I didn't use a Trie. The main data structures used are Linked List and Priority Queue.

The tokenization begins by transforming each character to a token. After that merges are applied in priority order as long as merges are possible.

The current state of tokenization is represented as a linked list where each node (token) points to the previous node and next node.

Nodes of the Linked List are added to a Priority Queue _if_ a merge to their corresponding "next node" is possible according to vocabulary (we use a Hash Map to perform these checks fast). Even though we are technically adding nodes of a linked list into the Priority Queue, you can think of the Priority Queue as holding "potential merges" in the order of their priority (priority according to the trained tokenizer merge data).

When we poll a node from the priority queue, we first check that the merge is still possible (because the situation may have changed between the time the node was added to the priority queue, and the time when it was polled from the queue). If the merge is possible, then this is guaranteed to be the most highest-priority merge, so we apply the merge. At this point we need to do several things: we need to mark the previous nodes of the merge as "deleted", we need to create a new node representing the merged token, we need to update the pointers of the adjacent nodes in the linked list, and we need to check if new merges have become possible, and if they have, we need to add the corresponding nodes to the priority queue.

> I take it if you do greedily go from left to right, you end up with different tokenization and the model doesn't work properly because that isn't what it was trained with?

The way that the LLaMA tokenizer works is, a word is tokenized one way within a certain context, and a different way within a different context. If you go greedily from left to right, you will find mostly the same tokenizations for words, but occasionally the tokenization will be different. It will still be a legitimate tokenization for the word, though, so the model will not spew nonsense if you feed these tokens into it. I assume the outputs of the model would be slightly suboptimal, but the difference might be so small that nobody notices anything.

Anyway, I don't expect anyone to use this library in a manner where they will turn text to tokens with this library, and then feed the tokens to the model. I expect people to use this library to count tokens, dynamically iterate on the prompt to fit within the token limit, and then eventually send raw text to the model, which performs the tokenization by itself. If we think about this use case, and we consider what would happen if we just greedily tokenized from left to right, it would be mostly fine, because our token counts would be pretty close to the real token count. But occasionally it wouldn't be fine: occasionally our greedy tokenizer would say that we are below the token limit, when actually we're beyond the token limit. In this case the model would either return an error, or it would automatically trim some part of the prompt. If the prompt is automatically trimmed, it might be trimmed from the wrong place. For example, oobabooga trims the prompt from the beginning, when you typically would want to trim the prompt from the middle.

> Did the model designers choose this 'difficult' tokenization because it performs better?

I'm not sure. LLaMA is using a SentencePiece BPE tokenizer, and the most-often touted benefit of this tokenizer is that it can fluently deal with multiple different languages. So it's possible that they chose this to support multiple different languages, not to maximize the quality of output in the English language.