Invariant correlation: a general and straightforward method to quantify invariance in time-varying neural signals.

Recognizing information in natural stimuli is challenging because sensory inputs for different instances of the same feature often vary substantially. Successful recognition thus requires neural systems to generate representations that are invariant to such variation, posing a fundamental computational challenge for sensory coding. Much remains unknown about how sensory systems code invariant information in complex, temporally dynamic stimuli such as speech, in part due to methodological challenges in measuring and modeling invariance from noisy, time-varying neural responses. Here, we introduce the "invariant correlation", a straightforward and general method for directly quantifying the strength and temporal dynamics of invariance from time-varying neural signals and computational models. We demonstrate its utility by quantifying invariance to acoustic variation in neural representations of phonemes using spatiotemporally precise intracranial recordings from human auditory cortex. Our method successfully revealed substantial diversity in the strength and dynamics of invariance across the human auditory cortex and across different phonetic features within individual electrodes. We illustrate how many of these empirically measured patterns can be explained by applying the same analysis to the predictions from a simple computational model based on spectrotemporal tuning in a cochleagram representation of sound. Although we focus here on speech, the invariant correlation is a broadly applicable tool for characterizing the organization and computational mechanisms underlying invariant representations of dynamic stimuli across sensory modalities.