Related papers: From Local Pseudorandom Generators to Hardness of …
We revisit known constructions of efficient learning algorithms from various notions of constructive circuit lower bounds such as distinguishers breaking pseudorandom generators or efficient witnessing algorithms which find errors of small…
We study the problem of PAC learning one-hidden-layer ReLU networks with $k$ hidden units on $\mathbb{R}^d$ under Gaussian marginals in the presence of additive label noise. For the case of positive coefficients, we give the first…
"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…
We define the local complexity of a neural network with continuous piecewise linear activations as a measure of the density of linear regions over an input data distribution. We show theoretically that ReLU networks that learn…
The problem of learning $t$-term DNF formulas (for $t = O(1)$) has been studied extensively in the PAC model since its introduction by Valiant (STOC 1984). A $t$-term DNF can be efficiently learnt using a $t$-term DNF only if $t = 1$ i.e.,…
The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…
Density modelling is the task of learning an unknown probability density function from samples, and is one of the central problems of unsupervised machine learning. In this work, we show that there exists a density modelling problem for…
We study the complexity of PAC learning halfspaces in the presence of Massart noise. In this problem, we are given i.i.d. labeled examples $(\mathbf{x}, y) \in \mathbb{R}^N \times \{ \pm 1\}$, where the distribution of $\mathbf{x}$ is…
We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the…
The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…
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…
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…
Neural networks with random weights appear in a variety of machine learning applications, most prominently as the initialization of many deep learning algorithms and as a computationally cheap alternative to fully learned neural networks.…
We prove several hardness results for training depth-2 neural networks with the ReLU activation function; these networks are simply weighted sums (that may include negative coefficients) of ReLUs. Our goal is to output a depth-2 neural…
Free fermions are some of the best studied quantum systems. However, little is known about the complexity of learning free-fermion distributions. In this work we establish the hardness of this task in the particle number non-preserving…
While on some natural distributions, neural-networks are trained efficiently using gradient-based algorithms, it is known that learning them is computationally hard in the worst-case. To separate hard from easy to learn distributions, we…
This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…
The existence of local minima for one-hidden-layer ReLU networks has been investigated theoretically in [8]. Based on the theory, in this paper, we first analyze how big the probability of existing local minima is for 1D Gaussian data and…
In our recent work (Bubeck, Price, Razenshteyn, arXiv:1805.10204) we argued that adversarial examples in machine learning might be due to an inherent computational hardness of the problem. More precisely, we constructed a binary…
Recently, a spate of papers have provided positive theoretical results for training over-parameterized neural networks (where the network size is larger than what is needed to achieve low error). The key insight is that with sufficient…