What Constrains Adaptation After Pretraining? Representation Dynamics Under Inherited Data Manifolds

TMLR Paper7035 Authors

Abstract: Large language models are often adapted after pretraining under fixed objectives and training pipelines, yet their behavior across data settings can be difficult to anticipate. We study whether post pretraining adaptation is primarily constrained by optimization and supervision, or by geometric structure inherited from pretraining. Using controlled data selection, we treat training samples as structured populations in representation space and compare adaptation under matched architectures and training procedures while varying only geometric support. Across the controlled models and continued pretraining settings we study, adaptation mainly redistributes density within already occupied regions, with limited cross-region migration.

Submission Type: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

This revision addresses reviewer feedback as follows:

### 1. Core claim clarified
We sharpened the main takeaway: under controlled continued pretraining, adaptation mostly redistributes density inside already occupied regions, with limited cross region migration.

### 2. Scope and terminology tightened
We explicitly state that continued pretraining is used as a controlled probe of post pretraining adaptation, we do not model alignment, and “fine tuning” refers to continued pretraining rather than instruction SFT.

### 3. Experimental controls made explicit
We added a clean list of what is held fixed across comparisons, including architecture and initialization, training budget and preprocessing, update operator and hyperparameters, and the evaluation and representation extraction protocol.

### 4. Geometry metrics fully specified
We expanded the definitions and computation details for global distances, kNN neighborhood statistics, and the pairwise subsampling protocol, including the fixed pair sample size and seed reuse across checkpoints.

### 5. Geometry conditioned sampling clarified
We define dataset geometry and sampling rules in a frozen reference embedding space (BAAI bge m3) and evaluate all geometry only in the decoder model space, with tie handling documented for quantile partitions.

### 6. Reference versus model sanity check added
We report agreement between reference space and pretrained model space, including density ranking correlation and a separate pairwise proximity agreement test.

### 7. Broader coverage across scale and update operators
We include both 1B and 3B models and compare full parameter updates with LoRA under matched optimization settings to show the same qualitative behavior persists.

### 8. Dataset construction and evaluation protocol expanded
We provide concrete multilingual dataset budgets, sequence length constraints, packing length, and fixed random seeds, and we clarify evaluation set sizes used for geometry statistics.

Assigned Action Editor: ~Adin_Ramirez_Rivera1

Submission Number: 7035