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Title: Revisiting Bayes by Backprop

Paper content:
In this work we explore a straightforward variational Bayes scheme for Recurrent Neural Networks.
Firstly, we show that a simple adaptation of truncated backpropagation through time can yield good quality uncertainty estimates and superior regularisation at only a small extra computational cost during training, also reducing the amount of parameters by 80\%.
Secondly, we demonstrate how a novel kind of posterior approximation yields further improvements to the performance of Bayesian RNNs.
We incorporate local gradient information into the approximate posterior to sharpen it around the current batch statistics.
We show how this technique is not exclusive to recurrent neural networks and can be applied more widely to train Bayesian neural networks.
We also empirically demonstrate how Bayesian RNNs are superior to traditional RNNs on a language modelling benchmark and an image captioning task, as well as showing how each of these methods improve our model over a variety of other schemes for training them.
We also introduce a new benchmark for studying uncertainty for language models so future methods can be easily compared.
Recurrent Neural Networks (RNNs) achieve state-of-the-art performance on a wide range of sequence prediction tasks BID0 BID22 BID50 BID32 .
In this work we examine how to add uncertainty and regularisation to RNNs by means of applying Bayesian methods to training.
This approach allows the network to express uncertainty via its parameters.
At the same time, by using a prior to integrate out the parameters to average across many models during training, it gives a regularisation effect to the network.
Recent approaches either justify dropout BID43 and weight decay as a variational inference scheme BID12 , or apply Stochastic Gradient Langevin dynamics (Welling & Teh, 2011, SGLD) to truncated backpropagation in time directly BID13 .
Interestingly, recent work has not explored further directly applying a variational Bayes inference scheme BID3 for RNNs as was done in BID14 .
We derive a straightforward approach based upon Bayes by Backprop that we show works well on large scale problems.
Our strategy is a simple alteration to truncated backpropagation through time that results in an estimate of the posterior distribution on the weights of the RNN.
This formulation explicitly leads to a cost function with an information theoretic justification by means of a bits-back argument BID18 where a KL divergence acts as a regulariser.The form of the posterior in variational inference shapes the quality of the uncertainty estimates and hence the overall performance of the model.
We shall show how performance of the RNN can be improved by means of adapting ("sharpening") the posterior locally to a batch.
This sharpening adapts the variational posterior to a batch of data using gradients based upon the batch.
This can be viewed as a hierarchical distribution, where a local batch gradient is used to adapt a global posterior, forming a local approximation for each batch.
This gives a more flexible form to the typical assumption of Gaussian posterior when variational inference is applied to neural networks, which reduces variance.
This technique can be applied more widely across other Bayesian models.The contributions of our work are as follows:• We show how Bayes by Backprop (BBB) can be efficiently applied to RNNs.•
We develop a novel technique which reduces the variance of BBB, and which can be widely adopted in other maximum likelihood frameworks.•
We improve performance on two widely studied benchmarks outperforming established regularisation techniques such as dropout by a big margin.•
We introduce a new benchmark for studying uncertainty of language models.
We have shown how to apply the Bayes by Backprop (BBB) technique to RNNs.
We enhanced it further by introducing the idea of posterior sharpening: a hierarchical posterior on the weights of neural networks that allows a network to adapt locally to batches of data by a gradient of the model.We showed improvements over two open source, widely available models in the language modelling and image captioning domains.
We demonstrated that not only do BBB RNNs often have superior performance to their corresponding baseline model, but are also better regularised and have superior uncertainty properties in terms of uncertainty on out-of-distribution data.
Furthermore, BBB RNNs through their uncertainty estimates show signs of knowing what they know, and when they do not, a critical property for many real world applications such as self-driving cars, healthcare, game playing, and robotics.
Everything from our work can be applied on top of other enhancements to RNN/LSTM models (and other non-recurrent architectures), and the empirical evidence combined with improvements such as posterior sharpening makes variational Bayes methods look very promising.
We are exploring further research directions and wider adoption of the techniques presented in our work.

assistant: text: Variational Bayes scheme for Recurrent Neural Networks