Article: "How Good Are Frontier Models at Physics?
Expert Re-Grading Reveals Broken Evaluations and
Near-Saturation of Leading Benchmarks"
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.
I would be very surprised if any of the frontier models wasn't trained on all public physics benchmarks. Training data providers have been hiring people for exactly this task.
yeah, it would be almost shocking if an open source benchmark was NOT used ~somewhere in training. Perhaps just pre-training, but still.
Neural networks can be fairly robust to some mistakes in their training data, so maybe it doesn't even matter if some of them are incorrect. Who knows.
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.
This tracks with my experience. A core and integral part to make models actually shine involves post training and custom harness engineering, all specifically done for the purpose of getting them to settle into competent inputs and outputs that are relevant to you, optimized for the harness you build which better suits your domain. The weights are just a generalization. A block of marble to be sculpted.
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.
Sorry not an AI specialist, what exactly do you mean by 'custom harness engineering'? Some way of informing the model whether the output it is producing is good or bad based on the specific task in question?
Harnesses are the control surface the model interacts with. How it invokes tools, the tools it has access to, how agents are coordinated. It's like an interface or a shell. It's the magic that lets an LLM operate a computer. You can read more here: https://learn.microsoft.com/en-us/agent-framework/concepts/h...
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.
Also a trained physicist. Don’t you need tension to stop the weight of the top ball pushing the 3 supporting balls outward?
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).
If you have high friction (the problem said "smooth" not "slippery"), then the only way the supporting balls can go anywhere is by rolling apart. But the ball sitting on top cannot simultaneously rotate in a manner compatible with all of the lower balls rolling away, so the lower balls would need to slip against the top ball if the top ball were to move downward.
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?".
I would think of "smooth" as meaning "not having relevant bumps", in the way that a baseball has stitches and a rough surface has the kinds of bumps that would cause a rolling ball to experience vertical motion.
You need tension if the sphere-table contact is frictionless. But without friction the rope can’t stay on. If there is friction in the rope, there can’t be 0 tension in the rope before you put the top ball on because you need that tension to produce the rope/sphere friction.
Replying to myself: this is fun! Let's ask ChatGPT (whatever model the website currently feels like using) an improved question:
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!
When I click your share, it shows the model. When I click into my chat, it just says "High". I did ask the model what it was and it said "GPT-5.6 Sol".
Yeah, it's strange that people who should be knowledgeable in experimentation ignore that. "I heard that people enjoy skiing. I've tried skiing on whatever surface happened to be on a nearby hill and it didn't work!"
Excuse me? What would the other option be? Either outward separation is prevented or it isn't. Where else could the balls go?
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.
Have you tried Fable? I've been having fun running various science-fictional scenarios by it, like building a Dyson swarm. It comes up with much more detailed analyses than Opus, and avoids the howling mistakes that Opus occasionally made. But I'm not a physicist so I don't know how accurate it is.
I'm also a trained physicist, spent some time in industry, and taught a college freshman math class for a semester a couple decades ago.
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.
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.
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.
The odd thing is that we do train people to do real physics, somehow despite my cynical take. I see the education process as following heuristics that are believed to have some relationship to developing real world abilities, even if we don't know why. We all worked these problems, and now we're somehow able to do physics. In the end we don't know what turns people into physicists. Or musicians, artists, etc.
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.
Article: "How Good Are Frontier Models at Physics? Expert Re-Grading Reveals Broken Evaluations and Near-Saturation of Leading Benchmarks"
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.
I would be very surprised if any of the frontier models wasn't trained on all public physics benchmarks. Training data providers have been hiring people for exactly this task.
This study appears to be evidence against that: the model failed the benchmark but arrived at the correct answer.
Half of the benchmarks don't have published answers. That's why training data providers have been hiring physicists to solve them.
yeah, it would be almost shocking if an open source benchmark was NOT used ~somewhere in training. Perhaps just pre-training, but still. Neural networks can be fairly robust to some mistakes in their training data, so maybe it doesn't even matter if some of them are incorrect. Who knows.
This is interesting and actually very important for robotics.
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.
(Trained physicist here)
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:
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.
This tracks with my experience. A core and integral part to make models actually shine involves post training and custom harness engineering, all specifically done for the purpose of getting them to settle into competent inputs and outputs that are relevant to you, optimized for the harness you build which better suits your domain. The weights are just a generalization. A block of marble to be sculpted.
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.
Sorry not an AI specialist, what exactly do you mean by 'custom harness engineering'? Some way of informing the model whether the output it is producing is good or bad based on the specific task in question?
Harnesses are the control surface the model interacts with. How it invokes tools, the tools it has access to, how agents are coordinated. It's like an interface or a shell. It's the magic that lets an LLM operate a computer. You can read more here: https://learn.microsoft.com/en-us/agent-framework/concepts/h...
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.
Also a trained physicist. Don’t you need tension to stop the weight of the top ball pushing the 3 supporting balls outward?
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).
If you have high friction (the problem said "smooth" not "slippery"), then the only way the supporting balls can go anywhere is by rolling apart. But the ball sitting on top cannot simultaneously rotate in a manner compatible with all of the lower balls rolling away, so the lower balls would need to slip against the top ball if the top ball were to move downward.
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?".
Doesn’t smooth in these contexts mean zero friction?
I would think of "smooth" as meaning "not having relevant bumps", in the way that a baseball has stitches and a rough surface has the kinds of bumps that would cause a rolling ball to experience vertical motion.
But yes, the question, as phrased, is pretty bad.
You need tension if the sphere-table contact is frictionless. But without friction the rope can’t stay on. If there is friction in the rope, there can’t be 0 tension in the rope before you put the top ball on because you need that tension to produce the rope/sphere friction.
Replying to myself: this is fun! Let's ask ChatGPT (whatever model the website currently feels like using) an improved question:
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:
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:
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!
whatever model the website currently feels like using
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...
When I click your share, it shows the model. When I click into my chat, it just says "High". I did ask the model what it was and it said "GPT-5.6 Sol".
(I continue to despise the chatgpt.com frontend.)
Yeah, it's strange that people who should be knowledgeable in experimentation ignore that. "I heard that people enjoy skiing. I've tried skiing on whatever surface happened to be on a nearby hill and it didn't work!"
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.
Have you tried Fable? I've been having fun running various science-fictional scenarios by it, like building a Dyson swarm. It comes up with much more detailed analyses than Opus, and avoids the howling mistakes that Opus occasionally made. But I'm not a physicist so I don't know how accurate it is.
I'm also a trained physicist, spent some time in industry, and taught a college freshman math class for a semester a couple decades ago.
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.
The odd thing is that we do train people to do real physics, somehow despite my cynical take. I see the education process as following heuristics that are believed to have some relationship to developing real world abilities, even if we don't know why. We all worked these problems, and now we're somehow able to do physics. In the end we don't know what turns people into physicists. Or musicians, artists, etc.
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.
Nice thanks for sharing this!