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Comment by randomImmigrant | Hacker News Reader

Sliding past the mistakes pointed out, shifting goalposts and trying to recover I see.

Let’s say I’m a complete moron and don’t know what a sparse embedding is.

Pretty please, can you define it for me and then tell me, in detail, where in whatever region of the brain you think this is going on… how is it going on?

Explain how “memories must be stored as embeddings with single multi-neuron assemblies (cortical columns?) storing multiple embeddings as a kind of contents-addressable memory”

You have moved past the cortical column. But still seem to be insisting it’s a bunch of neurons, somewhere… or has that also conveniently changed? Whatever your current position is, please go ahead and explain what components of what cells or otherwise are involved in this process you’re describing.

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An embedding space is a (typically) high dimensional space that has enough dimensions such that examples of some type of entity (e.g. faces, words, or thoughts) can be represented as points in that space, positioned such that they are nearby to other entities with which they have things in common.

An entity embedding doesn't need to use all the dimensions of the space it is positioned in - some dimensions may be unused (sometimes represented as a coorrdinate of 0 in that dimension). These are called "sparse" embeddings. For example, an LLM's tokens are represented as embeddings in what is typcially an approximately ~1000 dimensional space, but start out as sparse embeddings just representing a short letter sequence (but then go on to be transformed/augmented with additional information and so become less sparse).

As an example, let's say an embedding space has 10 dimensions, then a couple of sparse embedding examples could be:

  [0 0 1 0 0 1 1 0 0 0]
  [1 1 0 0 0 0 0 1 0 0]

These two embeddings have no overlap (where both are non-zero), and the more dimensions you have the more likely it is that two random sparse embedding will have little in common.

Embeddings are used in many types of artificial neural networks, not just LLMs, for example face recognition networks, where they are trained such that similar faces (multiple photos of the same person) are close together in the embedding space, and post-training you can then "look up" any arbitrary photo (in the training set or not) by embedding it and seeing what is nearby in the embedding space, which will be similar looking faces.

Presumably real neural networks used embeddings in a similar way, since, for example, it obviously requires many neurons to represent the many differences between different faces, and there is going to be overlap between the neurons used to represent multiple faces (this is not a computer with one storage location for face #1, and a different location for face #2).

A neural network, real or artificial, uses groups of neurons (e.g. a cortical column) to represent an embedding space, with each neuron corresponding to a dimension. A single group of neurons (column) can store multiple embeddings (e.g. faces) represented as different activity patterns (which neurons are firing), and if these are sparse embeddings then the firing patterns corresponding to different memories stored in the same column will have little in common.

Now, I don't know how you believe associative recall is implemented in the brain - how does someone's voice, or half obscured face, recall their entire face, so feel free to imagine it as implemented however you will, but I'd suggest that in an assembly such as a cortical column that when a set of synaptic inputs are triggered the assembly as a whole will learn to reactivate the entire pattern when only part of the original set of synaptic inputs are triggered, and this is the basis of associative recall. There are papers that suggest exactly how this may work given the cortical column microcircuit.

So, with all that said, the suggestion I was making for why (or at least one reason why) memory degrades with age, with memories blending together, is that with a finite quantity of "storage" (cortical columns) you will eventually be storing so many memories (absent a deliberate forgetting mechanism) that there will inevitably be overlap between the sparse embedddings, and this associative recall will therefore not cleanly recall individual memories but rather recall blended memories according to what they have in common.

Obviously some types of memory are at least initially stored in the hippocampus, so no reason to focus on cortical columns, but I expect the use of embeddings is universal.

it makes sense now with this examples

Ok great, thanks. Now you’ve brought up facial recognition, and that’s actually a great example to show where the analogy breaks, and the idea of a few sparse cells encoding specific faces has been conclusively disproved:

https://authors.library.caltech.edu/records/znzhp-4j547

Faces live in a ~50-dimensional continuous space (25 shape axes, 25 appearance axes). They measured about 205 neurons across 2 macaques (human studies have substantiated much of this, some from the same lab), and the key thing is: every neuron participates in every face.

