arXiv subjects

Pascal Vincent

Publications and source records attributed to Pascal Vincent.

At least 73 records · Page 4Linked to original sources

arXiv2016

The Z-loss: a shift and scale invariant classification loss belonging to the Spherical Family

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size of problems we are able to tackle with current hardware. Second, it remains unclear how close it matches the task loss such as the top-k error rate or other non-differentiable evaluation metrics which we aim to optimize ultimately. In this paper, we introduce an alternative classification loss function, the Z-loss, which is designed to address these two issues. Unlike the log-softmax, it has the desirable property of belonging to the spherical loss family (Vincent et al., 2015), a class of loss functions for which training can be performed very efficiently with a complexity independent of the number of output classes. We show experimentally that it significantly outperforms the other spherical loss functions previously investigated. Furthermore, we show on a word language modeling task that it also outperforms the log-softmax with respect to certain ranking scores, such as top-k scores, suggesting that the Z-loss has the flexibility to better match the task loss. These qualities thus makes the Z-loss an appealing candidate to train very efficiently large output networks such as word-language models or other extreme classification problems. On the One Billion Word (Chelba et al., 2014) dataset, we are able to train a model with the Z-loss 40 times faster than the log-softmax and more than 4 times faster than the hierarchical softmax.

cs.LG↗

arXiv2016

Hierarchical Memory Networks

Memory networks are neural networks with an explicit memory component that can be both read and written to by the network. The memory is often addressed in a soft way using a softmax function, making end-to-end training with backpropagation possible. However, this is not computationally scalable for applications which require the network to read from extremely large memories. On the other hand, it is well known that hard attention mechanisms based on reinforcement learning are challenging to train successfully. In this paper, we explore a form of hierarchical memory network, which can be considered as a hybrid between hard and soft attention memory networks. The memory is organized in a hierarchical structure such that reading from it is done with less computation than soft attention over a flat memory, while also being easier to train than hard attention over a flat memory. Specifically, we propose to incorporate Maximum Inner Product Search (MIPS) in the training and inference procedures for our hierarchical memory network. We explore the use of various state-of-the art approximate MIPS techniques and report results on SimpleQuestions, a challenging large scale factoid question answering task.

stat.ML↗

arXiv2016

Recombinator Networks: Learning Coarse-to-Fine Feature Aggregation

Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create features that are more robust, and typically organized as lower resolution spatial feature maps. On some tasks, such as whole-image classification, max-pooling derived features are well suited; however, for tasks requiring precise localization, such as pixel level prediction and segmentation, max-pooling destroys exactly the information required to perform well. Precise localization may be preserved by shallow convnets without pooling but at the expense of robustness. Can we have our max-pooled multi-layered cake and eat it too? Several papers have proposed summation and concatenation based methods for combining upsampled coarse, abstract features with finer features to produce robust pixel level predictions. Here we introduce another model --- dubbed Recombinator Networks --- where coarse features inform finer features early in their formation such that finer features can make use of several layers of computation in deciding how to use coarse features. The model is trained once, end-to-end and performs better than summation-based architectures, reducing the error from the previous state of the art on two facial keypoint datasets, AFW and AFLW, by 30\% and beating the current state-of-the-art on 300W without using extra data. We improve performance even further by adding a denoising prediction model based on a novel convnet formulation.

cs.CV↗

arXiv2016

Universal Vectorial and Ultrasensitive Nanomechanical Force Field Sensor

Miniaturization of force probes into nanomechanical oscillators enables ultrasensitive investigations of forces on dimensions smaller than their characteristic length scale. Meanwhile it also unravels the force field vectorial character and how its topology impacts the measurement. Here we expose an ultrasensitive method to image 2D vectorial force fields by optomechanically following the bidimensional Brownian motion of a singly clamped nanowire. This novel approach relies on angular and spectral tomography of its quasi frequency-degenerated transverse mechanical polarizations: immersing the nanoresonator in a vectorial force field does not only shift its eigenfrequencies but also rotate eigenmodes orientation as a nano-compass. This universal method is employed to map a tunable electrostatic force field whose spatial gradients can even take precedence over the intrinsic nanowire properties. Enabling vectorial force fields imaging with demonstrated sensitivities of attonewton variations over the nanoprobe Brownian trajectory will have strong impact on scientific exploration at the nanoscale.

