{"ID":2889733,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.00901","arxiv_id":"2508.00901","title":"Provable Knowledge Acquisition and Extraction in One-Layer Transformers","abstract":"Large language models may encounter factual knowledge during pre-training yet fail to reliably use that knowledge after fine-tuning. Despite growing empirical evidence that MLP layers store factual associations and fine-tuning affects factual recall, the training-dynamics mechanisms linking next-token pre-training, knowledge storage, and post-fine-tuning extraction remain poorly understood. We study this problem in a stylized one-layer transformer with self-attention and MLP modules, trained by next-token prediction and subsequently fine-tuned on question-answering data. Under suitable regularity conditions, we first prove that the model reaches near-optimal pre-training loss while learning structured attention patterns and relation-specific feature directions, giving a mechanism for factual knowledge acquisition. We then show that fine-tuning can turn the Q\u0026A prompt format into a trigger for pre-trained relation features, enabling the model to extract facts that are not revisited during fine-tuning. Our analysis yields a relation-covering characterization of knowledge extraction: fine-tuning need not revisit every stored subject-answer pair, but it must cover enough latent relation-template directions through which facts were encoded during pre-training. Consequently, extraction improves with pre-training multiplicity and fine-tuning coverage, but becomes harder as the relation-template universe grows. Conversely, insufficient coverage leads to a failure regime in which facts may be stored but remain inaccessible, providing a stylized mechanism for hallucination. The theory applies to both full and low-rank fine-tuning, offering insight into why low-rank adaptation can recover pre-trained factual knowledge when relation coverage is sufficient. Experiments on synthetic data and PopQA-based GPT-2/Llama models support the predicted trends.","short_abstract":"Large language models may encounter factual knowledge during pre-training yet fail to reliably use that knowledge after fine-tuning. Despite growing empirical evidence that MLP layers store factual associations and fine-tuning affects factual recall, the training-dynamics mechanisms linking next-token pre-training, kno...","url_abs":"https://arxiv.org/abs/2508.00901","url_pdf":"https://arxiv.org/pdf/2508.00901v4","authors":"[\"Ruichen Xu\",\"Kexin Chen\"]","published":"2025-07-28T17:24:57Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CL\"]","methods":"[\"Transformer\",\"Language Model\"]","has_code":false}