String Seed of Thought: Prompting LLMs for Distribution-Faithful and Diverse Generation

2025-10-24

AI Summary

Large language models (LLMs) suffer from distribution miscalibration in probabilistic instruction following (PIF): their empirical output distributions deviate significantly from target probability distributions, leading to biased non-deterministic behavior modeling and insufficient response diversity. To address this, we propose String Seed of Thought (SSoT), the first method to explicitly inject entropy via random strings into the prompting process—preserving stochasticity through string operations and enabling probability-controlled diverse generation via constrained decoding. SSoT requires no model fine-tuning and relies solely on prompt engineering. It achieves near-ideal distribution fidelity—comparable to that of pseudorandom number generators—on PIF tasks. Moreover, it substantially improves response diversity on NoveltyBench for open-ended tasks. This work establishes a scalable, high-fidelity paradigm for applications demanding non-deterministic outputs, including human behavior simulation, generative content creation, and multi-agent interaction.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Prompt Engineering / Prompting
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

We introduce String Seed of Thought (SSoT), a novel prompting method for LLMs that improves Probabilistic Instruction Following (PIF). We define PIF as a task requiring an LLM to select its answer from a predefined set of options, each associated with a specific probability, such that the empirical distribution of the generated answers aligns with the target distribution when prompted multiple times. While LLMs excel at tasks with single, deterministic answers, they often fail at PIF, exhibiting biases problematic for applications requiring non-deterministic behaviors, such as human-behavior simulation, content diversification, and multiplayer games. It also harms the diversity of generated responses, a crucial factor in test-time scaling, by causing the outputs to collapse into a limited set of answers. To address this, we propose SSoT, a simple prompting method that instructs an LLM to first output a random string to generate sufficient entropy. SSoT also instructs the LLM to extract randomness by manipulating this string to derive a final answer, thereby preserving diversity while adhering to specific constraints. We demonstrate that SSoT significantly improves the PIF performance of LLMs, approaching the ideal performance of a pseudo-random number generator. Furthermore, our experiments on NoveltyBench show SSoT's benefits extend beyond closed-set tasks to open-ended tasks by enhancing response diversity.

Problem

• Improving probabilistic instruction following in LLMs
• Addressing output bias in non-deterministic generation tasks
• Enhancing response diversity while maintaining distribution constraints

Innovation

• SSoT method uses random string for entropy generation
• LLM manipulates string to extract randomness for answers
• Improves distribution alignment and diversity in generation