Learning Human-Understandable Description of Dynamical Systems from Feed-Forward Neural Networks

Tourret, Sophie; Gentet, Enguerrand; Inoue, Katsumi

doi:10.1007/978-3-319-59072-1_57

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…There are logical approaches to BN learning (Inoue, Ribeiro, and Sakama 2014;Tourret, Gentet, and Inoue 2017;Chevalier et al 2019). From a logical point of view, our work is considered as a matricized version of "learning from interpretation transition" in logic programming in which a BN is represented as a propositional normal logic program (Inoue, Ribeiro, and Sakama 2014).…”

Section: Constrained Learning and Relearningmentioning

confidence: 99%

“…The main difference is that we search for a solution by minimizing a differentiable cost function for scalability instead of applying logical operations such as resolution and subsumption in a symbolic space. Tourret et al extracted DNF formulas from parameters of a feed-forward neural network learned from state transitions and convert them to logical rules describing a BN (Tourret, Gentet, and Inoue 2017).…”

Section: Constrained Learning and Relearningmentioning

confidence: 99%

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Boolean Network Learning in Vector Spaces for Genome-wide Network Analysis

Sato

Kojima

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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Boolean networks (BNs) are one of the standard tools for modeling gene regulatory networks in biology but their learning has been limited to small networks due to computational difficulty. Aiming at unprecedented scalability, we focus on a subclass of BNs called AND/OR Boolean networks where Boolean formulas are restricted to a conjunction or a disjunction of literals. We represent an AND/OR BN with N nodes by an N x 2N binary matrix Q paired with an N dimensional integer vector theta called a threshold vector, a state of the BN by an N dimensional binary state vector s and a state transition by matrix operations on Q, theta and s. Given a list of state transitions S = s_0...s_L, we learn Q and theta in a continuous space by minimizing a cost function J(Q*,theta,S) w.r.t. a real number matrix Q* and theta while thresholding Q* into a binary matrix Q using theta so that Q represents an AND/OR BN realizing the target state transitions S. We conducted experiments with artificial and real data sets to check scalability and accuracy of our learning algorithm. First we randomly generated AND/OR BNs up to N=5,000 nodes and empirically confirmed O(N^2) learning time behavior using them. We also observed 99.8% bit-by-bit prediction accuracy (prediction accuracy = 1 - test error) with state transition data generated by AND/OR BNs. For real data, we learned genome-wide AND/OR BNs with 10,928 nodes for budding yeast from transcription profiling data sets, each containing 10,928 mRNAs and 40 transitions and achieved for instance 84.3% prediction accuracy and successfully extracted more than 6,000 small AND/ORs whose average prediction accuracy reaches much higher 94.9%.

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Section: Constrained Learning and Relearningmentioning

confidence: 99%

Section: Constrained Learning and Relearningmentioning

confidence: 99%

Boolean Network Learning in Vector Spaces for Genome-wide Network Analysis

Sato

Kojima

2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

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Learning from interpretation transition using differentiable logic programming semantics

et al. 2021

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Differentiable learning of matricized DNFs and its application to Boolean networks

Sato

Inoue

2023

Mach Learn

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Boolean networks (BNs) are well-studied models of genomic regulation in biology where nodes are genes and their state transition is controlled by Boolean functions. We propose to learn Boolean functions as Boolean formulas in disjunctive normal form (DNFs) by an explainable neural network Mat_DNF and apply it to learning BNs. Directly expressing DNFs as a pair of binary matrices, we learn them using a single layer NN by minimizing a logically inspired non-negative cost function to zero. As a result, every parameter in the network has a clear meaning of representing a conjunction or literal in the learned DNF. Also we can prove that learning DNFs by the proposed approach is equivalent to inferring interpolants in logic between the positive and negative data. We applied our approach to learning three literature-curated BNs and confirmed its effectiveness. We also examine how generalization occurs when learning data is scarce. In doing so, we introduce two new operations that can improve accuracy, or equivalently generalizability for scarce data. The first one is to append a noise vector to the input learning vector. The second one is to continue learning even after learning error becomes zero. The first one is explainable by the second one. These two operations help us choose a learnable DNF, i.e., a root of the cost function, to achieve high generalizability.

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Learning Human-Understandable Description of Dynamical Systems from Feed-Forward Neural Networks

Cited by 3 publications

References 13 publications

Boolean Network Learning in Vector Spaces for Genome-wide Network Analysis

Boolean Network Learning in Vector Spaces for Genome-wide Network Analysis

Learning from interpretation transition using differentiable logic programming semantics

Differentiable learning of matricized DNFs and its application to Boolean networks

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