alt Hacker NewsYou could have invented transformers from memory
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I think I can follow most of this, or probably will be able to do so with some help from Claude as we go through it with my questions, but I thought I'd ask humans first.
I've watched most of Karpathy's videos but it's been a while so if I ask a dumb question it's because I'm at a very basic level from a while ago.
To try to turn this into something concrete, let's say I want to store as facts the 50 state capitals. We'll do the most basic tokenization possible, so I have ['AL': 1, 'AK': 2, 'AZ': 3, ... 'WI': 49, 'WY': 50, 'Montgomery': 51, 'Juneau': 52, ... 'Cheyenne': 100]
(Do I need an embedding matrix here? I feel like I need a 100x64 embedding matrix, one for each "token", even for those very first linear examples? Maybe I need two 50x64 matrices?)
But then I'm learning randomly initialized V and K matrices by going through and dotting my 'AL' row by K and my 'Montgomery' row by V and then dotting them together, and going through all of the rest of the states similarly and then optimizing a loss function until I get a V and K that gives me good performance?
I kind of wanted to go one step further and adding two more tokens, a 'StateHasCapital' token and a 'IsCapitalOf' token (say 101 and 102), and somehow use that to learn with compound keys ['StateHasCapital'+'AL': 'Montgomery'] - if I'm really learning facts, can I train on all 50 States->Capitals and maybe 25 Capitals->States and then as a test to see if I'm learning "facts", use the remaining capitals that I didn't train on to see if I can look up what state has the capital city of Olympia?
I might be conflating a whole bunch of steps that don't make sense in that initial linear example and adding complexity, and maybe trying to fit too much into the later examples too (I don't see the 'Query' matrix in the any of the parts of the post that get into self-attention, and maybe this post is just about "here's how memory works, not how LLMs work"
Would be nice if articles defined the requirements to be a “you”.
So I saw this:
"Here are the terms we’ll use throughout. A memory store is a function $f$ that holds $M$ memories, for $i = 1, \ldots, M$. A memory is one key-value pair: a key $k_i \in \reals^{d_k}$, used for lookup based on similarity, and a value $v_i \in \reals^{d_v}$, which is what we want to retrieve. To use $f$, we query it with an input $x$, and it recalls an output $f(x)$. A good memory store recalls $v_i$ when we query it with $k_i$, or with another vector similar to $k_i$. In the literature, a memory store that recalls by similarity is called an associative memory."
And thought "I need to disable noscript because I get crappy page view". I disabled and it didn't help. It's a little sad that there is no explanation in the article what all that dollar signs mean. I feel excluded
Great post. I'm a first-year CS student without much math knowledge (also poor English). I'd like to check whether I got the key idea right. There are layers and each layer stores key, value pairs (normalized in this article). If I query Q then Q will be compared with every stored key "Q@A + Q@B + Q@C + ... = value". If A is the answer then Q@A will be 1, others will be interferences. D dimension only has d orthogonal directions, so if I store more keys than the dimension, I can't avoid remaining interferences. What we want is reducing them by going through function F. And this article introduces heuristic capacity results with different memory store functions (linear -> ReLU -> self attention). Is it roughly right?
self attention is the best way to suppress interferences?
This is a really interesting article! While I can’t profess to understand all the math it is a great way to demonstrate it.
I recall awhile back hearing someone ask whether intelligence was actually the same or similar to “compression” or storing all of this knowledge in weights - IE the ability to create something from reason or weights or relationships / connections. This article makes it even more interesting!
Funny how age shows up in some cases. For me the first thing that came to mind, when starting to read the article, was Ranulph Glanville's 1978: "What is memory that it can remember what it is?" (Progress in cybernetics and systems research - vol 4)
"interference-to-signal ratio", "capacity", ... These terms, and their context, are things a communications/electrical engineer would understand. I encourage comms engineers to start learning how AI works under the hood. Chances are, a lot of what you know about maximising channel capacity and throughput is applicable to AI (can be seen as a channel with memory?).
The animated bird, the kea is absolutely fabulous. I appreciate the effort and detail that went into this.
Great article. My favorite fact about "transformers as a hopfield network" is that transformers are so good at memorizing that they only need one step to find a suitable memory as opposed to multiple steps for a vanilla hopfield network
For anyone here who understands this stuff, help me out because the article dropped me at the end when drawing the connection from memory to LLMs.
For an LLM, the keys are the tokens in your context, and the values are … what exactly?
Wow!! I wish I had this perspective 13 years ago during those dull courses describing the mechanics of an MLP.
So refreshing to see actual human dialog at the start of an AI post/paper/explainer, instead of having that visceral "I'm just reading AI slop" feeling. Even if it's totally unrelated, the little bit about playing the Dune board game made me much more engaged and willing to listen to what the rest of the content had to say.
See also:
NNCP: Lossless Data Compression with Neural Networks (2019)
Goodness, someone posts a great article which IMO accessible math, and people get upset.
If you think that is crazy, ohh boy, just wait til you see all the other papers underlying LLMs, AI, and optimization in general.
I appreciate this post because starting from linear algebra is the correct way to form an intuition of the higher dimensional semantic spaces we're dealing with.
This perspective is great.
This sparks a thought that I have not seen revisited in the LLM age - memristors [1].
Who? Me?
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This article does two things which make it unhelpful for me:
1. It uses math notation. This is a software development site, wouldn't this be much more clear to this audience written as psuedo code instead of a complex series of greek and latin letters?
2. It doesn't step through a concrete example. What is hollow R raised to the (M * d_v) ? Is it a number, a set, a list, a matrix?
To use an example I understand: RAG used to seem complicated to me when only math people were talking about it in math words. For example, let's take a line from wikipedia on embeddings:
> the representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar in meaning
What made it clear was learning that generating an embedding is just a function(string) -> list[float], and RAG is just taking a list[float] for your prompt and finding other list[float] that are close to it in your dataset.
So what would make this article more clear, is step through a simplified example of putting a value into a memory store and querying that memory store, showing the actual data structures.
Hey author here! I have a short summary here if people find it helpful: https://x.com/heyyalexwang/status/2111158818730397932?s=46