[Paper Review] Augmenting Neural Networks with First-order Logic

Tao Li, Vivek Srikumar|arXiv (Cornell University)|Jun 14, 2019

Topic Modeling40 references4 citations

TL;DR

This paper proposes a framework to integrate first-order logic rules into neural networks by compiling them into differentiable computation graphs, enabling knowledge infusion without additional trainable parameters. The method enhances model performance—especially in low-data regimes—across machine comprehension, natural language inference, and text chunking tasks by providing logical inductive biases that guide training and prediction.

ABSTRACT

Today, the dominant paradigm for training neural networks involves minimizing task loss on a large dataset. Using world knowledge to inform a model, and yet retain the ability to perform end-to-end training remains an open question. In this paper, we present a novel framework for introducing declarative knowledge to neural network architectures in order to guide training and prediction. Our framework systematically compiles logical statements into computation graphs that augment a neural network without extra learnable parameters or manual redesign. We evaluate our modeling strategy on three tasks: machine comprehension, natural language inference, and text chunking. Our experiments show that knowledge-augmented networks can strongly improve over baselines, especially in low-data regimes.

Motivation & Objective

• To address the data hunger of neural networks by incorporating declarative world knowledge through first-order logic.
• To develop a method that integrates logical constraints into existing neural architectures without redesign or additional learnable parameters.
• To evaluate whether logical constraints can reduce data dependency and improve performance in low-resource settings.
• To compare the effectiveness of logic-augmented models against models relying solely on large-scale pre-trained representations.

Proposed method

• The framework compiles first-order logic rules into differentiable computation graphs that are integrated into existing neural network architectures.
• Logical rules are expressed as conditional statements (L → R), where L is a conjunction/disjunction of literals and R is a single literal, enabling systematic constraint encoding.
• The method uses soft constraints throughout, allowing for error tolerance in rules, and maps predicates in logic to specific neurons in the network.
• A differentiable relaxation of logic is employed to enable gradient-based optimization, preserving end-to-end training with standard backpropagation.
• The approach is compatible with off-the-shelf neural networks and applies constraints to interpretable layers such as attention mechanisms or CRF layers.
• The framework supports both local and global constraint integration, allowing for modular augmentation of neural components.

Experimental results

Research questions

• RQ1 Can first-order logic rules be systematically integrated into neural network training without modifying the learning procedure?
• RQ2 Can such logical constraints reduce the data requirements for neural network training?
• RQ3 How does incorporating domain-specific logical knowledge compare to relying on large-scale pre-trained representations?
• RQ4 Does the integration of logic improve model performance in low-data regimes across diverse NLP tasks?

Key findings

• The knowledge-augmented models significantly outperform standard baselines, especially in low-data regimes, with gains of up to 5.4% on the SQuAD dataset using only 5% of training data.
• On the SNLI entailment dataset, the constrained model achieved 88.6% accuracy with 5% of the data, outperforming the baseline and CRF models.
• In text chunking, the BiLSTM model augmented with constraints (C1:5) achieved 92.1% accuracy with 20% of the data, surpassing the baseline and CRF models.
• The combination of CRF and logical constraints yielded the best performance (95.0% accuracy) on the full data set, demonstrating complementary benefits.
• The CRF model underperformed the baseline with ≤40% of the data, indicating that global inference models require more data to learn scoring functions effectively.
• The framework successfully improves model performance across all three tasks without adding trainable parameters, confirming its efficiency and compatibility with existing architectures.