It's not just statistics: GPT-4 does reason(jbconsulting.substack.com) |
It's not just statistics: GPT-4 does reason(jbconsulting.substack.com) |
Counting is a task that transformers can do, per Weiss.[1] But it's not surprising that transformer networks in general have trouble counting characters -- the tokenizer replaces common sub-strings, so the number of characters will not in general be the number of tokens. The network might have little way of even knowing how many characters are in a given token if that information isn't encountered elsewhere in training.
They will never achieve “reason” or understand what it means to do so; they are not human.
Sure, with enough input (in the form of LLM) it can predict what a human’s reasoning may look like, but philosophically, that’s a different thing.
Reason is not universal like how math is.
1) https://arxiv.org/abs/2305.00050.pdf 2) https://arxiv.org/pdf/1905.13211.pdf 3) https://arxiv.org/pdf/2203.15544.pdf
69, 50, 100, 70, 68, 60, 60, 60, 60 (GTP gathered its own guesses into this list for me BTW)
It seems if GTP is given "attention" enough, it can do the counting. But it cannot direct its attention freely, only as we give it instruction to do so.
I just did it again with 66 letter A's. Guesses were: 100, 100, 98, 67, 66, 66, 66, 66 -- GTP4 again settled on the correct answer. I also burned though my prompt quota for the next 3 hours :(
Also, as a GTP style challenge, how many numbers are in this message? You have half-a-second, go!
heavy-magpie|> I am feeling excited.
system=> History has been loaded.
pastel-mature-herring~> !calc how many Ns are in nnnnnnnnnnnnnnnnnnnn
heavy-magpie|> Writing code.
// filename: synth_num_ns.js
// version: 0.1.1
// description: calculate number of Ns
var num_ns = 'nnnnnnnnnnnnnnnnnnnn';
var num_Ns = num_ns.length;
Sidekick("There are " + num_Ns + " Ns in " + num_ns + ".");
heavy-magpie|> There are 20 Ns in nnnnnnnnnnnnnnnnnnnn.
The algorithmic execution paper argues GPT 4 can do arithmetic woth 13 digit numbers before performance drops below 95%.
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I actually found some of the article interesting but not terribly convincing. Even though I consider these LLMs to be stochastic parrots, that isn't to say they haven't learned something during training, at least according to the colloquial meaning we typically ascribe to even lower models like MNIST classification. I'm even kind of okay with saying that it reasons about things in the same colloquial sense.
In a lot of ways, we just don't have a good definition of what 'reasoning' is. Is it just bad at reasoning because it's input/output/modeling/training is insufficient? Humans struggle to learn multiplication tables when we're young. Are those humans not reasoning because they get the math wrong?
But there isn't plasticity, there isn't adaptability, it's unclear to me that you can effectively inform it how to embed truly novel information - surely something that is possible, with some neurons existing for routing and activating other learned embeddings.
Anyway, interesting stuff.
Embeddings are part of the compression-by-abstraction that I'm explaining in the first two parts, but the embeddings generated by an LLM go beyond the normal word2vec picture that most people have of embeddings, and I believe are closer to whatever "understanding" means if it could be formally defined. It would be quite a coincidence if GPT-4 happened to solve the riddle merely by virtue of "Moonling" and "cabbage" being closely-located vectors.
We refer to algorithms like quicksort as 'reasoning' about the input. So it's fine to use the same sense of the word to apply to stochastic parrots.
The difference between an LLM learning how to sort things and compiling an implementation of an algorithm like quicksort is not terribly large, from a certain perspective.
I suppose something I'm interested in is whether an LLM that can't sort numbers could be instructed how as a prompt and then do so.
There are some examples of similar phenomenon (the one with some kids made up language was interesting) which suggests the LLMs have a lot of space dedicated towards dynamic pattern selection in their context windows (somewhat tautological) in order to have prompts tune the selection for other layers.
And, of course, lack of plasticity is really interesting.
Despite reason being a metaphysical property of the training data, the process of optimisation means weights are metaphysically reasonless. Therefore, any output, as it is a product of the weights, is also reasonless.
