Related papers: From Local Pseudorandom Generators to Hardness of …
We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…
We define a novel, basic, unsupervised learning problem - learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as…
While deep learning has demonstrated impressive progress, it remains a daunting challenge to learn from hard samples as these samples are usually noisy and intricate. These hard samples play a crucial role in the optimal performance of deep…
We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and…
In recent work it has been shown that determining a feedforward ReLU neural network to within high uniform accuracy from point samples suffers from the curse of dimensionality in terms of the number of samples needed. As a consequence,…
This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of…
Distributional assumptions have been shown to be necessary for the robust learnability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019). In this paper, we study…
We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the…
We consider the fundamental problem of ReLU regression, where the goal is to output the best fitting ReLU with respect to square loss given access to draws from some unknown distribution. We give the first efficient, constant-factor…
Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for…
We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging…
We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness. Among other results, we show a generic learning speedup lemma, equivalences between various learning models in the…
We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural networks. First, we emphatically show that it is unsurprising…
We prove the first superpolynomial lower bounds for learning one-layer neural networks with respect to the Gaussian distribution using gradient descent. We show that any classifier trained using gradient descent with respect to square-loss…
The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…
The study of graph products is a major research topic and typically concerns the term $f(G*H)$, e.g., to show that $f(G*H)=f(G)f(H)$. In this paper, we study graph products in a non-standard form $f(R[G*H]$ where $R$ is a "reduction", a…
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent…
We consider the well-studied problem of learning a linear combination of $k$ ReLU activations with respect to a Gaussian distribution on inputs in $d$ dimensions. We give the first polynomial-time algorithm that succeeds whenever $k$ is a…
We study the problem of PAC learning halfspaces in the reliable agnostic model of Kalai et al. (2012). The reliable PAC model captures learning scenarios where one type of error is costlier than the others. Our main positive result is a new…
This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived…