Slowness and sparseness have diverging effects on complex cell learning.

Area of Science:

• Computational neuroscience
• Visual system processing
• Machine learning for neuroscience

Background:

• Sparse coding principles have been proposed to explain complex cell receptive fields in the primary visual cortex.
• Previous studies suggested that receptive field properties could be derived from a slowness principle, similar to sparsity.

Purpose of the Study:

• To investigate whether slowness and sparsity principles lead to similar or different receptive field properties.
• To compare representations learned by slow subspace analysis (SSA) with those learned by independent subspace analysis (ISA).

Main Methods:

• Employed slow subspace analysis (SSA) to learn basis functions from natural movies and transformed natural images (translations, rotations, scalings).
• Directly paralleled SSA with independent subspace analysis (ISA), differing only in optimizing for slowness versus sparsity.
• Analyzed the discrepancy between filter shapes generated by SSA and ISA.

Main Results:

• Demonstrated that slowness and sparsity drive representations towards substantially different receptive field properties.
• Observed a large discrepancy between filter shapes learned using SSA and ISA.
• Interpreted SSA as a generalization of the Fourier transform, linking power spectra to maximally slow subspace energies.

Conclusions:

• Contradicts the claim that receptive field properties derived from slowness are equivalent to those derived from sparsity.
• Highlights the distinct nature of representations learned through slowness maximization versus sparsity maximization.
• Suggests further investigation into the trade-offs when combining slowness and sparseness in objective functions for neural representation learning.