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 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

The explosion of image data on the Internet has the potential to foster more sophisticated and robust models and algorithms to index, retrieve, organize and interact with images and multimedia data. But exactly how such data can be harnessed and organized remains a critical problem. We introduce here a new database called “ImageNet”, a large-scale ontology of images built upon the backbone of the WordNet structure. ImageNet aims to populate the majority of the 80,000 synsets of WordNet with an average of 500-1000 clean and full resolution images. This will result in tens of millions of annotated images organized by the semantic hierarchy of WordNet. This paper offers a detailed analysis of ImageNet in its current state: 12 subtrees with 5247 synsets and 3.2 million images in total. We show that ImageNet is much larger in scale and diversity and much more accurate than the current image datasets. Constructing such a large-scale database is a challenging task. We describe the data collection scheme with Amazon Mechanical Turk. Lastly, we illustrate the usefulness of ImageNet through three simple applications in object recognition, image classification and automatic object clustering. We hope that the scale, accuracy, diversity and hierarchical structure of ImageNet can offer unparalleled opportunities to researchers in the computer vision community and beyond.

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ImageNet: A large-scale hierarchical image database

State-of-the-art methods for video action recognition commonly use an ensemble of two networks: the spatial stream, which takes RGB frames as input, and the temporal stream, which takes optical flow as input. In recent work, both of these streams consist of 3D Convolutional Neural Networks, which apply spatiotemporal filters to the video clip before performing classification. Conceptually, the temporal filters should allow the spatial stream to learn motion representations, making the temporal stream redundant. However, we still see significant benefits in action recognition performance by including an entirely separate temporal stream, indicating that the spatial stream is "missing" some of the signal captured by the temporal stream. In this work, we first investigate whether motion representations are indeed missing in the spatial stream of 3D CNNs. Second, we demonstrate that these motion representations can be improved by distillation, by tuning the spatial stream to predict the outputs of the temporal stream, effectively combining both models into a single stream. Finally, we show that our Distilled 3D Network (D3D) achieves performance on par with two-stream approaches, using only a single model and with no need to compute optical flow.

D3D: Distilled 3D Networks for Video Action Recognition

We propose DeepV2D, an end-to-end deep learning architecture for predicting depth from video. DeepV2D combines the representation ability of neural networks with the geometric principles governing image formation. We compose a collection of classical geometric algorithms, which are converted into trainable modules and combined into an end-to-end differentiable architecture. DeepV2D interleaves two stages: motion estimation and depth estimation. During inference, motion and depth estimation are alternated and converge to accurate depth.

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DeepV2D: Video to Depth with Differentiable Structure from Motion

We address the problem of scene flow: given a pair of stereo or RGB-D video frames, estimate pixelwise 3D motion. We introduce RAFT-3D, a new deep architecture for scene flow. RAFT-3D is based on the RAFT model developed for optical flow but iteratively updates a dense field of pixelwise SE3 motion instead of 2D motion. A key innovation of RAFT-3D is rigid-motion embeddings, which represent a soft grouping of pixels into rigid objects. Integral to rigid-motion embeddings is Dense-SE3, a differentiable layer that enforces geometric consistency of the embeddings. Experiments show that RAFT-3D achieves state-of-the-art performance. On FlyingThings3D, under the two-view evaluation, we improved the best published accuracy (d < 0.05) from 34.3% to 83.7%. On KITTI, we achieve an error of 5.77, outperforming the best published method (6.31), despite using no object instance supervision. Code is available at this https URL.

RAFT-3D: Scene Flow using Rigid-Motion Embeddings.

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at this https URL.

Learning to Prove Theorems via Interacting with Proof Assistants

We study the problem of single-image depth estimation for images in the wild. We collect human annotated surface normals and use them to help train a neural network that directly predicts pixel-wise depth. We propose two novel loss functions for training with surface normal annotations. Experiments on NYU Depth, KITTI, and our own dataset demonstrate that our approach can significantly improve the quality of depth estimation in the wild.

Jia Deng

Papers

D3D: Distilled 3D Networks for Video Action Recognition

DeepV2D: Video to Depth with Differentiable Structure from Motion

RAFT-3D: Scene Flow using Rigid-Motion Embeddings.

Learning to Prove Theorems via Interacting with Proof Assistants

Surface Normals in the Wild