10 accepted papers
A main theoretical puzzle is why over-parameterized Neural Networks (NNs) generalize well when trained to zero loss (i.e., so they interpolate the data). Usually, the NN is trained with Stochastic Gradient Descent (SGD) or one of its variants. However, recent empirical work examined the generalizati…
Recent work has demonstrated the effectiveness of using patch based representations when learning from image data. Here we provide theoretical support for this observation, by showing that a simple semi-supervised algorithm that uses patch statistics can efficiently learn labels produced by a one-hi…
Learning functions over Boolean variables is a fundamental problem in machine learning. But not much is known about learning such functions using neural networks. Here we focus on learning read-once disjunctive normal forms (DNFs) under the uniform distribution with a convex neural network and gradi…
Fine-tuning is a common practice in deep learning, achieving excellent generalization results on downstream tasks using relatively little training data. Although widely used in practice, it is not well understood theoretically. Here we analyze the sample complexity of this scheme for regression with…
Max-Pooling operations are a core component of deep learning architectures. In particular, they are part of most convolutional architectures used in machine vision, since pooling is a natural approach to pattern detection problems. However, these architectures are not well understood from a theoreti…
Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer network with Leaky ReLU activations. The learned network can i…
When applying machine learning to sensitive data, one has to find a balance between accuracy, information security, and computational-complexity. Recent studies combined Homomorphic Encryption with neural networks to make inferences while protecting against information leakage. However, these method…
Empirical evidence suggests that neural networks with ReLU activations generalize better with over-parameterization. However, there is currently no theoretical analysis that explains this observation. In this work, we provide theoretical and empirical evidence that, in certain cases, overparameteriz…
Neural networks exhibit good generalization behavior in the over-parameterized regime, where the number of network parameters exceeds the number of observations. Nonetheless, current generalization bounds for neural networks fail to explain this phenomenon. In an attempt to bridge this gap, we study…
Deep learning models are often successfully trained using gradient descent, despite the worst case hardness of the underlying non-convex optimization problem. The key question is then under what conditions can one prove that optimization will succeed. Here we provide a strong result of this kind. We…