Delta N-gram: Forward-Only Continual Writing into a Language Model's Native N-gram Memory

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Our previous analysis found that a model's native hashed N-gram table is where continual updates disturb the base least, but its writes needed backpropagation and changed the pretrained table. We present Delta N-gram, a forward-only write path into that table. The pretrained table T^0 is never modified. Evidence is written into a sparse patch \Delta on the rows it addresses: a 4.1M-parameter writer emits a target and a gate per (position, hash head) event, and a block-averaged delta rule keeps each row a convex combination of its old value and the gated targets. The writer is trained offline on raw text with the pretraining objective; at use time writing takes forward passes only, and clearing \Delta restores the original model. A 0.6B prototype trained to answer questions keeps 16/16 facts after a second write; online gradient writes keep 2--4/16. We study two writers: a plain writer that encodes evidence with the T^0-only model, and a delta writer that reads its current memory while encoding. On Qwen3.8-Flash-Next, the plain writer's memory is document-specific: on 64 held-out news events it lowers continuation NLL by 0.068 nats/token against empty memory and by 0.024 against another document's memory, and 0.063 and 0.013 after 16 intervening articles. The delta writer's memory is more document-specific and keeps more of it under distraction (70% vs 54%). Over 35,000 writes on our previous seven-task chain both writers stay stable and the delta writer drifts less (layer-2 math drift 176% vs 188%); later accuracy changes by -0.26/-0.52pp (-7.29pp for gradient updates) and small-k_i drift is 17.9/17.5% (39.2%). Acquisition is negative, and general-input drift reaches 32.8% (20.75%): format rows read by every example grow to 4--12 times their pretrained norm. Zeroing eight such rows removes over 98% of layer-2 drift on math inputs, together with their NLL gain.

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