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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

As a popular channel pruning method for convolutional neural networks (CNNs), network slimming (NS) has a three-stage process: (1) it trains a CNN with $\ell_1$ regularization applied to the scaling factors of the batch normalization…

Computer Vision and Pattern Recognition · Computer Science 2024-01-31 Kevin Bui , Fanghui Xue , Fredrick Park , Yingyong Qi , Jack Xin

The success of neural networks over the past decade has established them as effective models for many relevant data generating processes. Statistical theory on neural networks indicates graceful scaling of sample complexity. For example,…

Machine Learning · Computer Science 2023-03-28 Yifan Zhu , Hong Jun Jeon , Benjamin Van Roy

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

Machine Learning · Computer Science 2016-08-12 Hrushikesh Mhaskar , Tomaso Poggio

We present an approach to learn a dense pixel-wise labeling from image-level tags. Each image-level tag imposes constraints on the output labeling of a Convolutional Neural Network (CNN) classifier. We propose Constrained CNN (CCNN), a…

Computer Vision and Pattern Recognition · Computer Science 2015-10-20 Deepak Pathak , Philipp Krähenbühl , Trevor Darrell

In this paper, we propose a novel deep neural network framework embedded with low-level features (LCNN) for salient object detection in complex images. We utilise the advantage of convolutional neural networks to automatically learn the…

Computer Vision and Pattern Recognition · Computer Science 2015-08-18 Hongyang Li , Huchuan Lu , Zhe Lin , Xiaohui Shen , Brian Price

We present ApproxConv, a novel method for compressing the layers of a convolutional neural network. Reframing conventional discrete convolution as continuous convolution of parametrised functions over space, we use functional approximations…

Computer Vision and Pattern Recognition · Computer Science 2022-10-18 Theo W. Costain , Victor Adrian Prisacariu

In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure…

Machine Learning · Computer Science 2023-04-05 Vugar Ismailov , Ekrem Savas

We study model recovery for data classification, where the training labels are generated from a one-hidden-layer neural network with sigmoid activations, also known as a single-layer feedforward network, and the goal is to recover the…

Machine Learning · Statistics 2020-05-07 Haoyu Fu , Yuejie Chi , Yingbin Liang

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon…

Machine Learning · Computer Science 2022-05-17 Hancheng Min , Salma Tarmoun , Rene Vidal , Enrique Mallada

We consider whether deep convolutional networks (CNNs) can represent decision functions with similar accuracy as recurrent networks such as LSTMs. First, we show that a deep CNN with an architecture inspired by the models recently…

One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies…

Machine Learning · Computer Science 2019-02-06 Simon S. Du , Xiyu Zhai , Barnabas Poczos , Aarti Singh

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…

Machine Learning · Computer Science 2018-06-08 Samet Oymak

Shallow supervised 1-hidden layer neural networks have a number of favorable properties that make them easier to interpret, analyze, and optimize than their deep counterparts, but lack their representational power. Here we use 1-hidden…

Machine Learning · Computer Science 2019-04-24 Eugene Belilovsky , Michael Eickenberg , Edouard Oyallon

Nowadays, deep learning can be employed to a wide ranges of fields including medicine, engineering, etc. In deep learning, Convolutional Neural Network (CNN) is extensively used in the pattern and sequence recognition, video analysis,…

Computer Vision and Pattern Recognition · Computer Science 2019-02-06 Rezoana Bente Arif , Md. Abu Bakr Siddique , Mohammad Mahmudur Rahman Khan , Mahjabin Rahman Oishe

In this paper, we study 1-bit convolutional neural networks (CNNs), of which both the weights and activations are binary. While efficient, the lacking of representational capability and the training difficulty impede 1-bit CNNs from…

Computer Vision and Pattern Recognition · Computer Science 2019-09-05 Zechun Liu , Wenhan Luo , Baoyuan Wu , Xin Yang , Wei Liu , Kwang-Ting Cheng

We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural networks. First, we emphatically show that it is unsurprising…

Numerical Analysis · Mathematics 2020-11-02 Austin R. Benson , Anil Damle , Alex Townsend

We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean…

Machine Learning · Computer Science 2016-11-01 Francis Bach

We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation, i.e., $f(\mathbf{Z}, \mathbf{w}, \mathbf{a}) = \sum_j a_j\sigma(\mathbf{w}^T\mathbf{Z}_j)$, in which both…

Machine Learning · Computer Science 2018-06-18 Simon S. Du , Jason D. Lee , Yuandong Tian , Barnabas Poczos , Aarti Singh

Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a…

Machine Learning · Computer Science 2020-06-26 Shuai Zhang , Meng Wang , Sijia Liu , Pin-Yu Chen , Jinjun Xiong