Research papers and code for "Yoshua Bengio":
A new prior is proposed for representation learning, which can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by the phenomenon of consciousness seen as the formation of a low-dimensional combination of a few concepts constituting a conscious thought, i.e., consciousness as awareness at a particular time instant. This provides a powerful constraint on the representation in that such low-dimensional thought vectors can correspond to statements about reality which are true, highly probable, or very useful for taking decisions. The fact that a few elements of the current state can be combined into such a predictive or useful statement is a strong constraint and deviates considerably from the maximum likelihood approaches to modelling data and how states unfold in the future based on an agent's actions. Instead of making predictions in the sensory (e.g. pixel) space, the consciousness prior allows the agent to make predictions in the abstract space, with only a few dimensions of that space being involved in each of these predictions. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in the form of facts and rules, although the conscious states may be richer than what can be expressed easily in the form of a sentence, a fact or a rule.

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We propose to exploit {\em reconstruction} as a layer-local training signal for deep learning. Reconstructions can be propagated in a form of target propagation playing a role similar to back-propagation but helping to reduce the reliance on derivatives in order to perform credit assignment across many levels of possibly strong non-linearities (which is difficult for back-propagation). A regularized auto-encoder tends produce a reconstruction that is a more likely version of its input, i.e., a small move in the direction of higher likelihood. By generalizing gradients, target propagation may also allow to train deep networks with discrete hidden units. If the auto-encoder takes both a representation of input and target (or of any side information) in input, then its reconstruction of input representation provides a target towards a representation that is more likely, conditioned on all the side information. A deep auto-encoder decoding path generalizes gradient propagation in a learned way that can could thus handle not just infinitesimal changes but larger, discrete changes, hopefully allowing credit assignment through a long chain of non-linear operations. In addition to each layer being a good auto-encoder, the encoder also learns to please the upper layers by transforming the data into a space where it is easier to model by them, flattening manifolds and disentangling factors. The motivations and theoretical justifications for this approach are laid down in this paper, along with conjectures that will have to be verified either mathematically or experimentally, including a hypothesis stating that such auto-encoder mediated target propagation could play in brains the role of credit assignment through many non-linear, noisy and discrete transformations.

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Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to impressive theoretical results, learning algorithms and breakthrough experiments, several challenges lie ahead. This paper proposes to examine some of these challenges, centering on the questions of scaling deep learning algorithms to much larger models and datasets, reducing optimization difficulties due to ill-conditioning or local minima, designing more efficient and powerful inference and sampling procedures, and learning to disentangle the factors of variation underlying the observed data. It also proposes a few forward-looking research directions aimed at overcoming these challenges.

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Stochastic neurons can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic neurons, i.e., can we "back-propagate" through these stochastic neurons? We examine this question, existing approaches, and present two novel families of solutions, applicable in different settings. In particular, it is demonstrated that a simple biologically plausible formula gives rise to an an unbiased (but noisy) estimator of the gradient with respect to a binary stochastic neuron firing probability. Unlike other estimators which view the noise as a small perturbation in order to estimate gradients by finite differences, this estimator is unbiased even without assuming that the stochastic perturbation is small. This estimator is also interesting because it can be applied in very general settings which do not allow gradient back-propagation, including the estimation of the gradient with respect to future rewards, as required in reinforcement learning setups. We also propose an approach to approximating this unbiased but high-variance estimator by learning to predict it using a biased estimator. The second approach we propose assumes that an estimator of the gradient can be back-propagated and it provides an unbiased estimator of the gradient, but can only work with non-linearities unlike the hard threshold, but like the rectifier, that are not flat for all of their range. This is similar to traditional sigmoidal units but has the advantage that for many inputs, a hard decision (e.g., a 0 output) can be produced, which would be convenient for conditional computation and achieving sparse representations and sparse gradients.

