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.

/pdf/imagenet-classification-with-deep-convolutional-neural-1190x9a6b9.pdf

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.

/pdf/going-deeper-with-convolutions-1yobw2o2ds.pdf

Going deeper with convolutions

Transfer learning enables prediction of myocardial injury from continuous single-lead electrocardiography

Approximate Dynamic Programming

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

Reducing methane emissions is essential for mitigating global warming. To attribute methane emissions to their sources, a comprehensive dataset of methane source infrastructure is necessary. Recent advancements with deep learning on remotely sensed imagery have the potential to identify the locations and characteristics of methane sources, but there is a substantial lack of publicly available data to enable machine learning researchers and practitioners to build automated mapping approaches. To help fill this gap, we construct a multi-sensor dataset called METER-ML containing 86,599 georeferenced NAIP, Sentinel-1, and Sentinel-2 images in the U.S. labeled for the presence or absence of methane source facilities including concentrated animal feeding operations, coal mines, landfills, natural gas processing plants, oil refineries and petroleum terminals, and wastewater treatment plants. We experiment with a variety of models that leverage different spatial resolutions, spatial footprints, image products, and spectral bands. We find that our best model achieves an area under the precision recall curve of 0.915 for identifying concentrated animal feeding operations and 0.821 for oil refineries and petroleum terminals on an expert-labeled test set, suggesting the potential for large-scale mapping. We make METER-ML freely available at https://stanfordmlgroup.github.io/projects/meter-ml/ to support future work on automated methane source mapping.

METER-ML: A Multi-Sensor Earth Observation Benchmark for Automated Methane Source Mapping

We propose a selective learning method using meta-learning and deep reinforcement learning for medical image interpretation in the setting of limited labeling resources. Our method, MedSelect, consists of a trainable deep learning selector that uses image embeddings obtained from contrastive pretraining for determining which images to label, and a non-parametric selector that uses cosine similarity to classify unseen images. We demonstrate that MedSelect learns an effective selection strategy outperforming baseline selection strategies across seen and unseen medical conditions for chest X-ray interpretation. We also perform an analysis of the selections performed by MedSelect comparing the distribution of latent embeddings and clinical features, and find significant differences compared to the strongest performing baseline. We believe that our method may be broadly applicable across medical imaging settings where labels are expensive to acquire.

Andrew Y. Ng

Papers

Transfer learning enables prediction of myocardial injury from continuous single-lead electrocardiography

Approximate Dynamic Programming

Reinforcement learning and apprenticeship learning for robotic control

METER-ML: A Multi-Sensor Earth Observation Benchmark for Automated Methane Source Mapping

MedSelect: Selective Labeling for Medical Image Classification Combining Meta-Learning with Deep Reinforcement Learning