How Structured Prompts Could Make AI Outputs More Predictable

In the paper's words

Large language models (LLMs) are increasingly used as interchangeable components in automated pipelines, yet the same natural-language instruction produces materially different outputs across models, sampling seeds, and runs. This variance blocks the use of LLMs where reproducible execution matters: batch document processing, schema-constrained data extraction, and multi-step agentic workflows. The specific gap is that prompt engineering is practiced as a literary craft with no predictive model of how prompt form controls output variance, and the largest existing variance decomposition of LLM creative output attributes 36.43% of originality variance to prompts but does not separate prompt form from prompt content.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Under explicitly labeled illustrative assumptions, pinning four of six interpretation dimensions removes 82% of the prompt-attributable interpretation variance, bounded by the empirical decomposition to at most 29.9 percentage points of total variance; a 20-field schema at an assumed per-field compliance of 0.986 yields 75.4% full-compliance probability against 12.2% for an assumed prose baseline of 0.90 per field, a 3.57-fold reduction in violation probability.

   from Abstract

2. Worked numerical predictions under explicitly labeled illustrative assumptions: an 82% reduction of the prompt-attributable interpretation variance when four of six interpretation dimensions are pinned, a bound of 29.9 percentage points on total-variance reduction, a schema-compliance calculation giving 75.4% versus 12.2% full-compliance probability at 20 fields, and a Bayes-factor amplification for cross-model verification protocols from 8 to 16 under a halved null-convergence probability; derived in Section 4 and reported in Section 5.

   from 1. Introduction

3. If instead the structured prompt pinned the four smallest contributors, the residual would be $(0.30 + 0.25)/1.00 = 0.55$, only a 45% reduction: the framework predicts that which degrees of freedom a structured form eliminates matters more than how many, a directly testable corollary.

   from 4.2 Variance-reduction factor under illustrative sensitivity weights

4. At the lower-bound decomposition of [8], the prompt component is 36.43% of the 87.93% total, so the maximum total-variance reduction achievable by perfect elimination of interpretation divergence is $$0.3643 \times 0.82 = 0.298726 \approx 0.299,$$ i.e., roughly 29.9 percentage points of total variance under the illustrative weights, with the remainder of total variance (model identity and sampling stochasticity) untouched by prompt form.

   from 4.3 Bound from the empirical decomposition

5. A configuration-style prompt plausibly constrains the majority of its tokens; even a conservative $c = 0.50$ predicts a 50% total-variance reduction.

   from 4.8 Incoherence of the token-density model

6. The reported component shares are not additive over their ranges (lower-bound sum 87.93%, upper-bound sum 121.38%; Section 4.1).

   from 5. Results

How it is done

1. The framework converts prompt engineering into a specification discipline with measurable design targets and a falsifiable pilot protocol of 53 paired tasks.

   from Abstract

2. The claim is testable, and this paper does two things about it: it builds the formal machinery needed to state the claim precisely and predict its magnitude, and it specifies the experiment that would confirm or refute it.

   from 1. Introduction

3. On the measurement side, [3] investigates the sequential sampling method for reducing the variance of a simulation output performance measure in crossdocking systems, targeting a desired 95% confidence interval half-width with a minimum number of replications [3].

   from 2. Background and Related Work

4. We model an LLM $m$ as a conditional distribution $p_{\theta_m}(y \mid x)$ over outputs $y$ given a prompt $x$, following the probabilistic framing of [8].

   from 3.1 The model

What would falsify it

1. The framework converts prompt engineering into a specification discipline with measurable design targets and a falsifiable pilot protocol of 53 paired tasks.

   from Abstract

2. The claim is testable, and this paper does two things about it: it builds the formal machinery needed to state the claim precisely and predict its magnitude, and it specifies the experiment that would confirm or refute it.

   from 1. Introduction

3. A falsifiable pilot protocol — paired prose/structured prompt corpora, fixed temperature, multiple models, structural and semantic agreement metrics, sized at 53 paired tasks — with the specific outcome that would refute the central claim; specified in Section 7.

   from 1. Introduction

Where the claim stops

1. Every numerical value in Section 4 is either (i) taken from a cited work and attributed to it, or (ii) computed here from explicitly labeled illustrative assumptions.

   from 3.6 Modeling convention and scope

2. The result rests on the following assumptions, each with its sensitivity: The result rests on the following assumptions, each with its sensitivity: The six-dimension sensitivity weight vector (Section 4.2).

   from 6. Discussion

3. The 82% reduction figure is sensitive to them: if the four pinned parameters carried only half the weight the assumption assigns them ($\sum_{i=1}^{4} S_{T_i} = 0.41$ instead of $0.82$), the reduction would fall to 41%; if the interpretation space had ten dimensions with the top four carrying 0.60, the reduction would be 60%.

   from 6. Discussion

Where to read

1. Abstract241 words · 1 min
2. 1. Introduction687 words · 3 min
3. 2. Background and Related Work841 words · 4 min
4. 3. Methods649 words · 3 min
5. 4. Analysis1,729 words · 8 min
6. 5. Results417 words · 2 min
7. 6. Discussion1,024 words · 4 min
8. 7. Practical Implications and Engineering Pathways861 words · 4 min
9. 8. Conclusion288 words · 1 min
10. Provenance and AI Involvement240 words · 1 min