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This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…

Differential Geometry · Mathematics 2025-10-22 Tsemo Aristide

While deep learning is facing an homogenization across modalities led by Transformers, they are still challenged by shallow linear models in the time series forecasting task. Our hypothesis is that models should learn a direct link from…

Machine Learning · Computer Science 2026-05-15 Alexis-Raja Brachet , Pierre-Yves Richard , Céline Hudelot

The advent of deep learning has inspired research into end-to-end learning for a variety of problem domains in robotics. For navigation, the resulting methods may not have the generalization properties desired let alone match the…

Robotics · Computer Science 2021-03-03 Haoxin Ma , Justin S. Smith , Patricio A. Vela

Training deep neural networks on large-scale datasets requires significant hardware resources whose costs (even on cloud platforms) put them out of reach of smaller organizations, groups, and individuals. Backpropagation, the workhorse for…

Machine Learning · Computer Science 2020-09-22 Alexander Ororbia , Ankur Mali , Daniel Kifer , C. Lee Giles

This paper identifies a structural property of data distributions that enables deep neural networks to learn hierarchically. We define the "staircase" property for functions over the Boolean hypercube, which posits that high-order Fourier…

Machine Learning · Computer Science 2021-11-25 Emmanuel Abbe , Enric Boix-Adsera , Matthew Brennan , Guy Bresler , Dheeraj Nagaraj

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an…

Machine Learning · Statistics 2019-05-09 Arild Nøkland , Lars Hiller Eidnes

Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of…

Machine Learning · Computer Science 2024-11-04 Alan Jeffares , Alicia Curth , Mihaela van der Schaar

Deep learning approaches are nowadays ubiquitously used to tackle computer vision tasks such as semantic segmentation, requiring large datasets and substantial computational power. Continual learning for semantic segmentation (CSS) is an…

Computer Vision and Pattern Recognition · Computer Science 2021-03-12 Arthur Douillard , Yifu Chen , Arnaud Dapogny , Matthieu Cord

In this paper, we propose several novel deep learning methods for object saliency detection based on the powerful convolutional neural networks. In our approach, we use a gradient descent method to iteratively modify an input image based on…

Computer Vision and Pattern Recognition · Computer Science 2015-05-07 Hengyue Pan , Bo Wang , Hui Jiang

We describe a layer-by-layer algorithm for training deep convolutional networks, where each step involves gradient updates for a two layer network followed by a simple clustering algorithm. Our algorithm stems from a deep generative model…

Machine Learning · Computer Science 2018-06-26 Eran Malach , Shai Shalev-Shwartz

Recent advancements in the realm of deep learning, particularly in the development of large language models (LLMs), have demonstrated AI's ability to tackle complex mathematical problems or solving programming challenges. However, the…

Artificial Intelligence · Computer Science 2024-02-29 Xiaoxin Yin

Understanding the internal representations and decision mechanisms of deep neural networks remains a critical open challenge. While existing interpretability methods often identify influential input regions, they may not elucidate how a…

Machine Learning · Computer Science 2025-06-12 Farzaneh Mahdisoltani , Saeed Mahdisoltani , Roger B. Grosse , David J. Fleet

Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing and controlling the network Jacobian. We first provide a…

Machine Learning · Computer Science 2026-02-12 Alex Massucco , Davide Murari , Carola-Bibiane Schönlieb

The question of whether pre-training on geometric tasks is viable for downstream transfer to semantic tasks is important for two reasons, one practical and the other scientific. If the answer is positive, we may be able to reduce…

Computer Vision and Pattern Recognition · Computer Science 2024-07-19 Dong Lao , Fengyu Yang , Daniel Wang , Hyoungseob Park , Samuel Lu , Alex Wong , Stefano Soatto

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold…

Neurons and Cognition · Quantitative Biology 2026-02-27 Bruno Aristimunha , Ce Ju , Antoine Collas , Florent Bouchard , Ammar Mian , Bertrand Thirion , Sylvain Chevallier , Reinmar Kobler

The autoencoder is an effective unsupervised learning model which is widely used in deep learning. It is well known that an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost…

Machine Learning · Statistics 2019-01-01 Elad Plaut

Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…

Machine Learning · Statistics 2026-04-21 Hossein Taheri , Avishek Ghosh , Arya Mazumdar

Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a…

Machine Learning · Statistics 2022-06-15 Joowon Lee , Hanbaek Lyu , Weixin Yao

We present and discuss several novel applications of deep learning for the physical layer. By interpreting a communications system as an autoencoder, we develop a fundamental new way to think about communications system design as an…

Information Theory · Computer Science 2017-07-13 Timothy J. O'Shea , Jakob Hoydis

Features play a crucial role in computer vision. Initially designed to detect salient elements by means of handcrafted algorithms, features are now often learned by different layers in Convolutional Neural Networks (CNNs). This paper…

Computer Vision and Pattern Recognition · Computer Science 2021-11-18 Loris Nanni , Stefano Ghidoni , Sheryl Brahnam
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