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Deep Learning Is Applied Topology

theahura.substack.com

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Re: Deep Learning Is Applied Topology

#191
post #142

Earlier quoted context omitted.

Related to ways of understanding neural networks, I've seen these views expressed a lot, which to me seem like misconceptions: - LLMs are basically just slightly better `n-gram` models - The idea of "just" predicting the next token, as if next-token-prediction implies a model must be dumb (I wonder if this [1] popular response to Karpathy's RNN [2] post is partly to blame for people equating language neural nets with…

I guess I'll plug my hobby horse: The whole discourse of "stochastic parrots" and "do models understand" and so on is deeply unhealthy because it should be scientific questions about mechanism, and people don't have a vocabulary for discussing the range of mechanisms which might exist inside a neural network. So instead we have lots of arguments where people project meaning onto very fuzzy ideas and the argument does…

> The whole discourse of "stochastic parrots" and "do models understand" and so on is deeply unhealthy [...] So instead we have lots of arguments where people project meaning onto very fuzzy ideas and the argument doesn't ground out to scientific, empirical claims.

I would put it this way: the question "do LLMs, etc understand?" is rooted in a category mistake.

Meaning, I am not claiming that it is premature to answer such questions because we lack a sufficient grasp of neutral networks. I am asserting that LLMs don't understand, because the question of whether they do is like asking whether A-flat is yellow.

Re: Deep Learning Is Applied Topology

#192
This is an insightful read but at a place where a prompt churns out a whole model - that's yet far far away and extremely compute intensive.

Philosophical point being - if human brain is also all planes all the way down with trillion dimensional planes separating concepts.

I don't think so that is the case but yes - we might mimic something like that and such a thing will always malfunction more than their human counterparts in a given subject area and would always hit a wall where a human won't.

Re: Deep Learning Is Applied Topology

#193
post #98

Since this post is based on my 2014 blog post ( https://colah.github.io/posts/2014-03-NN-Manifolds-Topology/ ), I thought I might comment. I tried really hard to use topology as a way to understand neural networks, for example in these follow ups: - https://colah.github.io/posts/2014-10-Visualizing-MNIST/ - https://colah.github.io/posts/2015-01-Visualizing-Representa... There are places I've found the topological per…

Consider looking into fields related to machine learning to see how topology is used there. The main problem is that some of the cool math did not survive the transition to CS, e.g. the math for control theory is not quite present in RL.

In terms of topology, control theory has some very cool topological interpretations, e.g. toruses appear quite a bit in control theory.

Re: Deep Learning Is Applied Topology

#194

Earlier quoted context omitted.

My favorite argument against SP is zero shot translation. The model learns Japanese-English and Swahili-English and then can translate Japanese-Swahili directly. That shows something more than simple pattern matching happens inside. Besides all arguments based on model capabilities, there is also an argument from usage - LLMs are more like pianos than parrots. People are playing the LLM on the keyboard, making them '…

The translation happens because of token embeddings. We spent a lot of time developing rich embeddings that capture contextual semantics. Once you learn those, translation is “simply” embedding in one language, and disembedding in another. This does not show complex thinking behavior, although there are probably better examples. Translation just isn’t really one of them.

Furthermore: Learning additional languages fine tunes the embedding.

Re: Deep Learning Is Applied Topology

#195
Huge fan of the idea in fiction of Applied Topology is magic https://en.wikipedia.org/wiki/The_Laundry_Files

> Howard is recruited to work for the Q-Division of SOE, otherwise known as "the Laundry", the British government agency which deals with occult threats. "Magic" is described as being a branch of applied computation (mathematics), therefore computers and equations are just as useful, and perhaps more potent, than classic spellbooks, pentagrams, and sigils for the purpose of influencing ancient powers and opening gates to other dimensions.

Re: Deep Learning Is Applied Topology

#196
post #189

Earlier quoted context omitted.

