A Novel Neural-symbolic System under Statistical Relational Learning

TL;DR

NSF-SRL presents a general neural-symbolic framework that unifies deep learning with statistical relational learning via Markov Logic Networks to jointly model perception and reasoning. The approach alternates between concept learning (neural reasoning module and symbolic reasoning module) and concept manipulation (transductive and inductive) to improve accuracy, generalization, and interpretability, while training with a variational EM objective and a differentiable concept network. Empirical results across digit addition, visual relationship detection, and zero-shot classification show competitive performance and strong generalization, aided by explicit logic rules that provide interpretable evidence for predictions. The work highlights a path toward interpretable, robust AI systems that can reason about relational structure in data and adapt to new tasks with learned concepts.

Abstract

A key objective in the field of artificial intelligence is to develop cognitive models that can exhibit human-like intellectual capabilities. One promising approach to achieving this is through neural-symbolic systems, which combine the strengths of deep learning and symbolic reasoning. However, current methodologies in this area face limitations in integration, generalization, and interpretability. To address these challenges, we propose a neural-symbolic framework based on statistical relational learning, referred to as NSF-SRL. This framework effectively integrates deep learning models with symbolic reasoning in a mutually beneficial manner.In NSF-SRL, the results of symbolic reasoning are utilized to refine and correct the predictions made by deep learning models, while deep learning models enhance the efficiency of the symbolic reasoning process. Through extensive experiments, we demonstrate that our approach achieves high performance and exhibits effective generalization in supervised learning, weakly supervised and zero-shot learning tasks. Furthermore, we introduce a quantitative strategy to evaluate the interpretability of the model's predictions, visualizing the corresponding logic rules that contribute to these predictions and providing insights into the reasoning process. We believe that this approach sets a new standard for neural-symbolic systems and will drive future research in the field of general artificial intelligence.

Figures (13)

• Figure 1: Overview of NSF-SRL. The concept learning phase acquires basic concepts such as "catlike", "tawny" and "spot" from the training data. In transductive concept manipulation, the learned concepts and toriginal rules are applied to test data whose labels were present in the training sets. This integration of learned concepts enhances the interpretability of NSF-SRL by providing insights into how predictions are made based on these concepts and the accompanying rules. Conversely, in inductive concept manipulation, the learned concepts serve as the rule body, and new rules are introduced to reason about samples with labels that have never appeared in the training set.
• Figure 2: Illustration of concept learning. The NRM aims to predict labels for raw data, generating pseudo-labels and feature vectors as outputs. The SRM is a probabilistic graphical model that incorporates both the pseudo-labels from the NRM and the ground atoms from the MLN. The entire model is trained end-to-end, using backpropagation to iteratively refine the pseudo-labels.
• Figure 3: Concept network. The inputs are feature vectors of object pairs (e.g., $e_{1}$ and $e_2$) or objects (e.g., $e_j$), and outputs are probabilities of affiliation relationship labels (e.g., $P_{binary}(A_{i}(e_{1},e_{2}))$) or object labels (e.g., $P_{unary}(A_{j}(e_{j}))$). $k$ represents tensor layer and each layer is a predicate.
• Figure 4: Illustration of concept manipulation. (a) Transductive concept manipulation. The trained neural reasoning module predicts results, while the symbolic reasoning module provides interpretability. (b) Inductive concept manipulation. The trained neural reasoning module generates feature vectors, which are used by the symbolic reasoning module for reasoning.
• Figure 5: Performance of NSF-SRL and comparison methods on digit image addition and zero-shot image classification tasks: (a) MNIST ; (b) AwA2 ; (c) CUB.