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Yann LeCun

Publications and source records attributed to Yann LeCun.

228 records · Page 13Linked to original sources
arXiv2013

Pushing Stochastic Gradient towards Second-Order Methods -- Backpropagation Learning with Transformations in Nonlinearities

Recently, we proposed to transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model the linear dependencies instead. We continue the work by firstly introducing a third transformation to normalize the scale of the outputs of each hidden neuron, and secondly by analyzing the connections to second order optimization methods. We show that the transformations make a simple stochastic gradient behave closer to second-order optimization methods and thus speed up learning. This is shown both in theory and with experiments. The experiments on the third transformation show that while it further increases the speed of learning, it can also hurt performance by converging to a worse local optimum, where both the inputs and outputs of many hidden neurons are close to zero.

cs.LG↗
arXiv2013

No More Pesky Learning Rates

The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any one time. The method relies on local gradient variations across samples. In our approach, learning rates can increase as well as decrease, making it suitable for non-stationary problems. Using a number of convex and non-convex learning tasks, we show that the resulting algorithm matches the performance of SGD or other adaptive approaches with their best settings obtained through systematic search, and effectively removes the need for learning rate tuning.

stat.ML↗
arXiv2013

Learning Stable Group Invariant Representations with Convolutional Networks

Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing mathematical properties, where convolutions, together with pooling operators, bring stability to additive and geometric perturbations of the input. Whereas physical transformation groups are ubiquitous in image and audio applications, they do not account for all the variability of complex signal classes. We show that the invariance properties built by deep convolutional networks can be cast as a form of stable group invariance. The network wiring architecture determines the invariance group, while the trainable filter coefficients characterize the group action. We give explanatory examples which illustrate how the network architecture controls the resulting invariance group. We also explore the principle by which additional convolutional layers induce a group factorization enabling more abstract, powerful invariant representations.

cs.AI↗
arXiv2013

Causal graph-based video segmentation

Numerous approaches in image processing and computer vision are making use of super-pixels as a pre-processing step. Among the different methods producing such over-segmentation of an image, the graph-based approach of Felzenszwalb and Huttenlocher is broadly employed. One of its interesting properties is that the regions are computed in a greedy manner in quasi-linear time. The algorithm may be trivially extended to video segmentation by considering a video as a 3D volume, however, this can not be the case for causal segmentation, when subsequent frames are unknown. We propose an efficient video segmentation approach that computes temporally consistent pixels in a causal manner, filling the need for causal and real time applications.

cs.CV↗
arXiv2012

Scene Parsing with Multiscale Feature Learning, Purity Trees, and Optimal Covers

Scene parsing, or semantic segmentation, consists in labeling each pixel in an image with the category of the object it belongs to. It is a challenging task that involves the simultaneous detection, segmentation and recognition of all the objects in the image. The scene parsing method proposed here starts by computing a tree of segments from a graph of pixel dissimilarities. Simultaneously, a set of dense feature vectors is computed which encodes regions of multiple sizes centered on each pixel. The feature extractor is a multiscale convolutional network trained from raw pixels. The feature vectors associated with the segments covered by each node in the tree are aggregated and fed to a classifier which produces an estimate of the distribution of object categories contained in the segment. A subset of tree nodes that cover the image are then selected so as to maximize the average "purity" of the class distributions, hence maximizing the overall likelihood that each segment will contain a single object. The convolutional network feature extractor is trained end-to-end from raw pixels, alleviating the need for engineered features. After training, the system is parameter free. The system yields record accuracies on the Stanford Background Dataset (8 classes), the Sift Flow Dataset (33 classes) and the Barcelona Dataset (170 classes) while being an order of magnitude faster than competing approaches, producing a 320 \times 240 image labeling in less than 1 second.

cs.CV↗
arXiv2012

Convolutional Neural Networks Applied to House Numbers Digit Classification

We classify digits of real-world house numbers using convolutional neural networks (ConvNets). ConvNets are hierarchical feature learning neural networks whose structure is biologically inspired. Unlike many popular vision approaches that are hand-designed, ConvNets can automatically learn a unique set of features optimized for a given task. We augmented the traditional ConvNet architecture by learning multi-stage features and by using Lp pooling and establish a new state-of-the-art of 94.85% accuracy on the SVHN dataset (45.2% error improvement). Furthermore, we analyze the benefits of different pooling methods and multi-stage features in ConvNets. The source code and a tutorial are available at eblearn.sf.net.

cs.CV↗
arXiv2012

Fast approximations to structured sparse coding and applications to object classification

We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We store a lookup table with the assignments and the pseudoinverses for each node, allowing for very fast inference. We give an algorithm for learning the tree, the dictionary and the dictionary element assignment, and In the process of describing this algorithm, we discuss the more general problem of learning the groups in group structured sparse modelling. We show that our method creates good sparse representations by using it in the object recognition framework of \cite{lazebnik06,yang-cvpr-09}. Implementing our own fast version of the SIFT descriptor the whole system runs at 20 frames per second on $321 \times 481$ sized images on a laptop with a quad-core cpu, while sacrificing very little accuracy on the Caltech 101 and 15 scenes benchmarks.

cs.CV↗
arXiv2011

Learning Representations by Maximizing Compression

We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The likelihood under the model can be calculated exactly, and arithmetic coding can be used directly for compression. When training on digits the algorithm learns filters similar to those of restricted boltzman machines and denoising autoencoders. Independent samples can be drawn from the model by a single sweep through the pixels. The algorithm has a good compression performance when compared to other methods that work under random ordering of pixels.

cs.CV↗
arXiv2011

Efficient Learning of Sparse Invariant Representations

We propose a simple and efficient algorithm for learning sparse invariant representations from unlabeled data with fast inference. When trained on short movies sequences, the learned features are selective to a range of orientations and spatial frequencies, but robust to a wide range of positions, similar to complex cells in the primary visual cortex. We give a hierarchical version of the algorithm, and give guarantees of fast convergence under certain conditions.

cs.CV↗
arXiv2010

Fast Inference in Sparse Coding Algorithms with Applications to Object Recognition

Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual object recognition tasks has been limited because of the prohibitive cost of the optimization algorithms required to compute the sparse representation. In this work we propose a simple and efficient algorithm to learn basis functions. After training, this model also provides a fast and smooth approximator to the optimal representation, achieving even better accuracy than exact sparse coding algorithms on visual object recognition tasks.

cs.CV↗
arXiv2010

Emergence of Complex-Like Cells in a Temporal Product Network with Local Receptive Fields

We introduce a new neural architecture and an unsupervised algorithm for learning invariant representations from temporal sequence of images. The system uses two groups of complex cells whose outputs are combined multiplicatively: one that represents the content of the image, constrained to be constant over several consecutive frames, and one that represents the precise location of features, which is allowed to vary over time but constrained to be sparse. The architecture uses an encoder to extract features, and a decoder to reconstruct the input from the features. The method was applied to patches extracted from consecutive movie frames and produces orientation and frequency selective units analogous to the complex cells in V1. An extension of the method is proposed to train a network composed of units with local receptive field spread over a large image of arbitrary size. A layer of complex cells, subject to sparsity constraints, pool feature units over overlapping local neighborhoods, which causes the feature units to organize themselves into pinwheel patterns of orientation-selective receptive fields, similar to those observed in the mammalian visual cortex. A feed-forward encoder efficiently computes the feature representation of full images.

cs.NE↗