Analysis of neural network optimization in the mean-field regime is important as the setting allows for feature learning. Existing theory has been developed mainly for neural networks in finite dimensions, i.e., each neuron has a finite-dimensional parameter. However, the setting of infinite-dimensional input naturally arises in machine learning problems such as nonparametric functional data analysis and graph classification. In this paper, we develop a new mean-field analysis of two-layer neural network in an infinite-dimensional parameter space. We first give a generalization error bound, which shows that the regularized empirical risk minimizer properly generalizes when the data size is sufficiently large, despite the neurons being infinite-dimensional. Next, we present two gradient-based optimization algorithms for infinite-dimensional mean-field networks, by extending the recently developed particle optimization framework to the infinite-dimensional setting. We show that the proposed algorithms converge to the (regularized) global optimal solution, and moreover, their rates of convergence are of polynomial order in the online setting and exponential order in the finite sample setting, respectively. To our knowledge this is the first quantitative global optimization guarantee of neural network on infinite-dimensional input and in the presence of feature learning.

Don't let the Artemis II astronauts have all the fun. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. The moon is bombarded by meteoroids the size of ping-pong balls every day. Breakthroughs, discoveries, and DIY tips sent six days a week. Establishing a long-term human presence on the moon is a daunting challenge.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of taskagnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Elon Musk Boosts New Yorker's Sam Altman Exposé on X as Trial Begins The move comes as the trial for Elon Musk's lawsuit against OpenAI kicks off in federal court in Oakland. Elon Musk is boosting a post on X promoting The New Yorker's extensive investigation into Sam Altman's allegedly deceptive behavior, WIRED has confirmed. The move comes just as Musk's lawsuit against OpenAI and Altman heads to a jury trial in a federal courtroom on Monday morning. People scrolling X on Monday reported seeing an April 6 post from Ronan Farrow, a coauthor on the New Yorker article, promoting the investigation. A pop-up on the post on X's mobile app says it was boosted by @elonmusk, who also owns the platform.

Images of Samsung's rumored smart glasses have leaked They are codenamed Jinju and could retail for somewhere between $380 and $500. Images and details about Samsung's upcoming smart glasses have leaked, . We knew these were, but we now have what could be actual photos and they look pretty nifty. The glasses are reportedly being developed under the codename Jinju and could cost anywhere from $380 to $500. These are the first smart glasses from Samsung and look to offer a similar feature set to stuff like and the forthcoming . Samsung's specs will run on the and will likely feature heavy integration with the Google Gemini chatbot.

Understanding how grid cells perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration by grid cells, where the 2D self-position is encoded as a higher dimensional vector, and the 2D self-motion is represented by a general transformation of the vector. We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration. The other is an isotropic scaling condition that ensures locally conformal embedding, so that the error in the vector representation translates conformally to the error in the 2D self-position. Then we investigate the simplest transformation, i.e., the linear transformation, uncover its explicit algebraic and geometric structure as matrix Lie group of rotation, and explore the connection between the isotropic scaling condition and a special class of hexagon grid patterns. Finally, with our optimization-based approach, we manage to learn hexagon grid patterns that share similar properties of the grid cells in the rodent brain. The learned model is capable of accurate long distance path integration.

Understanding the behavior of non-human primates is crucial for improving animal welfare, modeling social behavior, and gaining insights into distinctively human and phylogenetically shared behaviors. However, the lack of datasets on non-human primate behavior hinders in-depth exploration of primate social interactions, posing challenges to research on our closest living relatives. To address these limitations, we present ChimpACT, a comprehensive dataset for quantifying the longitudinal behavior and social relations of chimpanzees within a social group. Spanning from 2015 to 2018, ChimpACT features videos of a group of over 20 chimpanzees residing at the Leipzig Zoo, Germany, with a particular focus on documenting the developmental trajectory of one young male, Azibo.

The recent explosion of interest in multimodal applications has resulted in a wide selection of datasets and methods for representing and integrating information from different modalities. Despite these empirical advances, there remain fundamental research questions: How can we quantify the interactions that are necessary to solve a multimodal task? Subsequently, what are the most suitable multimodal models to capture these interactions? To answer these questions, we propose an information-theoretic approach to quantify the degree of redundancy, uniqueness, and synergy relating input modalities with an output task. We term these three measures as the PID statistics of a multimodal distribution (or PID for short), and introduce two new estimators for these PID statistics that scale to high-dimensional distributions. To validate PID estimation, we conduct extensive experiments on both synthetic datasets where the PID is known and on large-scale multimodal benchmarks where PID estimations are compared with human annotations. Finally, we demonstrate their usefulness in (1) quantifying interactions within multimodal datasets, (2) quantifying interactions captured by multimodal models, (3) principled approaches for model selection, and (4) three real-world case studies engaging with domain experts in pathology, mood prediction, and robotic perception where our framework helps to recommend strong multimodal models for each application.

Hiking sticks, hats, and other simple tricks can keep your hike web-free. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. You're striding confidently down what seems to be a clear, open path, and then you feel it. The more you try to backtrack and flail your way out of it the more you feel like Frodo wrapped in Shelob the spider's deadly web, your luckier friends snickering like orcs ready to take you back to Mordor .