Multi-channel learning has gained significant attention in recent applications, where neural networks with t-product layers (t-NNs) have shown promising performance through novel feature mapping in the transformed domain. However, despite the practical success of t-NNs, the theoretical analysis of their generalization remains unexplored. We address this gap by deriving upper bounds on the generalization error of t-NNs in both standard and adversarial settings. Notably, it reveals that t-NNs compressed with exact transformed low-rank parameterization can achieve tighter adversarial generalization bounds compared to non-compressed models. While exact transformed low-rank weights are rare in practice, the analysis demonstrates that through adversarial training with gradient flow, highly over-parameterized t-NNs with the ReLU activation can be implicitly regularized towards a transformed low-rank parameterization under certain conditions. Moreover, this paper establishes sharp adversarial generalization bounds for t-NNs with approximately transformed low-rank weights. Our analysis highlights the potential of transformed low-rank parameterization in enhancing the robust generalization of t-NNs, offering valuable insights for further research and development.

Successful adoption of deep learning (DL) in the wild requires models to be: (1) compact, (2) accurate, and (3) robust to distributional shifts. Unfortunately, efforts towards simultaneously meeting these requirements have mostly been unsuccessful. This raises an important question: "Is the inability to create Compact, Accurate, and Robust Deep neural networks (CARDs) fundamental?" To answer this question, we perform a large-scale analysis of popular model compression techniques which uncovers several intriguing patterns. Notably, in contrast to traditional pruning approaches (e.g., fine tuning and gradual magnitude pruning), we find that "lottery ticket-style" approaches can surprisingly be used to produce CARDs, including binary-weight CARDs. Specifically, we are able to create extremely compact CARDs that, compared to their larger counterparts, have similar test accuracy and matching (or better) robustness--simply by pruning and (optionally) quantizing. Leveraging the compactness of CARDs, we develop a simple domain-adaptive test-time ensembling approach (CARD-Deck) that uses a gating module to dynamically select appropriate CARDsfrom the CARD-Deckbased on their spectral-similarity with test samples. The proposed approach builds a "winning hand" of CARDsthat establishes a new state-of-the-art [8] on CIFAR-10-C accuracies (i.e., 96.8% standard and 92.75% robust) and CIFAR-100-C accuracies (i.e., 80.6% standard and 71.3% robust) with better memory usage than non-compressed baselines (pretrained CARDs available at [8]). Finally, we provide theoretical support for our empirical findings.

Nonetheless, the inherent variability of solar irradiance poses a significant challenge for seamlessly integrating solar power into the electrical grid. While the majority of prior research has centered on employing purely time series-based methodologies for solar forecasting, only a limited number of studies have taken into account factors such as cloud cover or the surrounding physical context. In this paper, we put forth a deep learning architecture designed to harness spatio-temporal context using satellite data, to attain highly accurate day-ahead time-series forecasting for any given station, with a particular emphasis on forecasting Global Horizontal Irradiance (GHI). We also suggest a methodology to extract a distribution for each time step prediction, which can serve as a very valuable measure of uncertainty attached to the forecast. When evaluating models, we propose a testing scheme in which we separate particularly difficult examples from easy ones, in order to capture the model performances in crucial situations, which in the case of this study are the days suffering from varying cloudy conditions. Furthermore, we present a new multi-modal dataset gathering satellite imagery over a large zone and time series for solar irradiance and other related physical variables from multiple geographically diverse solar stations. Our approach exhibits robust performance in solar irradiance forecasting, including zero-shot generalization tests at unobserved solar stations, and holds great promise in promoting the effective integration of solar power into the grid.

A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have inherent equivariances, such as rotation or permutation equivariance. In such tasks, even perturbations with large norm do not necessarily change an input's semantic content. Furthermore, there are perturbations for which a model's prediction explicitly needs to change. For the first time, we propose a sound notion of adversarial robustness that accounts for task equivariance.

What would happen if Yellowstone's'supervolcano' erupted today? Say goodbye to Montana, Wyoming, and Idaho. 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. This photo of a volcano in Iceland doesn't even begin to encapsulate the devastation that would happen if the Yellowstone volcano erupted. Breakthroughs, discoveries, and DIY tips sent six days a week.

Send the pool guy packing. One of these robotic buddies can maintain your water quality instead. Cleaning swimming pools is not fun. I learned this simple logic as a kid growing up in and around pools--it's the only way to survive summer in Houston, Texas. Four years ago, I became a pool owner myself, and I found that the rule still holds. Jumping into the pool on a hot day remains a rare treat, but if the pool is filled with leaves and dirt, that treat becomes a lot less delightful. And when the thermometer is reading over 100 degrees Fahrenheit, the thought of laboring on the pool deck, scooping out debris with a net, is downright cruel.

Will fusion power get cheap? New research suggests that cost declines could be slow for the technology. Fusion power could provide a steady, zero-emissions source of electricity in the future--if companies can get plants built and running. But a new study suggests that even if that future arrives, it might not come cheap. Technologies tend to get less expensive over time. Lithium-ion batteries are now about 90% cheaper than they were in 2013.