Geoffrey E. Hinton

Bio: Geoffrey E. Hinton is an academic researcher from Google. The author has contributed to research in topics: Artificial neural network & Generative model. The author has an hindex of 157, co-authored 414 publications receiving 409047 citations. Previous affiliations of Geoffrey E. Hinton include Canadian Institute for Advanced Research & Max Planck Society.

A Better Way to Pre-Train Deep Boltzmann Machines

Abstract: We describe how the pretraining algorithm for Deep Boltzmann Machines (DBMs) is related to the pretraining algorithm for Deep Belief Networks and we show that under certain conditions, the pretraining procedure improves the variational lower bound of a two-hidden-layer DBM. Based on this analysis, we develop a different method of pretraining DBMs that distributes the modelling work more evenly over the hidden layers. Our results on the MNIST and NORB datasets demonstrate that the new pretraining algorithm allows us to learn better generative models.

Hand-printed digit recognition using deformable models

Abstract: Deformable models are an attractive way for characterizing handwritten digits since they have relatively few parameters, are able to capture many topological variations, and incorporate much prior knowledge. We have described a system [8] that uses learned digit models consisting of splines whose shape is governed by a small number of control points. Images can be classi ed by separately tting each digit model to the image, and using a simple neural network to decide which model ts best. We use an elastic matching algorithm to minimize an energy function that includes both the deformation energy of the digit model and the log probability that the model would generate the inked pixels in the image. The use of multiple models for each digit can characterize the population of handwritten digits better. We show how multiple models may be used without increasing the time required for elastic matching.

Products of Hidden Markov Models: It Takes N>1 to Tango

Abstract: Products of Hidden Markov Models(PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This maybe in part due to their more computationally expensive gradient-based learning algorithm,and the intractability of computing the log likelihood of sequences under the model. In this paper, we demonstrate how the partition function can be estimated reliably via Annealed Importance Sampling. We perform experiments using contrastive divergence learning on rainfall data and data captured from pairs of people dancing. Our results suggest that advances in learning and evaluation for undirected graphical models and recent increases in available computing power make PoHMMs worth considering for complex time-series modeling tasks.

Subclass Distillation

Abstract: After a large "teacher" neural network has been trained on labeled data, the probabilities that the teacher assigns to incorrect classes reveal a lot of information about the way in which the teacher generalizes. By training a small "student" model to match these probabilities, it is possible to transfer most of the generalization ability of the teacher to the student, often producing a much better small model than directly training the student on the training data. The transfer works best when there are many possible classes because more is then revealed about the function learned by the teacher, but in cases where there are only a few possible classes we show that we can improve the transfer by forcing the teacher to divide each class into many subclasses that it invents during the supervised training. The student is then trained to match the subclass probabilities. For datasets where there are known, natural subclasses we demonstrate that the teacher learns similar subclasses and these improve distillation. For clickthrough datasets where the subclasses are unknown we demonstrate that subclass distillation allows the student to learn faster and better.

Parallelizing neural networks during training

Abstract: A parallel convolutional neural network is provided. The CNN is implemented by a plurality of convolutional neural networks each on a respective processing node. Each CNN has a plurality of layers. A subset of the layers are interconnected between processing nodes such that activations are fed forward across nodes. The remaining subset is not so interconnected.

Deep Residual Learning for Image Recognition

Abstract: 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.

Adam: A Method for Stochastic Optimization

Abstract: 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.

ImageNet Classification with Deep Convolutional Neural Networks

Abstract: 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.

Long short-term memory

Abstract: Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O. 1. Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.

Very Deep Convolutional Networks for Large-Scale Image Recognition

Abstract: 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.