Guillaume Hennequin

Optimal control of transient dynamics in balanced networks supports generation of complex movements.

Populations of neurons in motor cortex engage in complex transient dynamics of large amplitude during the execution of limb movements. Traditional network models with stochastically assigned synapses cannot reproduce this behavior. Here we introduce a class of cortical architectures with strong and random excitatory recurrence that is stabilized by intricate, fine-tuned inhibition, optimized from a control theory perspective. Such networks transiently amplify specific activity states and can be used to reliably execute multidimensional movement patterns. Similar to the experimental observations, these transients must be preceded by a steady-state initialization phase from which the network relaxes back into the background state by way of complex internal dynamics. In our networks, excitation and inhibition are as tightly balanced as recently reported in experiments across several brain areas, suggesting inhibitory control of complex excitatory recurrence as a generic organizational principle in cortex.

Synaptic Plasticity in Neural Networks Needs Homeostasis with a Fast Rate Detector

Hebbian changes of excitatory synapses are driven by and further enhance correlations between pre- and postsynaptic activities. Hence, Hebbian plasticity forms a positive feedback loop that can lead to instability in simulated neural networks. To keep activity at healthy, low levels, plasticity must therefore incorporate homeostatic control mechanisms. We find in numerical simulations of recurrent networks with a realistic triplet-based spike-timing-dependent plasticity rule (triplet STDP) that homeostasis has to detect rate changes on a timescale of seconds to minutes to keep the activity stable. We confirm this result in a generic mean-field formulation of network activity and homeostatic plasticity. Our results strongly suggest the existence of a homeostatic regulatory mechanism that reacts to firing rate changes on the order of seconds to minutes.

Non-normal amplification in random balanced neuronal networks

In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W not being normal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the trade-off between non-normal amplification and dynamical slowing in the spontaneous activity of large random neuronal networks composed of excitatory and inhibitory neurons. We use a Schur decomposition of W to separate the two amplification mechanisms. Assuming linear stochastic dynamics, we derive an exact expression for the expected amount of purely non-normal amplification. We find that amplification is very limited if dynamical slowing must be kept weak. We conclude that, to achieve strong transient amplification with little slowing, the connectivity must be structured. We show that unidirectional connections between neurons of the same type together with reciprocal connections between neurons of different types, allow for amplification already in the fast dynamical regime. Finally, our results also shed light on the differences between balanced networks in which inhibition exactly cancels excitation and those where inhibition dominates.

Stabilized supralinear network dynamics account for stimulus-induced changes of noise variability in the cortex

Variability and correlations in cortical activity are ubiquitously modulated by stimuli. Correlated variability is quenched following stimulus onset across multiple cortical areas, suppressing low-frequency components of the LFP and of Vm-LFP coherence. Modulation of Fano factors and correlations in area MT is tuned for stimulus direction. What circuit mechanisms underly these behaviors? We show that a simple model circuit, the stochastic Stabilized Supralinear Network (SSN), robustly explains these results. Stimuli modulate variability by modifying two forms of effective connectivity between activity patterns that characterize excitatory-inhibitory (E/I) circuits. Increases in the strength with which activity patterns inhibit themselves reduce correlated variability, while increases in feedforward connections between patterns (transforming E/I imbalance into balanced fluctuations) increase variability. These results suggest an operating regime of cortical dynamics that involves fast fluctuations and fast responses to stimulus changes, unlike previous models of variability suppression through suppression of chaos or networks with multiple attractors.

Motor primitives in space and time via targeted gain modulation in cortical networks

Motor cortex (M1) exhibits a rich repertoire of activities to support the generation of complex movements. Although recent neuronal-network models capture many qualitative aspects of M1 dynamics, they can generate only a few distinct movements. Additionally, it is unclear how M1 efficiently controls movements over a wide range of shapes and speeds. We demonstrate that simple modulation of neuronal input–output gains in recurrent neuronal-network models with fixed architecture can dramatically reorganize neuronal activity and thus downstream muscle outputs. Consistent with the observation of diffuse neuromodulatory projections to M1, we show that a relatively small number of modulatory control units provide sufficient flexibility to adjust high-dimensional network activity using a simple reward-based learning rule. Furthermore, it is possible to assemble novel movements from previously learned primitives, and one can separately change movement speed while preserving movement shape. Our results provide a new perspective on the role of modulatory systems in controlling recurrent cortical activity.

Null Ain’t Dull: New Perspectives on Motor Cortex

Classical work has viewed primary motor cortex (M1) as a controller of muscle and body dynamics. A recent brain-computer interface (BCI) experiment suggests a new, complementary perspective: M1 is itself a dynamical system under active control of other circuits.

The Dynamical Regime of Sensory Cortex: Stable Dynamics around a Single Stimulus-Tuned Attractor Account for Patterns of Noise Variability

Summary Correlated variability in cortical activity is ubiquitously quenched following stimulus onset, in a stimulus-dependent manner. These modulations have been attributed to circuit dynamics involving either multiple stable states (“attractors”) or chaotic activity. Here we show that a qualitatively different dynamical regime, involving fluctuations about a single, stimulus-driven attractor in a loosely balanced excitatory-inhibitory network (the stochastic “stabilized supralinear network”), best explains these modulations. Given the supralinear input/output functions of cortical neurons, increased stimulus drive strengthens effective network connectivity. This shifts the balance from interactions that amplify variability to suppressive inhibitory feedback, quenching correlated variability around more strongly driven steady states. Comparing to previously published and original data analyses, we show that this mechanism, unlike previous proposals, uniquely accounts for the spatial patterns and fast temporal dynamics of variability suppression. Specifying the cortical operating regime is key to understanding the computations underlying perception.

Neural networks subtract and conquer

Two theoretical studies reveal how networks of neurons may behave during reward-based learning.