Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking

This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications

Input and Weight Space Smoothing for Semi-supervised Learning

We propose regularizing the empirical loss for semi-supervised learning by acting on both the input (data) space, and the weight (parameter) space. We show that the two are not equivalent, and in fact are complementary, one affecting the minimality of the resulting representation, the other insensitivity to nuisance variability. We propose a method to perform such smoothing, which combines known input-space smoothing with a novel weight-space smoothing, based on a min-max (adversarial) optimization. The resulting Adversarial Block Coordinate Descent (ABCD) algorithm performs gradient ascent with a small learning rate for a random subset of the weights, and standard gradient descent on the remaining weights in the same mini-batch. It achieves comparable performance to the state-of-the-art without resorting to heavy data augmentation, using a relatively simple architecture