Revisiting the Equivalence of In-Context Learning and Gradient Descent: The Impact of Data Distribution
Bibliographic record
Abstract
Transformers exhibit in-context learning (ICL), enabling adaptation to various tasks via prompts without the need for computationally intensive fine-tuning. Recent research investigates ICL’s mechanisms under analytically tractable models, with some conjecturing that ICL with linear attention implements one step of gradient descent for simple linear regression tasks. This paper reevaluates this claim, revealing it relies on strong assumptions like feature independence. Relaxing these assumptions, we prove that ICL with linear attention resembles preconditioned gradient descent, with a pre-conditioner that depends on the data covariance. Our experiments support this finding. We also empirically explore softmax-attention and find that increasing the number of attention heads better approximates gradient descent. Our work offers a nuanced perspective on the connection between ICL and gradient descent, emphasizing data assumptions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".