TL;DR
This paper extends the concept of differential invariants in differentiable programming to arbitrary order, enhancing validation methods beyond the current first-order focus.
Contribution
It introduces a generalized framework for differential invariants of any order, advancing validation techniques in differentiable programming.
Findings
Generalized differential invariants for arbitrary order derived
Enhanced validation methods for higher-order differentiable programs
Theoretical foundation for future validation tools
Abstract
Validation is a major challenge in differentiable programming. The state of the art is based on algorithmic differentiation. Consistency of first-order tangent and adjoint programs is defined by a well-known first-order differential invariant. This paper generalizes the approach through derivation of corresponding differential invariants of arbitrary order.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Optimization Algorithms Research · Optimization and Mathematical Programming · Scheduling and Optimization Algorithms