Towards Robust, Locally Linear Deep Networks
This addresses the problem of unstable derivatives for sensitivity analysis and prediction explanation in deep learning, representing an incremental improvement.
The paper tackles the instability of derivatives in deep networks by proposing a learning problem to encourage stable derivatives over larger regions, focusing on networks with piecewise linear activation functions, and demonstrates results on image and sequence datasets using residual and recurrent networks.
Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to explain (obtain coordinate relevance for) a prediction. One key challenge is that such derivatives are themselves inherently unstable. In this paper, we propose a new learning problem to encourage deep networks to have stable derivatives over larger regions. While the problem is challenging in general, we focus on networks with piecewise linear activation functions. Our algorithm consists of an inference step that identifies a region around a point where linear approximation is provably stable, and an optimization step to expand such regions. We propose a novel relaxation to scale the algorithm to realistic models. We illustrate our method with residual and recurrent networks on image and sequence datasets.