A mathematical theory of semantic development in deep neural networks

An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, organize, and deploy abstract knowledge by integrating across many individual experiences? We address this question by mathematically analyzing the nonlinear dynamics of learning in deep linear networks. We find exact solutions to this learning dynamics that yield a conceptual explanation for the prevalence of many disparate phenomena in semantic cognition, including the hierarchical differentiation of concepts through rapid developmental transitions, the ubiquity of semantic illusions between such transitions, the emergence of item typicality and category coherence as factors controlling the speed of semantic processing, changing patterns of inductive projection over development, and the conservation of semantic similarity in neural representations across species. Thus, surprisingly, our simple neural model qualitatively recapitulates many diverse regularities underlying semantic development, while providing analytic insight into how the statistical structure of an environment can interact with nonlinear deep learning dynamics to give rise to these regularities

Dynamics of neural cryptography

Synchronization of neural networks has been used for novel public channel protocols in cryptography. In the case of tree parity machines the dynamics of both bidirectional synchronization and unidirectional learning is driven by attractive and repulsive stochastic forces. Thus it can be described well by a random walk model for the overlap between participating neural networks. For that purpose transition probabilities and scaling laws for the step sizes are derived analytically. Both these calculations as well as numerical simulations show that bidirectional interaction leads to full synchronization on average. In contrast, successful learning is only possible by means of fluctuations. Consequently, synchronization is much faster than learning, which is essential for the security of the neural key-exchange protocol. However, this qualitative difference between bidirectional and unidirectional interaction vanishes if tree parity machines with more than three hidden units are used, so that those neural networks are not suitable for neural cryptography. In addition, the effective number of keys which can be generated by the neural key-exchange protocol is calculated using the entropy of the weight distribution. As this quantity increases exponentially with the system size, brute-force attacks on neural cryptography can easily be made unfeasible.Comment: 9 pages, 15 figures; typos correcte

Model Learning for Look-ahead Exploration in Continuous Control

We propose an exploration method that incorporates look-ahead search over basic learnt skills and their dynamics, and use it for reinforcement learning (RL) of manipulation policies . Our skills are multi-goal policies learned in isolation in simpler environments using existing multigoal RL formulations, analogous to options or macroactions. Coarse skill dynamics, i.e., the state transition caused by a (complete) skill execution, are learnt and are unrolled forward during lookahead search. Policy search benefits from temporal abstraction during exploration, though itself operates over low-level primitive actions, and thus the resulting policies does not suffer from suboptimality and inflexibility caused by coarse skill chaining. We show that the proposed exploration strategy results in effective learning of complex manipulation policies faster than current state-of-the-art RL methods, and converges to better policies than methods that use options or parametrized skills as building blocks of the policy itself, as opposed to guiding exploration. We show that the proposed exploration strategy results in effective learning of complex manipulation policies faster than current state-of-the-art RL methods, and converges to better policies than methods that use options or parameterized skills as building blocks of the policy itself, as opposed to guiding exploration.Comment: This is a pre-print of our paper which is accepted in AAAI 201

A Self-Organizing System for Classifying Complex Images: Natural Textures and Synthetic Aperture Radar

A self-organizing architecture is developed for image region classification. The system consists of a preprocessor that utilizes multi-scale filtering, competition, cooperation, and diffusion to compute a vector of image boundary and surface properties, notably texture and brightness properties. This vector inputs to a system that incrementally learns noisy multidimensional mappings and their probabilities. The architecture is applied to difficult real-world image classification problems, including classification of synthetic aperture radar and natural texture images, and outperforms a recent state-of-the-art system at classifying natural texturns.Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-91-J-4100); Advanced Research Projects Agency (N00014-92-J-4015); Air Force Office of Scientific Research (F49620-92-J-0225, F49620-92-J-0334); National Science Foundation (IRI-90-00530, IRI-90-24877

A Self-Organizing System for Classifying Complex Images: Natural Textures and Synthetic Aperture Radar

A self-organizing architecture is developed for image region classification. The system consists of a preprocessor that utilizes multi-scale filtering, competition, cooperation, and diffusion to compute a vector of image boundary and surface properties, notably texture and brightness properties. This vector inputs to a system that incrementally learns noisy multidimensional mappings and their probabilities. The architecture is applied to difficult real-world image classification problems, including classification of synthetic aperture radar and natural texture images, and outperforms a recent state-of-the-art system at classifying natural texturns.Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-91-J-4100); Advanced Research Projects Agency (N00014-92-J-4015); Air Force Office of Scientific Research (F49620-92-J-0225, F49620-92-J-0334); National Science Foundation (IRI-90-00530, IRI-90-24877