Max P consists of a dynamic token filter which applies Winsorization to cap the probabilties of top tokens. Specifically, a base probability in the range of [0,1] is used to cap individual token probability; the sampler then redistributes excess proportionally. This proof of concept is implemented in PyTorch and transformers.

• Prevent overconfident predictions without breaking coherence
• Indirectly reduce long-range literal repetition by creating small variations that compound
• Nudge toward creativity without resorting to token bans or repetition penalties
• Complement min-p sampling in conjunction with temperature
• Be simple, principled mathematically, stateless, and composable
• Easy to implement and control (only one hyperparameter)

This proof of concept is implemented in PyTorch and designed to interact with the Hugging Face transformers pipeline.

pip install torch transformers

The core Max P logic is located in the repository's single executable Python file, which incorporates a working demonstration:

python maxp_sampler.py

Max P operates on the probability distribution $P$ of the next token, using a single hyperparameter, $\mathbf{p_{max}} \in [0, 1]$, as an absolute probability ceiling. The process is simple, principled, and executed in three steps:

• Capping: For every token $i$, if its probability $p_i > \mathbf{p_{max}}$, its new probability is set to $p'{i} = \mathbf{p{max}}$.
• Excess Collection: The total probability mass $E$ that was clipped is calculated from all capped tokens: $$E = \sum_{i | p_i > p_{max}} (p_i - p_{max})$$
• Proportional Redistribution: The excess mass $E$ is then proportionally distributed across all tokens whose probabilities were not capped.

This ensures the resulting distribution remains normalized ($\sum p'_i = 1$) while dynamically suppressing overconfident predictions.