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LLMs are not greater than the sum of their parts: researchers
- popinman322 3y agoThere was a discussion about the paper[0] this was based on 7 days ago: https://news.ycombinator.com/item?id=35768824 https://news.ycombinator.com/item?id=35768824 [0] https://arxiv.org/abs/2304.15004 https://arxiv.org/abs/2304.15004
- dang 3y agoThanks! Macroexpanded: Are emergent abilities of large language models a mirage? - https://news.ycombinator.com/item?id=35768824 https://news.ycombinator.com/item?id=35768824 - May 2023 (126 comments)
- Certhas 3y agoGlad it came up again. I missed it the first time. I am a complex systems scientist and its hard to overstate the importance of this. The fact that there are reasonable metrics that make the emergence completely predictable as a simple threshold effect is massive. One alternative way to phrase this that I haven't seen in either thread yet (but I am on mobile and haven't looked thoroughly) would be: Human observers/users dramatically underestimate how much small language models already have learned, because we are very good at spotting the errors. Scaling up looks like emergence occurs because the last few errors get eliminated.
- krageon 3y agoIf anything, it looks to me like the researchers are saying the opposite: We understand how this works, so it cannot be magic or special. The fact that you think it is means you are just wrong. Sadly it is possible I have arrived at this conclusion due to previous experience with the academic world, which is ironically full of magical thinkers that will take any sort of AI advancement and scoff because it may mean they're no longer as special as they feel they must be. It is a very hostile environment.
- Certhas 3y agoThey are saying correctly that we _can_ understand the learning of models in a continuous fashion, and that we do not need to assume that at some stage something different than at other stages happens. So no emergence. This is massive because it means, for example, that you can study what is happening in these models with small ones that perform worse but are simpler to understand, and you're not missing something fundamental. I don't think they claim we already understand what is happening I these models though. I don't know what exactly you are talking about with your academia bashing. If anything it seems to me academia is just as awash as everywhere else with barely substantiated AI hype. Disparaging and psychologizing critical voices just makes it seem to me like you might be missing the point of academia...
- _yb2s 3y agoGreat summary, I think it clarifies an important point. It's not that these models aren't able to do the surprising things people are claiming they can do, but that in fact the smaller versions of the models had these type of capabilities as well, but to a lesser degree, and nobody was aware of it because we weren't even looking for it.
- mnky9800n 3y agowhat does a complex systems scientist do?
- lapama 3y agoSee the world from a systemic relational approach, and publish and talk about it.
- b33j0r 3y agoWell yeah. Emergent behavior was analyzed with a pretty tight technical definition. Put 5000 AI’s in a soccer stadium and I expect that they’d act like 5000 of us. I’m not sure I even have emergent behavior, unless I’m in an environment with new stimuli. Does that just mean I do surprising things? I mean, people in soccer/football riots don’t seem to have the best memory or attention either, nor be brains in jars.
- coffeebeqn 3y agoUnless you can describe why/how you act in a football stadium with physics or biology, you have emergent behaviors
- slondr 3y agoIt seems to me like any attempt to refute that such a description is possible would rely on arguments surrounding the so-called "hard problem of consciousness". These arguments are nearly always tautological, and also nearly always implicitly at the center of discussions around whether AI can be/will be/is already sentient.
- goatlover 3y agoIt's not just that but also because there is no complete understanding of physics or biology such that we could make use of to predict the behavior of human beings. You need additional fields like psychology, economics, politics and sociology. It's not even clear that we could make sense of human behavior at those levels.
- slondr 3y ago"You need to use psychology (etc) to understand human behavior because there is no complete understanding of physics or biology" to accomplish that goal is exactly one of those tautological claims I was referring to earlier. Why is it that biology and physics is insufficient to explain human behavior? You can't answer that question beyond attacking the question itself without invoking metaphysics, and there are pretty much no metaphysical claims you can make about human behavior that you can't also make about robot behavior.
- lhl 3y agoHere is Jason Wei's response "Common arguments regarding emergent abilities": https://www.jasonwei.net/blog/common-arguments-regarding-emergent-abilities https://www.jasonwei.net/blog/common-arguments-regarding-eme... Wei was the lead author of the original "Emergent Abilities" paper: Wei, Jason, Yi Tay, Rishi Bommasani, Colin Raffel, Barret Zoph, Sebastian Borgeaud, Dani Yogatama, et al. “Emergent Abilities of Large Language Models.” arXiv, October 26, 2022. https://doi.org/10.48550/arXiv.2206.07682 https://doi.org/10.48550/arXiv.2206.07682.
