So what do you think the difference is between humans and an agent in this respect? What makes you think this has any relevance to the problem? everything is combinatorially explosive: the combination of words that we can string into sentences and essays is also combinatorially explosive and yet LLMs and humans have no problem with it. It's just the wrong frame of thinking for what's going on. These systems are obtaining higher and higher levels of abstractions because that is the most efficient thing for them to do to gain performance. That's what reasoning looks like: compositions of higher level abstractions. What you say may be true but I don't see how this is relevant.
"There is no sense in which they are mathematically destined to eventually program well"
- Yes there is and this belies and ignorance of the literature and how things work
- Again: RL has been around forever. Scaling laws have held empirically up to the largest scales we've tested. There are known RL scaling laws for both training and test time. It's ludicrous to state there is "no sense" in this, on the contrary, the burden of proof of this is squarely on yourself because this has already been studied and indeed is the primary reason why we're able to secure the eye-popping funding: contrary to popular HN belief, a trillion dollars of CapEx spend is based on rational evidence-based decision making.
> "How good are these types of algorithms at generalization"
There is a tremendously large literature and history of this. ULMFiT, BERT ==> NLP task generalization; https://arxiv.org/abs/2206.07682 ==> emergent capabilities, https://transformer-circuits.pub/2022/in-context-learning-an... ==> demonstrated circuits for in context learning as a mechanism for generalization, https://arxiv.org/abs/2408.10914 + https://arxiv.org/html/2409.04556v1 ==> code training produces downstream performance improvements on other tasks
> Verifiable domains are interesting. It is unquestionably why agents have come first for coding. But if you've played with claude you may have experienced it short-circuiting failing tests, cheating tests with code that does not generalize, writing meaningless tests, and at long last if you turn it away from all of these it may say something like "honest answer - this feature is really difficult and we should consider a compromise."
You say this and ignore my entire argument: you are right about all of your observations, yet
- Opus 4.6 compared to Sonnet 3.x is clearly more generalizable and less prone to these mistakes
- Verifiable domain performance SCALES, we have no reason to expect that this scaling will stop and our recursive improvement loop will die off. Verifiable domains mean that we are in alphago land, we're learning by doing and not by mimicking human data or memorizing a training set.