cond-mat.mes-hall↗

arXiv2016

An Exploration of Softmax Alternatives Belonging to the Spherical Loss Family

In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced by a softmax. This probabilistic mapping allows to use the maximum likelihood principle, which leads to the well-known log-softmax loss. However the choice of the softmax function seems somehow arbitrary as there are many other possible normalizing functions. It is thus unclear why the log-softmax loss would perform better than other loss alternatives. In particular Vincent et al. (2015) recently introduced a class of loss functions, called the spherical family, for which there exists an efficient algorithm to compute the updates of the output weights irrespective of the output size. In this paper, we explore several loss functions from this family as possible alternatives to the traditional log-softmax. In particular, we focus our investigation on spherical bounds of the log-softmax loss and on two spherical log-likelihood losses, namely the log-Spherical Softmax suggested by Vincent et al. (2015) and the log-Taylor Softmax that we introduce. Although these alternatives do not yield as good results as the log-softmax loss on two language modeling tasks, they surprisingly outperform it in our experiments on MNIST and CIFAR-10, suggesting that they might be relevant in a broad range of applications.

cs.NE↗

arXiv2016

Dropout as data augmentation

Dropout is typically interpreted as bagging a large number of models sharing parameters. We show that using dropout in a network can also be interpreted as a kind of data augmentation in the input space without domain knowledge. We present an approach to projecting the dropout noise within a network back into the input space, thereby generating augmented versions of the training data, and we show that training a deterministic network on the augmented samples yields similar results. Finally, we propose a new dropout noise scheme based on our observations and show that it improves dropout results without adding significant computational cost.

stat.ML↗

arXiv2015

Clustering is Efficient for Approximate Maximum Inner Product Search

Efficient Maximum Inner Product Search (MIPS) is an important task that has a wide applicability in recommendation systems and classification with a large number of classes. Solutions based on locality-sensitive hashing (LSH) as well as tree-based solutions have been investigated in the recent literature, to perform approximate MIPS in sublinear time. In this paper, we compare these to another extremely simple approach for solving approximate MIPS, based on variants of the k-means clustering algorithm. Specifically, we propose to train a spherical k-means, after having reduced the MIPS problem to a Maximum Cosine Similarity Search (MCSS). Experiments on two standard recommendation system benchmarks as well as on large vocabulary word embeddings, show that this simple approach yields much higher speedups, for the same retrieval precision, than current state-of-the-art hashing-based and tree-based methods. This simple method also yields more robust retrievals when the query is corrupted by noise.

cs.LG↗

arXiv2015

Artificial Neural Networks Applied to Taxi Destination Prediction

We describe our first-place solution to the ECML/PKDD discovery challenge on taxi destination prediction. The task consisted in predicting the destination of a taxi based on the beginning of its trajectory, represented as a variable-length sequence of GPS points, and diverse associated meta-information, such as the departure time, the driver id and client information. Contrary to most published competitor approaches, we used an almost fully automated approach based on neural networks and we ranked first out of 381 teams. The architectures we tried use multi-layer perceptrons, bidirectional recurrent neural networks and models inspired from recently introduced memory networks. Our approach could easily be adapted to other applications in which the goal is to predict a fixed-length output from a variable-length sequence.

cs.LG↗

arXiv2015

Efficient Exact Gradient Update for training Deep Networks with Very Large Sparse Targets

An important class of problems involves training deep neural networks with sparse prediction targets of very high dimension D. These occur naturally in e.g. neural language models or the learning of word-embeddings, often posed as predicting the probability of next words among a vocabulary of size D (e.g. 200 000). Computing the equally large, but typically non-sparse D-dimensional output vector from a last hidden layer of reasonable dimension d (e.g. 500) incurs a prohibitive O(Dd) computational cost for each example, as does updating the D x d output weight matrix and computing the gradient needed for backpropagation to previous layers. While efficient handling of large sparse network inputs is trivial, the case of large sparse targets is not, and has thus so far been sidestepped with approximate alternatives such as hierarchical softmax or sampling-based approximations during training. In this work we develop an original algorithmic approach which, for a family of loss functions that includes squared error and spherical softmax, can compute the exact loss, gradient update for the output weights, and gradient for backpropagation, all in O(d^2) per example instead of O(Dd), remarkably without ever computing the D-dimensional output. The proposed algorithm yields a speedup of D/4d , i.e. two orders of magnitude for typical sizes, for that critical part of the computations that often dominates the training time in this kind of network architecture.

cs.NE↗

arXiv2015

EmoNets: Multimodal deep learning approaches for emotion recognition in video

The task of the emotion recognition in the wild (EmotiW) Challenge is to assign one of seven emotions to short video clips extracted from Hollywood style movies. The videos depict acted-out emotions under realistic conditions with a large degree of variation in attributes such as pose and illumination, making it worthwhile to explore approaches which consider combinations of features from multiple modalities for label assignment. In this paper we present our approach to learning several specialist models using deep learning techniques, each focusing on one modality. Among these are a convolutional neural network, focusing on capturing visual information in detected faces, a deep belief net focusing on the representation of the audio stream, a K-Means based "bag-of-mouths" model, which extracts visual features around the mouth region and a relational autoencoder, which addresses spatio-temporal aspects of videos. We explore multiple methods for the combination of cues from these modalities into one common classifier. This achieves a considerably greater accuracy than predictions from our strongest single-modality classifier. Our method was the winning submission in the 2013 EmotiW challenge and achieved a test set accuracy of 47.67% on the 2014 dataset.

