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Bayesian polynomial neural networks and polynomial neural ordinary differential equations

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Colby Fronk, Jaewoong Yun, Prashant Singh, Linda Petzold

Machine Learning · Submitted 17 Aug 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We have found the Laplace approximation to be the best method for this class of problems.

how it is stated · asserted 1.00 read the record →

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arXiv ID2308.10892 (version 2)
Pith IDPXF2GYDO, Pith's permanent record of this paper and its review
CitationColby Fronk, Jaewoong Yun, Linda Petzold, Prashant Singh. "Bayesian polynomial neural networks and polynomial neural ordinary differential equations." arXiv:2308.10892 (2023). https://pith.science/paper/PXF2GYDO
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,193 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.37 · human participants 0.02 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.62 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. background 1.00 0.04 0.03 asserted 1.00
s1 However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. gap 0.95 0.09 0.03 asserted 1.00
s2 We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. contribution 0.76 0.93 0.07 asserted 0.98
s3 We have found the Laplace approximation to be the best method for this class of problems. result 0.99 0.96 0.66 asserted 1.00
s4 Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs. future work 0.74 0.33 0.06 asserted 0.51

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.96.

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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.

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1 arXiv paper cite this in 2 sentences

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What it cites

Uses the method or tool of 1 paper
  • We used gradient descent [ref] and Adam [ref] to minimize the negative log-likelihood, with the constant term $1/2 β^2$ dropped.

    Adam: A Method for Stochastic Optimization · Approach #1: Laplace Approximation · 1.00

Cites as background 7 papers

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