用卷积模型树实现图像旋转鲁棒回归，提升旋转下的预测稳定性。
Rotation-Robust Regression with Convolutional Model Trees
- 通过卷积平滑、倾斜主导约束等几何先验增强分裂方向的旋转鲁棒性。
- 部署时旋转搜索在严重旋转下提升性能，但标准朝向附近可能因置信度偏差导致下降。
- 适用于需要高旋转鲁棒性的图像回归任务，如手写数字识别。
我们研究使用卷积模型树（CMTs）进行图像输入的旋转鲁棒学习，其分裂与叶节点系数可在图像网格上结构化，并在部署时进行几何变换。在带有旋转不变回归目标的受控MNIST设置中，引入三种几何感知归纳偏置：卷积平滑、倾斜主导约束和基于重要性的剪枝，并量化其在平面内旋转下的鲁棒性影响。进一步评估了部署时的方向搜索策略，该策略在不更新模型参数的情况下选择使森林级置信度代理最大化的离散旋转。结果表明，方向搜索在严重旋转下可提升鲁棒性，但在标准朝向附近可能因置信度与正确性错位而产生负面影响。最后，在作为一对多回归实现的手写数字识别任务中观察到一致趋势，揭示了基于置信度的方向选择在模型树集成中的潜力与局限。
原文摘要 · Abstract (English)
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.
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