During limb movements, neurons of the primary motor cortex (M1) exhibit large, temporally complex, and short-lived activity transients. To account for these, we have recently proposed a new type of balanced architectures, in which strong and intricate recurrent excitation (E) is stabilized by detailed feedback inhibition (I) [1]. While we were able to construct such networks using algorithms from control theory and optimization, exactly how stabilizing feedback can be learned through realistic forms of inhibitory synaptic plasticity (ISP) remains unclear. Here we resolved this question in balanced networks with linear(ized) stochastic rate dynamics. First, we numerically confirmed a simple intuition: that Hebbian ISP [2], known to establish a detailed E/I balance in feedforward circuits, successfully stabilizes continuous growth in recurrent excitation. However, for strong enough excitation, ISP eventually fails. To understand – and ultimately circumvent – this limitation, we formulated optimal ISP as H2-norm minimization, a well-known control-theoretic approach to robust stability optimization. Through direct analytical comparisons with the optimal solution, we could show that Hebbian ISP always increases the degree of network stability, but becomes progressively less effective as excitatory connectivity builds up. Indeed, in that regime, knowledge of pre/post-synaptic activity correlations (the essence of Hebbian ISP) must be complemented by information about the network’s input sensitivity (“which inputs evoke the strongest collective responses?"). Surprisingly, this information can be collected locally via a spontaneous diffusion process running backwards through the synapses.We thus augmented Hebbian ISP with retrograde messengers, and obtained greatly enhanced stabilization performance over a much broader range of connectivity strengths. Our results provide the foundations for understanding how the brain reaches global objectives (here, stability) through local synaptic modifications, and suggest a new functional role for retrograde synaptic transmission.

References

• [1] Hennequin et al., Neuron (2014)
• [2] Vogels et al., Science (2011)