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It solves for the same thing a "train of thought" (internal vocalization) solves for in the human brain: there's a lot of stuff you "know" as episodic memories of words you've heard/read, but haven't yet internalized via practice into reflex reactions. It's a lot faster and cheaper to acquire a memory of some words, than it is to acquire an entire new skill, so you end up picking up far more memories-of-words than concrete skills from a given training corpus.

Reasoning (i.e. bubbling those remembered words up into your mental context, and then using a special "trigger effectively arbitrary synaptic activations dependent on the content of the attention-masked context and an ongoing state" bridging reflex on them, a.k.a. "system-2 thinking") is how you leverage memories-of-words into useful behavior. Rather than executing native skills embedded into your synaptic weights, you're running a single very fancy native skill that acts as an interpreter for word-memory data, slowly and strenuously turning words you're holding in mind into more words (synthesis), or into associations to other memories (word-memories or otherwise), or into actions/outputs, etc.

(An especially useful "trick" of this system is planning, i.e. chaining the interpreter through "mere words" that conjure more "mere words" to mind until you end up at words that form a declaration of what you're about to do. You can then rely on a special part of the bridging reflex, namely the "instruction-following" reflex, to react in a way where your actions are constrained by the plan you've generated.)

> Consider the problem: “what’s 1 +2 +3 +⋯ +10”? One solution is to add the numbers one at a time: 1, 3, 6, 10, and so on up to 55. Another way is to pair them from the outside in: 1 +10, 2 +9, 3 +8, 4 +7 and 5 +6 each make 11, and five pairs of 11 make 55. Both of these paths land on the correct answer, 55.

Watching my son work through difficult math problems has forced me into this realization. In my head there is one "correct" path, and I often have to stop myself from interrupting his chain of thought. He often is just getting there a different way.

I'm pretty sure that the current approach of baking in chain-of-thought reasoning into weights is not the end of the line. It just seems to accidental and ad-hoc.

P. S. The animated bird is truly magical!

Wang's argument contradicts the view that intelligence necessarily improves through more reasoning and undermines any assumption that recursive self-improvement (RSI) will automatically converge toward greater intelligence.

Content aside, that's a beautiful webiste

Normalizes user voice to goal so the action has more chances to success you can see this on model that dont hide traces sending very badly spelled or incomplete sentences

That is how I have been thinking about LLM reasoning pretty much since it arrived.

I am not sure I support his statement about RL “searching for successful paths and then training the model to reproduce them”.

Don’t we train the model to use a certain method to explore the space in search for an answer?

As soon as you have tool calling and a way to verify your result, such as a theorem prover for example you are essentially running an optimization algorithm.

My understanding of the math is weak (to say the least), but intuitively what I'm getting from this is:

1) Pretraining creates a bias _towards_ "correct answers" with each inference step

2) A longer walk is more likely to land in the correct region, given it's easier to verify you have the correct answer than to create it

3) RL selects the subset of walks that lands in the correct region and tilts the distribution in favor of such walks

4) By 2, that trains towards longer walks

...Is that correct?

EDIT: Wait, but this contradicts the post's claim that "The gains we credit to “thinking longer” come from the search we paid for during training, rather than at inference.". This requires that thinking longer is not at all causal for correct answers, which contradicts 2.

> reasoning as pathfinding through token space

Sounds like it's hillclimbing all the way down!

Cool framing. I'm excited for the parallel construction of ___ as pathfinding through weight space.

Mostly, it seems to be solving the problem of people thinking about things themselves.

What is the library, if any, used for the equation/formula rendering? Looks tastefully done.