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We propose a theory that relates difficulty of learning in deep architectures to culture and language. It is articulated around the following hypotheses: (1) learning in an individual human brain is hampered by the presence of effective local minima; (2) this optimization difficulty is particularly important when it comes to learning higher-level abstractions, i.e., concepts that cover a vast and highly-nonlinear span of sensory configurations; (3) such high-level abstractions are best represented in brains by the composition of many levels of representation, i.e., by deep architectures; (4) a human brain can learn such high-level abstractions if guided by the signals produced by other humans, which act as hints or indirect supervision for these high-level abstractions; and (5), language and the recombination and optimization of mental concepts provide an efficient evolutionary recombination operator, and this gives rise to rapid search in the space of communicable ideas that help humans build up better high-level internal representations of their world. These hypotheses put together imply that human culture and the evolution of ideas have been crucial to counter an optimization difficulty: this optimization difficulty would otherwise make it very difficult for human brains to capture high-level knowledge of the world. The theory is grounded in experimental observations of the difficulties of training deep artificial neural networks. Plausible consequences of this theory for the efficiency of cultural evolutions are sketched.

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Learning algorithms related to artificial neural networks and in particular for Deep Learning may seem to involve many bells and whistles, called hyper-parameters. This chapter is meant as a practical guide with recommendations for some of the most commonly used hyper-parameters, in particular in the context of learning algorithms based on back-propagated gradient and gradient-based optimization. It also discusses how to deal with the fact that more interesting results can be obtained when allowing one to adjust many hyper-parameters. Overall, it describes elements of the practice used to successfully and efficiently train and debug large-scale and often deep multi-layer neural networks. It closes with open questions about the training difficulties observed with deeper architectures.

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There are two widely known issues with properly training Recurrent Neural Networks, the vanishing and the exploding gradient problems detailed in Bengio et al. (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.

* Improved description of the exploding gradient problem and description and analysis of the vanishing gradient problem
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In this paper, we explore different ways to extend a recurrent neural network (RNN) to a \textit{deep} RNN. We start by arguing that the concept of depth in an RNN is not as clear as it is in feedforward neural networks. By carefully analyzing and understanding the architecture of an RNN, however, we find three points of an RNN which may be made deeper; (1) input-to-hidden function, (2) hidden-to-hidden transition and (3) hidden-to-output function. Based on this observation, we propose two novel architectures of a deep RNN which are orthogonal to an earlier attempt of stacking multiple recurrent layers to build a deep RNN (Schmidhuber, 1992; El Hihi and Bengio, 1996). We provide an alternative interpretation of these deep RNNs using a novel framework based on neural operators. The proposed deep RNNs are empirically evaluated on the tasks of polyphonic music prediction and language modeling. The experimental result supports our claim that the proposed deep RNNs benefit from the depth and outperform the conventional, shallow RNNs.

* Accepted at ICLR 2014 (Conference Track). 10-page text + 3-page references
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It has been noted in existing literature that over-parameterization in ReLU networks generally leads to better performance. While there could be several reasons for this, we investigate desirable network properties at initialization which may be enjoyed by ReLU networks. Without making any assumption, we derive a lower bound on the layer width of deep ReLU networks whose weights are initialized from a certain distribution, such that with high probability, i) the norm of hidden activation of all layers are roughly equal to the norm of the input, and, ii) the norm of parameter gradient for all the layers are roughly the same. In this way, sufficiently wide deep ReLU nets with appropriate initialization can inherently preserve the forward flow of information and also avoid the gradient exploding/vanishing problem. We further show that these results hold for an infinite number of data samples, in which case the finite lower bound depends on the input dimensionality and the depth of the network. In the case of deep ReLU networks with weight vectors normalized by their norm, we derive an initialization required to tap the aforementioned benefits from over-parameterization without which network fails to learn for large depth.

