# Same Targets, Different Computation: How Post-Training Divides Work Across Model Layers

arXiv: https://arxiv.org/abs/2605.07284 · HTML: https://mlsanity.com/paper/2605.07284/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 22 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 20 of 20)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching](https://mlsanity.com/paper/2311.17030/) (2023)
- [Hermes 3 Technical Report](https://mlsanity.com/paper/2408.11857/) (2024)
- [Overcoming Sparsity Artifacts in Crosscoders to Interpret Chat-Tuning](https://mlsanity.com/paper/2504.02922/) (2025)
- [How Post-Training Reshapes LLMs: A Mechanistic View on Knowledge, Truthfulness, Refusal, and Confidence](https://mlsanity.com/paper/2504.02904/) (2025)
- [Patches of Nonlinearity: Instruction Vectors in Large Language Models](https://mlsanity.com/paper/2602.07930/) (2026)

## Abstract (arXiv)

A late-layer change learned during post-training may work on the base model's earlier state, or it may depend on earlier computation learned with it. We distinguish these cases with a four-cell diagnostic that crosses base or descendant upstream states with base or descendant late stacks. A large late-stack effect need not imply strong upstream dependence. On math prompts, OpenMath2's late stack changes the target margin by +3.43 logits after base upstream state and +3.28 after its own, giving a near-zero interaction. Several instruction-following descendants of the same Llama-3.1-8B base show greater dependence, while controlled code and biomedical continuation-training runs sit near zero on the common support; seven released descendants span -0.54 to +2.20 logits. Because those checkpoints differ in many ways, we then isolate one training property. Two LoRA fine-tunes learn identical target responses requested either by familiar natural-language instructions or by newly learned nonce codes. Changing only this cue-to-response relation increases upstream dependence by +5.56 logits on Qwen3-4B and +4.18 on Llama-3.1-8B, with a positive paired shift in all six model-by-seed runs. The interaction is also positive in all five released base/instruction pairs we test, and late-stack replacement changes the full-vocabulary argmax in about half of events. Post-training can therefore organize the same target behavior with different dependencies between earlier and later computation. The diagnostic measures local next-token compatibility, not free-running component transplantation.