Distribution Prompting: Understanding the Expressivity of Language Models Through the Next-Token Distributions They Can Produce
Bibliographic record
Abstract
Autoregressive neural language models (LMs) generate a probability distribution over tokens at each time step given a prompt.In this work, we attempt to systematically understand the probability distributions that LMs can produce, showing that some distributions are significantly harder to elicit than others.Specifically, for any target next-token distribution over the vocabulary, we attempt to find a prompt that induces the LM to output a distribution as close as possible to the target, using either soft (Li and Liang, 2021) or hard (Wallace et al., 2019) gradient-based prompt tuning.We find that (1) in general, distributions with very low or very high entropy are easier to approximate than those with moderate entropy; (2) among distributions with the same entropy, those containing "outlier tokens" are easier to approximate; (3) target distributions generated by LMs-even LMs with different tokenizers-are easier to approximate than randomly chosen targets.These results offer insights into the expressiveness of LMs and the challenges of using them as probability distribution proposers.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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".