Dynamic Topology Neural-Spike Computing Networks

Abstract

This paper proposes a novel approach to computing leveraging dynamic topology neural-spike networks. The core idea centers on mimicking the self-adaptive topology structures found in biological neural networks to achieve higher efficiency and robustness in complex computational tasks. We introduce a programmable hardware platform composed of simulated neurons with dynamic connections and synaptic plasticity. Utilizing machine learning algorithms, specifically reinforcement learning, we continuously optimize the network topology in response to task demands, encompassing node addition, removal, and weight adjustments. This dynamic adaptation allows the network to real-time adjust to fluctuating input data, realizing adaptive computation. The innovation lies in the *dynamic* topology, contrasting with static structures or simplified models in existing neural-spike computing systems. By integrating parallel processing with machine learning optimization, our framework promises enhanced computational efficiency and resilience, representing a significant advancement over conventional neural-spike computing paradigms. The key mathematical framework revolves around representing the network topology as a graph (G = (V, E)), where V is the set of nodes (neurons) and E is the set of edges (connections) with associated weights. The dynamics of the network are governed by the following stochastic differential equations: d*s*i/dt = ∑j∈N(i) *w*ij *s*j + *f*i, where *s*i is the state of neuron *i*, *w*ij is the synaptic weight connecting neuron *i* to neuron *j*, *N(i)* is the set of neurons connected to neuron *i*, and *f*i represents a stochastic input or intrinsic noise. The learning process is formulated as a Markov Decision Process (MDP), and the policy is learned using reinforcement learning algorithms, aiming to maximize the expected reward. The core of the system can be represented as: R = ∑i αi *s*i, where αi is the activation function of neuron *i*. The system is designed to minimize the error between the output and the desired output, using a cost function: E = ∑i || *s*i - *t*i||2.