TY - JOUR

T1 - Frequency Propagation

T2 - Multimechanism Learning in Nonlinear Physical Networks

AU - Anisetti, Vidyesh Rao

AU - Kandala, Ananth

AU - Scellier, Benjamin

AU - Schwarz, J. M.

N1 - Publisher Copyright:
© 2024 Massachusetts Institute of Technology.

PY - 2024/3/21

Y1 - 2024/3/21

N2 - We introduce frequency propagation, a learning algorithm for nonlinear physical networks. In a resistive electrical circuit with variable resistors, an activation current is applied at a set of input nodes at one frequency and an error current is applied at a set of output nodes at another fre-quency. The voltage response of the circuit to these boundary currents is the superposition of an activation signal and an error signal whose coefficients can be read in different frequencies of the frequency domain. Each conductance is updated proportionally to the product of the two coefficients. The learning rule is local and proved to perform gradient descent on a loss function. We argue that frequency propagation is an in-stance of a multimechanism learning strategy for physical networks, be it resistive, elastic, or flow networks. Multimechanism learning strategies incorporate at least two physical quantities, potentially governed by in-dependent physical mechanisms, to act as activation and error signals in the training process. Locally available information about these two signals is then used to update the trainable parameters to perform gradient descent. We demonstrate how earlier work implementing learning via chemical signaling in flow networks (Anisetti, Scellier, et al., 2023) also falls under the rubric of multimechanism learning.

AB - We introduce frequency propagation, a learning algorithm for nonlinear physical networks. In a resistive electrical circuit with variable resistors, an activation current is applied at a set of input nodes at one frequency and an error current is applied at a set of output nodes at another fre-quency. The voltage response of the circuit to these boundary currents is the superposition of an activation signal and an error signal whose coefficients can be read in different frequencies of the frequency domain. Each conductance is updated proportionally to the product of the two coefficients. The learning rule is local and proved to perform gradient descent on a loss function. We argue that frequency propagation is an in-stance of a multimechanism learning strategy for physical networks, be it resistive, elastic, or flow networks. Multimechanism learning strategies incorporate at least two physical quantities, potentially governed by in-dependent physical mechanisms, to act as activation and error signals in the training process. Locally available information about these two signals is then used to update the trainable parameters to perform gradient descent. We demonstrate how earlier work implementing learning via chemical signaling in flow networks (Anisetti, Scellier, et al., 2023) also falls under the rubric of multimechanism learning.

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U2 - 10.1162/neco_a_01648

DO - 10.1162/neco_a_01648

M3 - Article

C2 - 38457749

AN - SCOPUS:85189120174

SN - 0899-7667

VL - 36

SP - 596

EP - 620

JO - Neural Computation

JF - Neural Computation

IS - 4

ER -