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

Recent interpretability work has identified model-internal handles on post-trained behavior, including refusal directions, assistant/persona axes, and sparse chat-tuning features. These results localize where behaviors can be read out or controlled, often in middle-to-late layers. We ask how earlier computation and the late stack cooperate to turn those differences into next-token margins. To test this, we introduce first-divergence cross-patching: at the first token where pretrained base (PT) and instruction-tuned (IT) checkpoints disagree, we cross each model's earlier-layer state with each model's late stack. The diagnostic separates training recipes: same-base instruction-following descendants show late effects that depend on their own earlier-layer state, while OpenMath2 math-domain SFT and controlled code/biomed CPT controls with verified domain learning do not; for OpenMath2, the late effect is already largely portable from base earlier-layer state. Across five dense families (4B-32B), the IT late stack adds +0.76 logits from PT upstream and +2.44 from IT upstream, giving a +1.68 interaction that is positive in every family. Thus the late stack has a real PT-upstream effect, but its larger effect in the IT checkpoint appears only when it reads its own post-trained upstream state. Sparse features in final MLP layers partially mediate the effect and are driven by upstream patches, supporting a handoff from earlier state to final-layer feature activation to IT-token margin. Forced-token scoring shows that the local token choice can change later exact-answer success. Operationally, paired-checkpoint studies that localize a difference to late layers should test whether it survives under the other checkpoint's upstream state before treating the late stack as self-contained.

Syntactic convergence (the tendency of speakers to adapt in language towards the grammatical profiles of their interlocutors) is a well-documented feature of human dialogue widely considered to operate below conscious awareness. Whether large language models exhibit analogous syntactic convergence toward human users relative to human baselines and across a broad range of syntactic constructions remains an open question. Using substitution-paradigm data in which model generations replace one speaker's turns in pre-existing human dialogues, this study measures turn-adjacent reuse of context-free grammar (CFG) rules across sixteen open-weight Llama and Gemma models (1B-70B, pretrained and instruction-tuned) at 1,901 matched positions per model. Every model showed greater CFG-rule overlap with the preceding human turn than with a sampled unrelated human prime, and in every model this actual-versus-random difference was larger for lower-frequency rules. Each instruction-tuned model also showed greater natural-output overlap with the actual prime than the human response it replaced, and all eight matched architecture pairs exhibited greater actual-prime overlap after instruction tuning. However, relative to pretrained variants, instruction-tuned outputs overlapped more with unrelated primes, showed a smaller actual-versus-random increment, and had lower conditional rule-reuse odds once target rule-set size was held constant. In exploratory analyses, each model exhibited greater mean lexical and semantic similarity to the preceding turn than the matched human responses did. Instruction-tuned models additionally produced responses with greater mean semantic similarity than their pretrained counterparts in all eight architecture pairs, whereas the lexical similarity results were more heterogeneous.

Developers judge a model checkpoint by how it behaves. After supervised fine-tuning (SFT), two checkpoints that perform about the same across relevant benchmarks are treated as interchangeable, equally ready for the next alignment stage, typically preference optimization. We ask whether this judgment misses a pretraining imprint: a difference that no post-SFT benchmark reveals, yet that decides how each checkpoint responds to further training. To find out, we run a controlled experiment on the final window of pretraining, the last data trained on before instruction tuning. Six branches fork from one partially pretrained checkpoint and differ only in this window: 500 million tokens, 0.1% to 1% of the tokens that precede it. Each branch trains its window on a single data source: generic web text, filtered web text, normative discourse, safety text, mathematical text, or synthetic educational text. SFT and post-training are then identical. After SFT the branches behave near-identically, within about one point on instruction following, refusal, and capability, yet the same post-training carries them to very different endpoints, under both a direct preference optimization update and a reinforcement learning update with a verifiable reward. We measure this deviation through refusal of harmful requests: when post-training begins the safety text branch refuses no more than the web text branch, yet by the end it has lost far less of its refusal. The other four branches gain little or no protection, so the effect is selective to what the window contained. The protection requires the safety text to arrive last rather than earlier in pretraining, and it reproduces on a second model family. What a model is pretrained on last shapes how it reacts to alignment. Therefore, a checkpoint should not be evaluated by its post-SFT behavior alone, and what it was trained on last should be reported with it.