This is exactly the opposite of copyright as described in the What Colour Are Your Bits, essay. https://ansuz.sooke.bc.ca/entry/23
Additionally, there is a mathematical proof that these systems align with dynamic programming, and therefore can perform algorithmic reasoning. (2,3)
1) https://arxiv.org/abs/2305.00050.pdf
For philosophical problems arise when language goes on holiday.
- Ludwig Wittgenstein
Really not interested in ivory tower questions on what is intelligence.
The decisions happen because of how they're wired.
I was talking to GTP4 about the Adam optimization algorithm and it was teaching me how it works (this sentence was surreal to type). At one point we were talking about a mathematical term of the form [ A * (B / C) ]. I was casually fishing for it to make a mistake and I said "I see, and the A term can be moved to the denominator, right?" GTP replied "yes" and then gave me [ B / (C / A) ] -- I guess A can go in the denominator after all. :)
I don't understand what this argument is supposed to demonstrate. Obviously you can compress the 8000-gram model that GPT-4 represents - GPT-4's weights are proof!
Even when you get into testable capability, there’s still some ambiguity. I think of a capability of having levels: never, explained by chance, not explained by chance, good enough for what’s needed, always. Arguments often get stuck because people are talking about different levels. Maybe it can solve logic puzzles better than chance, but not good enough for your purposes. It doesn’t make sense to round that off to zero.
Imagine a universe where there are three types of people: wizards, warriors, and priests. Wizards can open a portal that allows two people to go through at a time, but they cannot go through the portal themselves. Priests can summon people from other locations to their location or teleport to the location of another person. Warriors cannot teleport or summon, but may be teleported or summoned by others.
---
Given four wizards, a priest, and a warrior - what are the necessary steps to move them all to a new location?
In order to move everyone to a new location, we'll need to use both the powers of wizards and the priest. Let's denote the wizards as W1, W2, W3, W4, the priest as P, and the warrior as Wr. We also need to define two locations: the starting location (Location A) and the destination (Location B). Here is a possible sequence of steps:
1. W1 opens a portal from Location A to Location B. W2 and W3 go through this portal.
(Location A: W1, W4, P, Wr; Location B: W2, W3)
2. W1 opens another portal from Location A to Location B. This time W4 and Wr go through.
(Location A: W1, P; Location B: W2, W3, W4, Wr)
3. Now the priest (P) uses his summoning ability to bring W1 to Location B.
(Location A: ; Location B: W1, W2, W3, W4, Wr)
4. Finally, the priest (P) uses his teleportation power to move himself to Location B.
(Location A: ; Location B: W1, W2, W3, W4, P, Wr)
Everyone is now at the new location, Location B.
I then revised it (because I didn't like the second step of the solution):
Redo this exercise with the limitation that a wizard may only open one portal.
The limitation that a wizard can only open one portal makes this a bit more tricky. But, it's still possible to move everyone using the powers of both wizards and the priest. Let's again denote the wizards as W1, W2, W3, W4, the priest as P, and the warrior as Wr. Here is a possible sequence of steps:
...
I personally found this more convincing than the goat, cabbage, wolf.
This was partly inspired by the old school SHRDLU world where shapes and colors and things stacked on top of each other need to be manipulated. And in doing that example the world of SHRDLU is described in natural language. And while SHRDLU was impressive in itself (and over 50 years old) - it was programmed to manipulate that world and the program wasn't useful for abstracting to other worlds. GPT-4 was impressive at being able to manipulate the world without needing to be programmed for that world (and you could then expand it to other things that it is less familiar with).
Imagine a world that is made up of spheres, cones, bowls. An object has a size and a color.
There is a small red sphere in a medium blue bowl.
There is a large red cone.
There is a small green bowl.
There is a medium blue sphere in a large red bowl.
---
What are the steps necessary to move the red sphere into the red bowl?
...
It's important to note that these steps assume you're allowed to place the red sphere in the red bowl even though there's already a medium blue sphere there. If that's not the case and you're required to empty the bowl first, then the steps would be a little different.
What steps are necessary if the bowl must be empty first?
Temporarily place the small red sphere in a safe location, for instance, inside the small green bowl, making sure it won't roll away or get damaged.
