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We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher…

Machine Learning · Statistics 2018-06-21 Xiao Zhang , Yaodong Yu , Lingxiao Wang , Quanquan Gu

Binary neural networks improve computationally efficiency of deep models with a large margin. However, there is still a performance gap between a successful full-precision training and binary training. We bring some insights about why this…

Machine Learning · Computer Science 2020-04-22 Xinlin Li , Vahid Partovi Nia

Randomly initialized neural networks are known to become harder to train with increasing depth, unless architectural enhancements like residual connections and batch normalization are used. We here investigate this phenomenon by revisiting…

Machine Learning · Statistics 2020-06-15 Hadi Daneshmand , Jonas Kohler , Francis Bach , Thomas Hofmann , Aurelien Lucchi

How can local-search methods such as stochastic gradient descent (SGD) avoid bad local minima in training multi-layer neural networks? Why can they fit random labels even given non-convex and non-smooth architectures? Most existing theory…

Machine Learning · Computer Science 2019-05-28 Zeyuan Allen-Zhu , Yuanzhi Li , Zhao Song

Recurrent Neural Networks (RNNs) are a class of machine learning algorithms used for applications with time-series and sequential data. Recently, there has been a strong interest in executing RNNs on embedded devices. However, difficulties…

Neural and Evolutionary Computing · Computer Science 2020-03-23 Nesma M. Rezk , Madhura Purnaprajna , Tomas Nordström , Zain Ul-Abdin

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

Probability · Mathematics 2021-02-17 Lukas Gonon , Lyudmila Grigoryeva , Juan-Pablo Ortega

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the…

Optimization and Control · Mathematics 2025-02-06 Christoph Plate , Mirko Hahn , Alexander Klimek , Caroline Ganzer , Kai Sundmacher , Sebastian Sager

Deep neural networks with millions of parameters are at the heart of many state of the art machine learning models today. However, recent works have shown that models with much smaller number of parameters can also perform just as well. In…

Machine Learning · Computer Science 2016-08-03 Suraj Srinivas , R. Venkatesh Babu

Advancements in parallel processing have lead to a surge in multilayer perceptrons' (MLP) applications and deep learning in the past decades. Recurrent Neural Networks (RNNs) give additional representational power to feedforward MLPs by…

Machine Learning · Statistics 2014-10-22 Saahil Ognawala , Justin Bayer

Echo State Networks (ESNs) are a special type of recurrent neural networks (RNNs), in which the input and recurrent connections are traditionally generated randomly, and only the output weights are trained. Despite the recent success of…

Machine Learning · Computer Science 2022-05-11 Peter Steiner , Azarakhsh Jalalvand , Peter Birkholz

Consider the following fundamental learning problem: given input examples $x \in \mathbb{R}^d$ and their vector-valued labels, as defined by an underlying generative neural network, recover the weight matrices of this network. We consider…

Data Structures and Algorithms · Computer Science 2018-11-06 Ainesh Bakshi , Rajesh Jayaram , David P. Woodruff

Rectified linear units, or ReLUs, have become the preferred activation function for artificial neural networks. In this paper we consider two basic learning problems assuming that the underlying data follow a generative model based on a…

Machine Learning · Statistics 2018-03-13 Arya Mazumdar , Ankit Singh Rawat

Reducing bit-widths of weights, activations, and gradients of a Neural Network can shrink its storage size and memory usage, and also allow for faster training and inference by exploiting bitwise operations. However, previous attempts for…

Machine Learning · Computer Science 2016-12-01 Qinyao He , He Wen , Shuchang Zhou , Yuxin Wu , Cong Yao , Xinyu Zhou , Yuheng Zou

Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases,…

Machine Learning · Statistics 2018-06-20 Kyle Helfrich , Devin Willmott , Qiang Ye

We introduce a method to train Binarized Neural Networks (BNNs) - neural networks with binary weights and activations at run-time. At training-time the binary weights and activations are used for computing the parameters gradients. During…

Machine Learning · Computer Science 2016-03-18 Matthieu Courbariaux , Itay Hubara , Daniel Soudry , Ran El-Yaniv , Yoshua Bengio

Recurrent neural networks have shown remarkable success in modeling sequences. However low resource situations still adversely affect the generalizability of these models. We introduce a new family of models, called Lattice Recurrent Units…

Machine Learning · Computer Science 2017-11-23 Chaitanya Ahuja , Louis-Philippe Morency

In this paper, we study the problem of node representation learning with graph neural networks. We present a graph neural network class named recurrent graph neural network (RGNN), that address the shortcomings of prior methods. By using…

Machine Learning · Computer Science 2019-08-27 Binxuan Huang , Kathleen M. Carley

There is an implicit assumption that by unfolding recurrent neural networks (RNN) in finite time, the misspecification of choosing a zero value for the initial hidden state is mitigated by later time steps. This assumption has been shown to…

Machine Learning · Computer Science 2019-02-12 Sam Wenke , Jim Fleming

Binary neural networks (BNNs) have received ever-increasing popularity for their great capability of reducing storage burden as well as quickening inference time. However, there is a severe performance drop compared with real-valued…

Machine Learning · Computer Science 2023-02-07 Sheng Xu , Yanjing Li , Teli Ma , Mingbao Lin , Hao Dong , Baochang Zhang , Peng Gao , Jinhu Lv

We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which…