An alternative to backpropagation through time

Recurrent neural networks for dynamical systems: Applications to ordinary differential equations, collective motion, and hydrological modeling

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development and implementation of linear methods are relatively simple, but they often do not capture non-linear relationships in the data. Thus, artificial neural networks (ANNs) are receiving attention from researchers in analyzing and forecasting dynamical systems. Recurrent neural networks (RNNs), derived from feed-forward ANNs, use internal memory to process variable-length sequences of inputs. This allows RNNs to be applicable for finding solutions for a vast variety of problems in spatiotemporal dynamical systems. Thus, in this paper, we utilize RNNs to treat some specific issues associated with dynamical systems. Specifically, we analyze the performance of RNNs applied to three tasks: reconstruction of correct Lorenz solutions for a system with a formulation error, reconstruction of corrupted collective motion trajectories, and forecasting of streamflow time series possessing spikes, representing three fields, namely, ordinary differential equations, collective motion, and hydrological modeling, respectively. We train and test RNNs uniquely in each task to demonstrate the broad applicability of RNNs in the reconstruction and forecasting the dynamics of dynamical systems.

Presynaptic spike-driven plasticity based on eligibility trace for on-chip learning system

Introduction

Recurrent spiking neural network (RSNN) performs excellently in spatio-temporal learning with backpropagation through time (BPTT) algorithm. But the requirement of computation and memory in BPTT makes it hard to realize an on-chip learning system based on RSNN. In this paper, we aim to realize a high-efficient RSNN learning system on field programmable gate array (FPGA).

Methods

A presynaptic spike-driven plasticity architecture based on eligibility trace is implemented to reduce the resource consumption. The RSNN with leaky integrate-and-fire (LIF) and adaptive LIF (ALIF) models is implemented on FPGA based on presynaptic spike-driven architecture. In this architecture, the eligibility trace gated by a learning signal is used to optimize synaptic weights without unfolding the network through time. When a presynaptic spike occurs, the eligibility trace is calculated based on its latest timestamp and drives synapses to update their weights. Only the latest timestamps of presynaptic spikes are required to be stored in buffers to calculate eligibility traces.

Results

We show the implementation of this architecture on FPGA and test it with two experiments. With the presynaptic spike-driven architecture, the resource consumptions, including look-up tables (LUTs) and registers, and dynamic power consumption of synaptic modules in the on-chip learning system are greatly reduced. The experiment results and compilation results show that the buffer size of the on-chip learning system is reduced and the RSNNs implemented on FPGA exhibit high efficiency in resources and energy while accurately solving tasks.

Discussion

This study provides a solution to the problem of data congestion in the buffer of large-scale learning systems.