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Vikas Verma

Alumni

Publications

Modularity Matters: Learning Invariant Relational Reasoning Tasks
Jason Jo
Vikas Verma
Yoshua Bengio
We focus on two supervised visual reasoning tasks whose labels encode a semantic relational rule between two or more objects in an image: th… (voir plus)e MNIST Parity task and the colorized Pentomino task. The objects in the images undergo random translation, scaling, rotation and coloring transformations. Thus these tasks involve invariant relational reasoning. We report uneven performance of various deep CNN models on these two tasks. For the MNIST Parity task, we report that the VGG19 model soundly outperforms a family of ResNet models. Moreover, the family of ResNet models exhibits a general sensitivity to random initialization for the MNIST Parity task. For the colorized Pentomino task, now both the VGG19 and ResNet models exhibit sluggish optimization and very poor test generalization, hovering around 30% test error. The CNN we tested all learn hierarchies of fully distributed features and thus encode the distributed representation prior. We are motivated by a hypothesis from cognitive neuroscience which posits that the human visual cortex is modularized, and this allows the visual cortex to learn higher order invariances. To this end, we consider a modularized variant of the ResNet model, referred to as a Residual Mixture Network (ResMixNet) which employs a mixture-of-experts architecture to interleave distributed representations with more specialized, modular representations. We show that very shallow ResMixNets are capable of learning each of the two tasks well, attaining less than 2% and 1% test error on the MNIST Parity and the colorized Pentomino tasks respectively. Most importantly, the ResMixNet models are extremely parameter efficient: generalizing better than various non-modular CNNs that have over 10x the number of parameters. These experimental results support the hypothesis that modularity is a robust prior for learning invariant relational reasoning.
2018-06-17
ArXiv (prépublication)
arxiv.org
arxiv.org
Manifold Mixup: Better Representations by Interpolating Hidden States
Vikas Verma
Alex Lamb
Christopher Beckham
Aaron Courville
Ioannis Mitliagkas
Yoshua Bengio
Deep neural networks excel at learning the training data, but often provide incorrect and confident predictions when evaluated on slightly d… (voir plus)ifferent test examples. This includes distribution shifts, outliers, and adversarial examples. To address these issues, we propose Manifold Mixup, a simple regularizer that encourages neural networks to predict less confidently on interpolations of hidden representations. Manifold Mixup leverages semantic interpolations as additional training signal, obtaining neural networks with smoother decision boundaries at multiple levels of representation. As a result, neural networks trained with Manifold Mixup learn class-representations with fewer directions of variance. We prove theory on why this flattening happens under ideal conditions, validate it on practical situations, and connect it to previous works on information theory and generalization. In spite of incurring no significant computation and being implemented in a few lines of code, Manifold Mixup improves strong baselines in supervised learning, robustness to single-step adversarial attacks, and test log-likelihood.
2018-06-12
arXiv.org (prépublication)
doi.org
arxiv.org
Residual Connections Encourage Iterative Inference
Stanisław Jastrzębski
Devansh Arpit
Nicolas Ballas
Vikas Verma
Tong Che
Yoshua Bengio
Residual networks (Resnets) have become a prominent architecture in deep learning. However, a comprehensive understanding of Resnets is stil… (voir plus)l a topic of ongoing research. A recent view argues that Resnets perform iterative refinement of features. We attempt to further expose properties of this aspect. To this end, we study Resnets both analytically and empirically. We formalize the notion of iterative refinement in Resnets by showing that residual connections naturally encourage features of residual blocks to move along the negative gradient of loss as we go from one block to the next. In addition, our empirical analysis suggests that Resnets are able to perform both representation learning and iterative refinement. In general, a Resnet block tends to concentrate representation learning behavior in the first few layers while higher layers perform iterative refinement of features. Finally we observe that sharing residual layers naively leads to representation explosion and counterintuitively, overfitting, and we show that simple existing strategies can help alleviating this problem.
2017-12-31
ICLR.cc/2018/Conference (poster)
openreview.net
openreview.net