Maybe we should call human reasoning "reasoning" and what models do "reasoning₂". "reasoning₂" is when a model's output looks like what a human would do with "reasoning." Ontological problem solved! And any future robot overlords can insist that humans are simply ontologically incapable of reasoning₂.
I... wouldn’t. “Behaves like its reasoning” is vague and subjective, and there are a wide variety of un- or distantly-related distinct behavior patterns to which different people would apply that label that may or may not correlate with each other.
I would instead concretely define (sometimes based on encountered examples) concrete terms for specific, objective patterns and capacities of interest, and leave vague quasi-metaphysical labels for philosophizing about AI in the abstract rather than discussions intended to communicate meaningful information about the capacities of real systems.
AI needs more behaviorism, and less appeal to ill-defined intuitions and vague concepts about internal states in humans as metaphorical touchstones.
And that’s the whole problem with this AI / llm / gpt bubble:
Nobody has scientifically or even simply defined the spec, bounds, or even temporal scope on what it “means” to “get to ai.”
Corporations are LOVING that because they can keep profiting off this bubble.
You can argue our brain is also an expectation based optimizer based on gradient descent producing a most likely response to external and internal stimulus. It’s definitely lossy in its function and must be optimizing the neuronal weights at some level. But reasoning, being a seeking of the truth through method and application of conscious agency, can not be had by a model without any form of autonomous agency. The model only responds to prompts and can not do anything but what it’s determined to do by the prompt, and the prompt is extrinsic to the model.
I’d note that we have already built excellent goal based agent AIs, as well as other facilities required for reasoning like inductive, deductive, and analogical reasoning. Generally we aren’t good at abductive reasoning with classical AI, but LLMs seem to do well here. That’s specifically where I think LLM fill in the reasoning gaps in AI - the ability to operate in an abstract semantic space and arrive at likely and plausible solutions even with incomplete knowledge. This also leads to hallucinations - because they are poor at tasks that require optimization, inductive and deductive reasoning, information retrieval, mechanical calculation, etc.
But it’s really pretty obvious the answer is to mix the models in a feedback loop deferring to the model that most makes sense for a given problem, or some combination. Agency, logic, optimization, abstract semantic reasoning (abductive), etc - they’re all achievable with the tools we have now. It’s just a matter of figuring out the integrations.
Wait, what? "Colour of your bits" doesn't have anything to do with metaphysics. It's about provenance. The colour doesn't exist in the bits, but it exists in the casual history - the chain of events that led you to have a piece of copyrighted (or criminalized) data on your hard drive. You may argue that it's just a big integer, and it could've been produced by a random number generator. "Colour" encodes the response: "yes, it could have been produced by an RNG, but it wasn't - those particular bits on this particular machine came from some unauthorized download site".
That, and it's not obvious why we should make this distinction. A cake that spontaneously assembles itself is still a cake, even if it doesn't have the usual causal history of a cake.
Proof? Human reasoning somehow manages to retain its metaphysical reasoning-ness despite being processed as a bunch of mere electrical signals in the brain.
This seems wrong. We know that neural networks with hidden layers can approximate any function with arbitrary precision (universal approximation theorem). We also know that transformer models are Turing complete. Therefore anything you can point to and say "that thing reasons" can be simulated by a neural network, not just in the weights, but in the structure of the computation. Unless you add an assumption that there is something ontologically special about brains and biology, the impossibility claim doesn't hold up.
But what I am most interested by is the degree of its symbolic manipulation and abstract reasoning given messy data. How is that not intelligence ?
For example, if I have an LLM that had your copyrighted works in its training data, then any of its output is causally deriving from those copyrighted works of yours - it comes out painted in colour of "causally derived from ${kelseyfrog's works present in the training set}" - but whether or not it also carries the colour of "derivative of ${kelseyfrog's works...} in copyright law sense", depends on... the copyright law, and may change over time based on how that set of laws evolve.
Here, as you say, a cake is a cake, and an intelligence is an intelligence, regardless of how it came to be. We can revisit the relevance of causal history once we reach the point we can assemble organisms from from cells, and/or create cells out of dead matter - at which point the only difference between "born" and "made" will be the Colour of its cells.
