The successful deployment of AI solutions relies heavily on the quality of underlying model assumptions and the learning algorithms they employ. The design of loss functions is therefore crucial in the process of model development to the specific tasks at hand. For instance, the Hyvärinen score matching principle has been widely applied in AI systems, particularly for tasks such as image generation. This project seeks to further develop and broaden the range of loss functions by incorporating concepts from differential geometry. Additionally, we leverage the theory of estimating functions to create optimal inference algorithms for the proposed loss functions, as well as for those previously introduced in the literature. These advancements hold significant potential for a wide range of applications, spanning scientific research and societal challenges at large.

2025

2029