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Although traditional optimization methods focus on finding a single optimalsolution, most objective functions in modern machine learning problems,especially those in deep learning, often have multiple or infinite numbers ofoptima. Therefore, it is useful to consider the problem of finding a set ofdiverse points in the optimum set of an objective function. In this work, weframe this problem as a bi-level optimization problem of maximizing a diversityscore inside the optimum set of the main loss function, and solve it with asimple population gradient descent framework that iteratively updates thepoints to maximize the diversity score in a fashion that does not hurt theoptimization of the main loss. We demonstrate that our method can efficientlygenerate diverse solutions on a variety of applications, includingtext-to-image generation, text-to-mesh generation, molecular conformationgeneration and ensemble neural network training.

How to Fill the Optimum Set? Population Gradient Descent with Harmless Diversity