CNS*2013 Tutorial on


Massively Parallel Time Encoding and Channel Identificaton Machines

Saturday, July 13, 2013

Paris, France


Aurel A. Lazar

Department of Electrical Engineering

Columbia University, New York, NY 10027


Overview

This two part tutorial focusses on Time Encoding Machines (part I) and Channel Identification Machines (part II). The tutorial will give an overview of (i) nonlinear decoding of stimuli encoded with neural circuits with biophysical neuron models, (ii) functional identification of biophysical neural circuits, and (iii) the duality between the two. Scaling to massively parallel neural circuits for both encoding and functional identification will be discussed throughout. The tutorial will provide numerous examples of neural decoding and functional identification using the Time Encoding Machines Toolbox and the Channel Identification Machines Toolbox. Tutorial material, programming code and demonstrations will be provided.

Part I: Time Encoding Machines

The nature of the neural code is fundamental to theoretical and systems neuroscience [1]. Can information about the sensory world be faithfully represented by a population of sensory neurons? What features of the stimulus are encoded by a multidimensional spike train? How can these features be decoded? Why does the cochlear nerve carry some 30,000 fibers and the optic nerve some 1,000,000? We will discuss these questions using a class of neural encoding circuits called Time Encoding Machines (TEMs) [2]. TEMs model the encoding of stimuli in early sensory systems with neural circuits with arbitrary connectivity and feedback. These circuits are realized with temporal, spectro-temporal and/or spatio-temporal receptive fields, and biophysical neuron models with stochastic conductances (Hodgkin-Huxley, Morris-Lecar, etc.) [3, 4, 5, 6]. The tutorial will review key theoretical results and provide numerous examples of massively parallel neural encoding circuits and stimulus decoding algorithms with the Time Encoding Machines Toolbox.

Part II: Channel Identification Machines

Parameter estimation is at the core of functional identification of neural circuits. How are estimates of model parameters affected by the stimuli employed in neurophysiology? What is a suitable metric to assess the faithfulness of identified parameters and the goodness of model performance? These are key open questions that are of relevance to both theoretical and experimental neuroscientists. We will discuss these questions using a class of algorithms called Channel Identification Machines (CIMs) [7, 8, 9] and give an overview of the functional identification of massively parallel neural circuit models of sensory systems arising in olfaction, audition and vision. These circuits are built with temporal, spectro-temporal and non-separable spatio-temporal receptive fields, and biophysical spiking neuron models. The tutorial will demonstrate how CIMs achieve the efficient identification of neural circuit models and will provide numerous examples of functional identification using the Channel Identification Machines Toolbox.

References

[1] Alexander G. Dimitrov, Aurel A. Lazar, and Jonathan D. Victor. Information Theory in Neuroscience. Journal of Computational Neuroscience, 30(1):1-5, February 2011.

[2] Aurel A. Lazar. Neural signal sampling and time encoding machines. In Dieter Jaeger and Ranu Jung, editors, Encyclopedia of Computational Neuroscience. Springer, 2013.

[3] Aurel A. Lazar. Population Encoding with Hodgkin-Huxley Neurons, IEEE Transactions on Information Theory, 56(2):821-837, February 2010.

[4] Aurel A. Lazar and Eftychios A. Pnevmatikakis. Video Time Encoding Machines. IEEE Transactions on Neural Networks, 22(3):461-473, March 2011.

[5] Aurel A. Lazar, Eftychios A. Pnevmatikakis, and Yiyin Zhou. Encoding Natural Scenes with Neural Circuits with Random Thresholds. Vision Research, 50(22):2200-2212, October 2010. Special Issue on Mathematical Models of Visual Coding.

[6] Aurel A. Lazar and Yiyin Zhou. Massively Parallel Neural Encoding and Decoding of Visual Stimuli. Neural Networks, 32:303-312, August 2012.

[7] Aurel A. Lazar and Yevgeniy B. Slutskiy. Identifying Dendritic Processing. Advances in Neural Information Processing Systems, 23:1261-1269, 2010.

[8] Anmo J. Kim and Aurel A. Lazar. Recovery of Stimuli Encoded with a Hodgkin-Huxley Neuron Using Conditional PRCs. In N.W. Schultheiss, A.A. Prinz, and R.J. Butera, editors, Phase Response Curves in Neuroscience. Springer, 2011.

[9] Aurel A. Lazar and Yevgeniy B. Slutskiy. Channel Identification Machines. Computational Intelligence and Neuroscience, 2012:1-20, July 2012.