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We introduce repriorisation, a data-dependent reparameterisation which transforms a Bayesian neural network (BNN) posterior to a distribution whose KL divergence to the BNN prior vanishes as layer widths grow. The repriorisation map acts directly on parameters, and its analytic simplicity complements the known neural network Gaussian process (NNGP) behaviour of wide BNNs in function space. Exploiting the repriorisation, we develop a Markov chain Monte Carlo (MCMC) posterior sampling algorithm which mixes faster the wider the BNN. This contrasts with the typically poor performance of MCMC in high dimensions. We observe up to 50x higher effective sample size relative to no reparametrisation for both fully-connected and residual networks. Improvements are achieved at all widths, with the margin between reparametrised and standard BNNs growing with layer width., Comment: ICML 2022

There is a previously identified equivalence between wide fully connected neural networks (FCNs) and Gaussian processes (GPs). This equivalence enables, for instance, test set predictions that would have resulted from a fully Bayesian, infinitely wide trained FCN to be computed without ever instantiating the FCN, but by instead evaluating the corresponding GP. In this work, we derive an analogous equivalence for multi-layer convolutional neural networks (CNNs) both with and without pooling layers, and achieve state of the art results on CIFAR10 for GPs without trainable kernels. We also introduce a Monte Carlo method to estimate the GP corresponding to a given neural network architecture, even in cases where the analytic form has too many terms to be computationally feasible. Surprisingly, in the absence of pooling layers, the GPs corresponding to CNNs with and without weight sharing are identical. As a consequence, translation equivariance, beneficial in finite channel CNNs trained with stochastic gradient descent (SGD), is guaranteed to play no role in the Bayesian treatment of the infinite channel limit - a qualitative difference between the two regimes that is not present in the FCN case. We confirm experimentally, that while in some scenarios the performance of SGD-trained finite CNNs approaches that of the corresponding GPs as the channel count increases, with careful tuning SGD-trained CNNs can significantly outperform their corresponding GPs, suggesting advantages from SGD training compared to fully Bayesian parameter estimation., Comment: Published as a conference paper at ICLR 2019

We explore the method of style transfer presented in the article "A Neural Algorithm of Artistic Style" by Leon A. Gatys, Alexander S. Ecker and Matthias Bethge (arXiv:1508.06576). We first demonstrate the power of the suggested style space on a few examples. We then vary different hyper-parameters and program properties that were not discussed in the original paper, among which are the recognition network used, starting point of the gradient descent and different ways to partition style and content layers. We also give a brief comparison of some of the existing algorithm implementations and deep learning frameworks used. To study the style space further we attempt to generate synthetic images by maximizing a single entry in one of the Gram matrices $\mathcal{G}_l$ and some interesting results are observed. Next, we try to mimic the sparsity and intensity distribution of Gram matrices obtained from a real painting and generate more complex textures. Finally, we propose two new style representations built on top of network's features and discuss how one could be used to achieve local and potentially content-aware style transfer., Comment: A short class project report (14 pages, 14 figures)