The paper shows faces are embedded, but as points in a dense linear space where neurons are axes, not as sparse activity patterns where neurons are on/off slots.

The mapping between the neuronal activity and the facial structures is invertible. Record these same cells, and their firing pattern can be used to reconstruct the face. Or, if you generate a novel face, you can predict the firing rates of these neurons for it. As far as I understand, this doesn’t work for sparse embeddings.

Some cells carry the shape coordinates and others carry the appearance coordinates, in a heirarchy.

There’s an embedding space, yes. But that space isn’t defined by a network of “on” and “off” neurons. The embedding space is instead constructed by the activity of neurons, and the differences in activity distinguish the faces, using the same set of neurons.

And distance in the ensemble activity of these neurons tracks the distance in face space.

If faces use sparse embeddings, you wouldn’t expect similar faces to evoke similar activity would you? Yet that is exactly what this paper shows, and the same has been shown in the human brain for faces.

There are places where it’s sparse activity of a subset of neurons that maps to specific memories. What you’re describing is what you’d see if you look at how the dentate gyrus (part of the hippocampus) handles your memories in the same location.

But even there, the sheer number of cells makes this combinatorially such a vastly overdetermined system for a lifetime that there’s no capacity limit of the kind you’re describing. Even 1% of these cells lighting up for a specific memory leaves you with so many possible combinations that you’d have to live for a few million years to be in the right scale to at least being to talk about capacity issues.

The brain just isn’t capacity limited by the number of neurons the way your intuition is pointing you.

If you say this has nothing to do with the Von Neumann bottleneck or computational functionalism, fine, but how do you square that with the statement below, which you made further down responding to another post?

> but it's hard to imagine that all of the classical chemistry, let alone quantum, details are important. It's necessarily built out of chemistry, but selection is happening at the level of behavior - presumably depending only on a much higher level set of abstract capabilities (ability to learn, etc), not the exact details of chemistry. The success of LLMs, a crude prediction mechanism built atop a crude ANN, does tend to support the idea that low level details don't matter. Timing will matter if we want to go beyond LLMs to AI that can learn time-based things and not just sequence order, but how much else will matter remains to be seen!

It’s really odd to see these two paragraphs, because the second actually tells you why your first is wrong.

Simply put, the biochemistry is timed. I urge you to study how temperature compensation of circadian rhythms is achieved. That anticipatory function goes all the way down to the molecular level.

It might go down to the quantum level too. In birds, magnetoception depends on a protein called cryptochrome IV, which uses a singlet born, entangled radical pair of electrons to sense the very weak magnetic field of earth.

Now cryptochrome 4 is bird specific and mammals don’t have it. Other cryptochromes are critical clock molecules. And the whole shebang of these evolved initially to be sensitive to blue light and repair DNA.

Try as you might, you can’t separate out the deep linkages from the molecular to the behavioral in biology.

Trying is perfectly fine for stuff like language models. But if you’re going to build models with internal time, best of luck if you ignore the molecular and the energetic considerations. Time emerges from the ground up, in biology, as in physics. Doubt we’ll get a free ride with computers.

Me:

> A neural network, real or artificial, uses groups of neurons (e.g. a cortical column) to represent an embedding space, with each neuron corresponding to a dimension.

You:

> The paper shows faces are embedded, but as points in a dense linear space where neurons are axes, not as sparse activity patterns where neurons are on/off slots.

So you are saying that neurons are axes (aka dimensions), exactly as I just said!

> If faces use sparse embeddings, you wouldn’t expect similar faces to evoke similar activity would you?

Yes, of course you would, because that is precisely how embeddings work, and how you recognize someone even though their head is turned or they are wearing a baseball cap or whatever.

This is the ENTIRE point of emebeddings and why evolution has discovered them as a way of representing things and a way to recall them. You may have seen someone a million times, and yet the sensory patterns your visual cortex is fed are likely different every single time because they are not in the exact same orientation, making the exact same facial expression, with the exact same haircut, etc, etc, etc.

To your brain these are merely similar inputs, similar faces, but there is only so much facial variation between individuals, and if the input is similar along dozens or hundreds of axes of variability (i.e. close in embeddign space) then it is alomst certainly the same individual.

