Generative AI is probability-based technology. It’s based on transformers, and transformer architecture has not changed. So how is an evolution from next token prediction to reasoning to solving highly complex mathematical problems possible? It’s happened partly by design, partly by accident, and partly through improvements and compute capacity.

From stochastic parrots to homing pigeons

When we talk about reasoning, we have to shift the mental image of what an LLM does from next token prediction and “stochastic parrots” to a different kind of bird, the homing pigeon.

Chain-of-thought reasoning is a language model writing out its working before it answers, so that each line it writes becomes material for the next line. The model underneath still does what it always did: predict the next piece of text. The leap from predicting text to working through a problem came from giving that prediction something to carry.

One bird, one trip

A homing pigeon does one thing. Take it anywhere, let it go, and it flies home. It knows one trip. For centuries people used that by tying a message to the bird’s leg. The bird stayed the same. It picked up a job.

A language model also does one thing. Given the text so far, it produces the next piece of text. That is the “stochastic parrot” of the famous critique: fluent speech from learned patterns, headed nowhere in particular. Ask it a hard question and demand the answer straight away, and it gets one flight to cover the whole distance.

A line of lofts

Picture a line of pigeon lofts stretching across a country. A message leaves the first loft on a bird that lives at the second. The keeper there reads it, writes what comes next underneath, and ties the longer note to a bird that lives at the third. Every bird knows only its own hop. The note that reaches the far end contains work no single flight could have carried.

Now the model. Ask it why customers are dropping out of a sign-up process. With one hop, it offers a familiar guess. With a relay, the first line works out where customers drop. The second line, starting from that finding, looks at the rule controlling that step. The third compares the rule with the affected customer records and finds a required field missing. The fourth names the cause. Each line was an ordinary next-word prediction, and each one started from a fuller note than the one before.

The note is the model’s only memory of the job. Its trained knowledge stays fixed while it works, so anything it needs three steps later has to be written down where later steps can read it. Writing more also means computing more. The model does a fixed amount of work for every word it produces, so a long worked answer gets hundreds of passes where a short one gets a handful.

But a reminder: probability and patterns are still at play. If loft two writes “the drop-off is a UX issue” and that’s wrong, every later loft treats it as fact and builds a fix for the wrong problem. Errors, if not checked, still cascade

First a hack, then training

In 2022, researchers at Google showed that putting a few examples of worked reasoning into a prompt made models better at arithmetic and logic problems. Months later another team got a similar effect with one added phrase: “Let’s think step by step.” The models were the same ones as before. Only the instructions had changed. That was the hack.

The labs then trained for it. Models attempt problems with checkable answers, mostly maths and code, and get rewarded when the final answer is right. Over many rounds they get better at what to write at each loft: how to split a problem, when to double-check, how to back out of a dead end. OpenAI’s o1, previewed in September 2024, was the first widely known result. What the industry now sells as “reasoning” is this: chain of thought, trained in and given more room to run.

Several relays, and someone to check the note

One relay can fail, so run several and compare the notes that arrive. If most of them agree, go with that answer. This is the brute-force part of reasoning, which can involve hundreds, thousands, even millions of different paths, depending on the complexity of the problem.

It works best when someone at the last “loft” can check the note. Code runs or it fails. A sum is right or wrong. This is one reason why models are so good at code and math and less proficient with other kinds of problems: where the answer can’t be verified or has variations, a confident note and a correct note look alike.

What the relay carries, it carries all the way

A keeper who miscopies a line sends the error down every loft after it, and later keepers build on it. A guess written down at loft two reads as a fact by loft six. The note also keeps getting longer, so the original question becomes a smaller and smaller share of what each keeper is reading.

The parrot is the same bird it always was. It got the pigeon’s job: carry this to the next loft. What the labs call reasoning is that one hop, repeated, with training on top.

Does it always get it right? No, these are still probability machines, and they will have varying degrees of success. Prompts and phrasing among other factors can make an enormous difference in accuracy. And a long answer is not free thought. It is hundreds of extra guesses. That is why the bill and the wait both go up when you turn “reasoning” on.

For a concrete example, OpenAI reported these results on 2024 AIME competition maths problems:

Trained reasoning made LLMs far better at solving problems and answering questions accurately. The next step in their evolution was moving toward “autonomy”, taking action and becoming agentic, which we’ll cover in the next article in this series.