基于差商聚类的多模态回归解决方法：快速粗粒度条件标签分配
Resolving Multi-Modal Regression by Difference-Quotient-Based Clustering:Fast Coarse Conditional-Label Assignment
- Guangdong Polytechnic Normal University（广东技术师范大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对多模态回归的均值崩溃问题，提出差商聚类（DQC）方法，通过最小化簇内差异分配标签，在合成基准上取得优于随机标签和均值崩溃的最小平方误差，为后续生成优化减轻负担。
AI中文摘要：
多模态回归存在均值崩溃问题：在平方损失下，无约束回归器会收敛到条件均值，当模态数K>1时，该均值与所有模态均不匹配。我们将此失败归因于成对矛盾——输入相近但输出差异大的样本——并提出差商聚类（Difference-Quotient Clustering, DQC），该方法通过划分数据以最小化簇内输出与输入的差异。每个样本被分配至使其最大矛盾率最小的簇；随后在生成的标签上训练logits生成器和条件网络。由于测试时生成模态未知，我们通过对所有K个真实输出取最小平方误差（minMSE）进行评估。在合成基准（K=5、10）上，DQC的测试minMSE为0.19（K=5，样本数nx=500），而最优模型（oracle）为0.09，随机标签为1.08，均值崩溃为1.33。我们观察到两个经验规律：簇内矛盾越大，所需网络越深；最优模型标签比聚类生成的标签从更少样本中泛化。该聚类是用于粗粒度条件分配的硬并行化O(n²/2)前端，可减轻下游生成式优化的负担。我们将残差误差的第二阶段重新聚类作为未来工作。
英文摘要：
Multimodal regression suffers from the mean-collapse pathology: under squared loss, an unconstrained regressor converges to the conditional mean, which for K > 1 lies away from all modes. We attribute this failure to pairwise contradictions--samples with nearly identical inputs but distant outputs--and propose Difference-Quotient Clustering (DQC), which partitions data to minimize intra-cluster output-vs-input discrepancy. Each sample is assigned to the cluster that minimizes its maximum contradiction ratio; a logits generator and a conditional network are then trained on the resulting labels. Since the generating modality is unknown at test time, we evaluate via minimum squared error (minMSE) against all K true outputs. On synthetic benchmarks (K=5, 10), DQC achieves test minMSE 0.19 (K=5, nx=500), versus 0.09 for an oracle, 1.08 for random labels, and 1.33 for mean collapse. We observe two empirical regularities: larger intra-cluster contradictions require deeper networks, and oracle labels generalize from fewer samples than cluster-derived equivalents. The clustering is a hard, parallelizable O(n^2/2) front-end for coarse conditional assignment, reducing the burden of downstream generative refinement. A second-stage re-clustering on residual errors is outlined as future work.
