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Register a new userInformation in Infinite Ensembles of Infinitely-Wide Neural Networks
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Added by
Alexander Alemi
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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In this preliminary work, we study the generalization properties of infinite ensembles of infinitely-wide neural networks. Amazingly, this model family admits tractable calculations for many information-theoretic quantities. We report analytical and empirical investigations in the search for signals that correlate with generalization.
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Splitting network computations between the edge device and a server enables low edge-compute inference of neural networks but might expose sensitive information about the test query to the server. To address this problem, existing techniques train the model to minimize information leakage for a given set of sensitive attributes. In practice, however, the test queries might contain attributes that are not foreseen during training. We propose instead an unsupervised obfuscation method to discard the information irrelevant to the main task. We formulate the problem via an information theoretical framework and derive an analytical solution for a given distortion to the model output. In our method, the edge device runs the model up to a split layer determined based on its computational capacity. It then obfuscates the obtained feature vector based on the first layer of the server model by removing the components in the null space as well as the low-energy components of the remaining signal. Our experimental results show that our method outperforms existing techniques in removing the information of the irrelevant attributes and maintaining the accuracy on the target label. We also show that our method reduces the communication cost and incurs only a small computational overhead.
We analyze the learning dynamics of infinitely wide neural networks with a finite sized bottle-neck. Unlike the neural tangent kernel limit, a bottleneck in an otherwise infinite width network al-lows data dependent feature learning in its bottle-neck representation. We empirically show that a single bottleneck in infinite networks dramatically accelerates training when compared to purely in-finite networks, with an improved overall performance. We discuss the acceleration phenomena by drawing similarities to infinitely wide deep linear models, where the acceleration effect of a bottleneck can be understood theoretically.
This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et al., 2012], we derive simple characterizations of the convex hulls of the corresponding atomic sets for this problem under several different constraints on the weights and biases of the network, thus obtaining equivalent convex formulations for these problems. A modest extension of our proposed framework to a binary classification problem is also presented. We explore the efficacy of the resulting formulations experimentally, and compare with networks trained via gradient descent.
We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural network-based techniques and widely used Poisson Surface Reconstruction (which, as we demonstrate, can also be viewed as a type of kernel method). Because our approach is based on a simple kernel formulation, it is easy to analyze and can be accelerated by general techniques designed for kernel-based learning. We provide explicit analytical expressions for our kernel and argue that our formulation can be seen as a generalization of cubic spline interpolation to higher dimensions. In particular, the RKHS norm associated with Neural Splines biases toward smooth interpolants.
Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this paper, we prove that implementing empirical risk minimization on DCNNs with expansive convolution (with zero-padding) is strongly universally consistent. Motivated by the universal consistency, we conduct a series of experiments to show that without any fully connected layers, DCNNs with expansive convolution perform not worse than the widely used deep neural networks with hybrid structure containing contracting (without zero-padding) convolution layers and several fully connected layers.
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