Analog Memories in a Balanced Rate-Based Network of E-I Neurons

The persistent and graded activity often observed in cortical circuits is sometimes seen as a signature of autoassociative retrieval of memories stored earlier in synaptic efficacies. However, despite decades of theoretical work on the subject, the mechanisms that support the storage and retrieval of memories remain unclear. Previous proposals concerning the dynamics of memory networks have fallen short of incorporating some key physiological constraints in a unified way. Specifically, some models violate Dale's law (i.e. allow neurons to be both excitatory and inhibitory), while some others restrict the representation of memories to a binary format, or induce recall states in which some neurons fire at rates close to saturation. We propose a novel control-theoretic framework to build functioning attractor networks that satisfy a set of relevant physiological constraints. We directly optimize networks of excitatory and inhibitory neurons to force sets of arbitrary analog patterns to become stable fixed points of the dynamics. The resulting networks operate in the balanced regime, are robust to corruptions of the memory cue as well as to ongoing noise, and incidentally explain the reduction of trial-to-trial variability following stimulus onset that is ubiquitously observed in sensory and motor cortices. Our results constitute a step forward in our understanding of the neural substrate of memory.

[1]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[2]  D. Hansel,et al.  On the Distribution of Firing Rates in Networks of Cortical Neurons , 2011, The Journal of Neuroscience.

[3]  Peter Dayan,et al.  Rate- and Phase-coded Autoassociative Memory , 2004, NIPS.

[4]  Nicholas J. Priebe,et al.  Direction Selectivity of Excitation and Inhibition in Simple Cells of the Cat Primary Visual Cortex , 2005, Neuron.

[5]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Haim Sompolinsky,et al.  Patterns of Ongoing Activity and the Functional Architecture of the Primary Visual Cortex , 2004, Neuron.

[7]  Henning Sprekeler,et al.  Inhibitory Plasticity Balances Excitation and Inhibition in Sensory Pathways and Memory Networks , 2011, Science.

[8]  Andrew M. Clark,et al.  Stimulus onset quenches neural variability: a widespread cortical phenomenon , 2010, Nature Neuroscience.

[9]  Peter E. Latham,et al.  Computing and Stability in Cortical Networks , 2004, Neural Computation.

[10]  P. Dayan,et al.  Matching storage and recall: hippocampal spike timing–dependent plasticity and phase response curves , 2005, Nature Neuroscience.

[11]  Treves,et al.  Graded-response neurons and information encodings in autoassociative memories. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[12]  Edmund T. Rolls,et al.  What determines the capacity of autoassociative memories in the brain? Network , 1991 .

[13]  C. Petersen,et al.  The Excitatory Neuronal Network of the C2 Barrel Column in Mouse Primary Somatosensory Cortex , 2009, Neuron.

[14]  Sen Song,et al.  Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS biology.

[15]  Alessandro Treves,et al.  Stable and Rapid Recurrent Processing in Realistic Autoassociative Memories , 1998, Neural Computation.

[16]  Peter E. Latham,et al.  A Balanced Memory Network , 2007, PLoS Comput. Biol..

[17]  Nicolas Brunel,et al.  Dynamics of a recurrent network of spiking neurons before and following learning , 1997 .

[18]  D. Ferster,et al.  The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. , 2000, Science.

[19]  Wim Michiels,et al.  The Smoothed Spectral Abscissa for Robust Stability Optimization , 2009, SIAM J. Optim..

[20]  Nicholas J. Priebe,et al.  The Emergence of Contrast-Invariant Orientation Tuning in Simple Cells of Cat Visual Cortex , 2007, Neuron.

[21]  Tongxing Lu,et al.  Solution of the matrix equation AX−XB=C , 2005, Computing.

[22]  Kenneth D. Miller,et al.  Analysis of the Stabilized Supralinear Network , 2012, Neural Computation.

[23]  Nicholas J. Priebe,et al.  Mechanisms underlying cross-orientation suppression in cat visual cortex , 2006, Nature Neuroscience.

[24]  A. Litwin-Kumar,et al.  Slow dynamics and high variability in balanced cortical networks with clustered connections , 2012, Nature Neuroscience.

[25]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[26]  Gustavo Deco,et al.  Neural Network Mechanisms Underlying Stimulus Driven Variability Reduction , 2012, PLoS Comput. Biol..

[27]  W. Gerstner,et al.  Optimal Control of Transient Dynamics in Balanced Networks Supports Generation of Complex Movements , 2014, Neuron.