相关论文: Topos and Stacks of Deep Neural Networks

Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with…

Recent research has seen many behavioral comparisons between humans and deep neural networks (DNNs) in the domain of image classification. Often, comparison studies focus on the end-result of the learning process by measuring and comparing…

Deep neural networks have been proven powerful at processing perceptual data, such as images and audio. However for tabular data, tree-based models are more popular. A nice property of tree-based models is their natural interpretability. In…

Despite the impressive performance of Deep Neural Networks (DNNs) on various vision tasks, they still exhibit erroneous high sensitivity toward semantic primitives (e.g. object pose). We propose a theoretically grounded analysis for DNN…

Deep neural networks have achieved remarkable success, yet our understanding of how they learn remains limited. These models can learn high-dimensional tasks, which is generally statistically intractable due to the curse of dimensionality.…

Graph-structured data consisting of objects (i.e., nodes) and relationships among objects (i.e., edges) are ubiquitous. Graph-level learning is a matter of studying a collection of graphs instead of a single graph. Traditional graph-level…

Graph Neural Networks (GNNs) have emerged as an efficient alternative to convolutional approaches for vision tasks such as image classification, leveraging patch-based representations instead of raw pixels. These methods construct graphs…

Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing…

Functions are rich in meaning and can be interpreted in a variety of ways. Neural networks were proven to be capable of approximating a large class of functions[1]. In this paper, we propose a new class of neural networks called "Neural…

The last decade of machine learning has seen drastic increases in scale and capabilities. Deep neural networks (DNNs) are increasingly being deployed in the real world. However, they are difficult to analyze, raising concerns about using…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

How perception and reasoning arise from neuronal network activity is poorly understood. This is reflected in the fundamental limitations of connectionist artificial intelligence, typified by deep neural networks trained via gradient-based…

The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate…

In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

The process of aggregation is ubiquitous in almost all deep nets models. It functions as an important mechanism for consolidating deep features into a more compact representation, whilst increasing robustness to overfitting and providing…

A long-standing proposition is that by emulating the operation of the brain's neocortex, a spiking neural network (SNN) can achieve similar desirable features: flexible learning, speed, and efficiency. Temporal neural networks (TNNs) are…

Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in…

Artificial neural networks (ANN), typically referred to as neural networks, are a class of Machine Learning algorithms and have achieved widespread success, having been inspired by the biological structure of the human brain. Neural…

Deep neural networks (DNNs) have achieved remarkable empirical success, yet their training dynamics remain understood mainly from optimization rather than statistical principles. Here we develop a statistical framework for DNN training in…