eXpLogic: Explaining Logic Types and Patterns in DiffLogic Networks

TL;DR

This work tackles the explainability challenge in DiffLogic networks by introducing eXpLogic, a unified algorithm that yields both local input saliency (which inputs drive a decision) and function-level explanations (which input patterns activate specific logic gates). It introduces SwitchDist, a metric designed to evaluate saliency methods in discrete classification settings, and demonstrates that eXpLogic often outperforms Vanilla Gradients and Integrated Gradients in predicting inputs that switch class scores. Additionally, the authors show how FANIN-based pruning can produce MiniNets that substantially reduce model size (~86%) and inference time (~10%) with modest class-wise accuracy loss (~3.8%). The approach highlights how architecture choices that embed logical structure can enhance explainability and enable practical efficiency gains, with potential impact in healthcare, defense, and law.

Abstract

Constraining deep neural networks (DNNs) to learn individual logic types per node, as performed using the DiffLogic network architecture, opens the door to model-specific explanation techniques that quell the complexity inherent to DNNs. Inspired by principles of circuit analysis from computer engineering, this work presents an algorithm (eXpLogic) for producing saliency maps which explain input patterns that activate certain functions. The eXpLogic explanations: (1) show the exact set of inputs responsible for a decision, which helps interpret false negative and false positive predictions, (2) highlight common input patterns that activate certain outputs, and (3) help reduce the network size to improve class-specific inference. To evaluate the eXpLogic saliency map, we introduce a metric that quantifies how much an input changes before switching a model's class prediction (the SwitchDist) and use this metric to compare eXpLogic against the Vanilla Gradients (VG) and Integrated Gradient (IG) methods. Generally, we show that eXpLogic saliency maps are better at predicting which inputs will change the class score. These maps help reduce the network size and inference times by 87\% and 8\%, respectively, while having a limited impact (-3.8\%) on class-specific predictions. The broader value of this work to machine learning is in demonstrating how certain DNN architectures promote explainability, which is relevant to healthcare, defense, and law.

Figures (2)

• Figure 1: Overview of several explanation tools that are enabled when using the DiffLogic network, which are referred to as the eXpLogic set of analyses
• Figure 2: Overview of eXpLogic, showing: (a) examples of the eXpLogic function explanations, where each exhibits input patterns which influence each digit class from the MNIST dataset; (b) a notional DiffLogic architecture that predicts three classes which is juxtapozed with a MiniNet derived from the FANIN of "class a;" (c) Local explanation method showing the evidence (important pixels) that support the decisions of class 2, 4, and 8 from the MNIST dataset. Each row shows either a TP, FP, or FN prediction where the image titles show the True (T) and Predicted (P) labels for the MNIST images, and the number of important inputs ($\Sigma$) identified for each explanation. Note that $\Sigma$ is not always highest for the predicted class. Light pixels represent important positive inputs, whereas dark pixels represent important zero inputs; (d) a graphical illustration of the SwithDist used to evaluate each saliency methods, where a current input, class 5 in this case, is modified in (e) three directions which either add, remove, or alter the important input pixels. Each image represents a baseline of class 5 modified per each unit direction from Table \ref{['tab:directions']}