Logarithmic nature of the brain 💡

The video contrasts two ways randomness can combine—addition and multiplication—and shows how each leads to qualitatively different distributions: Gaussian vs lognormal.

Many key neural variables, including firing rates and synaptic strengths, follow lognormal rather than Gaussian distributions, with a majority of small values and a minority of very large ones.

Lognormal firing and weight distributions support a functional division of labor in neural networks between “generalizer” neurons and “specialists,” forming a rich-club-like organization.

Changes in dendritic spine size—a proxy for synaptic strength—follow multiplicative dynamics that naturally produce lognormal distributions, offering a mechanistic explanation for skewed synaptic weights.

The “log-dynamic brain” perspective proposes that skewed, lognormal-like distributions are pervasive in neural systems, shaping everything from microcircuit operations to perception.