Mapping the Diffusion Network into a stochastic system in Very Large Scale Integration

Abstract

The Diffusion Network (DN) is a probabilistic model capable of recognising continuous-time, continuous valued biomedical data. As the stochastic process of the DN is described by stochastic differential equations, realising the DN with analogue circuits is important to facilitate real-time simulation of a large network. This paper presents the trans lation of the DN into analogue Very Large Scale Integration (VLSI). With extensive simulation, the dynamic ranges of parameters and their representation in VLSI are identified.The VLSI circuits realising the stochastic unit of the DN are further designed and interconnected to form a stochastic system using noise to induce stochastic dynamics in VLSI. The circuit simulation demonstrate that the VLSI translation of the DN is satisfactory and the DN system is capable of using noise-induced stochastic dynamics to regenerate various types of continuous time sequences. I. I NTRODUCTIONThe Diffusion Network (DN) proposed by Movellan is a stochastic recurrent network whose stochastic dynamics can be trained to model the probability distributions of continuous-time sequences by the Monte-Carlo Expectation Maximisation (EM) algorithm [1], [2]. As stochasticity is useful for generalising the natural variability in data [3][4], the DN is further shown suitable for recognising noisy, continuous-time biomedical data [5]. However, the stochastic dynamics of the DN is defined by a set of continuous-time, stochastic differential equations. The speed of simulating stochastic differential equations in a digital computer is inherently limited by the serial processing and numerical iterations of the computer. Translating the DN into analogue circuits is thus important for simulating a large DN in real time. The hardware implementation of the DN could further function as an intelligent embedded system capa ble of recognising in real time multichannel, time-varying biomedical signals, for example, the neural activity recorded by a microprobe array in a brain-machine interface. In such applications, a DN system would enable implantable mi crosystems to deliver bio-feedbacks or to control prosthetic devices in real time [6].This paper presents the translation of the DN into a stochastic VLSI system using analogue circuits with noise induced stochasticity. Although analogue circuits are more vulnerable to noise interferences and hardware non-idealities, stochastic behaviour in analogue circuits can actually dis courage the propagation of computational errors and thus enhance the robustness against interferences and errors, as 978-1-�8lWtle1$26':PO ©201 0 IEEE demonstrated in [7]. The proposed DN system in VLSI is thus designed to exhibit noise-induced, continuous-valued stochastic behaviour as [8]. Following a brief review on the DN model, the dynamic ranges of parameters essential for modelling data satisfactorily are first identified with Matlab simulation. The representation of parameters in VLSI are then defined, and the component circuits for realising the DN are designed. Finally, the si...