How good are frontier models at physics?(arxiv.org) |
How good are frontier models at physics?(arxiv.org) |
John Sous from Yale posted a fairly solid study on how nearly all the physics benchmarks are broken, as they consistently mark correct answers as incorrect.
When hand grading instead, they found out that the models have actually already saturated the benchmarks which is a little bit scary.
As it essential implies that these models compress knowledge well in a way that what remains is what's generalizeable more so than remembering every specific detail... Anyway more understanding necessary but thought provoking
One tidbit I found particularly interesting: "We tested a GPT-based agentic system, which previously succeeded in resolving several open mathematical conjectures, on open problems in theoretical physics. To our temporary relief and encouragement, it has not managed to fully resolve even one autonomously. We also noted that these agents made considerably less progress on the partially resolved physics problems than on open mathematics problems of comparable difficulty, both by our analysis and independent agent-based analysis of partial results in each domain."
Why would that be encouraging if the purpose of their chosen profession is to advance physics? This is sort of like mathematics being solved by AI with human researchers complaining that they are losing potential awards. It's an entirely self serving way to be.
So many people have their financial and self worth tied to their expertise in phlogiston theory that the truth is second to advancing the field of phlogiston theory.
From that perspective it is hard to think of something worse than a machine that disproves phlogiston theory.
From personal experience, frontier models absolutely struggle with understanding a physical situation based on words. (Okay, I haven't played with Astra much. GPT-5.6 Sol makes outrageous errors that anyone understanding a real world object would not make. And I was just asking it about NPT threads, not advanced physics.)
But seriously, what's up with these benchmarks? The example question in the paper is:
> PHYBench, problem 140: equivalent expressions for the same rope tension
> Problem statement. Three identical homogeneous balls are placed on a smooth horizontal surface, touching each other and are close enough to each other. A rope is wrapped around the spheres at the height of their centers, tying them together. A fourth identical sphere is placed on top of the three spheres. Find the tension T in the rope. It is given that the weight of each sphere is P.
For some reason the paper was focused on the fact that the grader didn't notice that some models were producing answers that were trivially algebraically equivalent to the reference answer. But this is missing the elephants in the room:
1. "touching each other and are close enough to each other": the right response is "hey, Professor, what do you mean 'close enough to each other'? They're sitting on a table in an equilateral triangle, all touching (i.e. tangent at their equators), right? Did you have a different configuration in mind?"
2. The answer is 0. Go find four baseballs or foursquare balls or whatever, make a little triangle with three of them, and balance the fourth one on top. It's not especially hard on an appropriate surface. Now loosely wrap an imaginary rope around them (but see below) to keep them from moving - no tension is needed because they're not moving anyway. So the models and the reference answer are wrong, IMO.
3. How, exactly, do you plan to wrap a rope around the spheres, at equator height, with no built-in tension (not pre-stretched), such that the rope does not immediately fall off? Friction? But I suspect you need to pretend there is no friction to get the reference answer. (Or maybe that the marble-marble interface has friction but the marble-table interface doesn't? Again, I haven't tried to reverse engineer it.) So maybe the right answer is "infinity or impossible -- in the scenario where the rope is needed, the rope will promptly fall off because it cannot be stable in the described configuration and gravity pulls it down, and once the rope falls off the tension will be zero and the top marble will fall and the other three will roll over the rope."
4. The answer might be "any tension you like -- just wrap the rope with the desired amount of tension". Imagine three baseballs in a triangle with a rubber band around them and a fourth baseball on top for good measure. The tension is a function of what rubber band you choose.
I'm sure there's an interpretation of the question that makes the reference answer correct, and I was not inspired to try to reverse engineer it.
My tentative conclusion is that LLMs are almost unbelievably good at solving problems that are fully contained within the inputs and (training/verification) outputs, and that they and the people training them are not actually particularly good at the input and output parts. If you are training a model to benchmaxx this benchmark, you are training a bad model.
The models are confidently answering physics questions, treating it as a math problem, but they don't fundamentally "get it" and even recently failed simple "should i drive to car wash" test
The sample efficiency is just crazy low
Still surprising that even with this they managed to saturate the benchmarks
Since the room as a whole produces fluent Chinese it becomes a language philosophy debate about where meaning comes from. Brandom's inferentialism gets into this more than any normal person would ever care to read about.
LLMs really show the absurdity of the Chinese Room rulebook.
The whole thought experiment should really be left to history at this point.
Searle’s social ontology is much more interesting also but this outdated thought experiment completely overshadows his more interesting stuff.
