Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

/pdf/deep-residual-learning-for-image-recognition-b75jg61qrq.pdf

Deep Residual Learning for Image Recognition

In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth using an architecture with very small (3x3) convolution filters, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. These findings were the basis of our ImageNet Challenge 2014 submission, where our team secured the first and the second places in the localisation and classification tracks respectively. We also show that our representations generalise well to other datasets, where they achieve state-of-the-art results. We have made our two best-performing ConvNet models publicly available to facilitate further research on the use of deep visual representations in computer vision.

Very Deep Convolutional Networks for Large-Scale Image Recognition

Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. 
The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

/pdf/generative-adversarial-nets-1ofhan3sbf.pdf

Generative Adversarial Nets

Machine learning models are notoriously difficult to interpret and debug. This is particularly true of neural networks. In this work, we introduce automated software testing techniques for neural networks that are well-suited to discovering errors which occur only for rare inputs. Specifically, we develop coverage-guided fuzzing (CGF) methods for neural networks. In CGF, random mutations of inputs to a neural network are guided by a coverage metric toward the goal of satisfying user-specified constraints. We describe how fast approximate nearest neighbor algorithms can provide this coverage metric. We then discuss the application of CGF to the following goals: finding numerical errors in trained neural networks, generating disagreements between neural networks and quantized versions of those networks, and surfacing undesirable behavior in character level language models. Finally, we release an open source library called TensorFuzz that implements the described techniques.

TensorFuzz: Debugging Neural Networks with Coverage-Guided Fuzzing

Two recently introduced criteria for estimation of generative models are both based on a reduction to binary classification Noise-contrastive estimation (NCE) is an estimation procedure in which a generative model is trained to be able to distinguish data samples from noise samples Generative adversarial networks (GANs) are pairs of generator and discriminator networks, with the generator network learning to generate samples by attempting to fool the discriminator network into believing its samples are real data Both estimation procedures use the same function to drive learning, which naturally raises questions about how they are related to each other, as well as whether this function is related to maximum likelihood estimation (MLE) NCE corresponds to training an internal data model belonging to the {\em discriminator} network but using a fixed generator network We show that a variant of NCE, with a dynamic generator network, is equivalent to maximum likelihood estimation Since pairing a learned discriminator with an appropriate dynamically selected generator recovers MLE, one might expect the reverse to hold for pairing a learned generator with a certain discriminator However, we show that recovering MLE for a learned generator requires departing from the distinguishability game Specifically: 
(i) The expected gradient of the NCE discriminator can be made to match the expected gradient of 
MLE, if one is allowed to use a non-stationary noise distribution for NCE, 
(ii) No choice of discriminator network can make the expected gradient for the GAN generator match that of MLE, and 
(iii) The existing theory does not guarantee that GANs will converge in the non-convex case 
This suggests that the key next step in GAN research is to determine whether GANs converge, and if not, to modify their training algorithm to force convergence

On distinguishability criteria for estimating generative models

Semi-supervised learning (SSL) provides a powerful framework for leveraging unlabeled data when labels are limited or expensive to obtain. SSL algorithms based on deep neural networks have recently proven successful on standard benchmark tasks. However, we argue that these benchmarks fail to address many issues that these algorithms would face in real-world applications. After creating a unified reimplementation of various widely-used SSL techniques, we test them in a suite of experiments designed to address these issues. We find that the performance of simple baselines which do not use unlabeled data is often underreported, that SSL methods differ in sensitivity to the amount of labeled and unlabeled data, and that performance can degrade substantially when the unlabeled dataset contains out-of-class examples. To help guide SSL research towards real-world applicability, we make our unified reimplemention and evaluation platform publicly available.

Realistic Evaluation of Deep Semi-Supervised Learning Algorithms.

Adversarial training provides a means of regularizing supervised learning algorithms while virtual adversarial training is able to extend supervised learning algorithms to the semi-supervised setting. However, both methods require making small perturbations to numerous entries of the input vector, which is inappropriate for sparse high-dimensional inputs such as one-hot word representations. We extend adversarial and virtual adversarial training to the text domain by applying perturbations to the word embeddings in a recurrent neural network rather than to the original input itself. The proposed method achieves state of the art results on multiple benchmark semi-supervised and purely supervised tasks. We provide visualizations and analysis showing that the learned word embeddings have improved in quality and that while training, the model is less prone to overfitting.

Virtual Adversarial Training for Semi-Supervised Text Classification

We consider the problem of object recognition with a large number of classes. In order to overcome the low amount of labeled examples available in this setting, we introduce a new feature learning and extraction procedure based on a factor model we call spike-and-slab sparse coding (S3C). Prior work on S3C has not prioritized the ability to exploit parallel architectures and scale S3C to the enormous problem sizes needed for object recognition. We present a novel inference procedure for appropriate for use with GPUs which allows us to dramatically increase both the training set size and the amount of latent factors that S3C may be trained with. We demonstrate that this approach improves upon the supervised learning capabilities of both sparse coding and the spike-and-slab Restricted Boltzmann Machine (ssRBM) on the CIFAR-10 dataset. We use the CIFAR-100 dataset to demonstrate that our method scales to large numbers of classes better than previous methods. Finally, we use our method to win the NIPS 2011 Workshop on Challenges In Learning Hierarchical Models' Transfer Learning Challenge.

/pdf/large-scale-feature-learning-with-spike-and-slab-sparse-2tcub66i6h.pdf

Ian Goodfellow

Papers

TensorFuzz: Debugging Neural Networks with Coverage-Guided Fuzzing

On distinguishability criteria for estimating generative models

Realistic Evaluation of Deep Semi-Supervised Learning Algorithms.

Virtual Adversarial Training for Semi-Supervised Text Classification

Large-Scale Feature Learning With Spike-and-Slab Sparse Coding