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Deep neural networks can learn complex and abstract representations, that are progressively obtained by combining simpler ones. A recent trend in speech and speaker recognition consists in discovering these representations starting from raw audio samples directly. Differently from standard hand-crafted features such as MFCCs or FBANK, the raw waveform can potentially help neural networks discover better and more customized representations. The high-dimensional raw inputs, however, can make training significantly more challenging. This paper summarizes our recent efforts to develop a neural architecture that efficiently processes speech from audio waveforms. In particular, we propose SincNet, a novel Convolutional Neural Network (CNN) that encourages the first layer to discover meaningful filters by exploiting parametrized sinc functions. In contrast to standard CNNs, which learn all the elements of each filter, only low and high cutoff frequencies of band-pass filters are directly learned from data. This inductive bias offers a very compact way to derive a customized front-end, that only depends on some parameters with a clear physical meaning. Our experiments, conducted on both speaker and speech recognition, show that the proposed architecture converges faster, performs better, and is more computationally efficient than standard CNNs.

* submitted to ICASSP 2019. arXiv admin note: substantial text overlap with arXiv:1811.09725, arXiv:1808.00158
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The capacity of meta-learning algorithms to quickly adapt to a variety of tasks, including ones they did not experience during meta-training, has been a key factor in the recent success of these methods on few-shot learning problems. This particular advantage of using meta-learning over standard supervised or reinforcement learning is only well founded under the assumption that the adaptation phase does improve the performance of our model on the task of interest. However, in the classical framework of meta-learning, this constraint is only mildly enforced, if not at all, and we only see an improvement on average over a distribution of tasks. In this paper, we show that the adaptation in an algorithm like MAML can significantly decrease the performance of an agent in a meta-reinforcement learning setting, even on a range of meta-training tasks.

* Workshop on Meta-Learning - 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), Montreal, Canada
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Learning good representations is of crucial importance in deep learning. Mutual Information (MI) or similar measures of statistical dependence are promising tools for learning these representations in an unsupervised way. Even though the mutual information between two random variables is hard to measure directly in high dimensional spaces, some recent studies have shown that an implicit optimization of MI can be achieved with an encoder-discriminator architecture similar to that of Generative Adversarial Networks (GANs). In this work, we learn representations that capture speaker identities by maximizing the mutual information between the encoded representations of chunks of speech randomly sampled from the same sentence. The proposed encoder relies on the SincNet architecture and transforms raw speech waveform into a compact feature vector. The discriminator is fed by either positive samples (of the joint distribution of encoded chunks) or negative samples (from the product of the marginals) and is trained to separate them. We report experiments showing that this approach effectively learns useful speaker representations, leading to promising results on speaker identification and verification tasks. Our experiments consider both unsupervised and semi-supervised settings and compare the performance achieved with different objective functions.

* Submitted to ICASSP 2019
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Deep learning is currently playing a crucial role toward higher levels of artificial intelligence. This paradigm allows neural networks to learn complex and abstract representations, that are progressively obtained by combining simpler ones. Nevertheless, the internal "black-box" representations automatically discovered by current neural architectures often suffer from a lack of interpretability, making of primary interest the study of explainable machine learning techniques. This paper summarizes our recent efforts to develop a more interpretable neural model for directly processing speech from the raw waveform. In particular, we propose SincNet, a novel Convolutional Neural Network (CNN) that encourages the first layer to discover more meaningful filters by exploiting parametrized sinc functions. In contrast to standard CNNs, which learn all the elements of each filter, only low and high cutoff frequencies of band-pass filters are directly learned from data. This inductive bias offers a very compact way to derive a customized filter-bank front-end, that only depends on some parameters with a clear physical meaning. Our experiments, conducted on both speaker and speech recognition, show that the proposed architecture converges faster, performs better, and is more interpretable than standard CNNs.

* In Proceedings of NIPS@IRASL 2018. arXiv admin note: substantial text overlap with arXiv:1808.00158
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In this paper, we prove that depth with nonlinearity creates no bad local minima in a type of arbitrarily deep ResNets studied in previous work, in the sense that the values of all local minima are no worse than the global minima values of corresponding shallow linear predictors with arbitrary fixed features, and are guaranteed to further improve via residual representations. As a result, this paper provides an affirmative answer to an open question stated in a paper in the conference on Neural Information Processing Systems (NIPS) 2018. We note that even though our paper advances the theoretical foundation of deep learning and non-convex optimization, there is still a gap between theory and many practical deep learning applications.

