Continual learning commonly relies on post-hoc mechanisms such as replay, elastic regularization, or distillation. This work argues that forgetting should instead be modeled directly as interference between tasks. In the frozen-feature regime, forgetting from learning a new task is exactly the interference energy induced on the old task. In deep networks, the same quantity is recovered through path-averaged curvature with minimal additional forward passes. When task supports are disjoint, forgetting can be eliminated structurally and when task supports overlap in conflicting directions, a non-zero distortion floor is unavoidable. The same geometry optimally merges models through task-aware orthogonalization. From this analysis we derive Interference-Gated Functional Allocation (IGFA), a replay-free, Fisher-free method that shares directions when tasks align and protects them when they conflict. Across benchmarks, IGFA achieves lossless retention when tasks are structurally separable and moves unavoidable cost from irreversible forgetting into deferred but recoverable plasticity when they are not. It matches the strongest replay-free structural baselines on dissimilar-task streams and improves on unconditional projection when similarity makes transfer worth preserving.
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.