Arithmetic, counting and letters

The familiar explanation for why a chatbot miscounts letters is that it never sees letters, only chunks. That is true about the input, but it weakly explains the counting failures: the one benchmark built to test it found tokenization properties only weakly predicted counting correctness, while word length and true character count predicted it more strongly.

A tokenizer breaks text into subword chunks: the word annoyingly might split into annoying and ly, or into other chunks depending on the vocabulary,¹ and the GPT-2 tokenizer splits the word numbers into n and umbers, a break that says nothing about spelling.⁹ Character-level splitting would avoid this, but sequences get much longer and performance suffers, so chunks are the deliberate trade.¹ A 2025 paper adds a second reason: written text almost never spells words out, since spelling is self-evident to a reader, so the training signal for a word's letters is nearly absent.²

CharBench's 2026 measurements evaluated character tasks over 175,000 strings sampled from MiniPile across the seven models it tested, GPT-4o among them.³ Average accuracy was 77.34 percent on counting how often a letter occurs and 47.96 percent on counting distinct characters. Its finding about causes matters more: tokenization correlated only weakly with counting correctness, while word length and true count mattered more. For positional questions the story flips: longer tokens do obscure where a character sits.³ A 2026 study of three open model families agrees: character counts were recoverable from internal layers at above 80 percent probe accuracy in most layers, while stated answers sat near a 33 percent random baseline, attenuated by later-layer components.⁴

Arithmetic has its own version: the RoBERTa tokenizer encodes 520 as one chunk while 521 splits into two, and that inconsistency can undermine reliable alignment of digits by place value.⁵ A 2023 study reports GPT-4 at 4.3 percent on multi-digit multiplication.⁶ Separately, a 2026 study defines an arithmetic load and places the point where predicted multiplication accuracy falls to half at about 68.6 for GPT-5.4 and about 52.9 for GPT-4o.⁷ Earlier work concludes that these tasks are handled by linearised subgraph matching rather than systematic reasoning, with performance declining rapidly as task complexity increases.⁸

None of this is one story. Chunking explains position errors and barely explains counting errors, the figures belong to the named models on their stated dates, and nothing here says the ceiling is fixed.