Search papers, labs, and topics across Lattice.
This paper addresses the mean-collapse pathology in multimodal regression by introducing Difference-Quotient Clustering (DQC), which minimizes intra-cluster discrepancies between outputs and inputs. The method effectively partitions data to assign conditional labels, leading to significant improvements in test minimum squared error (minMSE) compared to traditional approaches. On synthetic benchmarks with multiple outputs, DQC achieved a test minMSE of 0.19, outperforming random labels and mean collapse strategies, and demonstrating the potential for deeper networks to handle larger intra-cluster contradictions.
DQC reduces the mean-collapse issue in multimodal regression, achieving a remarkable test minMSE of 0.19鈥攆ar superior to random and mean collapse strategies.
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.
