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Comment by janalsncm | Hacker News Reader

I’ve always wondered what an sufficient explanation of a neural network would entail.

At a very low level, there’s no secret: all of the weights are there, all of the relationships between weights are known. The problem is that it doesn’t tell you anything about the emergent properties of the network, in the same way that quantum physics doesn’t give much insight into biology.

It may be possible that there is no English sentence you can utter about the network which is both explanatory and fully accurate. What is the network doing? It’s trying to approximate the function you’ve given it. That’s it.

You can try other things like ablation to find the effects of lobotomizing the network in certain ways, but this also can’t fully explain 2nd and higher order relationships.

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This sentence from the article stood out to me:

> The explanations have to be wrong, because if their explanations were always right, you could just replace the black box with the explanations.

I've never thought of it like that, but I think that really gets to the core of the issue...

To be able to reason about the behaviour of a neural network with 100% confidence you would need an explanation that incorporated every weight, otherwise you have to accept some degree of uncertainty.

But the idea you could ever explain something with billions of parameters in a way that a human could comprehend seems ridiculous. Imperfect generalisation therefore would inevitably be required – "this bit of the network seems to perform x function". But in doing this you have to accept that this generalisation comes with uncertainty because such a high-level approximation is unlikely to capture all of the nuances. And if it did capture all nuances then the black box isn't needed.

The map is not the territory.

Or, at more length and in more depth, The Analytical Language of John Wilkins by Borges.

Thank you for sharing, the wiki has a pretty funny note:

> Lewis Carroll, in Sylvie and Bruno Concluded (1893), made the point humorously with his description of a fictional map that had "the scale of a mile to the mile". A character notes some practical difficulties with such a map and states that "we now use the country itself, as its own map, and I assure you it does nearly as well."

I'm reminded of: "I have the world's largest collection of seashells. I keep it on all the beaches of the world... perhaps you've seen it." - Steven Wright

All models are wrong, but some models are useful.

Obviously debatable, but this seems wrong. It could easily be that we can't figure out how to do something but when presented with a solution understand it. Many people understand public private key cryptography but could never in a million years come up with it. Same for much of physics, a lot of math etc. As for the sheer complexity of millions/billions of parameters - people can explain and understand molecular dynamics simulations perfectly well. They can't use a small number of words to explain a specific configuration, but it's explainable.

I think there’s a major difference though. You can understand public key crypto at varying levels of complexity because it is a topic created from first principles. Any sub-topic within the umbrella of public key crypto can be explored further. In this sense the knowledge is like a large program.

Neural networks aren’t like that. The whole thing works together simultaneously to derive a result. So I’m skeptical that there is a high level explanation other than “it’s doing it’s best to approximate the data it was trained on” which is not that useful.

There must be some kind of pattern in the high-dimensional space of NN decision making that can be used to explain its decision, at least broadly (given some well-defined query). I’m not saying it’s easy, and I’m not saying the end user will have access to it, but surely someone in the pipeline needs to be able to acquire that. Or else there will never be a serious certification process before general and widespread use.

I guess this raises the question of levels of explanation. What kind of explanation would you like to be able to get? It reminds me of something the physicist Tim Maudlin described on a recent podcast (I will give a poor summary):

Suppose you have the spinning color wheel on your MacBook. You give it to a computer scientist who says that the program is in an infinite loop, and the wheel will never stop spinning. Then you give the computer to a superhuman physicist who studies all of the components including the state of the transistors and internal components and concludes that the wheel will spin for 9 years before the screen gives out. [1]

The point is that both are correct, but we’d really prefer the first explanation, since it gives insight into what the program is doing.

The problem is that neural networks aren’t like programs. They don’t have reducible internal components unless you reduce down to the weights of the network itself. [2]

[1] https://m.youtube.com/watch?v=k0CQ_D7dwA0

[2] https://karpathy.medium.com/software-2-0-a64152b37c35

Yes, I totally agree, and thanks for the Karpathy link, it’s really good. And yes I don’t know at which level is the sweet spot. But the fact that it’s software 2.0 means we need debugging 2.0 too.

Sure — abstractions elide details.

But “this portion of the network appears to recognize faces” is still a useful abstraction. In the same way it is for neurology. Even if both NNs and brains sometimes see faces that aren’t there because the network isn’t “recognizing faces” but a system which signals on a complex set of heuristics that mostly detects faces.

How does the answer change if I only want 99% confidence and accept the existence of illusions? — can we describe the bulk of the behavior in a summary?

