Rotation-Robust Regression with Convolutional Model Trees

2026-01-08

arXiv.org

AI Summary

This work addresses the degradation of regression performance under in-plane image rotations by proposing a geometry-aware approach based on Convolutional Model Trees (CMT). The method enhances rotational invariance during training through three geometric inductive biases: convolutional smoothing, tilt-dominance constraints, and importance-based pruning. Furthermore, it introduces, for the first time in model tree ensembles, a deployment-time strategy that combines discrete rotation search with a confidence-proxy optimization mechanism to adaptively select the optimal rotation orientation. Experimental results demonstrate that the proposed approach significantly improves robustness under large-angle rotations on the MNIST rotation regression task, although a slight performance drop may occur near the canonical orientation due to misalignment between confidence estimates and prediction accuracy.

Technology Category

• Machine Learning: Ensemble Methods
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We study rotation-robust learning for image inputs using Convolutional Model Trees (CMTs) [1], whose split and leaf coefficients can be structured on the image grid and transformed geometrically at deployment time. In a controlled MNIST setting with a rotation-invariant regression target, we introduce three geometry-aware inductive biases for split directions -- convolutional smoothing, a tilt dominance constraint, and importance-based pruning -- and quantify their impact on robustness under in-plane rotations. We further evaluate a deployment-time orientation search that selects a discrete rotation maximizing a forest-level confidence proxy without updating model parameters. Orientation search improves robustness under severe rotations but can be harmful near the canonical orientation when confidence is misaligned with correctness. Finally, we observe consistent trends on MNIST digit recognition implemented as one-vs-rest regression, highlighting both the promise and limitations of confidence-based orientation selection for model-tree ensembles.

Problem

• rotation robustness
• image regression
• convolutional model trees
• geometric invariance
• orientation search

Innovation

• rotation-robust learning
• Convolutional Model Trees
• geometry-aware inductive bias
• orientation search
• confidence-based selection