PROMPT2BOX:Improving LLM Weakness Discovery and Specificity Estimation by Uncovering Entailment Structure among Prompts
Neeladri Bhuiya, Shib Sankar Dasgupta, Andrew McCallum, Haw-Shiuan Chang
EMNLP 2026 Main
cs.CL
2026-03-23
Prompt2Box maps prompts to boxes: volume estimates specificity (45% lower error vs length) and clustering finds 13.5% more LLM weaknesses than vectors on UltraFeedback.
The usual way to find LLM weak spots is to embed prompts as vectors, cluster them, and look for clusters with low scores. Clio, EvalTree, and SkillVerse all do a version of this. Vectors collapse topical similarity: "write a romantic story" and "write a romantic adventure about a robot" land near each other. The second prompt is harder. Its low score poisons the cluster average, and the cluster gets tagged as a weakness even when the model is fine at generic romance.
Specificity, meaning how many constraints a prompt carries, has no standard meter. Length is the cheap proxy. It correlates with difficulty, but token count is not the same as constraint count.
Prompt2Box represents each prompt as a high-dimensional box: a center for topic, a width for semantic scope. General prompts get large boxes, specific ones get small boxes. Containment is treated as entailment, so the specific prompt entails the general one. Similarity is intersection volume. The entailment score is intersection divided by own volume, and equals 1 under full containment.
The encoder starts from MPNet-base with two MLP heads, about 2% more parameters than the vector baseline. Hard min/max operators are replaced with the Gumbel Box relaxation so intersection and containment stay differentiable.
Training uses 203,138 examples from five sources: 50k English prompt-response pairs from Infinity Instruct, which push related boxes to overlap; 50k MultiNLI triplets for sentence-level entailment; 50k synthetic hierarchies, built by asking GPT-4.1 to rewrite WildChat instructions into 20k groups of 4 to 10 generality levels; 50k SURI trees that treat sibling constraint subsets as hard negatives; and 3,138 linkage pairs that stitch Infinity Instruct into the WildChat hierarchy so the two objectives do not split the space.
Two geometric tools sit on top. Box-SNE compresses boxes to 2D while keeping both intersection and entailment. Hierarchical clustering merges the pair whose union box is smallest, so contained boxes join first. That is the opposite of Ward linkage on vectors, which only sees symmetric distance.
On FollowBench (688 queries), the task is to retrieve a more specific instruction from the same semantic group. Full Box hits 0.738 accuracy against 0.640 for vectors, 0.687 without entailment data, and 0.659 for hyperbolic embeddings. Dropping the linkage set peaks at 0.775, but STS-B Spearman falls from 0.760 to 0.661. The full model is the compromise between entailment and topical similarity.
On UltraFeedback, a top-5 kNN that predicts response scores for 17 LLMs gets RMSE 1.5280 with boxes, 16.47% better than random at 1.8293. Vectors land at 1.6059, a 12.21% gain.
Hierarchical trees are built on 500 UltraFeedback prompts per model:
| Metric | Random | Vector | Prompt2Box |
| Neighbor score-consistency gain | 0% | 9.32% | 12.88% |
| Depth vs specificity agreement | 50.00% | 52.71% | 68.34% |
| Weakness-cluster AUC gain | - | 0% | 13.47% |
Box volume was never a training target. Used as a specificity proxy, it cuts RMSE of a sigmoid fit by 45.3% versus prompt length on UltraFeedback and 18.3% on LMSYS-Chat-1M. For Llama-2-13b-Chat the drop is about 58%.
In 2D, WildBench prompts draw smaller boxes than WildChat, matching the claim that WildBench is a harder slice. Scaling LLaMA-2 from 7B to 70B turns large weak regions strong; multilingual prompts stay weak, and tiny failed boxes remain inside otherwise strong regions.
Eval and data-collection teams get a second axis: did the model fail the topic, or did the prompt pile on constraints. Vector clusters mix those two failure modes. Volume tracks difficulty better than token count, and the encoder was never asked to regress length.
This is a representation, not a new benchmark or trainer. It can plug into existing weakness-discovery pipelines. Parameter cost is tiny. The real cost is synthesizing entailment data and swapping the clusterer and the 2D projector.
The paper tests three applications. Downstream numbers lean on UltraFeedback, which is unusually wide in specificity and has multi-model scores. Synthesis quality is tied to GPT-4.1; low-resource domains and languages may not hold. Box-SNE overcrowds. Weakness clusters are scored with a 25th-percentile proxy, not expert review.
Specificity is defined as constraint count; underspecified prompts are excluded. On held-out SURI, hyperbolic embeddings and CSDelta beat Box on entailment accuracy (0.978 and 0.950 versus 0.868) while losing badly on FollowBench retrieval. Box wins on global structure, not on every entailment number. Four annotators on 50 pairs agree only 45.3% of the time, so the label is noisy; against aggregated human labels, box trees hit 66.2% and vector trees 37.2%.