2022/04/18 by Iván A. Davidovich, Davidovich, Iván A., Yasser Roudi +1
Computer Science · Neuroscience · #FOS: Biological sciences #Functional Brain Connectivity Studies #Neural Networks and Applications #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Quantitative Methods (q-bio.QM)
paper · pdf · doi:10.48550/arxiv.2204.08525
openalex publication_date 2022/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Power laws arise in a variety of phenomena ranging from matter undergoing phase transition to the distribution of word frequencies in the English language. Usually, their presence is only apparent when data is abundant, and accurately determining their exponents often requires even larger amounts of data. As the scale of recordings in neuroscience becomes larger, an increasing number of studies attempt to characterise potential power-law relationships in neural data. In this paper, we aim to discuss the potential pitfalls that one faces in such efforts and to promote a Bayesian interpolation framework for this purpose. We apply this framework to synthetic data and to data from a recent study of large-scale recordings in mouse primary visual cortex (V1), where the exponent of a power-law scaling in the data played an important role: its value was argued to determine whether the population's stimulus-response relationship is smooth, and experimental data was provided to confirm that this is indeed so. Our analysis shows that with such data types and sizes as we consider here, the best-fit values found for the parameters of the power law and the uncertainty for these estimates are heavily dependent on the noise model assumed for the estimation, the range of the data chosen, and (with all other things being equal) the particular recordings. It is thus challenging to offer a reliable statement about the exponents of the power law. Our analysis, however, shows that this does not affect the conclusions regarding the smoothness of the population response to low-dimensional stimuli but casts doubt on those to natural images. We discuss the implications of this result for the neural code in the V1 and offer the approach discussed here as a framework that future studies, perhaps exploring larger ranges of data, can employ as their starting point to examine power-law scalings in neural data.