Tokenisation fixes what a model can never afterwards distinguish.

Demonstration

A transformer never sees text. It sees a sequence of integers produced by a tokeniser, and every downstream layer operates on embeddings indexed by those integers. Whatever the tokeniser merges, the model receives already merged.

Take unhappiness. Under a word-level vocabulary it is one symbol, and the model has no route from it to unhappy or to happiness other than whatever the embedding space happens to learn from co-occurrence. Under a subword vocabulary it arrives as un + happi + ness, and the negation is a token the model has seen thousands of times elsewhere. Under character-level segmentation the morphology is fully exposed and the sequence is ten times longer, which costs quadratic attention.

The consequence is that certain failures are not modelling failures at all. A model that cannot do arithmetic on long numbers may be suffering from a tokeniser that splits 1234 into 12 and 34 in one context and 1, 234 in another. No amount of training fixes a distinction that was destroyed before layer one.

# Two strings that differ, and a segmentation that hides the difference.
tok.encode("1234")   # -> [16, 2019]
tok.encode(" 1234")  # -> [220, 4513]   different pieces entirely

Corollary

Before blaming the architecture, read the token ids. The input representation is the first place a capability can be lost, and the only place where the loss is silent.