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Rotation-Robust Regression with Convolutional Model Trees

Hongyi Li, William Ward Armstrong, Jun Xu

TL;DR

This work tackles rotation robustness for image inputs by using Convolutional Model Trees (CMTs) with geometry-aware split biases and a deployment-time orientation search (OS). By targeting a rotation-invariant perimeter regression on MNIST, the authors show that three inductive biases—convolutional smoothing, tilt-dominance, and importance pruning—improve robustness, particularly near the canonical orientation. The deployment-time OS further boosts performance under severe rotations but can hurt near zero rotation unless calibrated or priors are applied. Overall, geometry-guided CMTs offer a practical path to rotation-robust regression with manageable training costs, though confidence-based orientation selection requires careful calibration for reliable deployment.

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.

Rotation-Robust Regression with Convolutional Model Trees

TL;DR

This work tackles rotation robustness for image inputs by using Convolutional Model Trees (CMTs) with geometry-aware split biases and a deployment-time orientation search (OS). By targeting a rotation-invariant perimeter regression on MNIST, the authors show that three inductive biases—convolutional smoothing, tilt-dominance, and importance pruning—improve robustness, particularly near the canonical orientation. The deployment-time OS further boosts performance under severe rotations but can hurt near zero rotation unless calibrated or priors are applied. Overall, geometry-guided CMTs offer a practical path to rotation-robust regression with manageable training costs, though confidence-based orientation selection requires careful calibration for reliable deployment.

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.
Paper Structure (28 sections, 8 equations, 3 figures, 6 tables)

This paper contains 28 sections, 8 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Deployment-time orientation search (OS).
  3. Method
  4. Notation
  5. Task Definition: Perimeter Regression
  6. Midpoint Hyperplane Split
  7. Leaf Models: Least-Squares Direction (Ridge-Optional) via Adam
  8. Geometric Inductive Biases for Split Normals
  9. Convolutional smoothing (Conv).
  10. Importance pruning (Prune).
  11. Tilt dominance constraint (Tilt).
  12. Deployment-Time Orientation Search (OS)
  13. Experimental Setup
  14. Data and Evaluation Protocol
  15. Models and Ablations
  16. ...and 13 more sections

Figures (3)

  • Figure 1: Rotated MNIST examples used in evaluation (bilinear resampling). We report results on the seven evaluation-time rotations $\Theta=\{-60^\circ,-40^\circ,-20^\circ,0^\circ,20^\circ,40^\circ,60^\circ\}$.
  • Figure 2: Perimeter regression MAE versus rotation angle. For models that support OS, we plot both normal prediction and OS-based prediction.
  • Figure 3: Classification-as-regression accuracy versus rotation angle. For models that support OS, we plot both normal prediction and OS-based prediction.