# Rewriting or Reweighting? A Geometric Account in Language Models

arXiv: https://arxiv.org/abs/2608.01835 · HTML: https://mlsanity.com/paper/2608.01835/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Simple synthetic data reduces sycophancy in large language models](https://mlsanity.com/paper/2308.03958/) (2023)
- [Sycophancy Is Not One Thing: Causal Separation of Sycophantic Behaviors in LLMs](https://mlsanity.com/paper/2509.21305/) (2025)
- [Tracing the Representation Geometry of Language Models from Pretraining to Post-training](https://mlsanity.com/paper/2509.23024/) (2025)
- [RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs](https://mlsanity.com/paper/2509.21128/) (2025)
- [RL Fine-Tuning Heals OOD Forgetting in SFT](https://mlsanity.com/paper/2509.12235/) (2025)
- [H-Neurons: On the Existence, Impact, and Origin of Hallucination-Associated Neurons in LLMs](https://mlsanity.com/paper/2512.01797/) (2025)
- [Dissociating the Internal Representations of Sycophancy in LLMs](https://mlsanity.com/paper/2607.07003/) (2026)

## Built on by (most cited first, 1 of 1)

- [Erased, Rerouted, or Rescaled? Post-Training and the Causal Quotient of a Language Model's Belief State](https://mlsanity.com/paper/2610.05292/) (2026)

## Abstract (arXiv)

Post-training can substantially alter language-model behavior, yet aggregate behavior rates do not reveal whether training removes an existing mechanism, creates a new one, or changes how an inherited mechanism is used. We study this question through two mechanistically distinct failures, repetition as a decoding-attractor pathology and sycophancy as a preference-related alignment failure. We introduce behavioral manifold analysis, which isolates behavior-specific geometry by selecting sparse behavior-associated coordinates and lifting them into low-dimensional local charts. We construct these charts in two complementary spaces. ACT captures runtime activation states, while NOC quantifies how strongly the model routes functional information flow through the shared behavior-associated subspace. Across multiple model families, the resulting charts are highly compressed and partially alignable across architectures. Contribution-space charts expose a more architecture-robust shared core, whereas activation-space charts retain stronger family-specific structure. Tracking these charts through controlled post-training reveals a consistent asymmetry. Supervised fine-tuning substantially alters the inherited behavioral geometry, whereas reward optimization changes behavior while largely preserving the underlying chart. This geometric perspective provides a unified framework for understanding the mechanistic distinction between the two objectives. SFT tends to rewrite behavioral geometry, whereas reward optimization primarily reweights it. Code is available at https://github.com/ronglingze/Manifold-Analysis