Although very successfully used in conventional machine learning, convolution based neural network architectures - believed to be inconsistent in function space - have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a computer. We prove a universality theorem to show that CNOs can approximate operators arising in PDEs to desired accuracy. CNOs are tested on a novel suite of benchmarks, encompassing a diverse set of PDEs with possibly multi-scale solutions and are observed to significantly outperform baselines, paving the way for an alternative framework for robust and accurate operator learning.

The following section is answers to questions listed in datasheets for datasets. A.1 Motivation For what purpose was the dataset created? VisAlign is created to serve as a benchmark for measuring visual perception alignment between AI models and humans. Who created the dataset (e.g., which team, research group) and on behalf of which entity (e.g., company, institution, organization)? Who funded the creation of the dataset? If there is an associated grant, please provide the name of the grantor and the grant name and number. This work was supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST)) and National Research Foundation of Korea (NRF) grant (NRF2020H1D3A2A03100945), funded by the Korea government (MSIT). A.2 Composition What do the instances that comprise the dataset represent (e.g., documents, photos, people, countries)? VisAlign contains eight different types of images and their corresponding gold human labels. How many instances are there in total (of each type, if appropriate)? There are a total of 12500 images in the train set, distributed equally among the 10 classes. The open test set and the closed test each contain 900 images: 100 images each in Categories 1 to 7 and 200 images in Category 8. Does the dataset contain all possible instances or is it a sample (not necessarily random) of instances from a larger set?

AI alignment refers to models acting towards human-intended goals, preferences, or ethical principles. In this paper, we focus on the models' visual perception alignment with humans, further referred to as AI-human visual alignment. Specifically, we propose a new dataset for measuring AI-human visual alignment in terms of image classification. In order to evaluate AI-human visual alignment, a dataset should encompass samples with various scenarios and have gold human perception labels. Our dataset consists of three groups of samples, namely Must-Act (i.e., Must-Classify), Must-Abstain, and Uncertain, and further divided into eight categories. All samples have a gold human perception label; even Uncertain (e.g., severely blurry) sample labels were obtained via crowd-sourcing. The validity of our dataset is verified by sampling theory, statistical theories related to survey design, and experts in the related fields. Using our dataset, we analyze the visual alignment and reliability of five popular visual perception models and eight abstention methods.

Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the first time-uniform finite sample guarantees for online (regularized) PCR whenever data is collected adaptively. Since the proof techniques for analyzing PCR in the fixed design setting do not readily extend to the online setting, our results rely on adapting tools from modern martingale concentration to the error-in-variables setting. As an application of our bounds, we provide a framework for experiment design in panel data settings when interventions are assigned adaptively. Our framework may be thought of as a generalization of the synthetic control and synthetic interventions frameworks, where data is collected via an adaptive intervention assignment policy.

Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with ab initio accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions. We evaluate QuinNet on public datasets of small molecules, such as MD17 and its revised version, and show that it is compatible with other state-of-the-art models on these benchmarks.

Robust inference for non-linear regression models from the tsallis score:812 Application to coronavirus disease 2019 contagion in italy.