Hmm there was a bunch of back and forth on this point even before the first version of the post, with @Michael Oesterle and @metasemi arguing what you are arguing. My motivation for calling the token the state is that A) the math gets easier/cleaner that way and B) it matches my geometric intuitions. In particular, if I have a first-order dynamical system then is the state, not the trajectory of states . In this situation, the dynamics of the system only depend on the current state (that's because it's ...

Thanks for pointing this out! This argument made it into the revised version. I think because of finite precision it's reasonable to assume that such an always exists in practice (if we also assume that the probability gets rounded to *something* < 1).

Technically correct, thanks for pointing that out! This comment (and the ones like it) was the motivation for introducing the "non-degenerate" requirement into the text. In practice, the proposition holds pretty well - although I agree it would nice to have a deeper understanding of when to expect the transition rule to be "non-degenerate"

This work by Michael Aird and Justin Shovelain might also be relevant: "Using vector fields to visualise preferences and make them consistent"

And I have a post where I demonstrate that reward modeling can extract utility functions from non-transitive preference orderings: "Inferring utility functions from locally non-transitive preferences"

(Extremely cool project ideas btw)

Fantastic, thank you for the pointer, learned something new today! A unique and explicit representation would be very neat indeed.

I'm pretty confused here.

Yeah, the feeling's mutual 😅 But the discussion is also very rewarding for me, thank you for engaging!

I am in favor of learning-from-scratch, and I am also in favor of specific designed inductive biases, and I don't think those two things are in opposition to each other.

A couple of thoughts:

- Yes, I agree that the inductive bias (/genetically hardcoded information) can live in different components: the learning rule, the network architecture, or the initialization of the weights. So learning-from-scratch is logically compatible with

Here's an operationalization. Suppose someday we write computer code that can do the exact same useful computational things that the neocortex (etc.) does, for the exact same reason. My question is: Might that code look like a learning-from-scratch algorithm?

Hmm, I see. If this is the crux, then I'll put all the remaining nitpicking at the end of my comment and just say: I think I'm on board with your argument. Yes, it seems conceivable to me that a learning-from-scratch program ends up in a (functionally) very similar state to the brain. The trajectory of...

42y

Thanks for your interesting comments!
I'm pretty confused here. To me, that doesn't seem to support your point, which suggests that one of us is confused, or else I don't understand your point.
Specifically: If I switch from a fully-connected DNN to a ConvNet, I'm switching from one learning-from-scratch algorithm to a different learning-from-scratch algorithm.
I feel like your perspective is that {inductive biases, non-learning-from-scratch} are a pair that go inexorably together, and you are strongly in favor of both, and I am strongly opposed to both. But that's not right: they don't inexorably go together. The ConvNet example proves it.
I am in favor of learning-from-scratch, and I am also in favor of specific designed inductive biases, and I don't think those two things are in opposition to each other.
I think you're misunderstanding me. Random chunks of matter do not learn language, but the neocortex does. There's a reason for that—aspects of the neocortex are designed by evolution to do certain computations that result in the useful functionality of learning language (as an example). There is a reason that these particular computations, unlike the computations performed by random chunks of matter, are able to learn language. And this reason can be described in purely computational terms—"such-and-such process performs a kind of search over this particular space, and meanwhile this other process breaks down the syntactic tree using such-and-such algorithm…", I dunno, whatever. The point is, this kind of explanation does not talk about subplates and synapses, it talks about principles of algorithms and computations.
Whatever that explanation is, it's a thing that we can turn into a design spec for our own algorithms, which, powered by the same engineering principles, will do the same computations, with the same results.
In particular, our code will be just as data-efficient as the neocortex is, and it will make the same types of mistakes in the same type

2y8

Hey Steve! Thanks for writing this, it was an interesting and useful read! After our discussion in the LW comments, I wanted to get a better understanding of your thinking and this sequence is doing the job. Now I feel I can better engage in a technical discussion.

I can sympathize well with your struggle in section 2.6. A lot of the "big picture" neuroscience is in the stage where it's not even wrong. That being said, I don't think you'll find a lot of neuroscientists who nod along with your line of argument without raising objections here and there (neuro...

2y7

Thanks!

I don't think anyone except for Jeff Hawkin believes in literal cortical uniformity.

Not even him! Jeff Hawkins: "Mountcastle’s proposal that there is a common cortical algorithm doesn’t mean there are no variations. He knew that. The issue is how much is common in all cortical regions, and how much is different. The evidence suggests that there is a huge amount of commonality."

I mentioned "non-uniform neural architecture and hyperparameters". I'm inclined to put different layer thicknesses (including agranularity) in the category of "non-uniform hyp...

Thank you very much for pointing it out! Just checked the primary source there it's spelled correctly. But the misspelled version can be found in some newer books that cite the passage. Funny how typos spread...

I'll fix it!

Hi, thanks for the response! I apologize, the "Left as an exercise" line was mine, and written kind of tongue-in-cheek. The rough sketch of the proposition we had in the initial draft did not spell out sufficiently clearly what it was I want to demonstrate here and was also (as you point out correctly) wrong in the way it was stated. That wasted people's time and I feel pretty bad about it. Mea culpa.

I think/hope the current version of the statement is more complete and less wrong. (Although I also wouldn't be shocked if there are mistakes in there). Regar... (read more)