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Deep learning is progressively gaining popularity as a viable alternative to i-vectors for speaker recognition. Promising results have been recently obtained with Convolutional Neural Networks (CNNs) when fed by raw speech samples directly. Rather than employing standard hand-crafted features, the latter CNNs learn low-level speech representations from waveforms, potentially allowing the network to better capture important narrow-band speaker characteristics such as pitch and formants. Proper design of the neural network is crucial to achieve this goal. This paper proposes a novel CNN architecture, called SincNet, that encourages the first convolutional layer to discover more meaningful filters. SincNet is based on parametrized sinc functions, which implement band-pass filters. In contrast to standard CNNs, that learn all elements of each filter, only low and high cutoff frequencies are directly learned from data with the proposed method. This offers a very compact and efficient way to derive a customized filter bank specifically tuned for the desired application. Our experiments, conducted on both speaker identification and speaker verification tasks, show that the proposed architecture converges faster and performs better than a standard CNN on raw waveforms.

* Accepted at SLT 2018
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Recurrent Backpropagation and Equilibrium Propagation are supervised learning algorithms for fixed point recurrent neural networks which differ in their second phase. In the first phase, both algorithms converge to a fixed point which corresponds to the configuration where the prediction is made. In the second phase, Equilibrium Propagation relaxes to another nearby fixed point corresponding to smaller prediction error, whereas Recurrent Backpropagation uses a side network to compute error derivatives iteratively. In this work we establish a close connection between these two algorithms. We show that, at every moment in the second phase, the temporal derivatives of the neural activities in Equilibrium Propagation are equal to the error derivatives computed iteratively by Recurrent Backpropagation in the side network. This work shows that it is not required to have a side network for the computation of error derivatives, and supports the hypothesis that, in biological neural networks, temporal derivatives of neural activities may code for error signals.

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We introduce an incremental processing scheme for convolutional neural network (CNN) inference, targeted at embedded applications with limited memory budgets. Instead of processing layers one by one, individual input pixels are propagated through all parts of the network they can influence under the given structural constraints. This depth-first updating scheme comes with hard bounds on the memory footprint: the memory required is constant in the case of 1D input and proportional to the square root of the input dimension in the case of 2D input.

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Deep CNNs are known to exhibit the following peculiarity: on the one hand they generalize extremely well to a test set, while on the other hand they are extremely sensitive to so-called adversarial perturbations. The extreme sensitivity of high performance CNNs to adversarial examples casts serious doubt that these networks are learning high level abstractions in the dataset. We are concerned with the following question: How can a deep CNN that does not learn any high level semantics of the dataset manage to generalize so well? The goal of this article is to measure the tendency of CNNs to learn surface statistical regularities of the dataset. To this end, we use Fourier filtering to construct datasets which share the exact same high level abstractions but exhibit qualitatively different surface statistical regularities. For the SVHN and CIFAR-10 datasets, we present two Fourier filtered variants: a low frequency variant and a randomly filtered variant. Each of the Fourier filtering schemes is tuned to preserve the recognizability of the objects. Our main finding is that CNNs exhibit a tendency to latch onto the Fourier image statistics of the training dataset, sometimes exhibiting up to a 28% generalization gap across the various test sets. Moreover, we observe that significantly increasing the depth of a network has a very marginal impact on closing the aforementioned generalization gap. Thus we provide quantitative evidence supporting the hypothesis that deep CNNs tend to learn surface statistical regularities in the dataset rather than higher-level abstract concepts.

* Submitted
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Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the mutual information, are hard to estimate and optimize directly. We propose to learn independent features with adversarial objectives which optimize such measures implicitly. These objectives compare samples from the joint distribution and the product of the marginals without the need to compute any probability densities. We also propose two methods for obtaining samples from the product of the marginals using either a simple resampling trick or a separate parametric distribution. Our experiments show that this strategy can easily be applied to different types of model architectures and solve both linear and non-linear ICA problems.

* A preliminary version of this work was presented at the ICML 2017 workshop on implicit models
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We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point, or stationary distribution) towards a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged towards their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal 'back-propagated' during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not.

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