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[CS.AI] Distributed Utility and Fourier Recoding: Where Grokking Happens in Transformers

Published at: 2026-09-18 22:00 Last updated: 2026-09-20 12:54
#algorithm #AI #Machine Learning

We investigate where a Transformer shifts from memorization to generalization. To probe this, we introduce Transition Games, exact activation games aligned with model behavior and paired with non‑generalizing controls. Adding a prospective bias to block‑0 attention yields a distributed utility gain; degree‑two modes alone account for 67%–92% of the added contrast in replacement experiments. An exact path study shows that the block‑1 MLP mediates a larger share of this effect than any downstream path across all 12 tested pairs.

The conventional claim “MLP memorizes, attention generalizes” is reversed in our findings: information per example drops by $.331$ bits at the memory anchor, and all 12 pairs move opposite to the predicted direction. Hypotheses such as routing onset, global rank collapse, and a prime‑invariant architectural ridge also fail to explain the results. Together, the evidence points to grokking manifesting as a spectral (Fourier) recoding of an existing distributed circuit rather than a switch between modules.

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Original Source: https://arxiv.org/abs/2609.17571

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