arXiv Machine Learning November 2, 2026 By Xiaojun Wu, Cehao Yang, Xuhui Jiang, Chengjin Xu, Jia Li, Jian Guo

FARO: Function-Space Adaptive Return-to-Risk Optimization via Cross-Block Equal-Risk-Contribution Budget Allocation

Read the original on arXiv Machine Learning →

The paper introduces FARO, a function‑space adaptive optimizer that treats each parameter block as a decision unit, assigning geometry based on counterfactual return and reallocating budgets via cross‑block equal risk contribution (ERC). On a GPT‑style model trained on FineWeb, FARO‑Adaptive matches the best hand‑designed optimizer (NorMuonAndAdam) while FARO‑ERC further reduces clean‑data loss by an average of 0.0136 nats across six seeds, achieving a robust improvement without extra time or memory. The method works by trimming the riskiest blocks and remains effective even under corrupted data streams.

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