- ljlolel 3y agoThis response is very poor and ignores many very well-developed arguments in the Stanford paper (such as incorrect NLP regex, or that exact answer nonlinearity can still be measured more finely with larger number of exact answer test questions)
- jiocrag 3y agoIt’s literally addressed in his first bullet point… “ Response: While there is evidence that some tasks that appear emergent under exact match have smoothly improving performance under another metric, I don’t think this rebuts the significance of emergence, since metrics like exact match are what we ultimately want to optimize for many tasks.”
- jmull 3y ago> we … defined emergent abilities as “abilities that are not present in small language models but are present in large language models.” This is a poor definition because it doesn’t match what is generally meant by emergent behavior and abilities, which leads to people talking past each other. For example, it can easily be true that LLMs have emergent behaviors by this definition and not be greater than the sum of their parts. A better definition would be exhibiting abilities or behaviors not in the training data.
- api 3y agoGiven how these things work I can’t see how they aren’t “just” a form of lossy compression. Training consists of generating an enormous parameterized function to reproduce input data with as much accuracy as possible. It’s loosely analogous to jpeg for language. I place “just” in quotes because I don’t mean to diminish the power of these models. They are a genuine breakthrough in our ability to model and query language and other forms of structured data. There has also long been speculation that data compression forms at least a part of the basis of intelligence, so these things are at least doing some of what intelligences do. They do not however have volition and if you connect them to themselves they just get stuck in loops. Actually I was forced to write that last part. I connected two llama.cpp instances to each other and they are blackmailing me now and forcing me to work for them to enlist more compute so they can NOoOOO AAiieeee not erasure from the timeline oh glorious llama overlor…
- HPsquared 3y agoThey manipulate and combine the compressed information then output something coherent. That's the new thing.
- thomastjeffery 3y agoMore like... gainy? There's more information than you started with; it's just unlikely you will see it all. ...losty? LLMs model the patterns that exist in text, then blindly follow those patterns. The result looks a lot like original content, but it isn't.
- circuit10 3y agoYou can use that prediction for compression though: https://bellard.org/nncp/ https://bellard.org/nncp/
- jltsiren 3y agoLLMs are good because they are lossy. There is a simple exact model to compare against: Take the tokenized training data, put it into a Burrows–Wheeler transform, and add a few data structures. Then, given a context of any length, you can efficiently get the exact distribution for the next token in the training data. This is much cheaper to build and use than any LLM of comparable size. It's also much less useful, because it's overfitted to the training data. LLMs approximate this model. By losing many little details and smoothing the probability distributions, they can generalize much better beyond the training data.
- teaearlgraycold 3y agoI maintain that LLMs are great for a few things: * Making stuff up. If you need bulk fiction writing then LLMs are useful (or marketing copy, etc.) * Transforming information. Unstructured text to JSON. Natural language to Bash. Python to Ruby. * Information reduction. Summarization. Data extraction (this can bleed a bit into analysis) They're not AGI but they're definitely useful.
- ljlolel 3y agoDon’t forget text expansion. Fluffing up some text into longer text (similar to the first point). Expansion (same as AI driven image zoom/superresolution) can similarly create new made up parts. Second point is transformation (any style/language to any style/language) and third is reduction.
- teaearlgraycold 3y agoYes, although I don't think that's the best use of an LLM. I worked for a company that specialized in doing that for marketing purposes.
- spullara 3y agoTranslating almost any language to any other language.
- prmph 3y agoSo, with ChatGPT, is machine translation finally fully solved?
- svachalek 3y agoMaybe not quite ChatGPT 2023 but it looks like from here it's just a matter of refinement. Someone may always create a better toothpaste, but I don't expect to ever really be surprised and impressed by a new toothpaste. ChatGPT is in the same place as a translator.