Note that "recall keys" (embeddings) are typically sparse even any stored embedding is not, since the face you are looking at may indeed be turned left or half obscured, and this partial/sparse pattern needs to recall the full one.

How can you be a neuroscientist, or even self-identify as one, if you are not already familiar with things like embeddings, and are making such basic 100% wrong assumptions as "you wouldn’t expect similar faces to evoke similar activity" ?!!!

> Now you’ve brought up facial recognition, and that’s actually a great example to show where the analogy breaks, and the idea of a few sparse cells encoding specific faces has been conclusively disproved

Well, my analogy was comparing computer hash tables collisions to sparse embedding collisions, so what you are discussing now is my suggestion itself (pertaining to embeddings and recall), not the analogy, which is fine!

The study we're discussing was nominally about associative recall, not faces per-se, and specifically about the hippocampus not the cortex (that Macaque face study).

> Memory accuracy for pairing faces with objects and scenes dropped sharply

https://studyfinds.com/aging-brains-blend-memories-together-...

That said, I wouldn't be so sure that face embeddings are fully dense, even if they are not particularly sparse either, given that not all faces have the same set of features, such as facial hair, glasses, blemishes, etc. OTOH, it's possible, perhaps likely, that similar faces are stored together, in which case they may be more dense.

> If faces use sparse embeddings, you wouldn’t expect similar faces to evoke similar activity would you? Yet that is exactly what this paper shows, and the same has been shown in the human brain for faces.

With embeddings in general, sparse or not, you'd expect individual dimensions/neurons to represent different axis of variability, so you would expect individual neurons to be active for multiple different faces that are similar along that same axis (e.g. eye color). Note that the study you are citing used individual neuron recordings as well as fMRI, but of course we don't currently have the ability to simultaneously record from the hundreds of neurons that are likely being used to embed faces, so I don't think this study has much to say about the degree of sparsity of these embeddings. Obviously IF faces both with and without glasses are stored in the same embedding space (same set of neurons), then one would expect the "glasses neuron" not to be firing for a face without glasses, which would confirm some degree of sparsity.

> The brain just isn’t capacity limited by the number of neurons the way your intuition is pointing you.

It's highly unlikely that our brains are wasteful and have unused capacity - this recalls daft pop-sci articles saying that we only use 10% of our brain ... We know that brains and memory do degrade with age, and the only question is how - maybe the encoding mechanism itself is failing resulting in embeddings that have more overlap than they should (or one could hypothesize a dozen other possble failure modes). Do you have any theory that explains the "aging brains blend memories" study that we're discussing, at the level of detail of the hippocampal patterns they are seeing?

> It’s really odd to see these two paragraphs, because the second actually tells you why your first is wrong.

> Try as you might, you can’t separate out the deep linkages from the molecular to the behavioral in biology.

Of course the linkages are there since our brain is built from chemistry, yet selection pressure is happening at a much higher functional level. The part of my response you are referring to is addressing the question of how much of this molecular level detail needs to be retained in an ARTIFICIAL neuron model sufficient for it support the same phenotype-level functional behavior, and the answer is we just don't know, because nobody has yet tried to do it.

Prior to LLMs a lot of speculation about what is necessary in the brain to learn language, e.g. Chompysky-ian language-organ nonsense, might have sounded logical and compelling, but now we have proof-by-existence that "prediction is all you need". We're going to need to wait until we have built an artificial brain, capable of learning time-based phenomena, and everything else our brain is capable of, to similarly be able to point at something (a future elaboration of an artificial neuron model), and then be able to say that this is the most that is needed.

As far as this specific point - how much of the detail of a real neuron is functionally necessary vs how much of it is just a reflection of how it is built, you could also compare the massive complexity of something like a digital circuit transistor or logic component if you get down in the weeds and look at the specific gate architecture, and how it operates via quantum tunneling etc, or you could instead look at the functional behavior as a circuit component, and realize that none of it actually matters, and that transistors are interchangeable as long as they are functionally equivalent.

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