Spiking, Bursting, and Population Dynamics in a Network of Growth Transform Neurons

Ahana Gangopadhyay, Shantanu Chakrabartty

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper investigates the dynamical properties of a network of neurons, each of which implements an asynchronous mapping based on polynomial growth transforms. In the first part of this paper, we present a geometric approach for visualizing the dynamics of the network where each of the neurons traverses a trajectory in a dual optimization space, whereas the network itself traverses a trajectory in an equivalent primal optimization space. We show that as the network learns to solve basic classification tasks, different choices of primal-dual mapping produce unique but interpretable neural dynamics like noise shaping, spiking, and bursting. While the proposed framework is general enough, in this paper, we demonstrate its use for designing support vector machines (SVMs) that exhibit noise-shaping properties similar to those of ΣΔ modulators, and for designing SVMs that learn to encode information using spikes and bursts. It is demonstrated that the emergent switching, spiking, and burst dynamics produced by each neuron encodes its respective margin of separation from a classification hyperplane whose parameters are encoded by the network population dynamics. We believe that the proposed growth transform neuron model and the underlying geometric framework could serve as an important tool to connect well-established machine learning algorithms like SVMs to neuromorphic principles like spiking, bursting, population encoding, and noise shaping.

Original languageEnglish
Pages (from-to)2379-2391
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number6
StatePublished - Jun 2018


  • Bursting
  • dynamical systems
  • growth transforms
  • population encoding
  • spike encoding
  • spiking neural network
  • support vector machines (SVMs)


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