AI BriefingHow to Find the Optimal Tokenizer
Key point
This proposes an algorithm that practically solves the theoretically intractable problem of finding the optimal Tokenizer via Integer Linear Programming (ILP).
Details
Finding the optimal Tokenization is theoretically a very hard (intractable) problem, but in practice it lies within a solvable range. This is similar to solving the Traveling Salesman Problem (TSP) using the Cutting-plane technique.
The existing BPE (Byte-Pair Encoding) is a decades-old greedy compression algorithm. However, recent research approaches Tokenization by connecting it to an Integer Linear Programming (ILP) problem.
The core structure of this model is as follows:
- Color variable: Assigned to every unique substring in the dataset, taking a value of 1 if that sequence is included in the Vocabulary, and 0 otherwise.
- Edge variable: Assigned to each token occurrence point in the dataset, taking a value of 1 if a specific token is used at that position.
- Constraints: Fixes the Vocabulary size and applies Flow constraints so that the dataset is tokenized in exactly one valid way.
However, there are also reasons why such optimization results may not necessarily be practically useful. This is because existing SOTA methods are already very close to the optimal value, and a Tokenizer optimized for training data may show reduced generalization performance on test data.
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