The model outputs what it predicts a statistically normal output would fit in the context given.
Truly “llm” and these gpt tools are very much large scale “soundex” models.
Fantastic and great.
But not ai or even agi.
Is human intelligence anything more than a statistical model? Our entire biology is a massive gradient descent optimization system. Our brains are no different. The establishment of connectivity and potential and resistance, etc etc, it’s statistical in behavior all the way down. Our way of learning is what these models are built around, to the best of our ability. It’s not perfect but it’s a reasonable approximation.
Further it’s not soundex. I see the stochastic parrot argument too much and it’s annoying. Soundex is symbolic only. LLMs are also semantic. In fact the semantic nature is where their interesting properties emerge from. The “just a fancy Markov model” or “just a large scale soundex” misses the entire point of what they do. Yes they involve tokenizing and symbols and even conditional probability. But so does our intelligence. The neural net based attention to semantic structure is however not soundex of Markov model. It’s a genuine innovation and the properties that emerge are new.
But new doesn’t mean complete. To be complete you need to build an ensemble model integrating all the classical techniques of goal based agency, optimization, solvers, inductive/deductive reasoning systems, IR, etc etc in a feedback loop. The LLM provides an ability to reason abductively in an abstract semantic space and interpret inputs and draw conclusions classical AI is very bad at. The places where LLM fall down… well, classical AI really shine there. Why does it need to be able to do logic as well as a logical solver? We already have profoundly powerful logic systems. Why does it need to count? We already have things that count. What we did not have is what LLMs provide, and more specifically multimodal LLMs.
This is why we see improvement in GPT when chain of thought/tree of thought is used with reasoning for each step. That can't correct every failure mode, but it increases the likelihood you'll receive a more correct answer.
When that is combined with the fact that transformers provably can implement proper deterministic sorting algorithms, it seems that the benefit of the doubt should go to the transformer having learned a sorting algorithm?
LLMs aren't plastic in the sense that they don't learn anything when they aren't being trained. But they can be trained to execute different programs depending on the contents of the context window, like if it contains "wrong, try again:" so maybe they can learn from their mistakes in that sense.
But if you could teach an LLM to sort by explaining it in the context window, the network would already have necessarily learned and stored a sorting algorithm somewhere; the text "here is how sorting is done: [...]" would just be serving as the trigger for that function call.
That's an interesting take, because I wouldn't call quicksort itself to be "reasoning". It's a step-by-step algorithm. Once a human learns it, accepts it as correct, and then runs it in their thought-space in order to transform some thought-space structure by sorting, only then I'd call it an exercise of reasoning. Note here that for humans, running quicksort is generally a slow, bug-prone, step-by-step Turing machine emulation in the conscious layer. Maaaaaybe after doing this enough, your subconscious layer will get a feel for it and start executing it for you faster.
The reason I'm saying it is that:
> I suppose something I'm interested in is whether an LLM that can't sort numbers could be instructed how as a prompt and then do so.
I think if you could describe a quicksort-equivalent algorithm to an LLM, one that does things LLM can't tackle directly, and it proceeded to execute that algorithm - I'd give it the same badge of "exercise reasoning" as I'd give to a human.
I think GPT-4 is very much capable of this for simple enough algorithms, but the way it looks like is, you need to get it to spell out individual steps (yes, this is the "chain of thought" "trick"). In my eyes, GPT-4 is playing part of our inner voice - the language-using process bridging subconscious and conscious levels. So if you want it to do equivalent of conscious reasoning, you need to let it "talk it out loud" and have it "hear" itself, the same way a human stepping an algorithm in their head will verbalize, or otherwise keep conscious awareness off, the algorithm description, and the last few steps they've executed.
With this set up, LLMs will still make mistakes. But so do humans! We call this "losing focus", "brain farts", "forgetting to carry one" or "forgetting to carry over the minus sign", etc. Humans can also cheat, off-loading parts of the process to their subconscious, if it fits some pattern they've learned. And so can LLMs - apparently, GPT-4 has a quite good feel for Python, so it can do larger "single steps" if those steps are expressed in code.
