相关论文: Topos and Stacks of Deep Neural Networks

Deep learning is a subset of a broader family of machine learning methods based on learning data representations. These models are inspired by human biological nervous systems, even if there are various differences pertaining to the…

It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what…

Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This…

Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically,…

The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…

We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the…

I aim to show that models, classification or generating functions, invariances and datasets are algorithmically equivalent concepts once properly defined, and provide some concrete examples of them. I then show that a) neural networks (NNs)…

Deep neural networks (DNNs) have achieved unprecedented performance on a wide range of complex tasks, rapidly outpacing our understanding of the nature of their solutions. This has caused a recent surge of interest in methods for rendering…

Deep neural networks (DNNs) exhibit crackling-like avalanches whose origin lacks a mechanistic explanation. Here, I derive a stochastic theory of deep information propagation (DIP) by incorporating Central Limit Theorem (CLT)-level…

While deep neural networks (DNNs) have become a standard architecture for many machine learning tasks, their internal decision-making process and general interpretability is still poorly understood. Conversely, common decision trees are…

Deep neural networks (DNNs) have demonstrated impressive performance on a wide array of tasks, but they are usually considered opaque since internal structure and learned parameters are not interpretable. In this paper, we re-examine the…

We rigorously study the thermodynamic limit of deep neural networks (DNNS) and recurrent neural networks (RNNs), assuming that the activation functions are sigmoids. A thermodynamic limit is a continuous neural network, where the neurons…

Deep Convolutional Neural Networks (CNNs) have been one of the most influential recent developments in computer vision, particularly for categorization. There is an increasing demand for explainable AI as these systems are deployed in the…

Understanding neural networks is challenging due to their high-dimensional, interacting components. Inspired by human cognition, which processes complex sensory data by chunking it into recurring entities, we propose leveraging this…

Deep Convolutional Neural Networks (CNNs) are playing important roles in state-of-the-art visual recognition. This paper focuses on modeling the spatial co-occurrence of neuron responses, which is less studied in the previous work. For…

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

The Artificial Neural Networks (ANNs) have been originally designed to function like a biological neural network, but does an ANN really work in the same way as a biological neural network? As we know, the human brain holds information in…

Tree-like structures, such as blood vessels, often express complexity at very fine scales, requiring high-resolution grids to adequately describe their shape. Such sparse morphology can alternately be represented by locations of centreline…

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…