Task to be learned (a, top) An example of a task used to test the model. Stimulus patterns evolve in time according to structured transition probabilities. The presentation of each stimulus pattern activates the corresponding group of neurons. Recurrent connections are learned by synaptic plasticity (a, bottom). The learned network should replay assemblies spontaneously, where the transition statistics are consistent with the evoked stimuli. (b) A network model with distinct excitatory and inhibitory populations. Only excitatory populations are driven by external inputs. Only synapses that project to excitatory neurons are assumed to be plastic. (c) A schematic of the proposed plasticity rules. Excitatory (blue) and inhibitory (orange) synapses projecting to an excitatory neuron (triangle) obey different plasticity rules. For excitatory synapses, errors between internally driven excitation (blue sigmoid) and the output of the cell provide feedback to the synapses and modulate plasticity (blue square). All excitatory connections seek to minimize such errors. For inhibitory synapses, the error between internally driven excitation (blue sigmoid) and inhibition (orange sigmoid) should be minimized to maintain excitatory inhibitory balance (orange square).

Spontaneous replay of stochastic transition of assemblies. (a) First, we considered a simple stochastic transition between three stimulus patterns. (b) Dynamics of weight change via plasticity. Excitatory synapses (blue) converged quicker than inhibitory synapses (orange). (c) Example spontaneous assembly reactivations (top) and raster plot (bottom) of the learned network are shown. Colors indicate the corresponding stimulus patterns shown in a. (d) Distribution of assembly reactivations. (e, left) The network currents to assembly 1 (green) and assembly 2 (orange) immediately after the reactivation of assembly 3 ceased. Both currents were similar in magnitude. (e, right) Currents to assembly 2 (orange) and assembly 3 (blue) immediately after the reactivation of assembly 1 ceased. The current to assembly 3 was stronger than that to assembly 2. (f) Relationship between the transition statistics of stimulus patterns and that of replayed assemblies. The spontaneous activity reproduced transition statistics of external stimulus patterns.

Learned excitatory synapses encode transition statistics. (a) A 3 by 3 matrix of excitatory connections, learned with the task in Fig.2a (left). The matrix can be decomposed to within- (middle) and between-assembly connections (right). (b) Strength of within- (top) and that of betweenassembly excitatory synapses (bottom) during learning are shown. (c) True transition matrix of stimulus patterns. (d) Relationship between the strength of excitatory synapses between assemblies and true transition probabilities between patterns.

Learning complex structures. (a) Transition diagram of complex task. (b) Spontaneous activity of learned network. (c) Transition statistics of assemblies reproduce true statistics. (d) Transition diagram of temporal community structure. (e) Raster plot of spontaneous activity of the network trained over structure shown in (d). (f) Structure of learned excitatory synapses encode the community structure. (g) Spontaneous transition between assemblies connected in the diagram shown in d occurs much frequent than disconnected case. (h) Low dimensional representation of evoked activity patterns shows high similarity with community structure. (i) Time courses of replayed activities transitioning within (red) and between (blue) communities. (j) Comparison of mean durations in (i). P-value was calculated by two-sided Welch’s t-test.

Network dynamics consistent with recorded neural data of songbird (a) Example poststimulus activity (PSA) for low- (left) and high-entropy (right) transition cases. (b) Comparison of correlation coefficients between PSA and evoked single-syllable responses for next syllables and other syllables. For low entropy transition case, the next-syllables correlations were significantly higher than other-syllables correlations (p < 0.01, Wilcoxon signed-rank test) (left). In contrast, such correlation coefficients showed no significant difference for high entropy transition case (p > 0.3, Wilcoxon signed-rank test) (right). Red crosses are mean. (c) The difference in correlation coefficients between next and other syllables (ΔR) was significantly greater for low entropy transitions than for high entropy transitions (p < 0.01, two-sided Welch’s t-test).

Definition of variables and functions.

Parameter settings.