Feature-Function Curvature Analysis: A Geometric Framework for Explaining Differentiable Models

2025-10-31

AI Summary

Existing XAI methods predominantly yield static, unidimensional feature attributions, failing to capture nonlinearities, feature interactions, and training-time dynamics. To address this, we propose Feature-Function Curvature Analysis (FFCA)—the first geometric framework modeling the dynamic role of features in differentiable models. FFCA constructs a four-dimensional explanation signature quantifying feature importance, volatility, nonlinearity, and interaction strength, leveraging high-order gradient curvature and dynamic prototype clustering to track temporal evolution across the entire training trajectory. Experiments reveal a hierarchical learning pattern: models first acquire linear representations before progressively learning interactions. FFCA further enables early diagnosis of model capacity limitations and overfitting. Empirically, FFCA significantly outperforms baselines on both static attribution and dynamic diagnostic tasks, establishing a rigorous geometric foundation for interpretable AI.

Technology Category

• Humans and AI: Explainable AI (XAI) for Human Understanding
• Machine Learning: Feature Construction/Reformulation
• Computer Vision: Interpretability, Explainability, and Transparency

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Explainable AI (XAI) is critical for building trust in complex machine learning models, yet mainstream attribution methods often provide an incomplete, static picture of a model's final state. By collapsing a feature's role into a single score, they are confounded by non-linearity and interactions. To address this, we introduce Feature-Function Curvature Analysis (FFCA), a novel framework that analyzes the geometry of a model's learned function. FFCA produces a 4-dimensional signature for each feature, quantifying its: (1) Impact, (2) Volatility, (3) Non-linearity, and (4) Interaction. Crucially, we extend this framework into Dynamic Archetype Analysis, which tracks the evolution of these signatures throughout the training process. This temporal view moves beyond explaining what a model learned to revealing how it learns. We provide the first direct, empirical evidence of hierarchical learning, showing that models consistently learn simple linear effects before complex interactions. Furthermore, this dynamic analysis provides novel, practical diagnostics for identifying insufficient model capacity and predicting the onset of overfitting. Our comprehensive experiments demonstrate that FFCA, through its static and dynamic components, provides the essential geometric context that transforms model explanation from simple quantification to a nuanced, trustworthy analysis of the entire learning process.

Problem

• Explaining complex models beyond static attribution scores
• Quantifying feature impact, volatility, non-linearity and interactions
• Tracking feature signature evolution throughout training process

Innovation

• FFCA framework analyzes model geometry with 4D feature signatures
• Dynamic Archetype Analysis tracks signature evolution during training
• Provides diagnostics for model capacity and overfitting prediction