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Reliable uncertainty estimation is critical for deploying neural networks (NNs) in real-world applications. While existing calibration techniques often rely on post-hoc adjustments or coarse-grained binning methods, they remain limited in…

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…

Many structured prediction tasks in machine vision have a collection of acceptable answers, instead of one definitive ground truth answer. Segmentation of images, for example, is subject to human labeling bias. Similarly, there are multiple…

The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? It is known that many different parameter…

Multi-task learning leverages structural similarities between multiple tasks to learn despite very few samples. Motivated by the recent success of neural networks applied to data-scarce tasks, we consider a linear low-dimensional shared…

Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain…

Multiple operator learning concerns learning operator families $\{G[\alpha]:U\to V\}_{\alpha\in W}$ indexed by an operator descriptor $\alpha$. Training data are collected hierarchically by sampling operator instances $\alpha$, then input…

We prove bounds for the approximation and estimation of certain binary classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guarantees for empirical risk minimization using networks of a…

Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…

Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose…

Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs…

We present a new algorithm to generate minimal, stable, and symbolic corrections to an input that will cause a neural network with ReLU activations to change its output. We argue that such a correction is a useful way to provide feedback to…

The big problem for neural network models which are trained to count instances is that whenever test range goes high training range generalization error increases i.e. they are not good generalizers outside training range. Consider the case…

We show that $n$-variable tree-structured Ising models can be learned computationally-efficiently to within total variation distance $\epsilon$ from an optimal $O(n \ln n/\epsilon^2)$ samples, where $O(\cdot)$ hides an absolute constant…

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high…

We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…

Neural architectures tend to fit their data with relatively simple functions. This "simplicity bias" is widely regarded as key to their success. This paper explores the limits of this principle. Building on recent findings that the…

Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…