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

Self-supervised contrastive learning approaches leverage modality-specific context or invariances to pretrain models using unlabeled data. While contrastive learning has demonstrated promising on results in the image domain, there has been limited work on determining how to exploit modality-specific invariances in biosignals such as the electrocardiogram. In this work, we propose 3KG, a method to generate positive pairs for contrastive learning using physiologically-inspired 3D augmentations of the 12-lead electrocardiogram. We evaluate representation quality by fine-tuning a linear layer for the downstream task of 24-class diagnosis on the PhysioNet 2020 challenge training data, and find that models trained with physiologically-inspired augmentations both outperform and complement standard time-series augmentations. Our best performing strategy, which incorporates spatial rotation, spatial scaling, and time masking, achieves a performance increase of 0.16, .086, and .046 in mean AUROC over a randomly initialized baseline at 1%, 10%, and 100% label fractions respectively. Additionally, we show that the strength of spatial augmentations does not significantly affect the quality of the learned representations. Finally, we investigate the clinical relevance of how physiologically-inspired augmentations affect the performance of our classifier on different disease subgroupings. As expert annotations are often expensive and scarce for medical contexts, our approach highlights the potential of machine learning to tackle medical problems with large quantities of unlabeled biosignal data by exploiting their unique biological properties.

Andrew Y. Ng

Papers

3KG: Contrastive Learning of 12-Lead Electrocardiograms using Physiologically-Inspired Augmentations.