The Convergence Gap: Instruction-Tuned Language Models Stabilize Later in the Forward Pass

• URL: http://arxiv.org/abs/2605.07282v1
• Date: Fri, 08 May 2026 05:45:52 GMT
• Title: The Convergence Gap: Instruction-Tuned Language Models Stabilize Later in the Forward Pass
• Abstract summary: Final outputs hide when a checkpoint commits to its next-token prediction.<n>We introduce the convergence gap, a model-diffing diagnostic that decodes each layer's next-token distribution and measures its distance to the model's own final distribution.
• Score: 9.8812664524155
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Final outputs hide when a checkpoint commits to its next-token prediction. We introduce the convergence gap, a model-diffing diagnostic that decodes each layer's next-token distribution and measures its distance to the model's own final distribution. Across six paired pretrained and instruction-tuned checkpoints in native prompting regimes, instruction-tuned checkpoints remain farther from their final predictions later into the stack. The effect persists under endpoint-matched raw and tuned readouts, endpoint-free same-history checks, and fixed-history template replay. Matched-prefix interventions identify late MLP windows as the largest tested leverage point: late IT grafts into PT hosts increase late KL by +0.34 nats, while PT-late swaps into IT hosts reduce it by -0.51 nats; matched random late perturbations give only +0.003 versus +0.327 for the true late graft. A preselected Gemma case study provides behavior-facing plausibility for the same late swap, without serving as a benchmark claim. These results identify a robust predictiondynamics signature of post-training: released instruction-following checkpoints tend to settle later, and late MLP computation is the strongest tested bidirectional handle on that delay under matched histories.

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