Yoshua Bengio

Bio: Yoshua Bengio is an academic researcher from Université de Montréal. The author has contributed to research in topics: Artificial neural network & Deep learning. The author has an hindex of 202, co-authored 1033 publications receiving 420313 citations. Previous affiliations of Yoshua Bengio include McGill University & Centre de Recherches Mathématiques.

Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net

Abstract: We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameterized energy function. The energy function is then modified so the model and data distributions match, with no guarantee on the number of steps required for the Markov chain to converge. Moreover, the detailed balance condition is highly restrictive: energy based models corresponding to neural networks must have symmetric weights, unlike biological neural circuits. In contrast, we develop a method for directly learning arbitrarily parameterized transition operators capable of expressing non-equilibrium stationary distributions that violate detailed balance, thereby enabling us to learn more biologically plausible asymmetric neural networks and more general non-energy based dynamical systems. The proposed training objective, which we derive via principled variational methods, encourages the transition operator to "walk back" in multi-step trajectories that start at data-points, as quickly as possible back to the original data points. We present a series of experimental results illustrating the soundness of the proposed approach, Variational Walkback (VW), on the MNIST, CIFAR-10, SVHN and CelebA datasets, demonstrating superior samples compared to earlier attempts to learn a transition operator. We also show that although each rapid training trajectory is limited to a finite but variable number of steps, our transition operator continues to generate good samples well past the length of such trajectories, thereby demonstrating the match of its non-equilibrium stationary distribution to the data distribution. Source Code: this http URL

Gradient Based Optimization of Hyper Parameters

Abstract: Many machine learning algorithms can be formulated as the minimiza tion of a training criterion which involves a hyper parameter This hyper parameter is usually chosen by trial and error with a model selection cri terion In this paper we present a methodology to optimize several hyper parameters based on the computation of the gradient of a model selection criterion with respect to the hyper parameters In the case of a quadratic training criterion the gradient of the selection criterion with respect to the hyper parameters is e ciently computed by back propagating through a Cholesky decomposition In the more general case we show that the implicit function theorem can be used to derive a formula for the hyper parameter gradient involving second derivatives of the training criterion

Problems in the deployment of machine-learned models in health care.

Abstract: [See related articles at www.cmaj.ca/lookup/doi/10.1503/cmaj.202434][1] and [www.cmaj.ca/lookup/doi/10.1503/cmaj.210036][2] KEY POINTS In a companion article, Verma and colleagues discuss how machine-learned solutions can be developed and implemented to support medical decision-making.[1][3] Both

On the challenge of learning complex functions.

Abstract: A common goal of computational neuroscience and of artificial intelligence research based on statistical learning algorithms is the discovery and understanding of computational principles that could explain what we consider adaptive intelligence, in animals as well as in machines. This chapter focuses on what is required for the learning of complex behaviors. We believe it involves the learning of highly varying functions, in a mathematical sense. We bring forward two types of arguments which convey the message that many currently popular machine learning approaches to learning flexible functions have fundamental limitations that render them inappropriate for learning highly varying functions. The first issue concerns the representation of such functions with what we call shallow model architectures. We discuss limitations of shallow architectures, such as so-called kernel machines, boosting algorithms, and one-hidden-layer artificial neural networks. The second issue is more focused and concerns kernel machines with a local kernel (the type used most often in practice) that act like a collection of template-matching units. We present mathematical results on such computational architectures showing that they have a limitation similar to those already proved for older non-parametric methods, and connected to the so-called curse of dimensionality. Though it has long been believed that efficient learning in deep architectures is difficult, recently proposed computational principles for learning in deep architectures may offer a breakthrough.

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.

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.

Deep learning

Abstract: Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.

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---8x deeper than VGG nets 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 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.