"lacks internal computation" is not part of the definition of markov chains. Only that the output depends only on the current state (the whole context, not just the last token) and no previous history, just like llms do. They do not consider tokens that slid out of the current context, because they are not part of the state anymore.

And it wouldn't be a cache unless you decide to start invalidating entries, which you could just, not do.. it would be a table with token-alphabet-size^context length size, with each entry being a vector of size token_alphabet_size. Because that would be too big to realistically store, we do not precompute the whole thing, and just approximate what each table entry should be using a neural network.

The pi example was just to show that how you implement a function (any function) does not matter, as long as the inputs and outputs are the same. Or to put it another way if you give me an index, then you wouldn't know whether I got the result by doing some computations or using a precomputed table.

Likewise, if you give me a sequence of tokens and I give you a probability distribution, you can't tell whether I used A NN or just consulted a precomputed table. The point is that given the same input, the table will always give the same result, and crucially, so will an llm. A table is just one type of implementation for an arbitrary function.

There is also no requirement for the state transiiltion function (a table is a special type of function) to be understandable by humans. Just because it's big enough to be beyond human comprehension, doesn't change its nature.

Dog has a very clear definition, so when you call a sausage in a bun a "Hot Dog", you are actually a fool.

Smart has a very clear definition, so no, you do not have a "Smart Phone" in your pocket.

Also, that is not the definition of intelligence. But the crux of the issue is that you are making up a definition for AI that suits your needs.

By that metric, you can argue Kasparov isn’t thinking during chess

Kasparov's thinking fits pretty much all biological definitions of thinking. Which is the entire point.

A well trained model should consider both types of lime. Failure is likely down to temperature and other model settings. This is not a measure of intelligence.

It's all "one instruction at a time" regardless of high processor speeds and words like "intelligent" being bandied about. "Reason" discussions should fall into the same query bucket as "sentience".

I don't think the article summarizes the research paper well. The researchers gave the AI models simple-but-large (which they confusingly called "complex") puzzles. Like Towers of Hanoi but with 25 discs.

The solution to these puzzles is nothing but patterns. You can write code that will solve the Tower puzzle for any size n and the whole program is less than a screen.

The problem the researchers see is that on these long, pattern-based solutions, the models follow a bad path and then just give up long before they hit their limit on tokens. The researchers don't have an answer for why this is, but they suspect that the reasoning doesn't scale.

It's not just the memorization of patterns that matters, it's the recall of appropriate patterns on demand. Call it what you will, even if AI is just a better librarian for search work, that's value - that's the new Google.

My impression of LLM training and deployment is that it's actually massively parallel in nature - which can be implemented one instruction at a time - but isn't in practice.

I think as we approach the uncanny valley of machine intelligence, it's no longer a cute cartoon but a menacing creepy not-quite imitation of ourselves.

While a fair idea there are two issues with that even still - Hallucinations and the cost of running the models.

Unfortunately, it take significant compute resources to perform even simple responses, and these responses can be totally made up, but still made to look completely real. It's gotten much better sure, but blindly trusting these things (Which many people do) can have serious consequences.

The AI stands for Actually Indians /s

I'm not trained or paid to reason, I am trained and paid to follow established corporate procedures. On rare occasions my input is sought to improve those procedures, but the vast majority of my time is spent executing tasks governed by a body of (not quite complete, sometimes conflicting) procedural instructions.

If AI can execute those procedures as well as, or better than, human employees, I doubt employers will care if it is reasoning or not.

When are people going to realize, in its current state , an LLM is not intelligent. It doesn’t reason. It does not have intuition. It’s a word predictor.

That indicates that this particular model does not follow instructions, not that it is architecturally fundamentally incapable.

OK, and? A car doesn't run like a horse either, yet they are still very useful.

I'm fine with the distinction between human reasoning and LLM "reasoning".

Then use a different word. "AI" and "reasoning" makes people think of Skynet, which is what the weird tech bros want the lay person to think of. LLMs do not "think", but that's not to say I might not be persuaded of their utility. But thats not the way they are being marketed.

Machine learning based pattern matching is indeed very useful and profitable when applied correctly. Identify (with confidence levels) features in data that would otherwise take an extremely well trained person. And even then it's just for the cursory search that takes the longest before presenting the highest confidence candidate results to a person for evaluation. Think: scanning medical data for indicators of cancer, reading live data from machines to predict failure, etc.

And what we call "AI" right now is just a much much more user friendly version of pattern matching - the primary feature of LLMs is that they natively interact with plain language prompts.

Not "This particular model". Frontier LRMs s OpenAI’s o1/o3,DeepSeek-R, Claude 3.7 Sonnet Thinking, and Gemini Thinking.

The paper shows that Large Reasoning Models as defined today cannot interpret instructions. Their architecture does not allow it.

Sure. We weren't discussing if AI creates value or not. If you ask a different question then you get a different answer.

Is thinking necessarily biologic?