Sparse coding models predict a spectral bias in the development of primary visual cortex (V1) receptive fields

It is well known that sparse coding models trained on natural images learn basis functions whose shapes resemble the receptive fields (RFs) of simple cells in the primary visual cortex (V1). However, few studies have considered how these basis functions develop during training. In particular, it is unclear whether certain types of basis functions emerge more quickly than others, or whether they develop simultaneously. In this work, we train an overcomplete sparse coding model (Sparsenet) on natural images and find that there is indeed order in the development of its basis functions, with basis functions tuned to lower spatial frequencies emerging earlier and higher spatial frequency basis functions emerging later. We observe the same trend in a biologically plausible sparse coding model (SAILnet) that uses leaky integrate-and-fire neurons and synaptically local learning rules, suggesting that this result is a general feature of sparse coding. Our results are consistent with recent experimental evidence that the distribution of optimal stimuli for driving neurons to fire shifts towards higher frequencies during normal development in mouse V1. Our analysis of sparse coding models during training yields an experimentally testable prediction for V1 development that this shift may be due in part to higher spatial frequency RFs emerging later, as opposed to a global shift towards higher frequencies across all RFs, which may also play a role. We also find that at least two explanations could account for the order of RF development: 1) high frequency RFs require more information to be specified accurately, and thus may require more visual experience in order to learn, and 2) early development of low frequency RFs improves the sparseness and fidelity of the visual representation more than early development of high frequency RFs. Author summary We are interested in how visual neurons learn representations of the natural world. In particular, we want to know whether certain visual features are learned by the visual cortex earlier in development than others. To address this question, we turn to a class of algorithms that can learn to represent natural scenes in a sparse fashion, with only a few neurons active at any given time (population sparseness). While sparse coding has been used extensively to model the response properties of neurons in the visual cortex, we use it here to arrive at a quantitative description of the way neurons might learn to encode visual information during development. We find that receptive fields (RFs) tuned to lower spatial frequencies develop earlier in our sparse coding models compared to high frequency RFs. If our prediction is accurate, such a description would provide a general framework for understanding the development of the functional properties of V1 neurons and serve as a guide for future experimental studies. It could also lead to new computational models that learn from input statistics, as well as advances in the design of devices that can augment or replace human vision. ### Competing Interest Statement The authors have declared no competing interest.