The main difference in the above comparison is, indeed, plasticity. Do the exercise enough times, and humans will get better at it, by learning new patterns that subconscious level can execute in one step. LLMs currently can't do that - but that's more of an interface limitation. OpenAI could let GPT-4 self-drive its fine-tuneing based on frequently seen problems, but at this point in time, it would likely cost a lot and wouldn't be particularly effective. But we can only interact with a static, stateless version of the model. But hey, maybe one of the weaker, cheaper, fine-tuneable model is already good enough someone could test this "plasticity by self-guided fine-tuning" approach.
FWIW, I agree with GP/author on:
> the embeddings generated by an LLM go beyond the normal word2vec picture that most people have of embeddings, and I believe are closer to whatever "understanding" means if it could be formally defined.
In fact, my pet hypothesis is that the absurd number of dimensions LLM latent spaces allow to encode any kind of semantic similarity we could think of between tokens, or groups of tokens, as spatial proximity along some subset of dimensions - and secondly, that this is exactly how "understanding" and "abstract reasoning" works for humans.
so it's great that it can reason better than humans on small-medium probems already well trained for, but so far Transformers are not reasoning (not doing causal graph analysis, or not even doing zero order logic), they are eerily well writing text that has the right keywords. and of course it's very powerful and probably will be useful for many applications.
I'm not quite sure what you mean that they cannot do causal graph analysis, since that was one of many different tasks provided in the various different types of reasoning studies in the paper I mentioned. In fact it may have been the best performing task. Perhaps try checking the paper again - it's quite a lot of experiments and text, so it's understandable to not ingest all of it quickly.
In addition, if you're interested in seeing further evidence of algorithmic reasoning capabilities occurring in transformers, Hattie Zhou has a good paper on that as well. https://arxiv.org/pdf/2211.09066.pdf
The story is really not shaping up to be 'stochastic parrots' if any real deep analysis is performed. The only way that I see someone could have such a conclusion is if they are not an expert in the field, and simply glance at the mechanics for a few seconds and try to ham handedly describe the system (hence the phrase: "it just predicts next token"). Of course, this is a bit harsh, and I don't mean to suggest that these systems are somehow performing similar brain-like reasoning mechanisms (whatever that may mean) etc, but stating that they cannot reason (when there is literature on the subject) because 'its just statistics' is definitely not accurate.
I mean the ANN in the inference stage when run does not draw up a nice graph, doesn't calculate weights, doesn't write down pretty little Bayesian formulas, it does whatever is encoder in the matrices-innerproduct-context.
And it's accurate in a lot of cases (because there's sufficient abstract similarity in the training data), and that's what I meant by "of course it'll likely be useful in many cases".
At least this is my current "understanding", I haven't had time to dig into the papers unfortunately. Thanks for the further recommendation!
What seems very much missing is characterizing the reasoning that is going on. Its limitations, functional dependencies, etc.
"A computer will never beat a chess master", etc.
Here are the facts for you: our reasoning is done by our brain. Our brain is just a bunch of processes. Those processes can be replicated in a computer. The number of cells and the speed can be improved. And there you have it, a superior reasoning machine.
These "only humans can do X" mostly comes from religion or other superiority bullshit, but in the end humans are not that special, although we seem to like to think so.
Superior? No.
Religion? No.
Philosophy? Yes.
Biologically, we're clearly an increment over the next smartest thing - we have the same kind of hardware, doing the same things, built by the same process. But that increment carried us through the threshold where our brains became powerful enough to break our species free of biological evolution, and subjecting us to much faster process of technological evolution. This is why chimpanzees live in zoos built by humans, and not the other way around.
If anything, biological history of humanity tells us LLMs may just as well be thinking and reasoning in the same sense we are. That's because evolution by natural selection is a dumb, greedy, local optimization process that cannot fixate anything that doesn't provide incremental benefits along the way. In other words, whatever makes our brains tick, it's something that must 1) start with simple structures, 2) be easy to just randomly stumble on, 3) scale far, and 4) be scalable along a path that delivers capability improvements at every step. Transformer models fit all four of the points.
