Related papers: Learning algorithms from circuit lower bounds

The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…

Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…

We study the problem of PAC learning $\gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoff suggesting an inherent gap between the sample complexity of the problem and the sample…

We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to…

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

We show a relation between quantum learning theory and algorithmic hardness. We use the existence of efficient, local learning algorithms for energy estimation -- such as the classical shadows algorithm -- to prove that finding near-ground…

We show that most arithmetic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique…

We propose a multi-step training method for designing generalized linear classifiers. First, an initial multi-class linear classifier is found through regression. Then validation error is minimized by pruning of unnecessary inputs.…

We give an algorithm for PAC learning intersections of $k$ halfspaces with a $\rho$ margin to within error $\varepsilon$ that runs in time $\textsf{poly}(k, \varepsilon^{-1}, \rho^{-1}) \cdot \exp \left(O(\sqrt{n \log(1/\rho) \log…

Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…

This work addressed the problem of learning a network with communication between vertices. The communication between vertices is presented in the form of perturbation on the measure. We studied the scenario where samples are drawn from a…

We consider the problems of robust PAC learning from distributed and streaming data, which may contain malicious errors and outliers, and analyze their fundamental complexity questions. In particular, we establish lower bounds on the…

The seminal work of Linial, Mansour, and Nisan gave a quasipolynomial-time algorithm for learning constant-depth circuits ($\mathsf{AC}^0$) with respect to the uniform distribution on the hypercube. Extending their algorithm to the setting…

In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest model able to…

We give an efficient algorithm for learning a binary function in a given class C of bounded VC dimension, with training data distributed according to P and test data according to Q, where P and Q may be arbitrary distributions over X. This…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…

End-to-end deep neural networks have achieved remarkable success across various domains but are often criticized for their lack of interpretability. While post hoc explanation methods attempt to address this issue, they often fail to…

We present a general framework for analyzing the complexity of subdivision-based algorithms whose tests are based on the sizes of regions and their distance to certain sets (often varieties) intrinsic to the problem under study. We call…