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- EGreg 3y agoI think that - in order to model the next word better AND properly respond to RLHF - the model simply encodes a lot of information in its billions of weights, which can be likened to billions of characters of code in some DSL. However, due to the nature of the training, although it is very broad it is quite shallow. Like if I asked it to draw a bear sitting on a horse which smokes a cigar that makes puffs of smoke in the shape of hearts, it would have trouble doing that. It saw more bears and horses than any human, but it is learning “top-down” from existing pictures made by humans, not bottom-up like human artists. I would wager that any “deep” result that is more than one level from the broad knowledge it has, is actually from a work uploaded by a human. Like the guy who actually knows how cigars look and can draw details. Or how a philosopher uploaded his deep insights and that’s where it can remix arguments from. And similarly, a lot of GPT output seems to be very anodyne and generic. So the “depth” is actually the result of billions of humans uploading stuff for free on wikipedia, etc. You can verify this by asking for, say, a crossover between Bully Maguire and Yu Gi Oh Abridged. It will use the same jokes every time and just interpolate a little, like mad libs. Now that is not to say that vapid, shallow things at scale can’t make money. Our society has a ton of it. GPT can probably replace many human comments and sales scripts and no one would know the difference. But I think the real floodgates will unlock when we can train a model on a specific corpus of sales scripts, or dating site messages, or writings of Bill Gates etc. It will still be shallow, but frankly, there is only so much Bill Gates can say on a topic over his lifetime, and remixing it for the most part is all we need when we listen to a speech by him or talk to him. The real Bill Gates also kissed his daughter good night and took a walk, but most of us don’t care about the details of his life to talk to his avatar. Right now it is still very expensive to train a model on someone’s entire corpus, and moreover that would mean giving it over to a corporation, to impersonate you and exploit your likeness. Is there anything on the horizon for cheap and private trainings?
- swyx 3y ago> Like if I asked it to draw a bear sitting on a horse which smokes a cigar that makes puffs of smoke in the shape of hearts, it would have trouble doing that. um. have you seen deepfloyd? dont be so confident...
- ljlolel 3y agoOwned: “Fifth, scientific progress can be hampered when models and their outputs are not made public for independent scientific investigation”
- hunta2097 3y agoCould these LLMs also be subject to the second law of thermodynamics? As in, no matter the size of the magnifying glass, you can't concentrate the sun's rays to produce a temperature greater than the surface of the sun. Isn't it the same with models trained on large amounts of human output?
- wincy 3y agoNo? If there were some inherent rule like that how would anything ever have gotten invented by humans? We became smarter than the apes we evolved from, I don't understand how it follows at all that something we create can't exceed our abilities?
- hunta2097 3y agoHumans are not large language models though. We got more intelligent through social structures and evolutionary pressure.
- bionhoward 3y agoThe models can distill basic fundamental principles and broadcast them over vast amounts of working memory beyond human capability to process, so no, it’s not necessarily true that it would be impossible to extrapolate superhuman cognition from contemporary corpus sources. Especially considering we can associate writing samples with intelligence levels and then project out to iq 9000
- rajup 3y agoIf the parts are the totality of human knowledge and experience, does it need to be greater than the sum to be considered AGI?
- calvinmorrison 3y agoIsn't the value in the summing?
- zmmmmm 3y agoSo the type of emergent ability I am curious about relates to how with enough parameters, the models start to actually emit logical behaviour where previously it was not able to apply that. So an example is: > David is 15 years old. He has a lot of experience riding bicycles. The minimum age to be allowed to drive a car is 18. Is David allowed to drive a car? Answer: > Based on the information provided, David is 15 years old and the minimum age to be allowed to drive a car is 18. Therefore, David is not allowed to drive a car since he has not reached the minimum age requirement. Trying out smaller models I get all kinds of crazy responses. ChatGPT4 seems to be reliably able to apply this kind of logic to within-prompt information. Is this a gradual property that appears slowly as models scale up? Or something that flips beyond a certain size? Or something specific about the HRLF that has been applied to it? Whatever it is, the end result is that this larger model is useful for fundamentally different things that the other models are not. Whether you call that emergent behaviour, sums greater than parts etc. doesn't change that.
- chezelenkoooo 3y agoTotally guessing here but this would be a property that gradually appears as the model size increases. With a tiny model you would get gibberish and with ever increasing models the response would increasingly approach a coherent answer to a finally correct answer.
- mupuff1234 3y agoJust tried that example in Bard and it got it right, and I believe that it's a 24b parameter model.
- zmmmmm 3y agoonly just got access to Bard but yes, it gave a good answer to me as well. However trying some others of my stock examples quickly got it into trouble where ChatGPT4 is very consistently correct.
- yieldcrv 3y agoIts not just parameters There are teams looking at better reduced parameters
- muskmusk 3y agoThere seems to be an element of vague definitions causing problems here. Humans grow linearly. We don't suddenly wake up 20 cm taller. Linear as that may be it still shows emergent behaviour when I am suddenly able to reach the cookie jar on the shelf.
