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Neurons, the fundamental units of the brain and nervous system, communicate through complex electrochemical signals that underpin all cognitive and bodily functions. This communication is primarily facilitated by a process involving the generation and propagation of an action potential along the axon of the neuron. When the internal electrical charge of a neuron surpasses a certain threshold, an action potential is triggered. This rapid change in voltage travels swiftly along the axon to the...
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Neuromorphic log-domain silicon synapse circuits obey bernoulli dynamics: a unifying tutorial analysis.

Konstantinos I Papadimitriou1, Shih-Chii Liu2, Giacomo Indiveri2

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Frontiers in Neuroscience
|February 6, 2015
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Summary

A new generalized Bernoulli Cell Formalism (GBCF) unifies the analysis of log-domain neuromorphic silicon synapse circuits. This mathematical framework offers a systematic approach and demonstrates improved speed for circuit analysis.

Keywords:
analog VLSI (aVLSI)generalized bernoulli cell formalismlog-domain circuitssubthreshold MOSFETssynaptic dynamics

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Area of Science:

  • Neuromorphic Engineering
  • Analog Circuit Design
  • Computational Neuroscience

Background:

  • Log-domain circuits are crucial for implementing neuromorphic silicon synapses.
  • Existing analysis methods for these circuits can be complex and fragmented.
  • A unified and systematic mathematical framework is needed for efficient circuit design and analysis.

Purpose of the Study:

  • To propose a parsimonious mathematical framework for analyzing neuromorphic silicon synapse circuits.
  • To generalize the Bernoulli Cell Formalism (BCF) to a Generalized Bernoulli Cell Formalism (GBCF).
  • To demonstrate the framework's applicability and efficiency through circuit examples.

Main Methods:

  • Extension of the Bernoulli Cell Formalism (BCF) by introducing new Bernoulli Cell (BC) operators.
  • Development of the Generalized Bernoulli Cell Formalism (GBCF) to encompass new MOS transistor and capacitor combinations.
  • Tutorial analysis of three established log-domain neuromorphic silicon synapse circuits using the GBCF.

Main Results:

  • The GBCF provides a unified theoretical framework for analyzing various log-domain neuromorphic circuits.
  • The formalism accommodates two novel combinations of MOS transistors and linear capacitors.
  • Comparative analysis shows the GBCF offers a speed advantage for high-order circuit transfer function determination.

Conclusions:

  • The GBCF is a powerful and systematic tool for the analysis of neuromorphic silicon synapse circuits.
  • This generalized formalism simplifies and unifies previous analysis approaches.
  • The proposed framework enhances the efficiency of designing and analyzing complex neuromorphic systems.