Zhang–Jiang balanced-splitting conjecture
For every finite horizon , in each of the symmetric recursive frameworks called the primitive and OBS-S constructions for predetermined-step gradient descent on smooth convex functions, an optimal recursive composition is obtained by balanced splitting at every recursive level: whenever a horizon is split into two admissible subhorizons, their sizes differ by at most one, subject to the framework's recursive constraints.
References
Primary source
Additional references
- Optimal Recursive Composition and Dyadic Phase Laws for Gradient Descent with Predetermined Stepsizes — arXiv — Yu Liu, Kang Chen, Rujun Jiang, Tianyu Wang
Progress summary
A September 2026 preprint claims to prove the conjecture’s optimal recursive strategy, but the result is unrefereed and limited to specified frameworks.
The Zhang–Jiang balanced-splitting conjecture predicts an exact finite-horizon description of optimal predetermined-step methods within its stated recursive setting.
September 10, 2026 claimed proof
Yu Liu, Kang Chen, Rujun Jiang, and Tianyu Wang claim to prove the conjectured optimal recursive structure and derive a nonconstant log-periodic modulation in the rate. Their result concerns only the specified recursive frameworks and is unrefereed.
Current status (as of September 2026): A claimed proof covers the stated recursive frameworks, but it remains unverified and does not establish a broader result.
Sources
Solutions 0
No solutions have been posted yet.