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FAME: Introducing Fuzzy Additive Models for Explainable AI

Omer Bahadir Gokmen, Yusuf Guven, Tufan Kumbasar

TL;DR

FAM and FAME address the transparency gap in deep learning by integrating fuzzy single-input single-output rules within a three-layer additive framework. The Projection Layer compresses inputs to a low-dimensional space; each reduced feature passes through a SFLS; outputs are aggregated additively to yield predictions. FAME further improves interpretability by sculpting the antecedent space using Gauss2MFs, achieving fewer active rules with comparable performance. A DL-based learning framework optimizes the model with either $L_2$ or $L_F$ loss, and experiments across six datasets show competitive RMSE with enhanced explainability, supporting FAME as a practical XAI tool.

Abstract

In this study, we introduce the Fuzzy Additive Model (FAM) and FAM with Explainability (FAME) as a solution for Explainable Artificial Intelligence (XAI). The family consists of three layers: (1) a Projection Layer that compresses the input space, (2) a Fuzzy Layer built upon Single Input-Single Output Fuzzy Logic Systems (SFLS), where SFLS functions as subnetworks within an additive index model, and (3) an Aggregation Layer. This architecture integrates the interpretability of SFLS, which uses human-understandable if-then rules, with the explainability of input-output relationships, leveraging the additive model structure. Furthermore, using SFLS inherently addresses issues such as the curse of dimensionality and rule explosion. To further improve interpretability, we propose a method for sculpting antecedent space within FAM, transforming it into FAME. We show that FAME captures the input-output relationships with fewer active rules, thus improving clarity. To learn the FAM family, we present a deep learning framework. Through the presented comparative results, we demonstrate the promising potential of FAME in reducing model complexity while retaining interpretability, positioning it as a valuable tool for XAI.

FAME: Introducing Fuzzy Additive Models for Explainable AI

TL;DR

FAM and FAME address the transparency gap in deep learning by integrating fuzzy single-input single-output rules within a three-layer additive framework. The Projection Layer compresses inputs to a low-dimensional space; each reduced feature passes through a SFLS; outputs are aggregated additively to yield predictions. FAME further improves interpretability by sculpting the antecedent space using Gauss2MFs, achieving fewer active rules with comparable performance. A DL-based learning framework optimizes the model with either or loss, and experiments across six datasets show competitive RMSE with enhanced explainability, supporting FAME as a practical XAI tool.

Abstract

In this study, we introduce the Fuzzy Additive Model (FAM) and FAM with Explainability (FAME) as a solution for Explainable Artificial Intelligence (XAI). The family consists of three layers: (1) a Projection Layer that compresses the input space, (2) a Fuzzy Layer built upon Single Input-Single Output Fuzzy Logic Systems (SFLS), where SFLS functions as subnetworks within an additive index model, and (3) an Aggregation Layer. This architecture integrates the interpretability of SFLS, which uses human-understandable if-then rules, with the explainability of input-output relationships, leveraging the additive model structure. Furthermore, using SFLS inherently addresses issues such as the curse of dimensionality and rule explosion. To further improve interpretability, we propose a method for sculpting antecedent space within FAM, transforming it into FAME. We show that FAME captures the input-output relationships with fewer active rules, thus improving clarity. To learn the FAM family, we present a deep learning framework. Through the presented comparative results, we demonstrate the promising potential of FAME in reducing model complexity while retaining interpretability, positioning it as a valuable tool for XAI.

Paper Structure

This paper contains 15 sections, 12 equations, 2 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Fuzzy Additive Models: FAM and FAME
  3. Inference Structure
  4. Projection Layer
  5. Fuzzy Layer
  6. Aggregation Layer
  7. SFLSs: Inference and Feature partitioning
  8. Inference
  9. Sculpting the antecedent space
  10. Learning Framework for FAM/FAME
  11. Performance Analysis
  12. Design of Experiments
  13. Impact of Feature Space on FAM and FAME Performance
  14. Assessing the Performance of FAM and FAME vs MFLS
  15. Conclusion and Future Work

Figures (2)

  • Figure 1: FAM/FAME is composed of three main layers: Projecton Layer maps the original input space $\boldsymbol{X}$ to the feature space $\boldsymbol{Z}$. In the Fuzzy Layer, each reduced dimension $z_i \in \boldsymbol{Z}$ is passed through an SFLS. The Aggregation Layer combines the outputs of the Fuzzy Layer by summing them.
  • Figure 2: Visualization of MFs in the effective universe of discourse, defined by the max and min values of learned $z_i$'s, and indicated by dashed lines.