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The backpropagation algorithm remains the dominant and most successful method for training deep neural networks (DNNs). At the same time, training DNNs at scale comes at a significant computational cost and therefore a high carbon…

The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

This paper proposes a new equation from continuous adjoint theory to compute the gradient of quantities governed by the Transport Theory of light. Unlike discrete gradients ala autograd, which work at the code level, we first formulate the…

Threshold activation functions are highly preferable in neural networks due to their efficiency in hardware implementations. Moreover, their mode of operation is more interpretable and resembles that of biological neurons. However,…

This work makes a substantial step in the field of split computing, i.e., how to split a deep neural network to host its early part on an embedded device and the rest on a server. So far, potential split locations have been identified…

Machine learning optimization often depends on stochastic gradient descent, where the precision of gradient estimation is vital for model performance. Gradients are calculated from mini-batches formed by uniformly selecting data samples…

In this paper, we advocate for two stages in a neural network's decision making process. The first is the existing feed-forward inference framework where patterns in given data are sensed and associated with previously learned patterns. The…

This paper introduces feature gradient flow, a new technique for interpreting deep learning models in terms of features that are understandable to humans. The gradient flow of a model locally defines nonlinear coordinates in the input data…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

We introduce a new technique for gradient normalization during neural network training. The gradients are rescaled during the backward pass using normalization layers introduced at certain points within the network architecture. These…

The performance and efficiency of distributed training of Deep Neural Networks highly depend on the performance of gradient averaging among all participating nodes, which is bounded by the communication between nodes. There are two major…

Note: This paper describes an older version of DeepLIFT. See https://arxiv.org/abs/1704.02685 for the newer version. Original abstract follows: The purported "black box" nature of neural networks is a barrier to adoption in applications…

Understanding the asymptotic behavior of gradient-descent training of deep neural networks is essential for revealing inductive biases and improving network performance. We derive the infinite-time training limit of a mathematically…

This paper presents a compact, matrix-based representation of neural networks in a self-contained tutorial fashion. Specifically, we develop neural networks as a composition of several vector-valued functions. Although neural networks are…

Training deep neural networks on large datasets containing high-dimensional data requires a large amount of computation. A solution to this problem is data-parallel distributed training, where a model is replicated into several…

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…

While feed-forward neurons in pre-trained language models (PLMs) can encode knowledge, past research targeted a small subset of neurons that heavily influence outputs. This leaves the broader role of neuron activations unclear, limiting…

Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models -- contrary to…

Importance sampling has been successfully used to accelerate stochastic optimization in many convex problems. However, the lack of an efficient way to calculate the importance still hinders its application to Deep Learning. In this paper,…

Deep neural networks (DNNs) demonstrate outstanding performance across most computer vision tasks. Some critical applications, such as autonomous driving or medical imaging, also require investigation into their behavior and the reasons…