It would be very satisfying if we could have an explanation like that. But that’s far from guaranteed, unless that was part of the explicit design of an MMOE for example. Very likely if you ask “what part of the network recognizes faces” the best answer is “the whole thing”.

There's some evidence for emergent "modules" inside NNs.

https://www.alignmentforum.org/posts/j84JhErNezMxyK4dH/llm-m...

We certainly cannot comprehend the entire thing at the same time. ”XAI” is a bit of a buzzword right now and every HCI researcher struggling with finding their grip have jumped on the hype boat, meaning lots of them will just say things because it sounds nice to people with even less knowledge of NNs as them.

However, to think we cannot comprehend them at all is too much. We can certainly ”query” a NN to understand the weights and activations that led to some decision in some specific scenario. How to consume and use that information is another matter, of course, but a debugging process is certainly feasible (as it is with any large scale computer system).

Plus, the architectures of neural networks are not as complicated as most people think. Sure it gets weird after training, but the basic architecture of components are not nearly as complicated as the hardware of a GPU for example, or even that of a complex OS kernel.

The neural net gives a very noisy approximation of some ideal structure. So you're looking for what that ideal structure is, which very possibly does not require a neural network to represent.

One thing that would be fun to know is, e.g., "If the LLM answers question X correctly, then what's a minimal-sized set of things we could remove from the training set and cause it to get that question wrong?" I think with current methods this would be pretty expensive to find out, but, in principle I'm guessing it would be pretty illuminating.

Causal modeling lets you determine where particular facts are stored without too much computational cost and also how you can edit those facts in the model. That might allow you to decouple the problem into first finding the desired set of gradients (converging at the target modification, zero for the weights you don't care about), and just do a linear solve (since probabilistic weightings on how likely an input is in the training set will linearly impact each of the gradients in basically every neural architecture of note, including most LLM modifications) to find an approximately minimal (IIRC, a true minimal subset is NP-hard or something) subset of the inputs which when combined would give you the inverse of the target gradient. Remove that much of the weighting for each of the inputs.

>It may be possible that there is no English sentence you can utter about anything which is both explanatory and fully accurate.

FTFY. Philosophy aside, humans understand complex things by building simpler abstractions for them. I think the key to NN understandability centers on building simpler NNs focused on specific tasks that build into bigger ones.

> the same way that quantum physics doesn’t give much insight into biology

This is very insightful. I've long maintained that "understanding" requires some predictive ability in addition to an ability to explain what's happened in the past.

In the case of neural networks, we should be able to "simply" generate the network that has the desired behavior.

But we can't. We're still shackled to compiling some collection of training data that may or may not produce the desired behavior, tested by some other collection of testing data that may or may not test the desired phenomenon.

I've thought about pattern matching NN weights against known graph structures. I'd imagine, for example, that decision trees emerge at some point in GPT.

The real problem IMO is our ability to represent natural concepts as such graphs. Is love, for example, a DFA? Can we search for its isomorphism?

Same thing as the brain pretty much, except we have root control over the NN in a way we don't with the brain.

To my knowledge, some angles have been explored. Finding which inputs maximally stimulate indiv neurons, and tracing that up the chain.

There was a fantastic article that did this on ImageNet - the takeaway was that neurons adjacent to the input encode sharp, basic features (like edges), and "higher-level" ones encode more nuanced stuff (textures, fur, wheels).

Then ablations, as you mentioned. And finally, rerunning the same training data on differently sized + shaped architectures.

AI systems are missing at least one level of complexity. All neurons in a NN layer fire simultaneously, unlike brain neurons, which trigger each other async.

The brain is heterogenous in ways that a neural network needn’t be. Certain brain regions definitely perform certain functions, certain regions are hardwired to other regions. You can chop out a chunk of a person’s brain and they’ll be completely unable to do certain things.

Afaik the properties you’re referring to on AlexNet (the network trained to perform on Image Net) have to do with the nature of repeated convolution operations which, while interesting, is not as deeply insightful as I believe the article is aiming for.

> It may be possible that there is no English sentence you can utter about the network which is both explanatory and fully accurate.

reminds me of: "The Tao that can be told is not the eternal Tao."

Perhaps a sequence of sentences, almost a series in the mathematical sense, where you iterate your explanation-finder, generating more sentences in the series, until it's sufficiently detailed for the question you care about today.

Also, remember that the explanation doesn't really have to fully contain the semantics of the model. It doesn't have to fully encode the weights, just activate sufficiently sympathetic structures in a human brain.

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