I am using syntax in a general form to mean patterns. We are talking about LLMs and the debate seems to be around whether learning about non-verbal concepts through verbal patterns (i.e. syntax that includes all the rules of word use, including constraints reflecting relations between words meaning, but not communication any of that meaning in more direct ways) constitutes semantic understanding or not. In the end, a…

> In the end, all the meaning we have is constructed from the patterns our senses relay to us. We construct meaning from those patterns. Appears quite bold. What sense-relays inform us about infinity or other mathematical concepts that don't exist physically? Is math-sense its own sense that pulls from something extra-physical? Doesn't this also go against Chomsky's work, the poverty of stimulus. That it's the recurs…

> Appears quite bold. What sense-relays inform us about infinity or other mathematical concepts that don't exist physically?

A great point. A fantastic question.

My guess is:

1. We learn useful patterns that are not explicitly in our environment, but are good simpler approximations to work with.

Some of these patterns only mean something in a given context, or are statistical happenstance.

But some of them are actual or approximate abstractions, potentially applicable to many other things.

2. Then we reason about these patterns.

Sometimes we create new patterns that reveal deeper insights about our environment.

Sometimes we create nonsense, which is either obviously nonsense, fools those who don't reason carefully (i.e. bullshit). And some nonsense is so psychologically attractive that it helps some of us pose and believe we are special and connected to higher planes.

And sometimes we create patterns that offer deeper insights into patterns themselves. I.e. abstractions, like counting numbers, arithmetic, logic, and infinity.

--

It is worth considering, that the progression of abstractions, from unary counting, to more scalable number notations, zero as a number, negative numbers, etc. took a couple hundred thousands years to get going. But once we got going, every small new abstraction helped progress compound faster and faster.

At the level of abstract thinking, I view humans as intelligent as a species, not as individuals. Even the greatest minds, a very small proportion of us, had to stand on innumerable inherited abstractions to make significant progress.

Now many people contribute to new abstractions, but we have inherited powerful abstractions about abstractions to work with.

Erase all that accumulated knowledge for a new generation of humans, and very few would make much or any accumulated progress in explicit abstractions for a very long time.

Re: Deep Learning Is Applied Topology

#197
post #183
post #176

Earlier quoted context omitted.

>Am I really dealing in semantics? Or have I just learned the graph-like latent representation for (statistical or reliable) invariant relationships in a bunch of syntax? This and the rest of the comment are philosophical skepticism, and Kant blew this apart back when Hume's "bundle of experience" model of human subjects was considered an open problem in epistemology.

Can you get into more detail and share some links? Inquiring minds want to know

This gives a good survey: https://plato.stanford.edu/entries/hume/#CopyPrin

>All our simple ideas in their first appearance are deriv’d from simple impressions, which are correspondent to them, and which they exactly represent.

>...he is so confident the correspondence holds that he challenges anyone who doubts it to produce an example of a simple impression without a corresponding simple idea, or a simple idea without a corresponding simple impression...

In other words, Hume thought that your ideas about things are a result, and only a result, of your impression of the thing. Knowledge must be, then, a posteriori. Indeed he reduces our "selves" into "bundles", which is to say nothing more than an accumulation of the various impressions we've received while living.

The problem with this is that it raises the question: How do we come up with novel thoughts that are not just reproducing things we have observed? (This is called synthetic a priori knowledge)

You can see at this point that this question is very similar to the one posed to AI right now. If it's nothing more than a bundle of information related to impressions it has received (by way of either text or image corpora), then can it really ever create anything novel that doesn't draw directly from an impression?

Kant delivered a decisive response to this with his Critique of Pure Reason and his Prolegomena to Any Future Metaphysics. He focused initially on Hume's biggest skepticism (about causality). Hume claimed that when we expect an effect from a cause, it's not because we're truly understanding how an effect can proceed from a cause, but rather because we've just observed it often enough that we expect it out of habit. Kant addresses this and expands it to any synthetic a priori statements.

