Introducing Pivotal Token Search (PTS): Targeting Critical Decision Points in LLM Training

codelion Asankhaya Sharma

Overview

Today I'm excited to release Pivotal Token Search (PTS), a new technique for identifying and optimizing critical decision points in language model generations. Inspired by the recent Phi-4 paper from Microsoft, PTS helps identify specific "pivotal tokens" that dramatically shift the probability of a successful generation.

The Problem

Traditional Direct Preference Optimization (DPO) treats all tokens equally when learning from preferences. However, in many complex reasoning tasks, the success of a generation often hinges on just a handful of critical decisions. For example, when solving a math problem, choosing "cross-multiplying" versus "multiplying both sides" can dramatically affect whether the model reaches the correct solution, even though both approaches are mathematically valid.

How PTS Works

PTS uses a binary search algorithm to identify tokens that cause significant shifts in the probability of generation success:

1. For a given prompt and completion, we estimate P(success|prefix) at various points in the generation
2. We recursively subdivide the sequence to find points where adding a single token causes a large change in this probability
3. We then create preference pairs focused specifically on these pivotal tokens

This targeted approach offers several advantages over standard DPO:

• More efficient learning signal by focusing on critical decisions
• Better handling of cases where both preferred/rejected responses contain valid reasoning
• Enhanced ability to improve reasoning without additional data

Released Resources

Implementation

Our GitHub repository contains:

• Full implementation of the PTS algorithm
• Data generation pipelines
• Evaluation tools and metrics
• Usage examples

Datasets

We're releasing several PTS-generated datasets for different domains:

• pts: The pivotal tokens discovered using PTS
• pts-dpo-pairs: The exported preference pairs using pivotal tokens that can be used for DPO
• pts-steering-vectors: Activation vectors exported from pivotal tokens that can be used for steering during inference

Models

Try our fine-tuned models that have been optimized using PTS:

• Base models fine-tuned with PTS preference pairs
• Specialized models for DeepSeek-R1 and Qwen3

Example Use Case

When fine-tuning a model to solve math problems, traditional approaches might provide an entire correct solution as a preference example. With PTS, we can identify that the critical decision was choosing to factor a quadratic rather than complete the square. By creating a preference pair focused on just that pivotal token, we provide a cleaner learning signal.

Future Directions

We're actively exploring:

• Multi-token pivotal sequences
• Applications to agent trajectory optimization
• Using PTS for model interpretability
• Combining PTS with other alignment techniques

Get Involved

We welcome community contributions! Try out PTS on your own tasks, experiment with our datasets, or contribute to the codebase.

• 📦 GitHub: https://github.com/codelion/pts
• 📊 Datasets: https://huggingface.co/datasets?other=pts
• 🤖 Models: https://huggingface.co/models?other=pts

Let me know if you have questions or feedback in the comments!