Reproduce “JacNet: Learning Functions with Structured Jacobians” on OpenResearch

About this paper

Jonathan Lorraine, Safwan Hossain

The JacNet framework introduces a neural network approach that learns functions by directly modeling and integrating their Jacobians, enabling the explicit enforcement of derivative properties. The method demonstrates that specific output activations for the Jacobian-learning network can guarantee properties like global invertibility and k-Lipschitz continuity, as shown by successful approximations of target functions like exponential and absolute value.

Key insights

• Learning a function by modeling and integrating its Jacobian offers a principled way to explicitly control and guarantee derivative properties of the learned function.
• Output activations can be designed to directly translate desired regularity conditions (e.g., positive definite Jacobian for invertibility, tanh for Lipschitz bounds) into the structure of the learned derivatives.
• The combination of a learned Jacobian with differentiable numerical integration provides an end-to-end framework for 'function learning with certified derivative properties'.

Summary by alphaXiv.