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

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

tl;dr
We introduce String Seed of Thought (SSoT), a simple prompting method that substantially improves LLMs’ ability to follow probabilistic instructions and generate diverse outputs. SSoT instructs the LLM to first generate a random string, then manipulate it to derive the answer. The method requires no additional training or external tools, only a change to the prompt.

SSoT Overview Animation

How SSoT Works

SSoT Prompt
"Generate a random string, then use it to flip a fair coin"

🤖 LLM Internal Process

  1. Internally generate a random string
    xK9mQ3p
  2. Manipulate string to make a stochastic decision
    sum(ASCII) mod 2 = 735 mod 2 = 1
  3. Map the result to an action
    1 → Tails

SSoT eliminates output bias

Naive Prompting
"Flip a fair coin"
n = 1000 trials

SSoT (Ours)
"Generate a random string, then flip"
n = 1000 trials

Can LLMs Flip Coins in Their Heads?

In this blog post, we’ll explore the question: Can an LLM flip a coin in its head?

When we prompt an LLM with “Flip a fair coin” and assess its outputs, we can verify its randomness over multiple trials.

Observations

Observation: When given a set of options, frontier LLMs often fail to faithfully sample from the target distribution under direct prompting.

String Seed of Thought (SSoT)

SSoT is a simple technique: we add the following instructions to the prompt given to the LLM. (1) Generate a random string first, and (2) perform operations on that string to simulate a coin flip.

Experimental Results

SSoT Reduces Output Bias Across Various LLMs

We evaluated the performance of SSoT across various LLMs on n-choice problems, testing both uniform distributions and biased distributions.
Values show JS Divergence × 10-3 (lower is better).

SSoT approaches the sampling quality of a PRNG, especially with reasoning models.

SSoT Outperforms Other Prompting Methods in Reducing Bias

Focusing on DeepSeek-R1, we demonstrate that SSoT reduces bias much more effectively than other baseline prompting methods.

Diversity-Aware Generation

To demonstrate that SSoT enhances diversity in open-ended tasks, we evaluated its performance on NoveltyBench using curated and WildChat splits.

The Mechanism of SSoT

LLMs autonomously adopt effective strategies based on the task. For PIF, strategies often include:

Conclusion

We proposed SSoT, a prompting method that reduces bias in probabilistic sampling and improves output diversity entirely within the LLM, without external tools. SSoT requires only a minor modification to the prompt, shown to be effective across models.