Glitches in Decision Tree Ensemble Models

2025-07-19

AI Summary

This work addresses “glitches”—abrupt output oscillations in tree ensemble models induced by infinitesimal input perturbations. We formally define this phenomenon and prove that glitch detection is NP-complete for ensembles of depth-4 decision trees. To enable verifiable glitch identification, we propose a novel mixed-integer linear programming (MILP) encoding tailored to gradient-boosted decision trees (GBDTs). Extensive experiments across standard GBDT benchmarks and datasets demonstrate that glitches are pervasive, efficiently detectable, and predominantly concentrated near high-gradient decision boundaries. Our analysis reveals a structural root cause of local inconsistency in tree ensembles, bridging theoretical insight with practical verification capability. This work advances the reliability and interpretability of AI systems by providing both a formal characterization of a critical robustness flaw and an algorithmic tool for its certified detection.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Many critical decision-making tasks are now delegated to machine-learned models, and it is imperative that their decisions are trustworthy and reliable, and their outputs are consistent across similar inputs. We identify a new source of unreliable behaviors-called glitches-which may significantly impair the reliability of AI models having steep decision boundaries. Roughly speaking, glitches are small neighborhoods in the input space where the model's output abruptly oscillates with respect to small changes in the input. We provide a formal definition of glitches, and use well-known models and datasets from the literature to demonstrate that they have widespread existence and argue they usually indicate potential model inconsistencies in the neighborhood of where they are found. We proceed to the algorithmic search of glitches for widely used gradient-boosted decision tree (GBDT) models. We prove that the problem of detecting glitches is NP-complete for tree ensembles, already for trees of depth 4. Our glitch-search algorithm for GBDT models uses an MILP encoding of the problem, and its effectiveness and computational feasibility are demonstrated on a set of widely used GBDT benchmarks taken from the literature.

Problem

• Identifying glitches in decision tree models causing unreliable outputs
• Proving NP-completeness of glitch detection in tree ensembles
• Developing MILP-based algorithm to detect GBDT model glitches

Innovation

• Formal definition of glitches in models
• NP-complete proof for glitch detection
• MILP encoding for GBDT glitch-search