Firing rate predictions in optimal balanced networks

How are firing rates in a spiking network related to neural input, connectivity and network function? This is an important problem because firing rates are a key measure of network activity, in both the study of neural computation and neural network dynamics. However, it is a difficult problem, because the spiking mechanism of individual neurons is highly non-linear, and these individual neurons interact strongly through connectivity. We develop a new technique for calculating firing rates in optimal balanced networks. These are particularly interesting networks because they provide an optimal spike-based signal representation while producing cortex-like spiking activity through a dynamic balance of excitation and inhibition. We can calculate firing rates by treating balanced network dynamics as an algorithm for optimising signal representation. We identify this algorithm and then calculate firing rates by finding the solution to the algorithm. Our firing rate calculation relates network firing rates directly to network input, connectivity and function. This allows us to explain the function and underlying mechanism of tuning curves in a variety of systems.

[1]  R. Freeman,et al.  Orientation selectivity in the cat's striate cortex is invariant with stimulus contrast , 2004, Experimental Brain Research.

[2]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[3]  Eric Shea-Brown,et al.  Impact of Network Structure and Cellular Response on Spike Time Correlations , 2011, PLoS Comput. Biol..

[4]  D. Tank,et al.  Functional dissection of circuitry in a neural integrator , 2007, Nature Neuroscience.

[5]  Prof. Dr. Valentino Braitenberg,et al.  Anatomy of the Cortex , 1991, Studies of Brain Function.

[6]  A. Aertsen,et al.  Spectro-temporal receptive fields of auditory neurons in the grassfrog , 1980, Biological Cybernetics.

[7]  T. M. Mayhew,et al.  Anatomy of the Cortex: Statistics and Geometry. , 1991 .

[8]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[9]  Bruce W. Knight,et al.  Dynamics of Encoding in a Population of Neurons , 1972, The Journal of general physiology.

[10]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[11]  Christian K. Machens,et al.  Linearity of Cortical Receptive Fields Measured with Natural Sounds , 2004, The Journal of Neuroscience.

[12]  Christian K. Machens,et al.  Predictive Coding of Dynamical Variables in Balanced Spiking Networks , 2013, PLoS Comput. Biol..

[13]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[14]  Sophie Denève,et al.  Spike-Based Population Coding and Working Memory , 2011, PLoS Comput. Biol..

[15]  David J. Field,et al.  How Close Are We to Understanding V1? , 2005, Neural Computation.

[16]  Mark D. Humphries,et al.  Population-wide distributions of neural activity during perceptual decision-making , 2013, Progress in Neurobiology.

[17]  Alexandre Pouget,et al.  Insights from a Simple Expression for Linear Fisher Information in a Recurrently Connected Population of Spiking Neurons , 2011, Neural Computation.

[18]  E. Salinas.  How Behavioral Constraints May Determine Optimal Sensory Representations , 2006, PLoS biology.

[19]  D. McCormick,et al.  Neocortical Network Activity In Vivo Is Generated through a Dynamic Balance of Excitation and Inhibition , 2006, The Journal of Neuroscience.

[20]  E. Adrian,et al.  The impulses produced by sensory nerve‐endings , 1926 .

[21]  Christian K. Machens,et al.  Learning optimal spike-based representations , 2012, NIPS.

[22]  Sompolinsky,et al.  Theory of correlations in stochastic neural networks. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.