Learning from interpretation transition using differentiable logic programming semantics

Gao, Kun; Wang, Hanpin; Cao, Yongzhi; Inoue, Katsumi

doi:10.1007/s10994-021-06058-8

Cited by 6 publications

(2 citation statements)

References 34 publications

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“…Then P is represented by the matrix MP ∈ [0,1] m×n . Each element akj in MP is defined as follows (Gao et al 2021):…”

Section: A Matrix Representation Of Lpmentioning

confidence: 99%

“…To employ KAN to learn the SH matrix of an LP, a differentiable logic semantics used in [replaces the logical 'or' operator with the product t-norm (Chapter ? ?,Gao et al, 2021) and uses the differentiable function ϕ(x − 1) in to replace the θ(x) function. The hyperparameter γ controls the slope similarity between the functions ϕ and θ:∅(𝑥) = 1 1 + 𝑒 −𝛾𝑥After the conversion into propositional form, the relational facts are transformed into pairs of interpretation vectors (vi,vo).…”

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confidence: 99%

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Kolmogorov-Arnold network for word-level explainable meaning representation

Galitsky

2024

Preprint

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We leverage the explainability feature of KAN network and build an explainable language model where certain neurons encode individual words and neuron activation is fully interpretable in terms of the basis of a word. To do that, we propose a continuous word2vec model where a meaning of a word is expressed by a continuous profile of distances of this word from the words in the basis of words which is interpolated. As a result, the whole KAN network can be interpreted as a sequential procedure with word expressions. We then proceed from words to logic programs and develop a clause learning technique based on KAN. A logic program construction process from facts now become fully interpretable. We follow the differentiable inductive logic programming technique, representing a logic program as a matrix learned by KAN. Hence, we obtain an efficient and fully interpretable rule learning approach.

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“…Then P is represented by the matrix MP ∈ [0,1] m×n . Each element akj in MP is defined as follows (Gao et al 2021):…”

Section: A Matrix Representation Of Lpmentioning

confidence: 99%

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confidence: 99%

Kolmogorov-Arnold network for word-level explainable meaning representation

Galitsky

2024

Preprint

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Algebraic Connection Between Logic Programming and Machine Learning (Extended Abstract)

Inoue

2024

Lecture Notes in Computer Science

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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 from interpretation transition using differentiable logic programming semantics

Cited by 6 publications

References 34 publications

Kolmogorov-Arnold network for word-level explainable meaning representation

Kolmogorov-Arnold network for word-level explainable meaning representation

Algebraic Connection Between Logic Programming and Machine Learning (Extended Abstract)

Differentiable learning of matricized DNFs and its application to Boolean networks

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