December 20, 2014
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June 1, 2018
Theoretical understanding of deep learning is one of the most important tasks facing the statistics and machine learning communities. While deep neural networks (DNNs) originated as engineering methods and models of biological networks in neuroscience and psychology, they have quickly become a centerpiece of the machine learning toolbox. Unfortunately, DNN adoption powered by recent successes combined with the open-source nature of the machine learning community, has outpaced...
February 24, 2017
This paper is a review of the evolutionary history of deep learning models. It covers from the genesis of neural networks when associationism modeling of the brain is studied, to the models that dominate the last decade of research in deep learning like convolutional neural networks, deep belief networks, and recurrent neural networks. In addition to a review of these models, this paper primarily focuses on the precedents of the models above, examining how the initial ideas a...
June 24, 2012
The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implem...
October 18, 2022
Machine learning (ML) formalizes the problem of getting computers to learn from experience as optimization of performance according to some metric(s) on a set of data examples. This is in contrast to requiring behaviour specified in advance (e.g. by hard-coded rules). Formalization of this problem has enabled great progress in many applications with large real-world impact, including translation, speech recognition, self-driving cars, and drug discovery. But practical instant...
July 25, 2019
Data augmentation is a widely used trick when training deep neural networks: in addition to the original data, properly transformed data are also added to the training set. However, to the best of our knowledge, a clear mathematical framework to explain the performance benefits of data augmentation is not available. In this paper, we develop such a theoretical framework. We show data augmentation is equivalent to an averaging operation over the orbits of a certain group that ...
August 28, 2019
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing branches of deep learning theory through the lens of dynamical system and optimal control. By viewing deep neural networks as discrete-time nonlinear dynamical systems, we can analyze how information propagates through layers using me...
September 20, 2020
A big mystery in deep learning continues to be the ability of methods to generalize when the number of model parameters is larger than the number of training examples. In this work, we take a step towards a better understanding of the underlying phenomena of Deep Autoencoders (AEs), a mainstream deep learning solution for learning compressed, interpretable, and structured data representations. In particular, we interpret how AEs approximate the data manifold by exploiting the...
January 6, 2017
This workshop explores the interface between cognitive neuroscience and recent advances in AI fields that aim to reproduce human performance such as natural language processing and computer vision, and specifically deep learning approaches to such problems. When studying the cognitive capabilities of the brain, scientists follow a system identification approach in which they present different stimuli to the subjects and try to model the response that different brain areas h...
October 16, 2017
This paper provides theoretical insights into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, nonrobustness, and sharp minima, responding to an open question in the literature. We also discuss approaches to provide non-vacuous generalization guarantees for deep learning. Based on theoretical observations, we propose new open problems and discuss the limitations of our results.
December 27, 2019
Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called "network motifs". In this article we show that network science tools can be successfully applied also to the study of artificial neural networks operating according to self-organizing (learning) principles. In particular, we study the emergence ...