The simple, elegant approach of training convolutional neural networks (CNNs) directly from RGB pixels has enjoyed overwhelming empirical success. But could more performance be squeezed out of networks by using different input representations? In this paper we propose and explore a simple idea: train CNNs directly on the blockwise discrete cosine transform (DCT) coefficients computed and available in the middle of the JPEG codec. Intuitively, when processing JPEG images using CNNs, it seems unnecessary to decompress a blockwise frequency representation to an expanded pixel representation, shuffle it from CPU to GPU, and then process it with a CNN that will learn something similar to a transform back to frequency representation in its first layers. Why not skip both steps and feed the frequency domain into the network directly? In this paper, we modify libjpeg to produce DCT coefficients directly, modify a ResNet-50 network to accommodate the differently sized and strided input, and evaluate performance on ImageNet. We find networks that are both faster and more accurate, as well as networks with about the same accuracy but 1.77x faster than ResNet-50.

Few ideas have enjoyed as large an impact on deep learning as convolution. For any problem involving pixels or spatial representations, common intuition holds that convolutional neural networks may be appropriate. In this paper we show a striking counterexample to this intuition via the seemingly trivial coordinate transform problem, which simply requires learning a mapping between coordinates in (x,y) Cartesian space and coordinates in one-hot pixel space. Although convolutional networks would seem appropriate for this task, we show that they fail spectacularly. We demonstrate and carefully analyze the failure first on a toy problem, at which point a simple fix becomes obvious. We call this solution CoordConv, which works by giving convolution access to its own input coordinates through the use of extra coordinate channels. Without sacrificing the computational and parametric efficiency of ordinary convolution, CoordConv allows networks to learn either complete translation invariance or varying degrees of translation dependence, as required by the end task. CoordConv solves the coordinate transform problem with perfect generalization and 150 times faster with 10--100 times fewer parameters than convolution. This stark contrast raises the question: to what extent has this inability of convolution persisted insidiously inside other tasks, subtly hampering performance from within? A complete answer to this question will require further investigation, but we show preliminary evidence that swapping convolution for CoordConv can improve models on a diverse set of tasks. Using CoordConv in a GAN produced less mode collapse as the transform between high-level spatial latents and pixels becomes easier to learn. A Faster R-CNN detection model trained on MNIST detection showed 24% better IOU when using CoordConv, and in the Reinforcement Learning (RL) domain agents playing Atari games benefit significantly from the use of CoordConv layers.

The simple, elegant approach of training convolutional neural networks (CNNs) directly from RGB pixels has enjoyed overwhelming empirical success. But could more performance be squeezed out of networks by using different input representations? In this paper we propose and explore a simple idea: train CNNs directly on the blockwise discrete cosine transform (DCT) coefficients computed and available in the middle of the JPEG codec. Intuitively, when processing JPEG images using CNNs, it seems unnecessary to decompress a blockwise frequency representation to an expanded pixel representation, shuffle it from CPU to GPU, and then process it with a CNN that will learn something similar to a transform back to frequency representation in its first layers. Why not skip both steps and feed the frequency domain into the network directly? In this paper, we modify libjpeg to produce DCT coefficients directly, modify a ResNet-50 network to accommodate the differently sized and strided input, and evaluate performance on ImageNet. We find networks that are both faster and more accurate, as well as networks with about the same accuracy but 1.77x faster than ResNet-50.

We introduce the Metropolis-Hastings generative adversarial network (MH-GAN), which combines aspects of Markov chain Monte Carlo and GANs. The MH-GAN draws samples from the distribution implicitly defined by a GAN's discriminator-generator pair, as opposed to sampling in a standard GAN which draws samples from the distribution defined by the generator. It uses the discriminator from GAN training to build a wrapper around the generator for improved sampling. With a perfect discriminator, this wrapped generator samples from the true distribution on the data exactly even when the generator is imperfect. We demonstrate the benefits of the improved generator on multiple benchmark datasets, including CIFAR-10 and CelebA, using DCGAN and WGAN.

Few ideas have enjoyed as large an impact on deep learning as convolution. For any problem involving pixels or spatial representations, common intuition holds that convolutional neural networks may be appropriate. In this paper we show a striking counterexample to this intuition via the seemingly trivial coordinate transform problem, which simply requires learning a mapping between coordinates in (x,y) Cartesian space and one-hot pixel space. Although convolutional networks would seem appropriate for this task, we show that they fail spectacularly. We demonstrate and carefully analyze the failure first on a toy problem, at which point a simple fix becomes obvious. We call this solution CoordConv, which works by giving convolution access to its own input coordinates through the use of extra coordinate channels. Without sacrificing the computational and parametric efficiency of ordinary convolution, CoordConv allows networks to learn either perfect translation invariance or varying degrees of translation dependence, as required by the task. CoordConv solves the coordinate transform problem with perfect generalization and 150 times faster with 10--100 times fewer parameters than convolution. This stark contrast raises the question: to what extent has this inability of convolution persisted insidiously inside other tasks, subtly hampering performance from within? A complete answer to this question will require further investigation, but we show preliminary evidence that swapping convolution for CoordConv can improve models on a diverse set of tasks. Using CoordConv in a GAN produced less mode collapse as the transform between high-level spatial latents and pixels becomes easier to learn. A Faster R-CNN detection model trained on MNIST detection showed 24% better IOU when using CoordConv, and in the RL domain agents playing Atari games benefit significantly from the use of CoordConv layers.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less.

This is the Proceedings of NIPS 2017 Symposium on Interpretable Machine Learning, held in Long Beach, California, USA on December 7, 2017

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less. Code: https://github.com/google/svcca/

Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic science that is interesting in its own right---similar to why we study the human brain---and will enable researchers to further improve DNNs. One path to understanding how a neural network functions internally is to study what each of its neurons has learned to detect. One such method is called activation maximization, which synthesizes an input (e.g. an image) that highly activates a neuron. Here we dramatically improve the qualitative state of the art of activation maximization by harnessing a powerful, learned prior: a deep generator network. The algorithm (1) generates qualitatively state-of-the-art synthetic images that look almost real, (2) reveals the features learned by each neuron in an interpretable way, (3) generalizes well to new datasets and somewhat well to different network architectures without requiring the prior to be relearned, and (4) can be considered as a high-quality generative method (in this case, by generating novel, creative, interesting, recognizable images).