Symbolic Knowledge Extraction Research Articles

Untying black boxes with clustering-based symbolic knowledge extraction

Machine learning black boxes, exemplified by deep neural networks, often exhibit challenges in interpretability due to their reliance on complicated relationships involving numerous internal parameters and input features. This lack of transparency from a human perspective renders their predictions untrustworthy, particularly in critical applications. In this paper, we address this issue by introducing the design and implementation of CReEPy, an algorithm for symbolic knowledge extraction based on explainable clustering. Specifically, CReEPy leverages the underlying clustering performed by the ExACT or CREAM algorithms to generate human-interpretable Prolog rules that mimic the behaviour of opaque models. Additionally, we introduce CRASH, an algorithm for the automated tuning of hyper-parameters required by CReEPy. We present experiments evaluating both the human readability and predictive performance of the proposed knowledge-extraction algorithm, employing existing state-of-the-art techniques as benchmarks for comparison in real-world applications.

Special Issue: Selected papers from the AIxIA 2023 Workshops

The 2023 edition of the AIxIA Conference, held in Rome, brought together a large number of researchers and practitioners to discuss the most recent and important advancements in Artificial Intelligence (AI). The conference featured 19 workshops, organized by 77 experts, attracting 248 submissions and resulting in 16 proceedings. This special issue presents extended versions of selected papers initially showcased at these workshops. Each paper underwent rigorous review and represents a diverse array of topics, reflecting the multifaceted nature of the Italian AI community. The topics covered include ethical foundations to symbiotic AI, symbolic knowledge extraction from black-box models, creative influence prediction using graph theory, AI approaches to multidimensional poverty prediction, an assessment of AI-based supports for informal caregivers, deep learning-based EEG denoising, AI-assisted board-game-based learning, large language models for assessment and feedback in higher education, geometric reasoning in the Traveling Salesperson Problem, defeasible reasoning in weighted knowledge bases, and conditional computation in neural networks. These contributions demonstrate the innovative and interdisciplinary research within the AI community, offering valuable insights and advancing the field.

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

In this article, we focus on the opacity issue of sub-symbolic machine learning predictors by promoting two complementary activities— symbolic knowledge extraction (SKE) and symbolic knowledge 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 may 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.

Towards a unified model for symbolic knowledge extraction with hypercube-based methods

The XAI community is currently studying and developing symbolic knowledge-extraction (SKE) algorithms as a means to produce human-intelligible explanations for black-box machine learning predictors, so as to achieve believability in human-machine interaction. However, many extraction procedures exist in the literature, and choosing the most adequate one is increasingly cumbersome, as novel methods keep on emerging. Challenges arise from the fact that SKE algorithms are commonly defined based on theoretical assumptions that typically hinder practical applicability. This paper focuses on hypercube-based SKE methods, a quite general class of extraction techniques mostly devoted to regression-specific tasks. We first show that hypercube-based methods are flexible enough to support classification problems as well, then we propose a general model for them, and discuss how they support SKE on datasets, predictors, or learning tasks of any sort. Empirical examples are reported as well –based upon the PSyKE framework –, showing the applicability of hypercube-based methods to actual classification tasks.

Symbolic knowledge extraction for explainable nutritional recommenders

Background and objective:This paper focuses on nutritional recommendation systems (RS), i.e. AI-powered automatic systems providing users with suggestions about what to eat to pursue their weight/body shape goals. A trade-off among (potentially) conflictual requirements must be taken into account when designing these kinds of systems, there including: (i) adherence to experts’ prescriptions, (ii) adherence to users’ tastes and preferences, (iii) explainability of the whole recommendation process. Accordingly, in this paper we propose a novel approach to the engineering of nutritional RS, combining machine learning and symbolic knowledge extraction to profile users—hence harmonising the aforementioned requirements.MethodsOur contribution focuses on the data processing workflow. Stemming from neural networks (NN) trained to predict user preferences, we use CART Breiman et al.(1984) to extract symbolic rules in Prolog Körner et al.(2022) form, and we combine them with expert prescriptions brought in similar form. We can then query the resulting symbolic knowledge base via logic solvers, to draw explainable recommendations.ResultsExperiments are performed involving a publicly available dataset of 45,723 recipes, plus 12 synthetic datasets about as many imaginary users, and 6 experts’ prescriptions. Fully-connected 4-layered NN are trained on those datasets, reaching ∼86% test-set accuracy, on average. Extracted rules, in turn, have ∼80% fidelity w.r.t. those NN. The resulting recommendation system has a test-set precision of ∼74%. The symbolic approach makes it possible to devise how the system draws recommendations.ConclusionsThanks to our approach, intelligent agents may learn users’ preferences from data, convert them into symbolic form, and extend them with experts’ goal-directed prescriptions. The resulting recommendations are then simultaneously acceptable for the end user and adequate under a nutritional perspective, while the whole process of recommendation generation is made explainable.

