Responses to transient perturbation can distinguish intrinsic from latent criticality in spiking neural populations

The critical brain hypothesis posits that neural circuitry operates near criticality to reap the computational benefits of accessing a wide range of timescales. The theory of critical phenomena generally predicts heavy-tailed (power-law) correlations in space and time near criticality, but it has been argued that in the brain such correlations could be inherited from ``latent variables,'' such as external sensory signals that are not directly observed when recording from neural circuitry. Distinguishing whether heavy-tailed correlations in neural activity are intrinsically generated within a neural circuit or are driven by unobserved latent variables is crucial for properly interpreting circuit functions. We argue that measuring neural responses to sudden perturbative inputs, rather than correlations in ongoing activity, can disambiguate these cases. We demonstrate this approach in a model of stochastic spiking neuron populations receiving external latent input that can be tuned to a critical state. We propose a scaling theory for the covariance and response functions of the spiking network, which we validate with simulations. We end by discussing how our approach might generalize to models of neural populations with more realistic biophysical details.