Layer-wise Learning of Kernel Dependence Networks

Due to recent debate over the biological plausibility of backpropagation (BP), finding an alternative network optimization strategy has become an active area of interest. We design a new type of kernel network, that is solved greedily, to theoretically answer several questions of interest. First, if BP is difficult to simulate in the brain, are there instead "trivial network weights" (requiring minimum computation) that allow a greedily trained network to classify any pattern. Perhaps a simple repetition of some basic rule can yield a network equally powerful as ones trained by BP with Stochastic Gradient Descent (SGD). Second, can a greedily trained network converge to a kernel? What kernel will it converge to? Third, is this trivial solution optimal? How is the optimal solution related to generalization? Lastly, can we theoretically identify the network width and depth without a grid search? We prove that the kernel embedding is the trivial solution that compels the greedy procedure to converge to a kernel with Universal property. Yet, this trivial solution is not even optimal. By obtaining the optimal solution spectrally, it provides insight into the generalization of the network while informing us of the network width and depth

Explanation Uncertainty with Decision Boundary Awareness

Post-hoc explanation methods have become increasingly depended upon for understanding black-box classifiers in high-stakes applications, precipitating a need for reliable explanations. While numerous explanation methods have been proposed, recent works have shown that many existing methods can be inconsistent or unstable. In addition, high-performing classifiers are often highly nonlinear and can exhibit complex behavior around the decision boundary, leading to brittle or misleading local explanations. Therefore, there is an impending need to quantify the uncertainty of such explanation methods in order to understand when explanations are trustworthy. We introduce a novel uncertainty quantification method parameterized by a Gaussian Process model, which combines the uncertainty approximation of existing methods with a novel geodesic-based similarity which captures the complexity of the target black-box decision boundary. The proposed framework is highly flexible; it can be used with any black-box classifier and feature attribution method to amortize uncertainty estimates for explanations. We show theoretically that our proposed geodesic-based kernel similarity increases with the complexity of the decision boundary. Empirical results on multiple tabular and image datasets show that our decision boundary-aware uncertainty estimate improves understanding of explanations as compared to existing methods