Related papers: Neural Network Layer Matrix Decomposition reveals …
We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…
In this paper, we investigate lossy compression of deep neural networks (DNNs) by weight quantization and lossless source coding for memory-efficient deployment. Whereas the previous work addressed non-universal scalar quantization and…
Despite deep neural networks' powerful representation learning capabilities, theoretical understanding of how networks can simultaneously achieve meaningful feature learning and global convergence remains elusive. Existing approaches like…
We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more.…
Deep learning has shown promising results in many machine learning applications. The hierarchical feature representation built by deep networks enable compact and precise encoding of the data. A kernel analysis of the trained deep networks…
Recurrent neural networks (RNN) are powerful tools to explain how attractors may emerge from noisy, high-dimensional dynamics. We study here how to learn the ~N^(2) pairwise interactions in a RNN with N neurons to embed L manifolds of…
While deep learning models and techniques have achieved great empirical success, our understanding of the source of success in many aspects remains very limited. In an attempt to bridge the gap, we investigate the decision boundary of a…
The Linear Representation Hypothesis (LRH) states that neural networks learn to encode concepts as directions in activation space, and a strong version of the LRH states that models learn only such encodings. In this paper, we present a…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…
We present the Input-Connected Multilayer Perceptron (IC-MLP), a feedforward neural network architecture in which each hidden neuron receives, in addition to the outputs of the preceding layer, a direct affine connection from the raw input.…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an…
Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
The Convolutional Neural Network (CNN) is one of the most prominent neural network architectures in deep learning. Despite its widespread adoption, our understanding of its universal approximation properties has been limited due to its…
We provide the first global optimization landscape analysis of $Neural\;Collapse$ -- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of neural networks during the terminal phase of training. As…
In this paper, we present a framework for modeling quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks using the core ideas presented by Linden et al. (2009), where the entangling and…
In this work, we present some applications of random matrix theory for the training of deep neural networks. Recently, random matrix theory (RMT) has been applied to the overfitting problem in deep learning. Specifically, it has been shown…