[p1esk]

Artificial neural networks are the closest working model of a brain we have today.

Lots of graph nodes, with weighted connections, performing distributed computation (mainly hierarchical pattern matching), learning from data by gradually updating weights, using selective attention (and/or recurrence, and/or convolutional filters).

Which of the above is not happening in our brains? Which of the above is not biologically inspired?

In fact this description equally applies to both a brain and GPT4.

[aeternum]

Many organisms have just a handful of neurons yet exhibit complex behavior that would be impossible given the weighted connections model. Not to mention single-celled organisms that exhibit ability to navigate.

The model can be the closest working model but that doesn't mean it is complete. It's very likely that cells can store memories/information independent from weights.

[p1esk]

We can’t do that not because our mathematical neurons are too simple. We can’t do that because we don’t know the algorithms those biological neurons are running.

Do you see the difference?

[__loam]

There is of course a difference between the two things you say. They're both the reason we can't recreate the brain in software though.

[p1esk]

There are two separate goals: to simulate the brain in software, and to understand brain algorithms. They overlap, but they are still distinct, and appeal to different groups of people. Neuroscientists want to understand detailed brain operations. They are primarily interested in the brain itself. AI researchers want to understand intelligence, they are primarily interested in higher brain functions (e.g. reasoning, attention, short/long memory, emotions, motivations, goal setting, etc).

We can't (fully) recreate the brain in software partly because we don't know enough, and partly because it's too computationally complex - for example, we can't simulate an entire modern CPU at the transistor level - even though we know how each transistor works, and what each transistor does in the CPU - because each transistor requires a detailed physical model with hundreds of parameters. It's simply not computationally feasible using current supercomputers. Brain is even less feasible to simulate if we want to accurately simulate each individual neuron in it - even if we knew exactly how it works.

But the second goal is much more feasible, and we have made great progress simply by scaling up simple known algorithms which approximate some information processing functions in the brain (mainly pattern matching/prediction and attention). I can talk to GPT4 today just like I talk to other humans, and by the way, this is only possible because out of all AI/ML algorithms people have tried over the last 70 years, the most brain-like one have won (ANNs). If we want to make further progress in AI or if we want to make GPT5 to be more human-like (not sure we do), we don't necessarily need to simulate brain at a neuronal level, we simply need to understand a little bit more about higher level brain functions. Today, we (ML researchers) might actually benefit more from studying psychology than neuroscience.

[ben_w]

> Many organisms have just a handful of neurons yet exhibit complex behavior that would be impossible given the weighted connections model.

That's rather a bold claim given that artificial neural networks are universal function approximators.

[agalunar]

Impossible given that number of neurons.

It's perhaps not terribly surprising that it becomes possible with unlimited width or depth (or an arbitrarily complex activation function).

https://en.wikipedia.org/wiki/Universal_approximation_theore...

[simiones]

It's incredible to me how widely this is misunderstood.

The universal function approximator theorem only applies for continuous functions. Non-continuous functions can only be approximated to the extent that they are of the same "class" as the activation function.

Additionally, the theorem only proves that for any given continuous function, there exists a particular NN with particular weight that can approximate that function to a given precision. Training is not necessarily possible, and the same NN isn't guaranteed to approximate any other function to some desired precision.

It seems pretty obvious to me that most interesting behaviors in the real world can't be modelled by a mathematical function at all (that is, for each input having a single output); if we further restrict to continuous functions, or step functions, or whatever restriction we get from our chosen activation function.

[ben_w]

> The universal function approximator theorem only applies for continuous functions. Non-continuous functions can only be approximated to the extent that they are of the same "class" as the activation function.

Yes, and?

> Training is not necessarily possible

That would be surprising, do you have any examples?

> and the same NN isn't guaranteed to approximate any other function to some desired precision.

Well duh. Me speaking English doesn't mean I can tell 你好[0] from 泥壕[1] when spoken.

> It seems pretty obvious to me that most interesting behaviours in the real world can't be modelled by a mathematical function at all (that is, for each input having a single output)

I think all of physics would disagree with you there, what with it being built up from functions where each input has a single output. Even Heisenberg uncertainty and quantised results from the Stern-Gerlach setup can be modelled that way in silico to high correspondence with reality, despite the result of testing the Bell inequality meaning there can't be a hidden variable.

