Symbolic Knowledge Extraction and Injection with Sub-symbolic Predictors: A Systematic Literature Review

TL;DR

The paper tackles the opacity of sub-symbolic predictors by formalizing symbolic knowledge extraction (SKE) and symbolic knowledge injection (SKI) as complementary strategies within an explainable AI framework. It delivers general meta-models and two bottom-up taxonomies for SKE and SKI, built from a systematic literature review of 132 SKE and 117 SKI methods, including an assessment of runnable software implementations. The authors introduce a TEFI loop to integrate SKE and SKI into the ML workflow and discuss the role of symbolic knowledge as a lingua franca for heterogeneous intelligent systems. The work provides practical guidance for data scientists and researchers to select methods, identify gaps, and drive future development of SKE/SKI techniques and tools. Overall, the paper advances a unified view of how symbolic and sub-symbolic AI can be combined to improve interpretability, controllability, and interoperability in AI systems.

Abstract

In this paper we focus on the opacity issue of sub-symbolic machine learning predictors by promoting two complementary activities, namely, symbolic knowledge extraction (SKE) and injection (SKI) from and into sub-symbolic predictors. We consider as symbolic any language being intelligible and interpretable for both humans and computers. Accordingly, we propose general meta-models for both SKE and SKI, along with two taxonomies for the classification of SKE and SKI methods. By adopting an explainable artificial intelligence (XAI) perspective, we highlight how such methods can be exploited to mitigate the aforementioned opacity issue. Our taxonomies are attained by surveying and classifying existing methods from the literature, following a systematic approach, and by generalising the results of previous surveys targeting specific sub-topics of either SKE or SKI alone. More precisely, we analyse 132 methods for SKE and 117 methods for SKI, and we categorise them according to their purpose, operation, expected input/output data and predictor types. For each method, we also indicate the presence/lack of runnable software implementations. Our work may be of interest for data scientists aiming at selecting the most adequate SKE/SKI method for their needs, and also work as suggestions for researchers interested in filling the gaps of the current state of the art, as well as for developers willing to implement SKE/SKI-based technologies.

Figures (16)

• Figure 1: Interpretability/performance trade-off for some common sorts of black-box predictors.
• Figure 2: Venn diagram categorising SKE methods w.r.t. translucency: pedagogical (P) or decompositional (D). For decompositional methods, we report the target predictor type: ANN$\langle n \rangle$ = artificial NN (possibly, having exactly $\langle n \rangle$ layers), CNN = convolutional NN, GNN = graph NN, FNN = fuzzy NN, SVM = support vector machines, DTE = decision tree ensembles, LC = linear classifiers.
• Figure 3: Venn diagram categorising SKE methods w.r.t. the input data type required by the underlying predictor: binary (B), discrete (D), continuous (C), images (I), text (T), graphs (G).
• Figure 4: Venn diagram categorising SKE methods w.r.t. the output knowledge's shape: rule lists (L), decision trees (DT) or tables (TA), knowledge graphs (KG).
• Figure 5: Venn diagram categorising SKE methods w.r.t. the output knowledge's expressiveness: propositional (P), $M$-of-$N$ (MN), fuzzy (F), or oblique (O) rules; or triplets (T).