2️⃣We also use ALM to directly transfer knowledge from a large teacher (with one tokenizer) to a smaller student (with another tokenizer).

We test this by distilling a large maths-specialized Llama into a small Gemma model.🔢

1️⃣continued: we can also transfer different base models to the same tokenizer, then ensemble them by combining their logits.

This would not be possible if they had different tokenizers.

We try ensembling Gemma, Llama and Qwen. They perform better together than separately!🤝

We investigate two use cases of ALM in detail (but there's definitely more!)

1️⃣Tokenizer transfer: the teacher is the model with its original tokenizer; the student is the same model with a new tokenizer.

Here, ALM even lets us distill subword models to a byte-level tokenizer😮

Chunks of tokens with different tokenization biases are not fairly comparable!⚠️⚠️

We thus develop a method to find chunks with low tokenization bias differences (making them *approximately comparable*), then learn to match the likelihoods of those✅

Our greatest adversary in this endeavour is *tokenization bias*.

Due to tokenization bias, a sequence of subword tokens can leak information about the future contents of the text they encode.

Most distillation methods so far needed the teacher and the student to have the same tokenizer.

We lift this restriction by first identifying comparable chunks of tokens in a sequence (surprisingly, this is not so easy!), then minimizing the difference between their likelihoods.

We created Approximate Likelihood Matching, a principled (and very effective) method for *cross-tokenizer distillation*!

With ALM, you can create ensembles of models from different families, convert existing subword-level models to byte-level and a bunch more🧵