FARO: Function-Space Adaptive Return-to-Risk Optimization via Cross-Block Equal-Risk-Contribution Budget Allocation
arXiv:2610.40858v1 Announce Type: new Abstract: Training a large language model is compute-bound, and current recipes divide the work between optimizers by hand: orthogonalized momentum for attention and MLP matrices, Adam-style updates for the rest. This division rests on human priors about which layer type deserves which geometry, and it fixes a single global update budget that every parameter block shares. We introduce FARO, a function-space adaptive optimizer that makes the partition of parameters into blocks the unit of decision. FARO gives each block a geometry by its realized counterfac
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