Quantifying neural coding noise in linear threshold models

Neurons integrating sensory stimulus features are found in many brain areas up to cortical level, and their understanding is essential for building and improving neural prostheses. Here, we focus on auditory neural coding in the inferior colliculus (IC). Much work has been conducted to identify the primary spectro-temporal sound features. However, a description of how reliable these features are encoded at IC level remains an open question. In a simplified model, the encoding process can be described by a linear integrator followed by a threshold nonlinearity that creates a binary spike sequence. To account for variability in neural responses, coding noise has to be taken into account. However, coding noise reduces the certainty about the stimulus features encoded. Traditional approaches to quantify the amount of noise based on information theory are prone to sampling bias and cannot be bounded in a simply way, making it hard to interpret the results obtained and to compare them across neural populations. Here, we reformulate neural coding as a spike detection task and show that methods from signal detection theory allow an alternative description to quantify coding noise. Using neural responses from the IC in Mongolian gerbils to acoustic stimuli, we demonstrate that this approach allows a reliable description of neural coding noise, particularly in the small data limit, while being highly correlated with information-theoretic quantities in the large-data regime.