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We present novel empirical observations regarding how stochastic gradient descent (SGD) navigates the loss landscape of over-parametrized deep neural networks (DNNs). These observations expose the qualitatively different roles of learning…
Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…
This paper proposes a new mean-field framework for over-parameterized deep neural networks (DNNs), which can be used to analyze neural network training. In this framework, a DNN is represented by probability measures and functions over its…
Deep Neural Networks (DNNs) are inherently computation-intensive and also power-hungry. Hardware accelerators such as Field Programmable Gate Arrays (FPGAs) are a promising solution that can satisfy these requirements for both embedded and…
We study the complexity of training neural network models with one hidden nonlinear activation layer and an output weighted sum layer. We analyze Gradient Descent applied to learning a bounded target function on $n$ real-valued inputs. We…
Gating is a key feature in modern neural networks including LSTMs, GRUs and sparsely-gated deep neural networks. The backbone of such gated networks is a mixture-of-experts layer, where several experts make regression decisions and gating…
Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms.…
Successfully training deep neural networks often requires either batch normalization, appropriate weight initialization, both of which come with their own challenges. We propose an alternative, geometrically motivated method for training.…
Deep artificial neural networks achieve surprising generalization abilities that remain poorly understood. In this paper, we present a new approach to analyzing generalization for deep feed-forward ReLU networks that takes advantage of the…
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…
We extend the ReLU Transition Graph (RTG) framework into a comprehensive graph-theoretic model for understanding deep ReLU networks. In this model, each node represents a linear activation region, and edges connect regions that differ by a…
The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…
Deep neural networks (DNNs) are widely studied in various applications. A DNN consists of layers of neurons that compute affine combinations, apply nonlinear operations, and produce corresponding activations. The rectified linear unit…
Recently, theoretical analyses of deep neural networks have broadly focused on two directions: 1) Providing insight into neural network training by SGD in the limit of infinite hidden-layer width and infinitesimally small learning rate…
Activation functions are core components of all deep learning architectures. Currently, the most popular activation functions are smooth ReLU variants like GELU and SiLU. These are self-gated activation functions where the range of the…
Gradient descent (GD) type optimization methods are the standard instrument to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation. Despite the great success of GD type optimization methods in numerical…
In recent years, deep neural networks (DNNs) achieved unprecedented performance in many low-level vision tasks. However, state-of-the-art results are typically achieved by very deep networks, which can reach tens of layers with tens of…
In this work, we investigate a particular implicit bias in gradient descent training, which we term "Feature Averaging," and argue that it is one of the principal factors contributing to the non-robustness of deep neural networks. We show…
Deep neural networks, which employ batch normalization and ReLU-like activation functions, suffer from instability in the early stages of training due to the high gradient induced by temporal gradient explosion. In this study, we analyze…
Activation functions influence behavior and performance of DNNs. Nonlinear activation functions, like Rectified Linear Units (ReLU), Exponential Linear Units (ELU) and Scaled Exponential Linear Units (SELU), outperform the linear…