解决多模态回归的均值坍缩问题，通过差商聚类实现快速粗粒度标签分配。
Resolving Multi-Modal Regression by Difference-Quotient-Based Clustering:Fast Coarse Conditional-Label Assignment
- 基于差商聚类划分数据，最小化簇内输出与输入的不一致性。
- 在合成数据上测试时，minMSE低至0.19（K=5, nx=500），接近0.09的最优值。
- 适合需要高效多模态输出生成的场景，如图像/视频多解生成任务。
多模态回归面临均值坍缩问题：在平方损失下，无约束回归器会收敛到条件均值，而当模态数K > 1时，该均值远离所有真实模式。我们将其归因于样本间成对矛盾——输入几乎相同但输出相距甚远。为此提出差商聚类（DQC），通过最小化簇内输出与输入的差异来划分数据。每个样本被分配到使其最大矛盾比最小的簇；随后使用生成的标签训练逻辑斯蒂生成器与条件网络。由于测试时生成模态未知，采用与所有真实输出的最小平方误差（minMSE）进行评估。在合成基准（K=5, 10）上，DQC测试minMSE为0.19（K=5, nx=500），优于0.09的理论最优、1.08的随机标签和1.33的均值坍缩。观察到两个经验规律：簇内矛盾越大，需更深网络；而最优标签可从更少样本中泛化出，优于聚类所得标签。该聚类为硬性、可并行的O(n²/2)前处理流程，用于粗粒度条件标签分配，减轻下游生成精调负担。未来工作将包括基于残差误差的二次重聚类。
原文摘要 · Abstract (English)
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.
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