FOGO: Forgetting-aware Orthogonalization Optimizer

• URL: http://arxiv.org/abs/2606.10406v1
• Date: Tue, 09 Jun 2026 04:30:49 GMT
• Title: FOGO: Forgetting-aware Orthogonalization Optimizer
• Abstract summary: We argue that forgetting is not confined to continual learning but is a general optimization phenomenon.<n>We introduce FOGO, a scalable gradient that continuously detects and resolves interference across both regimes.<n> FOGO consistently improves convergence and knowledge retention, outperforming Adam and Muon.
• Score: 21.464454254585387
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We argue that forgetting is not confined to continual learning but is a general optimization phenomenon: during standard training, dominant mini-batch gradients suppress rare but useful update directions, causing short-term forgetting at every step. When such knowledge is never revisited, these losses compound into long-term forgetting-the classical failure mode of continual learning. We introduce FOGO, a scalable optimizer that continuously detects and resolves gradient interference across both regimes. FOGO spectrally orthogonalizes momentum updates to prevent dominant directions from monopolizing optimization, then stores representative past directions in a compact codebook memory built on random projection, where pairwise distances are provably preserved in low-dimensional space. At each step, conflicts between the current update and stored directions are resolved via lightweight orthogonal correction and lifted back through a proximal step, with minimal overhead and no data storage. Across class-imbalanced classification, continual visual learning under domain and class shifts, continual fine-tuning of LLaVA-7B, and GPT-2 pretraining, FOGO consistently improves convergence and knowledge retention, outperforming Adam and Muon.

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