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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".