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.

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Deep Residual Learning for Image Recognition

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

Adam: A Method for Stochastic Optimization

We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overriding in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.

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ImageNet Classification with Deep Convolutional Neural Networks

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

This paper presents to integrate the auxiliary information (e.g., additional attributes for data such as the hashtags for Instagram images) in the self-supervised learning process. We first observe that the auxiliary information may bring us useful information about data structures: for instance, the Instagram images with the same hashtags can be semantically similar. Hence, to leverage the structural information from the auxiliary information, we present to construct data clusters according to the auxiliary information. Then, we introduce the Clustering InfoNCE (Cl-InfoNCE) objective that learns similar representations for augmented variants of data from the same cluster and dissimilar representations for data from different clusters. Our approach contributes as follows: 1) Comparing to conventional self-supervised representations, the auxiliary-information-infused self-supervised representations bring the performance closer to the supervised representations; 2) The presented Cl-InfoNCE can also work with unsupervised constructed clusters (e.g., k-means clusters) and outperform strong clustering-based self-supervised learning approaches, such as the Prototypical Contrastive Learning (PCL) method; 3) We show that Cl-InfoNCE may be a better approach to leverage the data clustering information, by comparing it to the baseline approach - learning to predict the clustering assignments with cross-entropy loss. For analysis, we connect the goodness of the learned representations with the statistical relationships: i) the mutual information between the labels and the clusters and ii) the conditional entropy of the clusters given the labels.

Integrating Auxiliary Information in Self-supervised Learning.

In many machine learning systems that jointly learn from multiple modalities, a core research question is to understand the nature of multimodal interactions: the emergence of new task-relevant information during learning from both modalities that was not present in either alone. We study this challenge of interaction quantification in a semi-supervised setting with only labeled unimodal data and naturally co-occurring multimodal data (e.g., unlabeled images and captions, video and corresponding audio) but when labeling them is time-consuming. Using a precise information-theoretic definition of interactions, our key contributions are the derivations of lower and upper bounds to quantify the amount of multimodal interactions in this semi-supervised setting. We propose two lower bounds based on the amount of shared information between modalities and the disagreement between separately trained unimodal classifiers, and derive an upper bound through connections to approximate algorithms for min-entropy couplings. We validate these estimated bounds and show how they accurately track true interactions. Finally, two semi-supervised multimodal applications are explored based on these theoretical results: (1) analyzing the relationship between multimodal performance and estimated interactions, and (2) self-supervised learning that embraces disagreement between modalities beyond agreement as is typically done.

Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications

While there are many real-world problems that might benefit from reinforcement learning, these problems rarely fit into the MDP mold: interacting with the environment is often prohibitively expensive and specifying reward functions is challenging. Motivated by these challenges, prior work has developed data-driven approaches that learn entirely from samples from the transition dynamics and examples of high-return states. These methods typically learn a reward function from the high-return states, use that reward function to label the transitions, and then apply an offline RL algorithm to these transitions. While these methods can achieve good results on many tasks, they can be complex, carefully regularizing the reward function and using temporal difference updates. In this paper, we propose a simple and scalable approach to offline example-based control. Unlike prior approaches (e.g., ORIL, VICE, PURL) that learn a reward function, our method will learn an implicit model of multi-step transitions. We show that this implicit model can represent the Q-values for the example-based control problem. Thus, whereas a learned reward function must be combined with an RL algorithm to determine good actions, our model can directly be used to determine these good actions. Across a range of state-based and image-based offline control tasks, we find that our method outperforms baselines that use learned reward functions, and additional experiments demonstrate improved robustness and scaling with dataset size.

Contrastive Example-Based Control

Adversarial robustness has emerged as a desirable property for neural networks. Prior work shows that robust networks perform well in some out-of-distribution generalization tasks, such as transfer learning and outlier detection. We uncover a different kind of out-of-distribution generalization property of such networks, and find that they also do well in a task that we call nearest category generalization (NCG) - given an out-of-distribution input, they tend to predict the same label as that of the closest training example. We empirically show that this happens even when the out-of-distribution inputs lie outside the robustness radius of the training data, which suggests that these networks may generalize better along unseen directions on the natural image manifold than arbitrary unseen directions. We examine how performance changes when we change the robustness regions during training. We then design experiments to investigate the connection between out-of-distribution detection and nearest category generalization. Taken together, our work provides evidence that robust neural networks may resemble nearest neighbor classifiers in their behavior on out-of-distribution data. The code is available at this https URL

Robustness and Generalization to Nearest Categories

How can a reinforcement learning (RL) agent prepare to solve downstream tasks if those tasks are not known a priori? One approach is unsupervised skill discovery, a class of algorithms that learn a set of policies without access to a reward function. Such algorithms bear a close resemblance to representation learning algorithms (e.g., contrastive learning) in supervised learning, in that both are pretraining algorithms that maximize some approximation to a mutual information objective. While prior work has shown that the set of skills learned by such methods can accelerate downstream RL tasks, prior work offers little analysis into whether these skill learning algorithms are optimal, or even what notion of optimality would be appropriate to apply to them. In this work, we show that unsupervised skill discovery algorithms based on mutual information maximization do not learn skills that are optimal for every possible reward function. However, we show that the distribution over skills provides an optimal initialization minimizing regret against adversarially-chosen reward functions, assuming a certain type of adaptation procedure. Our analysis also provides a geometric perspective on these skill learning methods.

Ruslan Salakhutdinov

Papers

Integrating Auxiliary Information in Self-supervised Learning.

Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications

Contrastive Example-Based Control

Robustness and Generalization to Nearest Categories

The Information Geometry of Unsupervised Reinforcement Learning