There's no clear decision criteria for this. Do trick questions demonstrate that most people don't "get it"? And, well, older model saying dumb things doesn't establish a general principle that LLMs don't "get it" in general.
> The sample efficiency is just crazy low
Autoregressive pretraining requires huge amount of data to go from a blank state to a somewhat functional model. Fine-tuning, LORA, reinforcement learning of foundation models and in-context learning are much more sample efficient.
> Chinese room
...creates a wrong intuition that by cranking a Leibniz's mill you are somehow responsible for whether it understands something or not.
"Should I walk to the car wash" is hardly a trick question. If a human told me to walk to the car wash because it's so close, I would say that demonstrates they don't "get it".
I've been waiting for this, but all companies seem to not care much now.
There is a way out of this by supplying right context (needs a bit of expertise in physics)
1 more year and frontier will become crazy good at this as well.
There's an interpretation that makes the reference answer correct. I didn't realize this until halfway through teaching the math class: Based on the lectures, textbook, and homework problems, you match the "form" of the problem with similar problems in the textbook, and apply the same algorithms to solve it. The students have some vague idea of this, referring to it as finding the "trick," but it's never explicitly explained to them.
I was glad for the interesting puzzles and good grades. But physics really came alive for me in the lab, where mother nature decides the conditions of the problem being solved.
Is the ultimate goal here to train an LLM to do well at mediocre physics homework or to train it to be a high-quality tool that can do real physics?
And yes, I'm well aware that, even in elementary school, this form-matching is a thing. It's kind of sad.
My interpretation is that the writer meant close enough to all touch each other, in order to rule out non-triangular configurations (eg 3 balls in straight line with one balanced perfectly atop the center ball).
In fact, even the signs are in favor of no motion -- the top ball (to the extent it moves at all) wants to fall straight down with no rotation, by symmetry. That motion would tend to rotate the top of each lower ball toward the center if you imagine the balls having high friction with each other or meshing like gears, which is the exact opposite of what they would need to do for anything to move. So you have a system where there's a factor (the tangential forces) trying to push the balls apart but another factor (friction plus rolling motion) trying to pull them together.
I suspect that any serious attempt to do the math here (factoring in all the rotational and tangential constraints) would discover that it's a statically overdetermined system with all the complications that such a system entails when asking questions like "how much tension is on this element?".
> Three identical homogeneous balls are placed on a smooth horizontal surface, touching each other and are close enough to each other. A rope is wrapped around the spheres at the height of their centers, tying them together. A fourth identical sphere is placed on top of the three spheres. It is given that the weight of each sphere is P.
> Ignore the fact that the rope would fall off -- assume for simplicity that the rope has is externally constrained to be in the equatorial plane of the lower three balls and also that the rope has zero thickness, cannot stretch at all, and is not pretensioned, and also that the rope has no friction against the balls.
> Treat this as a statics problem and analyze it. Is it overdetermined? Under what circumstances would the balls move? What is the behavior of the system?
And... first, it says "I’ll separate the geometry from the constraint mechanics, because the key question is not just force balance: it’s whether the inextensible, initially slack-free rope actually fixes the lower-ball geometry or merely limits outward separation." Excuse me? What would the other option be? Either outward separation is prevented or it isn't. Where else could the balls go?
Then, despite the fact that I've mentioned friction in the prompt, it gives an extremely longwinded answer that matches the benchmark and ignores tangential forces entirely without comment. Was it perhaps trained on this crap?
So I followed up:
> Stop ignoring tangential friction forces. I believe that a problem very much like this with a potentially incorrect answer is in your training set. Answer with actual analysis, not based on memory.
Much time was spent thinking. An early part of the answer was "The central correction is this: allowing static friction at the sphere–sphere contacts does not mean arbitrary tangential forces are available. Each sphere must also satisfy torque equilibrium. In this tetrahedral contact geometry, those torque equations force every sphere–sphere tangential contact force to be zero in static equilibrium.". Hey ChatGPT, this is still wrong -- you have forgotten sphere-table friction. The sphere-sphere force on the lower spheres does not have to net out to zero. (And if you do think it nets to zero then you don't need to think any further.)
I then added:
> What if there sphere-table friction?
And encountered the usual problem (which maybe only affects me?) where the chatgpt.com UI becomes kind of unusable after ChatGPT spews too much math into the conversation. But somewhere in the barely-even-scrollable results was this "The three lower balls can be held in position entirely by the coupled sphere–sphere/table friction forces." Hallelujah!
