Related papers: Convolutional neural networks with fractional orde…
The increasing complexity of deep learning architectures is resulting in training time requiring weeks or even months. This slow training is due in part to vanishing gradients, in which the gradients used by back-propagation are extremely…
This article introduces the multi-objective adaptive order Caputo fractional gradient descent (MOAOCFGD) algorithm for solving unconstrained multi-objective problems. The proposed method performs equally well for both smooth and non-smooth…
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into the network -- it ensures all layers are connected to one…
The vanilla fractional order gradient descent may oscillatively converge to a region around the global minimum instead of converging to the exact minimum point, or even diverge, in the case where the objective function is strongly convex.…
Convolutional networks are one of the most widely employed architectures in computer vision and machine learning. In order to leverage their ability to learn complex functions, large amounts of data are required for training. Training a…
We propose a new formulation for pruning convolutional kernels in neural networks to enable efficient inference. We interleave greedy criteria-based pruning with fine-tuning by backpropagation - a computationally efficient procedure that…
We propose a scalable Forward-Forward (FF) algorithm that eliminates the need for backpropagation by training each layer separately. Unlike backpropagation, FF avoids backward gradients and can be more modular and memory efficient, making…
Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…
Due to the substantial computational cost, training state-of-the-art deep neural networks for large-scale datasets often requires distributed training using multiple computation workers. However, by nature, workers need to frequently…
Convolutional Neural Networks (CNNs) has revolutionized computer vision, but training very deep networks has been challenging due to the vanishing gradient problem. This paper explores Residual Networks (ResNet), introduced by He et al.…
This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A…
A method to increase the precision of feedforward networks is proposed. It requires a prior knowledge of a target function derivatives of several orders and uses this information in gradient based training. Forward pass calculates not only…
Recurrent Neural Networks (RNNs) achieve state-of-the-art results in many sequence-to-sequence modeling tasks. However, RNNs are difficult to train and tend to suffer from overfitting. Motivated by the Data Processing Inequality (DPI), we…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Neural networks are trained primarily based on their inputs and outputs, without regard for their internal mechanisms. These neglected mechanisms determine properties that are critical for safety, like (i) transparency; (ii) the absence of…
In this paper, the problem of optimal gradient lossless compression in Deep Neural Network (DNN) training is considered. Gradient compression is relevant in many distributed DNN training scenarios, including the recently popular federated…
In this paper, we give some new thoughts about the classical gradient method (GM) and recall the proposed fractional order gradient method (FOGM). It is proven that the proposed FOGM holds a super convergence capacity and a faster…
We propose a novel Caputo fractional derivative-based optimization algorithm. Upon defining the Caputo fractional gradient with respect to the Cartesian coordinate, we present a generic Caputo fractional gradient descent (CFGD) method. We…
We propose a new way of training neural networks, with the goal of reducing training cost. Our method uses approximate predicted gradients instead of the full gradients that require an expensive backward pass. We derive a…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…