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

We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

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Going deeper with convolutions

Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models However, measuring disentanglement has been challenging and inconsistent, often dependent on an ad-hoc external model or specific to a certain dataset To address this, we present a method for quantifying disentanglement that only uses the generative model, by measuring the topological similarity of conditional submanifolds in the learned representation This method showcases both unsupervised and supervised variants To illustrate the effectiveness and applicability of our method, we empirically evaluate several state-of-the-art models across multiple datasets We find that our method ranks models similarly to existing methods We make our code publicly available at https://githubcom/stanfordmlgroup/disentanglement

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Evaluating the Disentanglement of Deep Generative Models through Manifold Topology

Many control problems, such as autonomous helicopter flight, legged robot locomotion, and autonomous driving are difficult because (i) It is hard to write down, in closed form, a formal specification of the control task (for example, what is the cost function for ”driving well”?), (ii) It is difficult to learn good models of the robot's dynamics, and (iii) It is expensive to find closed-loop controllers for high dimensional, highly stochastic domains. Using apprenticeship learning—in which we learn from a human demonstration of a task—as a unifying theme, I will present formal results showing how many control problems can be efficiently addressed given access to a demonstration. In presenting these ideas, I will also draw from a number of case studies, including applications in autonomous helicopter flight, quadruped obstacle negotiation, snake robot locomotion, and high-speed off-road navigation.

Finally, I will also describe the application of these ideas to the STAIR (STanford AI Robot) project, which has the long term goal of integrating methods from all major areas of AI—including spoken dialog/NLP, manipulation, vision, navigation, and planning—to build a general-purpose, “intelligent” home/office robotic assistant.

Reinforcement learning and apprenticeship learning for robotic control

Data augmentation has led to substantial improvements in the performance and generalization of deep models, and remain a highly adaptable method to evolving model architectures and varying amounts of data---in particular, extremely scarce amounts of available training data. In this paper, we present a novel method of applying Mobius transformations to augment input images during training. Mobius transformations are bijective conformal maps that generalize image translation to operate over complex inversion in pixel space. As a result, Mobius transformations can operate on the sample level and preserve data labels. We show that the inclusion of Mobius transformations during training enables improved generalization over prior sample-level data augmentation techniques such as cutout and standard crop-and-flip transformations, most notably in low data regimes.

Data augmentation with Mobius transformations

Similarity measures for text have historically been an important tool for solving information retrieval problems. In this paper we consider extended similarity metrics for documents and other objects embedded in graphs, facilitated via a lazy graph walk. We provide a detailed instantiation of this framework for email data, where content, social networks and a timeline are integrated in a structural graph. The suggested framework is evaluated for the task of disambiguating names in email documents. We show that reranking schemes based on the graph-walk similarity measures often outperform base-line methods, and that further improvements can be obtained by use of appropriate learning methods.

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A Graphical Framework for Contextual Search and Name Disambiguation in Email

While emerging deep-learning systems have outclassed knowledge-based approaches in many tasks, their application to detection tasks for autonomous technologies remains an open field for scientific exploration. Broadly, there are two major developmental bottlenecks: the unavailability of comprehensively labeled datasets and of expressive evaluation strategies. Approaches for labeling datasets have relied on intensive hand-engineering, and strategies for evaluating learning systems have been unable to identify failure-case scenarios. Human intelligence offers an untapped approach for breaking through these bottlenecks. This paper introduces Driverseat, a technology for embedding crowds around learning systems for autonomous driving. Driverseat utilizes crowd contributions for (a) collecting complex 3D labels and (b) tagging diverse scenarios for ready evaluation of learning systems. We demonstrate how Driverseat can crowdstrap a convolutional neural network on the lane-detection task. More generally, crowdstrapping introduces a valuable paradigm for any technology that can benefit from leveraging the powerful combination of human and computer intelligence.

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Andrew Y. Ng

Papers

Evaluating the Disentanglement of Deep Generative Models through Manifold Topology

Reinforcement learning and apprenticeship learning for robotic control

Data augmentation with Mobius transformations

A Graphical Framework for Contextual Search and Name Disambiguation in Email

Driverseat: Crowdstrapping Learning Tasks for Autonomous Driving.