FDSML: Formula-Driven Supervised Metric Learning with Parameter-Aware Triplet Loss

FDSML. Formula-Driven Supervised Metric Learning with Parameter-Aware Triplet Loss. By Hina Otake and five others, from Waseda University, the Waseda Research Institute for Science and Engineering, and two other institutions. Published on the twenty-ninth of October.

Formula-Driven Supervised Learning, or FDSL, makes it possible to pre-train vision models without any real images. But existing methods frame that pre-training as classification over discretized labels. Doing so throws away the continuity that exists in the generative process that made the images. Images produced by nearby formula parameters are related, and images from distant parameters less so, but a class label records only membership. Two images in one class count as equally alike, and two images in different classes count as equally unlike, however close their parameters were.

Formula-Driven Supervised Metric Learning, FDSML, keeps that continuity. It derives relational supervision from the image-generation parameters themselves, going beyond discrete class labels.

Two pieces make it up. The first is FineFractalDB, a refined fractal dataset with higher intra-class variation and more stable structures. The second is a Parameter-Aware Triplet Loss, or PA-Triplet. It assigns positives and negatives according to distances in the underlying Iterated Function System parameter space. The effect is that embeddings are trained to respect relative similarity orderings derived from those parameters. In place of a class label, the supervision becomes a statement about order: this image should sit closer to that one than to a third.

FDSML improves transferability to image retrieval, while staying competitive on downstream classification and improving robustness under several corruption settings. Compared with FDSL pre-training on ResNet-50, Recall@1 on Stanford Online Products rises from sixty-five point six to seventy-four percent. On Stanford Cars it rises from fifty-six point two to seventy-eight point four percent.

The shift is from asking which class an image belongs to, toward asking how close two images are in the parameters that generated them. The authors read their results as suggesting that this relational signal is a stronger synthetic pre-training signal than label-based classification, for transfer beyond recognition.