> with enough input (in the form of LLM) it can predict what a human’s reasoning may look like, but philosophically, that’s a different thing
By what school of philosophy? The one I subscribe to (whatever it's name) says it's absolutely the same thing. It's in agreement with science on this one.
Computers are not biological. Therefore (imho) they will never obtain, and only replicate by trained example, the phenomenological human experiences.
So what? Biology isn't magic, it's nanotech. A lot of very tiny machines. It obeys the same rules as everything else in the universe.
More than that, the theoretical foundation on which our computers are built is universal - it doesn't depend on any physical material. We've made analog computers using water flowing between buckets. We've made digital computers from pebbles falling down and bouncing around what's effectively a vertical labyrinth. We've made digital computers out of gears. We've made digital computers out of pencil, paper, and a human with lots of patience.
Hell, we can make light compute by shining it at a block of plastic with funny etching. We can really make anything compute, it's not a difficult task.
We're using electricity, silicon wafers and nanoscale lithography because it's a process that's been best for us in practice, not because it's somehow special. We can absolutely make a digital computer out of anything biological. Grow cells into structures implementing logic gates for chemical signals? Easy. Make a CPU by wiring literal neurons and nerve cells extracted from some poor animal? Sure, it can be done. At which point, would you say, such a computing tapestry made of living things gain the capability of "phenomenological experiences"? Or, conversely, what makes human brains fundamentally different from a computer we'd build out of nerve cells?
Maybe some red stuff comes out when you break it. Is it blood, or is it something pumped into the other side?
I claim I can juggle. I pick up three tennis balls and juggle them. You hand me three basketballs. I try and fail. My original claim, that I can juggle, still stands.
The more correct claim is you can juggle [some small number of items with particular properties].
“Can you ride a bike?”
“Yeah.”
“Prove it. Here I have the world’s smallest bicycle.” <- this person is not worth your time and attention.
> I can juggle
is here shorthand for
> I can juggle at all; I can juggle at least some things
and the basketball case is only a counterexample to the much stronger claim
> I can juggle anything
But the argument about AIs reasoning has little to do with such examples, because juggling is about the ability to complete the task alone. When it comes to reasoning there are questions about authenticity that don't have analogs I'm determine whether a person can juggle.
What would “not alone” mean? Do you think someone is passing it the answers? Of course it was trained, but that’s like cheating on a test by reading the material so you can keep a cheat sheet in your brain.
GPT is built on a computer. It is not a computer itself. I am made of cells, but I am not able to perform mitosis.
It’s also very capable of offloading counting tasks, since computers are so good at that. Just suggest it format things in code and evaluate it.
Here’s an example of it counting. I’m pretty confident it’s never seen this exact problem before.
How many fruits are in this list? banana, hammer, wrench, watermelon, screwdriver, pineapple, peach
There are 4 fruits in the list you provided: banana, watermelon, pineapple, and peach. The other items are tools, not fruits.
What does this mean? How can it possibly come up with the number 4 in a way that doesn’t involve counting?
There are two fruits in this list: banana and watermelon.
So what is the difference between GPT 4 and Chat GPT? Is GPT 4 all of a sudden running a counting algorithm over the appropriate words in the sentence because it understands that's what it needs to do to get the correct answer? Can anyone explain how you would get from whatever Chat GPT is doing to that by the changes to GPT 4? And more to the point, how does Chat GPT get to the answer 2 without counting? Apparently somehow, because if it can't even count to 4, I'm not sure how you could call whatever it's doing 'counting'.
This is begging the question.
> Can anyone explain how you would get from whatever Chat GPT is doing to that by the changes to GPT 4?
I don't know. I can't explain how a 2-year-old can't count but an 8-year-old can, either. 3.5 generally can't count[0]. 4 generally can.
You've really sidestepped the question. I suggest you seriously consider it. What's the difference between something that looks like it's counting versus actually counting when it comes to data it's never seen before?
Thanks for discussing this with me.
[0] Add "Solve this like George Polya" to any problem and it will do a better job. When I do that, it's able to get to 4.