Stability versus Neuronal Specialization for STDP: Long-Tail Weight Distributions Solve the Dilemma

Abstract:

The majority of distinct motor (and sensory) events are encountered as temporally ordered sequences with rich probabilistic structure. Although much is known about how linear sequences are produced and learned, much less is known about more general probabilistic sequences. Using the Bengalese finch, a songbird that sings probabilistically sequenced songs, as a model system of sequence production, we show that sequence probability, mean inter-syllable timing, and timing variability are positively correlated, almost necessarily. Further, we show that a simple synaptic chain-like circuit is sufficient to recapitulate the observed sequential-temporal structure of song.

Interestingly, this circuit is functionally similar to circuits for optimal decision-making, suggesting that sequence generation in birds can be viewed as a kind of sequential decision-making task. Furthermore, this circuit motivates a theoretical investigation of the Hebbian mechanisms that engrain experienced sequential statistics in the outgoing/incoming synaptic weights of a neuron. Through both simulations and analytic calculations, we show that a Hebbian synaptic plasticity rule with pre-synaptic competition develops synaptic weights that represent the conditional forward transition probabilities present in the input sequence while post-synaptic competition gives rise to a synaptic representation of the conditional backward probabilities of the same input sequence. We demonstrate that to stably but flexibly reflect the conditional probability of a neurons inputs/outputs, local Hebbian plasticity should balance the magnitude of synaptic depression relative to potentiation (strength of competitive force) with the weight dependence of synaptic change (strength of homogenizing force). These forces interact to control both the rate at which structure emerges and the entropy of the final distribution of synaptic weights. These results demonstrate that the site of synaptic competition dictates the learned probabilistic structure and highlights the necessity of balancing competitive and homogenizing forces in learning.