[0] Nǐ hǎo, meaning "hello"

[1] Ní háo, which google says is "mud trench", but I wouldn't know

[simiones]

> Yes, and?

It means that there is no guarantee that, given a non-continuous function function f(x), there exists an NN that approximates it over its entire domain withing some precision p.

> That would be surprising, do you have any examples?

Do you know of a universal algorithm that can take a continuous function and a target precision, and return an NN architecture (number of layers, number of neurons per layer) and a starting set of weights for an NN, and a training set, such that training the NN will reach the final state?

All I'm claiming is that there is no known algorithm of this kind, and also that the existence of such an algorithm is not guaranteed by any known theorem.

> Well duh. Me speaking English doesn't mean I can tell 你好[0] from 泥壕[1] when spoken.

My point was relevant because we are discussing whether an NN might be equivalent to the human brain, and using the Universal Approximation Theorem to try to decide this. So what I'm saying is that even if "knowning English" were a continuous function and "knowing French" were a continuous function, so by the theorem we know there are NNs that can approximate either one, there is no guarantee that there exists a single NN which can approximate both. There might or might not be one, but the theorem doesn't promise one must exist.

> I think all of physics would disagree with you there, what with it being built up from functions where each input has a single output.

It is built up of them, but there doesn't exist a single function that represents all of physics. You have different functions for different parts of physics. I'm not saying it's not possible a single function could be defined, but I also don't think it's proven that all of physics could be represented by a single function.

[ben_w]

> It means that there is no guarantee that, given a non-continuous function function f(x), there exists an NN that approximates it over its entire domain withing some precision p.

And why is this important?

> Do you know of a universal algorithm that can take a continuous function and a target precision, and return an NN architecture (number of layers, number of neurons per layer) and a starting set of weights for an NN, and a training set, such that training the NN will reach the final state?

> All I'm claiming is that there is no known algorithm of this kind, and also that the existence of such an algorithm is not guaranteed by any known theorem.

I think so: the construction proof of the claim that they are universal function approximators seems to meet those requirements.

Even better: it just goes direct to giving you the weights and biases.

> My point was relevant because we are discussing whether an NN might be equivalent to the human brain, and using the Universal Approximation Theorem to try to decide this. So what I'm saying is that even if "knowning English" were a continuous function and "knowing French" were a continuous function, so by the theorem we know there are NNs that can approximate either one, there is no guarantee that there exists a single NN which can approximate both. There might or might not be one, but the theorem doesn't promise one must exist.

I still don't understand your point. It still doesn't seem to matter?

If any organic brain can't do $thing, surely it makes no difference either way whether or not that $thing can or can't be done by whatever function is used by an ANN?

> It is built up of them, but there doesn't exist a single function that represents all of physics. You have different functions for different parts of physics. I'm not saying it's not possible a single function could be defined, but I also don't think it's proven that all of physics could be represented by a single function.

I could point you to this: https://www.youtube.com/watch?v=PHiyQID7SBs

But that would be unfair, given the QM/GR incompatibility.

That said, ultimately I think the onus is on you to demonstrate that it can't be done when all the (known) parts not only already exist separately in such a form, but also, AFAICT, we don't even have a way to describe any possible alternative that wouldn't be made of functions.

[simiones]

> Lots of graph nodes

Neurons are not connected by a simple graph, there are plenty of neurons which affect all the neurons physically close to them. There are also many components in the body which demonstrably affect brain activity but are not neurons (hormone glands being among the most obvious).

> with weighted connections

Probably, though we don't fully understand how synapses work

> performing distributed computation (mainly hierarchical pattern matching)

This is a description of purpose, not form, so it's irrelevant.

> learning from data by gradually updating weights

We have exactly 0 idea how biological neural nets learn at the moment. What we do know for sure is that a single neuron when alone can adjust its behavior based on previous inputs, so the only thing that is really clear is that individual neurons learn as well, it's not just the synapses with their weights which modifies behavior. Even more, non-neuron cells also learn, as is obvious from the complex behaviors of many single-cell organisms, but also some non-neuron cells in multicellular organisms. So potentially, learning in a human is not completely limited to the brain's neural net, but it could include certain other parts of the body (again, glands come to mind).

> using selective attention (and/or recurrence, and/or convolutional filters).

This is completely unknown.

So no, overall, there is almost no similarity between (artificial) neural nets and brains, at least none profound enough that they wouldn't share with a GPU.