network-based models have shown great success in many machine learning10 applications such as natural language processing [Collobert and Weston, 2008, Goldberg et al., 2018],11 computer vision and pattern recognition [Goodfellow et al., 2014, He and Sun, 2015].

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schrödinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step, has fast inference procedure, and allows handling small values of the entropy regularization coefficient which is of particular importance in some applied problems. Empirically, we show the performance of the method on several large-scale EOT tasks.

Gaussian mixture models (GMMs) are fundamental to machine learning due to their flexibility as approximating densities. However, uncertainty quantification of GMMs remains a challenge as differential entropy lacks a closed form. This paper explores polynomial approximations, specifically Taylor and Legendre, to the GMM entropy from a theoretical and practical perspective. We provide new analysis of a widely used approach due to Huber et al. (2008) and show that the series diverges under simple conditions. Motivated by this divergence we provide a novel Taylor series that is provably convergent to the true entropy of any GMM.

The company is the world's leading supplier of multilayer ceramic capacitors, essential components for every device that uses electricity because they regulate power flow. Murata Manufacturing has reported fourth-quarter earnings that beat analyst estimates, fueled by robust demand from artificial-intelligence data-center builders. Net income in the three months through March was ¥76.57 billion ($477 million), the Kyoto-based company said Thursday. Analysts had estimated ¥60 billion on average. Revenue was ¥460.62 billion, also better than expected.

China will ban the sale of drones in Beijing and require permits to fly them under new rules that take effect on Friday. Drones and key components will be prohibited from being sold, rented or brought into the Chinese capital. Drone owners will also be required to register their devices with the police. China has gradually tightened regulations on drones in recent years, with authorities citing public safety concerns. Drones and flying taxis are part of the so-called low-altitude economy, a strategic priority for China that is expected to generate more than two trillion yuan ($290bn; £217bn) by 2035.

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density π(θ) exp( U(θ)), LMC iteratively generates the next sample by taking a step in the gradient direction U with added Gaussian perturbations. Expectations w.r.t. the target distribution π are estimated by averaging over LMC samples. In ordinary Monte Carlo, it is well known that the estimation error can be substantially reduced by replacing independent random samples by quasi-random samples like low-discrepancy sequences. In this work, we show that the estimation error of LMC can also be reduced by using quasirandom samples. Specifically, we propose to use completely uniformly distributed (CUD) sequences with certain low-discrepancy property to generate the Gaussian perturbations. Under smoothness and convexity conditions, we prove that LMC with a low-discrepancy CUD sequence achieves smaller error than standard LMC. The theoretical analysis is supported by compelling numerical experiments, which demonstrate the effectiveness of our approach.