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We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities, e.g., for applications involving bandits or active learning. One simple approach to this is to use online Monte Carlo methods, such as SGLD (stochastic gradient Langevin dynamics). Unfortunately, such a method needs to store many copies of the parameters (which wastes memory), and needs to make predictions using man
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Bayesian Dark Knowledge is a method for compressing the posterior predictive distribution of a neural network model into a more compact form. Specifically, the method attempts to compress a Monte Carlo approximation to the parameter posterior into a single network representing the posterior predictive distribution. Further, the authors show that this approach is successful in the classification setting using a student network whose architecture matches that of a single network in the teacher ensemble. In this work, we examine the robustness of Bayesian Dark Knowledge to higher levels of posterior uncertainty. We show that using a student network that matches the teacher architecture may fail to yield acceptable performance. We study an approach to close the resulting performance gap by increasing student model capacity.
Knowledge distillation is a popular technique for training a small student network to emulate a larger teacher model, such as an ensemble of networks. We show that while knowledge distillation can improve student generalization, it does not typically work as it is commonly understood: there often remains a surprisingly large discrepancy between the predictive distributions of the teacher and the student, even in cases when the student has the capacity to perfectly match the teacher. We identify difficulties in optimization as a key reason for why the student is unable to match the teacher. We also show how the details of the dataset used for distillation play a role in how closely the student matches the teacher -- and that more closely matching the teacher paradoxically does not always lead to better student generalization.
We present two algorithms for Bayesian optimization in the batch feedback setting, based on Gaussian process upper confidence bound and Thompson sampling approaches, along with frequentist regret guarantees and numerical results.
In most cases deep learning architectures are trained disregarding the amount of operations and energy consumption. However, some applications, like embedded systems, can be resource-constrained during inference. A popular approach to reduce the size of a deep learning architecture consists in distilling knowledge from a bigger network (teacher) to a smaller one (student). Directly training the student to mimic the teacher representation can be effective, but it requires that both share the same latent space dimensions. In this work, we focus instead on relative knowledge distillation (RKD), which considers the geometry of the respective latent spaces, allowing for dimension-agnostic transfer of knowledge. Specifically we introduce a graph-based RKD method, in which graphs are used to capture the geometry of latent spaces. Using classical computer vision benchmarks, we demonstrate the ability of the proposed method to efficiently distillate knowledge from the teacher to the student, leading to better accuracy for the same budget as compared to existing RKD alternatives.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
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