Channel Identification Machines
We pioneered a novel class of algorithms for the functional identification of spiking neural circuits called Channel Identification Machines (CIMs) . Our neural circuit models take explicitly into account the highly nonlinear nature of spike generation that has been shown to result in significant interactions between various stimulus features and to fundamentally affect the estimation of receptive fields. The employed test signals belong to spaces of bandlimited functions and bridge the gap between identification using synthetic and naturalistic stimuli. This makes our methodology particularly attractive in those sensory modalities (most notably olfaction), where it is difficult to produce stimuli that are white and/or have particular distribution/attributes. Furthermore, and in contrast to many existing methods, our approach can also estimate receptive fields directly from spike times produced by a neuron, thereby obviating the need to repeat experiments in order to compute the neuron’s instantaneous rate of response (e.g., PSTH).
We also investigated multi-input multi-output neural circuit architectures for nonlinear processing and encoding of stimuli consisting of a bank of dendritic stimulus processors (DSPs). DSPs execute nonlinear transformations of multiple temporal or spatiotemporal signals such as spike trains or auditory and visual stimuli in the analog domain. We demonstrated a fundamental duality between the identification of the dendritic stimulus processor of a single neuron and the decoding of stimuli encoded by a population of neurons with a bank of dendritic stimulus processors. We have also shown that identification algorithms can be effectively and intuitively evaluated in the stimulus space. In this space, a signal reconstructed from spike trains generated by the identified neural circuit can be compared to the original stimulus.
Functional Identification of Linear Receptive Fields and Biological Spike Generators
- Aurel A. Lazar and Yevgeniy B. Slutskiy, Channel Identification Machines, Computational Intelligence and Neuroscience, Volume 2012, pp. 1-20, July, 2012.
- Aurel A. Lazar and Yevgeniy B. Slutskiy, Functional Identification of Spike-Processing Neural Circuits, Neural Computation, Volume 26, Issue 2, pp. 264-305, February 2014.
- Aurel A. Lazar and Yevgeniy B. Slutskiy, Channel Identification Machines for Multidimensional Receptive Fields, Frontiers in Computational Neuroscience, Volume 8, Number 117, September 2014.
A visual demonstration of the identification of a non-separable spatio-temporal receptive field is shown below.
The original spatio-temporal kernel and the identified kernel are shown, respectively, in the first column. The Fourier amplitude spectrum of each of these kernels is respectively shown in the right column.
Functional Identification of Multisensory Dendritic Stimulus Processors
- Aurel A. Lazar and Yevgeniy B. Slutskiy, Multisensory Encoding, Decoding, and Identification, Advances in Neural Information Processing Systems 26 (NIPS*2013), edited by C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani and K.Q. Weinberger, December 2013.
- Aurel A. Lazar, Yevgeniy B. Slutskiy and Yiyin Zhou, Massively Parallel Neural Circuits for Stereoscopic Color Vision: Encoding, Decoding and Identification, Neural Networks, Volume 63, pp. 254-271, March 2015.
- Aurel A. Lazar and Yiyin Zhou, Identifying Multisensory Dendritic Stimulus Processors, IEEE Transactions on Molecular, Biological, and Multi-Scale Communications, Volume 2, Number 2, pp. 183-198, December 2016 , Special Issue on Biological Applications of Information Theory in Honor of Claude Shannon's Centennial, Part II (invited paper).
The videos below illustrate that the evaluation of the functional identification of a massively parallel neural circuit can be intuitively and in its entirety performed in the stimulus space. We quantitatively demonstrate how the quality of reconstruction of the encoded signal depends on the number of spikes used for identifying the circuit parameters.
The underlying massively parallel neural circuit for encoding color video consists of 30,000 IAF neurons with color sensitive receptive fields, covering a screen size of 160x90px. The IAF neurons all have the same parameters and are always assumed to be known. The underlying receptive fields are spatio-temporal non-separable in each of their color components and they resemble 2D Gabor filters spatially and rotate around their spatial center over time. However, the color receptive fields are assumed to be unknown and need to be identified. All the receptive fields are functionally identified using the same natural video, whose duration is up to 200 seconds. We identify the entire neural circuit based on 7 different settings. In one setting, each neuron's receptive field is identified using 1,000 spikes (measurements). In the other settings, each neuron's receptive field is identified using 2,000, 4,000, 6,000, 9,000, 13,000, 17,000 spikes (measurements), respectively.
A novel stimulus (the bee video shown here) encoded by the underlying circuit is then recovered. Instead of using the underlying circuit parameters, the identified circuit parameters are used in decoding. Note that the set of spikes used are still the ones generated by the same underlying circuit. The decoding quality then depends on how well the circuit is identified. The reconstructed video and the associated Signal-to-Noise Ratio (SNR) are shown in the above video for the circuit identified with different settings. As identification quality increases (more spikes are used), the quality of reconstruction converges to that of reconstruction using the underlying circuit parameters (known receptive fields/filters).
Functional Identification of Nonlinear Dendritic Stimulus Processors
- Aurel A. Lazar and Yevgeniy B. Slutskiy, Spiking Neural Circuits with Dendritic Stimulus Processors: Encoding, Decoding, and Identification in Reproducing Kernel Hilbert Spaces, Journal of Computational Neuroscience, Volume 38, No. 1, pp. 1-24, February 2015.
- Aurel A. Lazar and Yiyin Zhou, Volterra Dendritic Stimulus Processors and Biophysical Spike Generators with Intrinsic Noise Sources, Frontiers in Computational Neuroscience, Volume 8, Number 95, September 2014.
- Aurel A. Lazar, Nikul H. Ukani, and Yiyin Zhou, Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli, The Journal of Mathematical Neuroscience, Volume 8, Number 2, January 2018.
Examples of reconstruction of natural visual stimuli. Snapshots of the original videos encoded by a neural circuit with complex cells are shown on the top row. The reconstructions from the spike times are shown in the middle row and the error on the bottom row. Note that the color bar indicating the magnitude of the error was set to 10% of the input range. SNR of the recovered natural visual stimuli in each column: (A) 48.85 [dB]. (B) 46.92 [dB]. (C) 48.61 [dB]. (D) 50.76 [dB]. (E) 48.11 [dB].