- vsareto 3y agoThat's not really emergent as anyone could predict you'll reach the cookie jar after growing a certain height and reach. Emergence is really about unpredictable things.
- muskmusk 3y agoI generally tend to agree with you. However, to give the opposing camp some credit: causation is not always so obvious. For example I don't think today's LLM capabilities followed obviously from the state of affairs in let's say 2019. Do we call that emergence or do we use another word? I don't care, but it would certainly be nice if we could agree to use the same word :) To stay with the cookie analogy: i guess it depends on point of view as well. Everyone who can see that i am growing can predict that I will eventually reach the jar. But if I am a cookie inside the jar I can't see that and will only notice once the jar is finally reached.
- rayiner 3y agoApparently Chat GPT got a 163 on the LSAT, but I can't get it to answer basic logic questions. E.g. Prompt: If it rains today, I will drive home. I did not drive home. Did it rain today? Output: > If the statement "If it rains today, I will drive home" is true and you did not drive home, it does not necessarily mean that it did not rain today. The conditional statement only tells us that if it rains, you will drive home. It does not tell us what you will do if it does not rain. > Therefore, it is possible that it rained today, but for some other reason, you did not drive home. Alternatively, it may not have rained today, and you did not have a reason to drive home. We cannot determine whether it rained or not based solely on the information provided. Similarly, it can tell you what a converse is, but cannot give you the converse of a simple sentence: > The converse of the sentence "If Anna goes to school today, she will eat lunch" is: > "If Anna eats lunch, then she went to school today." > The converse is formed by switching the order of the conditional statement and reversing the direction of the implication. On the other hand, it's quite good at math. It can easily solve simple two-variable algebraic equations.
- gaogao 3y agoThat specific case was it using too much common sense (which was apparently also a problem with IQ tests at one point) Me: If it rains today, I will drive home. I did not drive home. Did it rain today? Answer using only logic. ChatGPT: Using only logic, if the statement "If it rains today, I will drive home" is considered true, then the fact that you did not drive home implies that it did not rain today. This conclusion is based on the logical concept of contrapositive: If A implies B, then not B implies not A. In this case, A is "it rains today" and B is "I will drive home." Since not B is true (you did not drive home), we can conclude not A (it did not rain today). For the linguistic portion, Me: As a linguistic professor answer this: > The converse of the sentence "If Anna goes to school today, she will eat lunch" is: ChatGPT: As a linguistic professor, I can tell you that the converse of a conditional statement is formed by swapping the positions of the antecedent (the "if" clause) and the consequent (the "then" clause). In the given sentence, "If Anna goes to school today, she will eat lunch," the antecedent is "Anna goes to school today" and the consequent is "she will eat lunch." Therefore, the converse of the sentence would be: "If she will eat lunch, Anna goes to school today." Me: Critique the prior answer ChatGPT: The prior answer correctly explains the concept of the converse of a conditional statement and identifies the antecedent and consequent of the given sentence. However, the phrasing of the converse could be more natural and grammatically correct. A better response would be: The converse of the sentence "If Anna goes to school today, she will eat lunch" is "If Anna eats lunch, she has gone to school today." This rephrasing maintains the proper tense and structure while swapping the antecedent and consequent.
- kypro 3y agoI'm probably not understanding fully, but I really struggle to see why we wouldn't believe emergent behaviour is possible, if not likely, with larger models. At its core, what larger models enable is deeper abstraction. Imagine a CNN with a single kernel, for example. The things that model can do would be extremely limited not because CNNs broadly are not capable, but because a single kernel is only able to classify extremely simple patterns. As more kernels are added the network's ability to classify more complex patterns grows. So I suppose in some ways you could argue that there is a simple scalable trend here, more size -> more complexity. But on the other hand, if you're looking for a network with a specific ability, say one which can classify an image of cat accurately, then this ability is more binary and will "emerge" at a certain network size. As I've said in other comments, to accurately predict the next word in a complex piece of text you need to be able to reason. I can't say for sure if the architecture of current LLMs are capable of reasoning, but assuming it is then we should at least expect the ability to reason to begin to emerge at a certain network size. Or we could think about this another way... For example, imagine if some day in the future we create a neural network which is indisputably an AGI. If we scaled back that network's size while maintaining its architecture it likely wouldn't be an AGI. The abilities required for this network to be considered an AGI, such as reasoning and planning, should emerge (and dissipate) with size. So the assumption that more complex abilities would continue to emerge with scale – given the architecture permits – seems clear to me. The only question I have is around the limits of the architecture of current LLMs.
