Learning First-Order Rules with Differentiable Logic Program Semantics

• URL: http://arxiv.org/abs/2204.13570v1
• Date: Thu, 28 Apr 2022 15:33:43 GMT
• Title: Learning First-Order Rules with Differentiable Logic Program Semantics
• Authors: Kun Gao, Katsumi Inoue, Yongzhi Cao, Hanpin Wang
• Abstract summary: We introduce a differentiable inductive logic programming model, called differentiable first-order rule learner (DFOL) DFOL finds the correct LPs from relational facts by searching for the interpretable matrix representations of LPs. Experimental results indicate that DFOL is a precise, robust, scalable, and computationally cheap differentiable ILP model.
• Score: 12.360002779872373
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model, called differentiable first-order rule learner (DFOL), which finds the correct LPs from relational facts by searching for the interpretable matrix representations of LPs. These interpretable matrices are deemed as trainable tensors in neural networks (NNs). The NNs are devised according to the differentiable semantics of LPs. Specifically, we first adopt a novel propositionalization method that transfers facts to NN-readable vector pairs representing interpretation pairs. We replace the immediate consequence operator with NN constraint functions consisting of algebraic operations and a sigmoid-like activation function. We map the symbolic forward-chained format of LPs into NN constraint functions consisting of operations between subsymbolic vector representations of atoms. By applying gradient descent, the trained well parameters of NNs can be decoded into precise symbolic LPs in forward-chained logic format. We demonstrate that DFOL can perform on several standard ILP datasets, knowledge bases, and probabilistic relation facts and outperform several well-known differentiable ILP models. Experimental results indicate that DFOL is a precise, robust, scalable, and computationally cheap differentiable ILP model.

Related papers

• Knowledge Composition using Task Vectors with Learned Anisotropic Scaling [51.4661186662329]
  We introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsicity of pre-trained models, with only a few coefficients being the learnable parameters. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives.
  arXiv  Detail & Related papers  (2024-07-03T07:54:08Z)
• Making Pre-trained Language Models Great on Tabular Prediction [50.70574370855663]
  The transferability of deep neural networks (DNNs) has made significant progress in image and language processing. We present TP-BERTa, a specifically pre-trained LM for tabular data prediction. A novel relative magnitude tokenization converts scalar numerical feature values to finely discrete, high-dimensional tokens, and an intra-feature attention approach integrates feature values with the corresponding feature names.
  arXiv  Detail & Related papers  (2024-03-04T08:38:56Z)
• Physics-informed neural networks for operator equations with stochastic data [0.6445605125467572]
  We consider the computation of statistical moments to operator equations with data. PINNs -- referred to as TPINNs -- allow to solve the induced tensor operator equations under minimal changes of existing PINNs code. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations.
  arXiv  Detail & Related papers  (2022-11-15T20:52:01Z)
• Assessing the Unitary RNN as an End-to-End Compositional Model of Syntax [0.0]
  We show that both an LSTM and a unitary-evolution recurrent neural network (URN) can achieve encouraging accuracy on two types of syntactic patterns.
  arXiv  Detail & Related papers  (2022-08-11T09:30:49Z)
• PROTOtypical Logic Tensor Networks (PROTO-LTN) for Zero Shot Learning [2.236663830879273]
  Logic Networks (LTNs) are neuro-symbolic systems based on a differentiable, first-order logic grounded into a deep neural network. We focus here on the subsumption or textttisOfClass predicate, which is fundamental to encode most semantic image interpretation tasks. We propose a common textttisOfClass predicate, whose level of truth is a function of the distance between an object embedding and the corresponding class prototype.
  arXiv  Detail & Related papers  (2022-06-26T18:34:07Z)
• Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks [65.23508422635862]
  We propose learning rules with the recently proposed logical neural networks (LNN) Compared to others, LNNs offer strong connection to classical Boolean logic. Our experiments on standard benchmarking tasks confirm that LNN rules are highly interpretable.
  arXiv  Detail & Related papers  (2021-12-06T19:38:30Z)
• Deep learning with transfer functions: new applications in system identification [0.0]
  This paper presents a linear dynamical operator endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end training of structured networks containing linear transfer functions and other differentiable units.
  arXiv  Detail & Related papers  (2021-04-20T08:58:55Z)
• NSL: Hybrid Interpretable Learning From Noisy Raw Data [66.15862011405882]
  This paper introduces a hybrid neural-symbolic learning framework, called NSL, that learns interpretable rules from labelled unstructured data. NSL combines pre-trained neural networks for feature extraction with FastLAS, a state-of-the-art ILP system for rule learning under the answer set semantics. We demonstrate that NSL is able to learn robust rules from MNIST data and achieve comparable or superior accuracy when compared to neural network and random forest baselines.
  arXiv  Detail & Related papers  (2020-12-09T13:02:44Z)
• Connecting Weighted Automata, Tensor Networks and Recurrent Neural Networks through Spectral Learning [58.14930566993063]
  We present connections between three models used in different research fields: weighted finite automata(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks. We introduce the first provable learning algorithm for linear 2-RNN defined over sequences of continuous vectors input.
  arXiv  Detail & Related papers  (2020-10-19T15:28:00Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.