**Meta Continual Learning**

Using neural networks in practical settings would benefit from the ability of the networks to learn new tasks throughout their lifetimes without forgetting the previous tasks. This ability is limited in the current deep neural networks by a problem called catastrophic forgetting, where training on new tasks tends to severely degrade performance on previous tasks. One way to lessen the impact of the forgetting problem is to constrain parameters that are important to previous tasks to stay close to the optimal parameters. Recently, multiple competitive approaches for computing the importance of the parameters with respect to the previous tasks have been presented. In this paper, we propose a learning to optimize algorithm for mitigating catastrophic forgetting. Instead of trying to formulate a new constraint function ourselves, we propose to train another neural network to predict parameter update steps that respect the importance of parameters to the previous tasks. In the proposed meta-training scheme, the update predictor is trained to minimize loss on a combination of current and past tasks. We show experimentally that the proposed approach works in the continual learning setting. … **Ripple Network**

To address the sparsity and cold start problem of collaborative filtering, researchers usually make use of side information, such as social networks or item attributes, to improve recommendation performance. This paper considers the knowledge graph as the source of side information. To address the limitations of existing embedding-based and path-based methods for knowledge-graph-aware recommendation, we propose Ripple Network, an end-to-end framework that naturally incorporates the knowledge graph into recommender systems. Similar to actual ripples propagating on the surface of water, Ripple Network stimulates the propagation of user preferences over the set of knowledge entities by automatically and iteratively extending a user’s potential interests along links in the knowledge graph. The multiple ‘ripples’ activated by a user’s historically clicked items are thus superposed to form the preference distribution of the user with respect to a candidate item, which could be used for predicting the final clicking probability. Through extensive experiments on real-world datasets, we demonstrate that Ripple Network achieves substantial gains in a variety of scenarios, including movie, book and news recommendation, over several state-of-the-art baselines. … **quasi-MCMC**

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior densities within the Bayesian framework, in particular for inverse problems. We introduce a general parallel Markov chain Monte Carlo (MCMC) framework, for which we prove a law of large numbers and a central limit theorem. We further extend this approach to the use of adaptive kernels and state conditions, under which ergodicity holds. As a further extension, an importance sampling estimator is derived, for which asymptotic unbiasedness is proven. We consider the use of completely uniformly distributed (CUD) numbers and non-reversible transitions within the above stated methods, which leads to a general parallel quasi-MCMC (QMCMC) methodology. We prove consistency of the resulting estimators and demonstrate numerically that this approach scales close to $n^{-1}$ as we increase parallelisation, instead of the usual $n^{-1/2}$ that is typical of standard MCMC algorithms. In practical statistical models we observe up to 2 orders of magnitude improvement compared with pseudo-random methods. … **Spatially Coherent Randomized Attention Map (SCRAM)**

Attention mechanisms and non-local mean operations in general are key ingredients in many state-of-the-art deep learning techniques. In particular, the Transformer model based on multi-head self-attention has recently achieved great success in natural language processing and computer vision. However, the vanilla algorithm computing the Transformer of an image with n pixels has O(n^2) complexity, which is often painfully slow and sometimes prohibitively expensive for large-scale image data. In this paper, we propose a fast randomized algorithm — SCRAM — that only requires O(n log(n)) time to produce an image attention map. Such a dramatic acceleration is attributed to our insight that attention maps on real-world images usually exhibit (1) spatial coherence and (2) sparse structure. The central idea of SCRAM is to employ PatchMatch, a randomized correspondence algorithm, to quickly pinpoint the most compatible key (argmax) for each query first, and then exploit that knowledge to design a sparse approximation to non-local mean operations. Using the argmax (mode) to dynamically construct the sparse approximation distinguishes our algorithm from all of the existing sparse approximate methods and makes it very efficient. Moreover, SCRAM is a broadly applicable approximation to any non-local mean layer in contrast to some other sparse approximations that can only approximate self-attention. Our preliminary experimental results suggest that SCRAM is indeed promising for speeding up or scaling up the computation of attention maps in the Transformer. …

# If you did not already know

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Mar 2022

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