He does so by dispensing with the idea that we can truly know everything there is to know about concepts. We simply schematize an understanding of the objects after observing them over time and use our sense of reason to generalize that collection of impressions into objects in our mind. From there, we can apply categorical reasoning that can be applied without the need for empirical evidence, and then produce synthetic a priori statements, to include expecting a specific effect from a specific cause. This is opposed to Hume, who said:

>It is far better, Hume concludes, to rely on “the ordinary wisdom of nature”, which ensures that we form beliefs “by some instinct or mechanical tendency”, rather than trusting it to “the fallacious deductions of our reason”

Hume's position was somewhat of a dead end, and Kant rescued philosophy (particularly epistemology and metaphysics) from it in many peoples' estimation.

The big difference between us and LLMs is that (right now), LLMs don't have a thinking component that transcends their empirical data modeling. It is conceivable that someone might produce an "AI" system that uses the LLM as a sensory apparatus and combines it with some kind of pure logic reasoning system (ironically, the kind of thing that old school AI focused on) to give it that kind of reasoning power. Because without something applying reasoning, all we have is some statistical patterns that we hope can give the best answer, but which can't guarantee anything.

Re: Deep Learning Is Applied Topology

#198
post #189

Earlier quoted context omitted.

I am using syntax in a general form to mean patterns. We are talking about LLMs and the debate seems to be around whether learning about non-verbal concepts through verbal patterns (i.e. syntax that includes all the rules of word use, including constraints reflecting relations between words meaning, but not communication any of that meaning in more direct ways) constitutes semantic understanding or not. In the end, a…

> In the end, all the meaning we have is constructed from the patterns our senses relay to us. We construct meaning from those patterns. Appears quite bold. What sense-relays inform us about infinity or other mathematical concepts that don't exist physically? Is math-sense its own sense that pulls from something extra-physical? Doesn't this also go against Chomsky's work, the poverty of stimulus. That it's the recurs…

What sense-relays inform us about infinity…

A waterfall that never seems to run dry. The ocean. Outer space. Time.

I think infinitude, i.e. a property of something which never ends, is a simplifying abstraction for the many things we come across in reality for which we can’t know where it ends or, in a specific context, we don’t care.

Re: Deep Learning Is Applied Topology

#199
>as long as we can separate good from bad we can train a neural network to sort out the topology for us.

10-ish years ago, I saw a project training networks to guess biological sex from face photos. They carefully removed makeup, moustache, hair, etc, so the model would be unbiased, yet they only reached 70 to 80% correct guesses. Yet it seemed like a great result, and they were trying to reach 99%.

First thing I did after reading their paper, was seek a paper where people would try and guess the biological sex from similar photos. And people weren't that much better at it. The difference between people and machine guessing was 1 or 2 percent.

I asked the guys that run the project, how they proved that such a division, based only on a photo, was even possible. They didn't understand the question, they just assumed that you can do it.

They couldn't improve their results in the end. Maybe they sucked at teaching neural networks, or maybe a lot of faces just are unisex if you remove gender markers.

I bring this anecdote because this guys, in my eyes, made a reasonable assumption. An assumption that since they in most situations can guess what's in someone pants by seeing someones face, the face has this information.

The assumption that we could somehow separate good from bad, when we rewrite school books every year, when we try to calculate "half-life of knowledge", when philosophy as a science isn't over, and every day there are political and ideological debates about what's best, is a very-very unreasonable assumption.

Re: Deep Learning Is Applied Topology

#200

>as long as we can separate good from bad we can train a neural network to sort out the topology for us. 10-ish years ago, I saw a project training networks to guess biological sex from face photos. They carefully removed makeup, moustache, hair, etc, so the model would be unbiased, yet they only reached 70 to 80% correct guesses. Yet it seemed like a great result, and they were trying to reach 99%. First thing I did…

I forgot to conclude:

In the end, it's not even reasonable to assume that such a divide between "good" and "bad" exists at all.

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