LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints

• URL: http://arxiv.org/abs/2309.15458v3
• Date: Tue, 16 Apr 2024 05:33:38 GMT
• Title: LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints
• Authors: Weidi Xu, Jingwei Wang, Lele Xie, Jianshan He, Hongting Zhou, Taifeng Wang, Xiaopei Wan, Jingdong Chen, Chao Qu, Wei Chu,
• Abstract summary: This paper proposes a novel neural layer, LogicMP, whose layers perform mean-field variational inference over an MLN. It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. Empirical results in three kinds of tasks over graphs, images, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.
• Score: 42.16663204729038
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, whose layers perform mean-field variational inference over an MLN. It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations effectively mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over graphs, images, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.

Related papers

• On Scaling Neurosymbolic Programming through Guided Logical Inference [1.124958340749622]
  We propose a new approach centered around an exact algorithmNL, that enables bypassing the computation of the logical provenance. We show that this approach can be adapted for approximate reasoning with $epsilon$ or $(epsilon, delta)$ guarantees, called ApproxDPNL.
  arXiv  Detail & Related papers  (2025-01-30T08:49:25Z)
• Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation [49.44309457870649]
  We present Layer-wise Feedback Propagation (LFP), a novel training principle for neural network-like predictors. LFP decomposes a reward to individual neurons based on their respective contributions to solving a given task. Our method then implements a greedy approach reinforcing helpful parts of the network and weakening harmful ones.
  arXiv  Detail & Related papers  (2023-08-23T10:48:28Z)
• Injecting Logical Constraints into Neural Networks via Straight-Through Estimators [5.6613898352023515]
  Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning.
  arXiv  Detail & Related papers  (2023-07-10T05:12:05Z)
• PAC-learning gains of Turing machines over circuits and neural networks [1.4502611532302039]
  We study the potential gains in sample efficiency that can bring in the principle of minimum description length. We use Turing machines to represent universal models and circuits. We highlight close relationships between classical open problems in Circuit Complexity and the tightness of these.
  arXiv  Detail & Related papers  (2021-03-23T17:03:10Z)
• Reinforcement Learning with External Knowledge by using Logical Neural Networks [67.46162586940905]
  A recent neuro-symbolic framework called the Logical Neural Networks (LNNs) can simultaneously provide key-properties of both neural networks and symbolic logic. We propose an integrated method that enables model-free reinforcement learning from external knowledge sources.
  arXiv  Detail & Related papers  (2021-03-03T12:34:59Z)
• Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems [59.804810122136345]
  We propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed. An efficient IAIDNN based on the structure of the classic weighted minimum mean-square error (WMMSE) iterative algorithm is developed. We show that the proposed IAIDNN efficiently achieves the performance of the iterative WMMSE algorithm with reduced computational complexity.
  arXiv  Detail & Related papers  (2020-06-15T02:57:57Z)
• The Curious Case of Convex Neural Networks [12.56278477726461]
  We show that the convexity constraints can be enforced on both fully connected and convolutional layers. We draw three valuable insights: (a) Input Output Convex Neural Networks (IOC-NNs) self regularize and reduce the problem of overfitting; (b) Although heavily constrained, they outperform the base multi layer perceptrons and achieve similar performance as compared to base convolutional architectures.
  arXiv  Detail & Related papers  (2020-06-09T08:16:38Z)
• Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems [83.98774574197613]
  We take one of the simplest inference methods, a truncated max-product Belief propagation, and add what is necessary to make it a proper component of a deep learning model. This BP-Layer can be used as the final or an intermediate block in convolutional neural networks (CNNs) The model is applicable to a range of dense prediction problems, is well-trainable and provides parameter-efficient and robust solutions in stereo, optical flow and semantic segmentation.
  arXiv  Detail & Related papers  (2020-03-13T13:11:35Z)
• Efficient Probabilistic Logic Reasoning with Graph Neural Networks [63.099999467118245]
  Markov Logic Networks (MLNs) can be used to address many knowledge graph problems. Inference in MLN is computationally intensive, making the industrial-scale application of MLN very difficult. We propose a graph neural network (GNN) variant, named ExpressGNN, which strikes a nice balance between the representation power and the simplicity of the model.
  arXiv  Detail & Related papers  (2020-01-29T23:34:36Z)

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.