Symbolic knowledge extraction from opaque predictors applied to cosmic-ray data gathered with LISA Pathfinder

Machine learning models are nowadays ubiquitous in space missions, performing a wide variety of tasks ranging from the prediction of multivariate time series through the detection of specific patterns in the input data. Adopted models are usually deep neural networks or other complex machine learning algorithms providing predictions that are opaque, i.e., human users are not allowed to understand the rationale behind the provided predictions. Several techniques exist in the literature to combine the impressive predictive performance of opaque machine learning models with human-intelligible prediction explanations, as for instance the application of symbolic knowledge extraction procedures. In this paper are reported the results of different knowledge extractors applied to an ensemble predictor capable of reproducing cosmic-ray data gathered on board the LISA Pathfinder space mission. A discussion about the readability/fidelity trade-off of the extracted knowledge is also presented.

Symbolic knowledge extraction from opaque ML predictors in PSyKE: Platform design & experiments

A common practice in modern explainable AI is to post-hoc explain black-box machine learning (ML) predictors – such as neural networks – by extracting symbolic knowledge out of them, in the form of either rule lists or decision trees. By acting as a surrogate model, the extracted knowledge aims at revealing the inner working of the black box, thus enabling its inspection, representation, and explanation. Various knowledge-extraction algorithms have been presented in the literature so far. Unfortunately, running implementations of most of them are currently either proofs of concept or unavailable. In any case, a unified, coherent software framework supporting them all – as well as their interchange, comparison, and exploitation in arbitrary ML workflows – is currently missing. Accordingly, in this paper we discuss the design of PSyKE, a platform providing general-purpose support to symbolic knowledge extraction from different sorts of black-box predictors via many extraction algorithms. Notably, PSyKE targets symbolic knowledge in logic form, allowing the extraction of first-order logic clauses. The extracted knowledge is thus both machine- and human-interpretable, and can be used as a starting point for further symbolic processing—e.g. automated reasoning.

From LSAT: The Progress and Challenges of Complex Reasoning

Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In this paper, we take a step forward in complex reasoning by systematically studying the three challenging and domain-general tasks of the Law School Admission Test (LSAT), including analytical reasoning, logical reasoning and reading comprehension. We propose a hybrid reasoning system to integrate these three tasks and achieve impressive overall performance on the LSAT tests. The experimental results demonstrate that our system endows itself a certain complex reasoning ability, especially the fundamental reading comprehension and challenging logical reasoning capacities. Further analysis also shows the effectiveness of combining the pre-trained models with the task-specific reasoning module, and integrating symbolic knowledge into discrete interpretable reasoning steps in complex reasoning. We further shed a light on the potential future directions, like unsupervised symbolic knowledge extraction, model interpretability, few-shot learning and comprehensive benchmark for complex reasoning.

Characterizing Image Sets Using Formal Concept Analysis

This article presents a new method for supervised image classification. Given a finite number of image sets, each set corresponding to a place of an environment, we propose a localization strategy, which relies upon supervised classification. For each place, the corresponding landmark is actually a combination of features that have to be detected in the image set. Moreover, these features are extracted using a symbolic knowledge extraction theory, formal concept analysis. This paper details the full landmark extraction process and its hierarchical organization. A real localization problem in a structured environment is processed as an illustration. This approach is compared with an optimized neural network-based classification, and validated with experimental results. Further research to build up hybrid classifier is outlined in the discussion.