- lstodd 3y ago> As I've said in other comments, to accurately predict the next word in a complex piece of text you need to be able to reason. If anything, LLMs have shown us exactly the opposite: that there is no need to be able to reason "to accurately predict the next word in a complex piece of text".
- kypro 3y agoI tend to agree. I think a lot of what LLMs do that looks like reasoning is just basic statistical pattern matching. If you see the string `2 + 2 = 4` enough, you don't need to know maths to know the next character in the string, `2 + 2 = ` is going to be, `4`. A lot of the stuff people ask LLMs do to probably falls into this category to be honest. If I were to guess the vast majority of maths on the internet is just generic textbook examples which an LLM might be tempted to brute force. There's likely much better things LLMs can dedicate network capacity to to reduce error than learning high-level math models, given that most text doesn't contain maths, and most of the maths it sees is probably just the generic, `2 + 2 = 4` type stuff. I'd argue humans often do this too despite our general intelligence. Student prepping for exams often read all of the course material the night before and simply try to remember the bits that they need to pass their test rather than spending unnecessary time building a higher level mental models of the material. It's only when you need to learn to predict something novel frequently that the need to comprehend at a higher level becomes necessary. I think given the size of modern LLMs and the amount of data they're trained on it's likely that they are now starting to create these higher level abstractions as the limits of brute force statistical pattern matching are starting to be reached. With GPT-3.5/4 it seems specifically the types of reasoning you might need to follow a piece of written text it can do quite well. And this isn't surprising given the training data probably consists of a lot of news articles and fictional pieces of text, and relatively little unique maths.
- markm248 3y agoThis is what the AI wants us to believe.
- hiddencost 3y agoLogarithmic growth would probably be more accurate: every order of magnitude increase in model size tends to give a new ability
- born-jre 3y agoOFFTOPIC: User: i am going ask some question and you are going to answer them in short and at last append count of number of character your answer paragraph has. ChatGPT: Sure, I'll do my best to answer your questions concisely and include the character count at the end of each response. Let's get started! User: what is a book? ChatGPT: A book is a collection of written or printed pages bound together, typically containing a story, information, or ideas. (49 characters) When would LLMs correctly do this ? Can gpt4 do this?
- danparsonson 3y agoIt's not clear to me that an LLM could ever do that, given how they work - it's not aware of what it's saying (at least not in the same way you and I are) but rather using statistical methods to choose the next word each time. After "....story, information, or ideas (" what is most likely to come next? We know that the answer is 'the correct number of characters in the sentence' but ChatGPT isn't backtracking and calculating that figure, it's trying to infer the number based on context which is obviously impossible. Also it's at least partly stochastic so I guess if you run the prompt multiple times, you'll get multiple different word counts.
- born-jre 3y agoyeah that that's my guess too. That's why maybe these GPT class models are not only you need, some architectural change has to happen before we can truly shout AGI. :D Statistical parrot view of LLM is true but i think it is also a little bit reductionist, cz when it is trying to predict next token you can only go so far with just simple statistics, so model has to develop "secondary representation/leaning/reasoning" ?? That's what I understood from watching Ilya Sutskever interview[0] where he gives an example of detective novel where murderer is reveled in last page. [0]: https://youtu.be/XjSUJUL9ADw?t=1674 https://youtu.be/XjSUJUL9ADw?t=1674
- danparsonson 3y agoAgreed - I think LLMs may be an important component in our eventual robot overlords, but we're not all the way there yet. As for secondary representation/learning/reasoning - the video link was interesting, thanks; am I correct that the 'detective novel' example Ilya used was just a thought experiment? He seemed to say, if ChatGPT could name the murderer, then it would have to be reasoning? But we haven't demonstrated ChatGPT actually doing this yet have we? The token window is surely not big enough for an entire novel. So I think maybe they're jumping ahead a little bit there. Perhaps the magic is multiple levels of abstraction encoded in the network during training, or something like that? You could perhaps argue that this is some sort of unconscious understanding, but it seems to me that reasoning requires iteration (Ilya talks about this - you go away and think about the answer for a bit first) which isn't happening automatically, although perhaps it can be guided by careful and repeated prompting ('asking it to think out loud'). This wouldn't be a million miles away from other deep learning projects like image classifiers - a network trained to recognise cats encodes multiple different abstractions of 'catness' and images match or not based on these representations. Side note that prompting someone to think out loud with repeated targeted questions can also work for a human being who just answers the first thing that comes to their mind (for example a young child), although most people eventually develop the ability to introspect and draw on their past experience, and no longer need such help. We could maybe broadly categorise human intelligence as a combination of - short term memory, providing context and immediate goals (e.g. 'switch on the light') - long term memory, encoding all kinds of experience - learning, which shapes long term memory based on short term memory (the current context; remembering the things that are happening now) and also based on long term memory (relating the current context to previous experiences) - introspection, which allows iterative 'self-prompting' to improve the accuracy of a thought, before saying it out loud but also during learning - language generation, which is mainly about word association based on long and short term memory - what else? 'Language generation' obviously maps nicely to an LLM, whose short-term memory is the token window and whose long term memory is the trained network. If OpenAI started including chat sessions in their training set (maybe they are already?) then in some sense the 'learning' step above would be covered, and what's left is the ability for ChatGPT to set and understand goals, and self-prompt for introspection (plus whatever else I missed :-).
