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

arXiv: https://arxiv.org/abs/2510.21150 · HTML: https://mlsanity.com/paper/2510.21150/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 12 of 12)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)
- [NoveltyBench: Evaluating Language Models for Humanlike Diversity](https://mlsanity.com/paper/2504.05228/) (2025)
- [Diverse Preference Optimization](https://mlsanity.com/paper/2501.18101/) (2025)
- [Heads, Tails, and AI Fails: LLMs, Randomness, and Human Judgments](https://mlsanity.com/paper/2406.00092/) (2024)
- [Enough Coin Flips Can Make LLMs Act Bayesian](https://mlsanity.com/paper/2503.04722/) (2025)

## Built on by (most cited first, 11 of 11)

- [Frontier Models Can Take Actions at Low Probabilities](https://mlsanity.com/paper/2603.02202/) (2026)
- [Sampling More, Getting Less: Calibration is the Diversity Bottleneck in LLMs](https://mlsanity.com/paper/2605.11128/) (2026)
- [Probabilistic Calibration Is a Trainable Capability in Language Models](https://mlsanity.com/paper/2605.11845/) (2026)
- [Where You Inject Diversity Matters: A Unified Framework for Diverse Generation](https://mlsanity.com/paper/2606.10302/) (2026)
- [Forty Shades of Blue: Quality-Diversity Alignment via Mode-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2609.14896/) (2026)
- [PAWBench: How Far Are We from Probabilistically Aligned World Modeling?](https://mlsanity.com/paper/2608.27345/) (2026)
- [Deep and shallow biases in language models](https://mlsanity.com/paper/2609.09901/) (2026)
- [RoboTalk: Learning Multi-Robot Communication and Coordination from Multimodal Demonstrations](https://mlsanity.com/paper/2609.23997/) (2026)
- [Sample What You Say: Aligning Language Models to Sample the Distributions They State](https://mlsanity.com/paper/2609.34929/) (2026)
- [Synthetic Data Characterization via Training Dynamics](https://mlsanity.com/paper/2609.39447/) (2026)
- [Gacha Decoding: Eliciting Diverse Generations Through Instruction Following](https://mlsanity.com/paper/2610.01382/) (2026)

## Abstract (arXiv)

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.