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.

翻译：本研究利用卷积模型树（CMTs）[1]探索图像输入的旋转鲁棒学习问题，该模型的分裂节点和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。在具有旋转不变回归目标的受控MNIST实验环境中，我们针对分裂方向引入了三种几何感知的归纳偏置——卷积平滑、倾斜主导约束和基于重要性的剪枝——并量化了它们在平面旋转下对模型鲁棒性的影响。我们进一步评估了部署时的方向搜索策略，该策略通过选择使森林级置信度代理最大化的离散旋转角度来优化预测，且无需更新模型参数。方向搜索在极端旋转条件下显著提升了鲁棒性，但当置信度与正确性失准时，在标准方向附近可能产生负面效果。最后，我们在以一对多回归形式实现的MNIST数字识别任务中观察到一致的趋势，这凸显了基于置信度的方向选择策略对模型树集成方法兼具潜力与局限性。