A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

Singh, Abhinav; Wiuf, Carsten; Behera, Abhishek; Gopalkrishnan, Manoj

doi:10.1007/978-3-030-26807-7_4

Cited by 6 publications

(7 citation statements)

References 46 publications

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“…In a similar vein, Singh et al 19 proposed a stochastic CRN scheme for the Baum–Welch algorithm used to learn the parameters of a Hidden Markov model (HMM). It is a variant of the expectation–maximization (EM) algorithm, an iterative procedure that optimizes a given cost function by first calculating the expected cost with the current parameters (expectation step) and then by updating the parameters to optimize the cost function until convergence.…”

Section: Survey Of Molecular Computing Approaches To Learningmentioning

confidence: 99%

A survey on molecular-scale learning systems with relevance to DNA computing

Nagipogu

Reif

2023

Nanoscale

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Section: Survey Of Molecular Computing Approaches To Learningmentioning

confidence: 99%

A survey on molecular-scale learning systems with relevance to DNA computing

Nagipogu

Reif

2023

Nanoscale

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“…There is a growing interest in synthetic chemical reaction networks that carry out some pre-determined task [1][2][3][4][5][6][7][8][9][10][11][12][13]. The field that develops and analyses these networks often goes by the name 'computation with chemical reaction networks'.…”

Section: Introductionmentioning

confidence: 99%

“…Figure10. Plots of trajectories from the ODEs associated with our reaction network construction after different numbers of iterations.…”

mentioning

confidence: 99%

On reaction network implementations of neural networks

Anderson

Joshi

Deshpande

2021

J. R. Soc. Interface.

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This paper is concerned with the utilization of deterministically modelled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differential equations (ODEs) associated with certain reaction network implementations of neural networks have desirable properties including (i) existence of unique positive fixed points that are smooth in the parameters of the model (necessary for gradient descent) and (ii) fast convergence to the fixed point regardless of initial condition (necessary for efficient implementation). We do so by first making a connection between neural networks and fixed points for systems of ODEs, and then by constructing reaction networks with the correct associated set of ODEs. We demonstrate the theory by constructing a reaction network that implements a neural network with a smoothed ReLU activation function, though we also demonstrate how to generalize the construction to allow for other activation functions (each with the desirable properties listed previously). As there are multiple types of ‘networks’ used in this paper, we also give a careful introduction to both reaction networks and neural networks, in order to disambiguate the overlapping vocabulary in the two settings and to clearly highlight the role of each network’s properties.

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“…There is a growing interest in synthetic chemical reaction networks that carry out some predetermined task [4,5,7,8,11,12,21,23,24,26,27,29,30]. The field that develops and analyzes these networks often goes by the name "Computation with chemical reaction networks (CRNs).…”

Section: Introductionmentioning

confidence: 99%

On reaction network implementations of neural networks

F.¹,

Joshi²,

Deshpande³

2020

Preprint

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This paper is concerned with the utilization of chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differential equations (ODEs) associated with certain reaction network implementations of neural networks have desirable properties including (i) existence of unique positive fixed points that are smooth in the parameters of the model (necessary for gradient descent), and (ii) fast convergence to the fixed point regardless of initial condition (necessary for efficient implementation). We do so by first making a connection between neural networks and fixed points for systems of ODEs, and then by constructing reaction networks with the correct associated set of ODEs. We demonstrate the theory by constructing a reaction network that implements a neural network with a smoothed ReLU activation function, though we also demonstrate how to generalize the construction to allow for other activation functions (each with the desirable properties listed previously). As there are multiple types of "networks" utilized in this paper, we also give a careful introduction to both reaction networks and neural networks, in order to disambiguate the overlapping vocabulary in the two settings and to clearly highlight the role of each network's properties.

show abstract

A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

Cited by 6 publications

References 46 publications

A survey on molecular-scale learning systems with relevance to DNA computing

A survey on molecular-scale learning systems with relevance to DNA computing

On reaction network implementations of neural networks

On reaction network implementations of neural networks

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