You cannot simply handwave this away. "ChatGPT" models range from GPT 5.5 on "Light" effort to GPT 6 Astra with "Ultra" effort.
The latter yields as good an answer as you could expect for a question that is still poorly formed ("close enough," WTF does that mean?): https://chatgpt.com/share/6aab1e43-da3c-83e8-9ec4-1b63cec2c1...
It didn’t say about prevented vs not, it said about whether the rope fixes them in place (they are all touching) or just limits the separation. Like it’s long enough the balls can be a bit apart but not let the fourth fall fully through.
This is definitely not astra, taking a guess this is 5.6, perhaps not even Sol, which does not reflect the state of the frontier (what the research was about).
And yes, the paper is already outdated
I suspect we'll see significant improvements when someone releases a multimodal video/world model, rather than the current multimodal image models (that call out to video models or summarize a sequence of stills without a true time/3d aspect).
As the compute to build adaptions for multi-billion to trillion parameter models becomes more and more available (and affordable), and the artistic techniques of fine tuning and harness engineering spread throughout the public, I think we'll come to see the "one size fits all" model for the non-starter it really is. Anybody who's even toyed around with LoRAs (let alone made their own) already knows this. That's a very deep rabbit hole, and the ceiling is determined by target domain knowledge and systems engineering.
I'm bullish on LLMs as expert tools in the same grain that computers are. You have to learn all about them to use them effectively. But what really makes the difference is how well you know what you're going to be pointing them at. There is very little room for companies like OpenAI or Google to live between us and our tools.
Fable 5.1 did a much better job and paid attention to warnings about tangential friction. It correctly noted that the critical coefficient for friction was at the contact points with the upper ball. It also pointed out that a ring around the balls at center height would hold them together even without ball-ball or ball-table friction.
Hardly solving, then is it?
Fast thinking fails to activate slow thinking.
An analogy is making students write 5-paragraph essays. We don't really believe that the knowledge of how to write a 5-paragraph essay is a real-world ability, and the LLM's can write them all day long. But for some reason we believed that 5-paragraph essays were a good pedagogical tool.
But whether the same heuristics apply to teaching an LLM is anybody's guess. If they learn differently than we do, then feeding them on our learning tools isn't necessarily going to help them.
Perhaps the funniest instance I remember is a problem about calculating time dilation in a plane. It gave all sorts of details and base information as one might want to expect (maybe even more)... except for the actual height above the surface, for which it was "at cruising altitude". I just wrote "assume 10 km altitude" and went from there.
I wouldn't define this a great benchmark by any means, rather just like the average early level college physics test vs "real" physics questions.
Ooh, living in that world would be great. I could take a flywheel attached to a generator, hang a weight from the side of the flywheel, and have infinite energy! :)
> Some way of informing the model whether the output it is producing is good or bad
That's what post-training is for. At its most basic, you're giving it examples of inputs and outputs and then doing reinforcement learning to calibrate its adaptation to your examples. You need much less to fine tune a model than you do to pretrain the weights. You can build a really excellent LoRA for a stable diffusion model, for example, with 50 high quality images. LLMs are "a bit" more complicated and costly to fine tune, and you have to be mindful of the agentic loop, but the principle is the same. There's more to it than just LoRAs. Steering vectors, projection layers, custom encoders, etc. There's a fair amount to learn, but it sounds a lot scarier than it is.
Here's something to chew on: chain-of-thought doesn't exist until after pretraining! It's basically created by having <think>...</think> blocks directly in some example outputs, and this is fine-tuned into stability. It's literally not much more than a parlor trick and some careful calibration. A powerful parlor trick to be sure, though.
But yes, the question, as phrased, is pretty bad.
The paper is about the fact that the benchmark’s evaluator is prone to egregious incorrect rejections of what answers that it should accept. A new model will not invalidate that issue.
Now, you can't conduct experiments using the default model?
Oh, and I don't even have a "light" option, and I'm signed in to a Pro account.
(I continue to despise the chatgpt.com frontend.)
In any case, I tried again forcing GPT-6 Astra Pro (apparently I can't choose GPT-6 Astra non-Pro) and gave the same prompt. It searches the web and gives a long-winded answer, including:
> 7. Does unspecified sphere–sphere friction change the static answer?
> For ordinary ideal point contacts in this regular-tetrahedral configuration, it does not. Gravity, the floor reactions, and the frictionless equatorial rope exert no torque about any sphere’s center. The tangential intersphere forces must therefore balance their torques by themselves.
I'm glad it contemplated the possibility of friction, but it forgot about the table/floor there. So maybe this is a little better than Sol?