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Nicolas Ballas

Alumni

Publications

Improved Conditional VRNNs for Video Prediction
Predicting future frames for a video sequence is a challenging generative modeling task. Promising approaches include probabilistic latent v… (voir plus)ariable models such as the Variational Auto-Encoder. While VAEs can handle uncertainty and model multiple possible future outcomes, they have a tendency to produce blurry predictions. In this work we argue that this is a sign of underfitting. To address this issue, we propose to increase the expressiveness of the latent distributions and to use higher capacity likelihood models. Our approach relies on a hierarchy of latent variables, which defines a family of flexible prior and posterior distributions in order to better model the probability of future sequences. We validate our proposal through a series of ablation experiments and compare our approach to current state-of-the-art latent variable models. Our method performs favorably under several metrics in three different datasets.
On the Relation Between the Sharpest Directions of DNN Loss and the SGD Step Length
Stanisław Jastrzębski
Amos Storkey
Stochastic Gradient Descent (SGD) based training of neural networks with a large learning rate or a small batch-size typically ends in well-… (voir plus)generalizing, flat regions of the weight space, as indicated by small eigenvalues of the Hessian of the training loss. However, the curvature along the SGD trajectory is poorly understood. An empirical investigation shows that initially SGD visits increasingly sharp regions, reaching a maximum sharpness determined by both the learning rate and the batch-size of SGD. When studying the SGD dynamics in relation to the sharpest directions in this initial phase, we find that the SGD step is large compared to the curvature and commonly fails to minimize the loss along the sharpest directions. Furthermore, using a reduced learning rate along these directions can improve training speed while leading to both sharper and better generalizing solutions compared to vanilla SGD. In summary, our analysis of the dynamics of SGD in the subspace of the sharpest directions shows that they influence the regions that SGD steers to (where larger learning rate or smaller batch size result in wider regions visited), the overall training speed, and the generalization ability of the final model.
Width of Minima Reached by Stochastic Gradient Descent is Influenced by Learning Rate to Batch Size Ratio
Stanisław Jastrzębski
Amos Storkey
Finding Flatter Minima with SGD
Stanisław Jastrzębski
Amos Storkey
SGD S MOOTHS THE S HARPEST D IRECTIONS
Stanisław Jastrzębski
Amos Storkey
Stochastic gradient descent (SGD) is able to find regions that generalize well, even in drastically over-parametrized models such as deep ne… (voir plus)ural networks. We observe that noise in SGD controls the spectral norm and conditioning of the Hessian throughout the training. We hypothesize the cause of this phenomenon is due to the dynamics of neurons saturating their non-linearity along the largest curvature directions, thus leading to improved conditioning.
LATTER M INIMA WITH SGD
Stanisław Jastrzębski
Amos Storkey
Residual Connections Encourage Iterative Inference
Stanisław Jastrzębski
Tong Che
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.
Three Factors Influencing Minima in SGD
Stanisław Jastrzębski
Amos Storkey
We study the statistical properties of the endpoint of stochastic gradient descent (SGD). We approximate SGD as a stochastic differential eq… (voir plus)uation (SDE) and consider its Boltzmann Gibbs equilibrium distribution under the assumption of isotropic variance in loss gradients.. Through this analysis, we find that three factors – learning rate, batch size and the variance of the loss gradients – control the trade-off between the depth and width of the minima found by SGD, with wider minima favoured by a higher ratio of learning rate to batch size. In the equilibrium distribution only the ratio of learning rate to batch size appears, implying that it’s invariant under a simultaneous rescaling of each by the same amount. We experimentally show how learning rate and batch size affect SGD from two perspectives: the endpoint of SGD and the dynamics that lead up to it. For the endpoint, the experiments suggest the endpoint of SGD is similar under simultaneous rescaling of batch size and learning rate, and also that a higher ratio leads to flatter minima, both findings are consistent with our theoretical analysis. We note experimentally that the dynamics also seem to be similar under the same rescaling of learning rate and batch size, which we explore showing that one can exchange batch size and learning rate in a cyclical learning rate schedule. Next, we illustrate how noise affects memorization, showing that high noise levels lead to better generalization. Finally, we find experimentally that the similarity under simultaneous rescaling of learning rate and batch size breaks down if the learning rate gets too large or the batch size gets too small.
A dataset and exploration of models for understanding video data through fill-in-the-blank question-answering
Anna Rohrbach
Christopher Pal
While deep convolutional neural networks frequently approach or exceed human-level performance at benchmark tasks involving static images, e… (voir plus)xtending this success to moving images is not straightforward. Having models which can learn to understand video is of interest for many applications, including content recommendation, prediction, summarization, event/object detection and understanding human visual perception, but many domains lack sufficient data to explore and perfect video models. In order to address the need for a simple, quantitative benchmark for developing and understanding video, we present MovieFIB, a fill-in-the-blank question-answering dataset with over 300,000 examples, based on descriptive video annotations for the visually impaired. In addition to presenting statistics and a description of the dataset, we perform a detailed analysis of 5 different models' predictions, and compare these with human performance. We investigate the relative importance of language, static (2D) visual features, and moving (3D) visual features; the effects of increasing dataset size, the number of frames sampled; and of vocabulary size. We illustrate that: this task is not solvable by a language model alone; our model combining 2D and 3D visual information indeed provides the best result; all models perform significantly worse than human-level. We provide human evaluations for responses given by different models and find that accuracy on the MovieFIB evaluation corresponds well with human judgement. We suggest avenues for improving video models, and hope that the proposed dataset can be useful for measuring and encouraging progress in this very interesting field.
A Closer Look at Memorization in Deep Networks
We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While dee… (voir plus)p networks are capable of memorizing noise data, our results suggest that they tend to prioritize learning simple patterns first. In our experiments, we expose qualitative differences in gradient-based optimization of deep neural networks (DNNs) on noise vs. real data. We also demonstrate that for appropriately tuned explicit regularization (e.g., dropout) we can degrade DNN training performance on noise datasets without compromising generalization on real data. Our analysis suggests that the notions of effective capacity which are dataset independent are unlikely to explain the generalization performance of deep networks when trained with gradient based methods because training data itself plays an important role in determining the degree of memorization.
Deep Nets Don't Learn Via Memorization
Recurrent Batch Normalization
We propose a reparameterization of LSTM that brings the benefits of batch normalization to recurrent neural networks. Whereas previous works… (voir plus) only apply batch normalization to the input-to-hidden transformation of RNNs, we demonstrate that it is both possible and beneficial to batch-normalize the hidden-to-hidden transition, thereby reducing internal covariate shift between time steps. We evaluate our proposal on various sequential problems such as sequence classification, language modeling and question answering. Our empirical results show that our batch-normalized LSTM consistently leads to faster convergence and improved generalization.