cs.LG↗

arXiv2015

GSNs : Generative Stochastic Networks

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. Because the transition distribution is a conditional distribution generally involving a small move, it has fewer dominant modes, being unimodal in the limit of small moves. Thus, it is easier to learn, more like learning to perform supervised function approximation, with gradients that can be obtained by back-propagation. The theorems provided here generalize recent work on the probabilistic interpretation of denoising auto-encoders and provide an interesting justification for dependency networks and generalized pseudolikelihood (along with defining an appropriate joint distribution and sampling mechanism, even when the conditionals are not consistent). We study how GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. Successful experiments are conducted, validating these theoretical results, on two image datasets and with a particular architecture that mimics the Deep Boltzmann Machine Gibbs sampler but allows training to proceed with backprop, without the need for layerwise pretraining.

cs.LG↗

arXiv2014

Frequency modulated self-oscillation and phase inertia in a synchronized nanowire mechanical resonator

Synchronization has been reported for a wide range of self-oscillating systems. However, even though it has been predicted theoretically for several decades, the experimental realization of phase self-oscillation, sometimes called phase trapping, in the high driving regime has been studied only recently. We explored in detail the phase dynamics in a synchronized field emission SiC nanoelectromechanical system with intrinsic feedback. A richer variety of phase behavior has been unambiguously identified, implying phase modulation and inertia. This synchronization regime is expected to have implications for the comprehension of the dynamics of interacting self-oscillating networks and for the generation of frequency modulated signals at the nanoscale

cond-mat.mes-hall↗

arXiv2014

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

cs.LG↗

arXiv2014

Bidimensional nano-optomechanics and topological backaction in a non-conservative radiation force field

Optomechanics, which explores the fundamental coupling between light and mechanical motion, has made important advances in both exploring and manipulating macroscopic mechanical oscillators down to the quantum level. However, dynamical effects related to the vectorial nature of the optomechanical interaction remain to be investigated. Here we study a nanowire with sub-wavelength dimensions strongly coupled to a tightly focused beam of light, enabling ultrasensitive readout of the nanoresonators dynamics. We experimentally determine the vectorial structure of the optomechanical interaction and demonstrate that bidimensional dynamical backaction governs the nanowire dynamics. Moreover, the non-conservative topology of the optomechanical interaction is responsible for a novel canonical signature of strong coupling between the nanoresonator mechanical modes, leading to a topological instability. These results have a universal character and illustrate the increased sensitivity of nanomechanical devices towards topologically varying interactions, opening fundamental perspectives in nanomechanics, optomechanics, ultrasensitive scanning probe force microscopy and nano-optics.

quant-ph↗

arXiv2013

Role of fluctuations and nonlinearities on field emission nanomechanical self-oscillators

A theoretical and experimental description of the threshold, amplitude, and stability of a self-oscillating nanowire in a field emission configuration is presented. Two thresholds for the onset of self-oscillation are identified, one induced by fluctuations of the electromagnetic environment and a second revealed by these fluctuations by measuring the probability density function of the current. The ac and dc components of the current and the phase stability are quantified. An ac to dc ratio above 100% and an Allan deviation of 1.3x10-5 at room temperature can be attained. Finally, it is shown that a simple nonlinear model cannot describe the equilibrium effective potential in the self-oscillating regime due to the high amplitude of oscillations.

cond-mat.mes-hall↗

arXiv2013

Generalized Denoising Auto-Encoders as Generative Models

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).

cs.LG↗

arXiv2012

High-dimensional sequence transduction

We investigate the problem of transforming an input sequence into a high-dimensional output sequence in order to transcribe polyphonic audio music into symbolic notation. We introduce a probabilistic model based on a recurrent neural network that is able to learn realistic output distributions given the input and we devise an efficient algorithm to search for the global mode of that distribution. The resulting method produces musically plausible transcriptions even under high levels of noise and drastically outperforms previous state-of-the-art approaches on five datasets of synthesized sounds and real recordings, approximately halving the test error rate.

cs.LG↗

arXiv2012

Modeling Temporal Dependencies in High-Dimensional Sequences: Application to Polyphonic Music Generation and Transcription

We investigate the problem of modeling symbolic sequences of polyphonic music in a completely general piano-roll representation. We introduce a probabilistic model based on distribution estimators conditioned on a recurrent neural network that is able to discover temporal dependencies in high-dimensional sequences. Our approach outperforms many traditional models of polyphonic music on a variety of realistic datasets. We show how our musical language model can serve as a symbolic prior to improve the accuracy of polyphonic transcription.

cs.LG↗