Symbolic knowledge extraction from trained neural networks: A sound approach

Although neural networks have shown very good performance in many application domains, one of their main drawbacks lies in the incapacity to provide an explanation for the underlying reasoning mechanisms. The “explanation capability” of neural networks can be achieved by the extraction of symbolic knowledge. In this paper, we present a new method of extraction that captures nonmonotonic rules encoded in the network, and prove that such a method is sound. We start by discussing some of the main problems of knowledge extraction methods. We then discuss how these problems may be ameliorated. To this end, a partial ordering on the set of input vectors of a network is defined, as well as a number of pruning and simplification rules. The pruning rules are then used to reduce the search space of the extraction algorithm during a pedagogical extraction, whereas the simplification rules are used to reduce the size of the extracted set of rules. We show that, in the case of regular networks, the extraction algorithm is sound and complete. We proceed to extend the extraction algorithm to the class of non-regular networks, the general case. We show that non-regular networks always contain regularities in their subnetworks. As a result, the underlying extraction method for regular networks can be applied, but now in a decompositional fashion. In order to combine the sets of rules extracted from each subnetwork into the final set of rules, we use a method whereby we are able to keep the soundness of the extraction algorithm. Finally, we present the results of an empirical analysis of the extraction system, using traditional examples and real-world application problems. The results have shown that a very high fidelity between the extracted set of rules and the network can be achieved.

Noisy Time Series Prediction using Recurrent Neural Networks and Grammatical Inference

Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, non-stationarity, and non-linearity. Neural networks have been very successful in a number of signal processing applications. We discuss fundamental limitations and inherent difficulties when using neural networks for the processing of high noise, small sample size signals. We introduce a new intelligent signal processing method which addresses the difficulties. The method proposed uses conversion into a symbolic representation with a self-organizing map, and grammatical inference with recurrent neural networks. We apply the method to the prediction of daily foreign exchange rates, addressing difficulties with non-stationarity, overfitting, and unequal a priori class probabilities, and we find significant predictability in comprehensive experiments covering 5 different foreign exchange rates. The method correctly predicts the direction of change for the next day with an error rate of 47.1%. The error rate reduces to around 40% when rejecting examples where the system has low confidence in its prediction. We show that the symbolic representation aids the extraction of symbolic knowledge from the trained recurrent neural networks in the form of deterministic finite state automata. These automata explain the operation of the system and are often relatively simple. Automata rules related to well known behavior such as tr end following and mean reversal are extracted.

Extracting rules from a (fuzzy/crisp) recurrent neural network using a self-organizing map

Although the extraction of symbolic knowledge from trained feedforward neural networks has been widely studied, research in recurrent neural networks (RNN) has been more neglected, even though it performs better in areas such as control, speech recognition, time series prediction, etc. Nowadays, a subject of particular interest is (crisp/fuzzy) grammatical inference, in which the application of these neural networks has proven to be suitable. In this paper, we present a method using a self-organizing map (SOM) for extracting knowledge from a recurrent neural network able to infer a (crisp/fuzzy) regular language. Identification of this language is done only from a (crisp/fuzzy) example set of the language. © 2000 John Wiley & Sons, Inc.

Extraction of rules from discrete-time recurrent neural networks

The extraction of symbolic knowledge from trained neural networks and the direct encoding of (partial) knowledge into networks prior to training are important issues. They allow the exchange of information between symbolic and connectionist knowledge representations. The focus of this paper is on the quality of the rules that are extracted from recurrent neural networks. Discrete-time recurrent neural networks can be trained to correctly classify strings of a regular language. Rules defining the learned grammar can be extracted from networks in the form of deterministic finite-state automata (DFAs) by applying clustering algorithms in the output space of recurrent state neurons. Our algorithm can extract different finite-state automata that are consistent with a training set from the same network. We compare the generalization performances of these different models and the trained network and we introduce a heuristic that permits us to choose among the consistent DFAs the model which best approximates the learned regular grammar.