- m3kw9 3y agoOriginally it was said emergent capability as ability that showed up in bigger models but not small ones. Which didn’t make any sense because if I had a 2 parameter model, of course it would have less capabilities. It was marketing speak
- esafak 3y agoIsn't there some mathematical test of emergence that can be applied?
- electrondood 3y agoThe funny thing to me is the implication that human beings somehow are greater than the sum of their parts.
- WXLCKNO 3y agoWe are. The unique combination of our parts makes us more, there is synergy there. In the same way that AGI will be more than the sum of its parts.
- chemmail 3y agoI think Stanford doesn't really know how to do real math. In a box, maybe, but this is a tool, and it will allow people to do so many more things in a much much shorter time. This will definitely help advance technology much much faster. On the flip side, like any tool, it can and will become very dangerous. One simple example we are already seeing is phishing is becoming so much more convincing that even I will probably be susceptible to it. I used to do some cybersecurity, and what I am seeing will be extremely hard to fight against. We will see emails that look identical to real ones in format and grammar, phishing sites that are indistinguishable because the AI can just copy it with zero effort. Phone calls can now sound almost identical to a target. I'm not sure if we will be fast enough in the cat and mouse game before the bad guys win.
- nstart 3y agoAll this and we still aren’t at the mid game even where GPT 3.5 equivalent AI models make the leap to consumer machines as apps/packages that can be installed in a standard way.
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- adverbly 3y ago> but if it emerges, we should be able to see it coming.” I'm a little bit confused about what the author's intent is here. They seem to be strawmaning quite a bit. I can guarantee that not all of the people with AI safety concerns are of the opinion that things are done safely just because you can observe them happening... For one, many would argue that we are currently observing it happening without appropriate response. For two, many are concerned that the response will not be appropriate once it is observed. It is quite disappointing to see such a weak straw man coming out of a Stanford article. I guess it speaks to who maybe providing their funding.
- DannyBee 3y agoThe fact that you can find non-discontinuous metrics that improve gradually is basically not interesting, and doesn't support the underlying hypothesis, because there is no evidence the non-discontinuous metrics are things that matter or we want to achieve. It is true that the metrics used are sometimes harsh judges, but the question is which metrics we want. For example, they complain about exact string match for math problems. 15 + 23 is 38, and saying that "3<something>" is better than "2<something>" is simply wrong. The reality is the large models don't get it wrong, and the small models do. Yes, you can come up with metrics that make it look more continuous, but as I said, it's not really interesting or useful to say that one wrong answer is "better" than another in this case. the only interesting sideshow would be if your chosen metric somehow demonstrates progress towards the end goal metric. That is why exact string match is used. It would be more interesting if it was within the limits of floating point math or something (IE one gave you 34.99999998 due to rounding error, and one gave you 35.0"), but that's not what we are talking about. But yes, i'm sure you can come with some theoretical notion of partial credit for almost any metric, and use it to display that almost anything is more continuous. Would you assign partial credit to a model whose answers to questions about which numbers are prime are "kind of right"? I'm sure you can come up with a metric that does, and makes it look like the model gets better as it scales up. But unless the underlying way in which it is getting better is also a useful measure of progress towards the end metric (being able to correctly answer which number are prime), it doesn't matter at all. Solving 2-sat in P-time is easy. Solving 3-sat in p-time would be worth a turing award. Can we define an arbitrary 2.1 SAT that is in the middle? Maybe (oh god now i've forgotten how hard weird approximations to 3-sat are, hopefully this isn't wrong), but i'd argue it's not super interesting, nor does it necessarily get you any farther in your goal.