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Neural networks are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this paper we build a category-theoretic formalism around a neural network system called…

Machine Learning · Computer Science 2020-09-16 Bruno Gavranović

The Java and Scala community has built a very successful big data ecosystem. However, most of neural networks running on it are modeled in dynamically typed programming languages. These dynamically typed deep learning frameworks treat…

Programming Languages · Computer Science 2023-07-25 Bo Yang , Zhihao Zhang Kirisame Marisa , Kai Shi

This document is a follow-up to our previous paper dedicated to a vectorized derivation of backpropagation in CNNs. Following the same principles and notations already put in place there, we now focus on transformer-based…

Machine Learning · Computer Science 2025-12-30 Laurent Boué

Self-supervised learning is showing great promise for monocular depth estimation, using geometry as the only source of supervision. Depth networks are indeed capable of learning representations that relate visual appearance to 3D properties…

Computer Vision and Pattern Recognition · Computer Science 2020-02-28 Vitor Guizilini , Rui Hou , Jie Li , Rares Ambrus , Adrien Gaidon

Deep learning, a multi-layered neural network approach inspired by the brain, has revolutionized machine learning. One of its key enablers has been backpropagation, an algorithm that computes the gradient of a loss function with respect to…

Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we…

Machine Learning · Statistics 2018-08-06 Nicholas G. Polson , Vadim O. Sokolov

The Backprop algorithm for learning in neural networks utilizes two mechanisms: first, stochastic gradient descent and second, initialization with small random weights, where the latter is essential to the effectiveness of the former. We…

Machine Learning · Computer Science 2022-05-06 Shibhansh Dohare , Richard S. Sutton , A. Rupam Mahmood

A Deep Neural Network (DNN) is a composite function of vector-valued functions, and in order to train a DNN, it is necessary to calculate the gradient of the loss function with respect to all parameters. This calculation can be a…

Machine Learning · Computer Science 2023-06-02 Saeed Damadi , Golnaz Moharrer , Mostafa Cham

Deep learning is a group of exciting new technologies for neural networks. Through a combination of advanced training techniques and neural network architectural components, it is now possible to create neural networks that can handle…

Machine Learning · Computer Science 2022-05-18 Jeff Heaton

Deep-predictive-coding networks (DPCNs) are hierarchical, generative models. They rely on feed-forward and feed-back connections to modulate latent feature representations of stimuli in a dynamic and context-sensitive manner. A crucial…

Artificial Intelligence · Computer Science 2021-09-27 Isaac J. Sledge , Jose C. Principe

Deep neural network architectures have recently produced excellent results in a variety of areas in artificial intelligence and visual recognition, well surpassing traditional shallow architectures trained using hand-designed features. The…

Computer Vision and Pattern Recognition · Computer Science 2016-04-15 Catalin Ionescu , Orestis Vantzos , Cristian Sminchisescu

This paper gives two new categorical characterisations of lenses: one as a coalgebra of the store comonad, and the other as a monoidal natural transformation on a category of a certain class of coalgebras. The store comonad of the first…

Programming Languages · Computer Science 2011-07-12 Russell O'Connor

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…

Machine Learning · Computer Science 2026-05-14 Yatin Dandi , Matteo Vilucchio , Luca Arnaboldi , Hugo Tabanelli , Florent Krzakala

Backpropagation is the core learning mechanism underlying deep learning. However, whether and how this algorithm is implemented in the brain remains highly debated. In particular, while forward activations of pretrained models reliably map…

Neural Networks sequentially build high-level features through their successive layers. We propose here a new neural network model where each layer is associated with a set of candidate mappings. When an input is processed, at each layer,…

Machine Learning · Computer Science 2014-10-03 Ludovic Denoyer , Patrick Gallinari

Representations are fundamental to artificial intelligence. The performance of a learning system depends on the type of representation used for representing the data. Typically, these representations are hand-engineered using domain…

Machine Learning · Computer Science 2017-04-28 Vivek Veeriah , Shangtong Zhang , Richard S. Sutton

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…

Machine Learning · Computer Science 2025-11-12 Sander Dalm , Joshua Offergeld , Nasir Ahmad , Marcel van Gerven

In this work, a non-gradient descent learning (NGDL) scheme was proposed for deep feedforward neural networks (DNN). It is known that an autoencoder can be used as the building blocks of the multi-layer perceptron (MLP) DNN, the MLP is…

Machine Learning · Computer Science 2021-08-25 P. Guo , K. Wang , X. L. Zhou

Understanding the training dynamics of deep learning models is perhaps a necessary step toward demystifying the effectiveness of these models. In particular, how do data from different classes gradually become separable in their feature…

Machine Learning · Computer Science 2021-10-13 Jiayao Zhang , Hua Wang , Weijie J. Su

Establishing accurate morphological measurements of galaxies in a reasonable amount of time for future big-data surveys such as EUCLID, the Large Synoptic Survey Telescope or the Wide Field Infrared Survey Telescope is a challenge. Because…

Instrumentation and Methods for Astrophysics · Physics 2017-06-14 D. Tuccillo , M. Huertas-Company , E. Decenciere , S. Velasco-Forero