Exposure Bias and State Matching in Recurrent Neural Network Virtual Analog Models

Virtual analog (VA) modeling using neural networks (NNs) has great potential for rapidly producing high-fidelity models. Recurrent neural networks (RNNs) are especially appealing for VA due to their connection with discrete nodal analysis. Furthermore, VA models based on NNs can be trained efficiently by directly exposing them to the circuit states in a gray-box fashion. However, exposure to ground truth information during training can leave the models susceptible to error accumulation in a free-running mode, also known as “exposure bias” in machine learning literature. This paper presents a unified framework for treating the previously proposed state trajectory network (STN) and gated recurrent unit (GRU) networks as special cases of discrete nodal analysis. We propose a novel circuit state-matching mechanism for the GRU and experimentally compare the previously mentioned networks for their performance in state matching, during training, and in exposure bias, during inference. Experimental results from modeling a diode clipper show that all the tested models exhibit some exposure bias, which can be mitigated by truncated backpropagation through time. Furthermore, the proposed state matching mechanism improves the GRU modeling performance of an overdrive pedal and a phaser pedal, especially in the presence of external modulation, apparent in a phaser circuit.