Neural Networks Are Still Waiting for Their Thermodynamics

In October 2024, Training Data hosts Sonya Huang and Pat Grady sat down with Dan Roberts, a former Sequoia AI Fellow who had just joined OpenAI as a researcher. The episode was recorded on his second-to-last day at Sequoia, before he knew he would become a core contributor to o1, internally known as Strawberry. Roberts is a quantum physicist who did undergraduate research on invisibility cloaks, earned a PhD at MIT, and completed a postdoc at the Institute for Advanced Study in Princeton. The hosts wanted two things from him: what physics can teach AI, and what AI might teach physics about how the world works.

Asked who he is, Roberts reaches for a stock answer he still believes: he was an annoying three-year-old who never grew up. His 19-month-old son follows the washing-machine repairman around the house just to look inside the drum, and Roberts says he simply kept that habit into adulthood. People who are more quantitatively oriented than not, he argues, tend to veer into physics rather than philosophy when they keep asking how the world works. The inward-facing questions about people felt less quantitative to him, more like the humanities; the outward-facing stuff—what is all this other material in the universe—was what pulled him in.

Huang jokes that they should be recruiting the 19-month-old already. Roberts reports that the child has grown out of a Sequoia onesie and into a toddler T-shirt, and is “ready to be a future founder.” It is a light beat, but it sets the tone for the rest of the conversation: curiosity as a method, not a personality quirk. A physicist who never stopped looking inside the machine is about to explain why that habit is useful in AI labs.

The switch toward AI did not happen in undergrad. Roberts took an AI class that was classic good-old-fashioned AI: hardcoded if-this-then-that rules, plus some game playing. He found it algorithmic and interesting, but unrelated to what it means to be intelligent, and he wrote the field off. Grady interrupts with the question Roberts does not have a stock answer for: what *does* it mean to be intelligent? Roberts is careful not to “say nonsense.” What excites him is systems that do what humans do, and the chance to trace a few lines of Python through to an output—classifying a cat, writing a poem.

That, he says, is a much shorter chain than studying human intelligence, which requires going from biology through neuroscience through psychology to higher-level accounts. AI takes pieces of what humans do and offers a simple, studyable example. He then went to the UK for the first part of graduate school, discovered machine learning, and found a statistical approach that made sense: you have examples of a task, you write a flexible algorithm, and it adapts. He graduated college in 2009, found machine learning in 2010–2011, and 2012 was the big year for deep learning. He got lucky, he says: a scientific framework he understood started to show real progress almost immediately.

Why so many ex-physicists in AI? Roberts says yes to coincidence, herd behavior, *and* genuine fit. Physicists have infiltrated many subjects with their hammers; historically, those who left academia went into quantitative finance, then data science. Machine learning felt different because it feels a lot like actual physics, on a problem everyone is excited about. The methods also differ from traditional computer science. Physics lives on a tight loop between theory and experiment: propose a model, run experiments, collect data, invent toy models, and move understanding forward. Deep learning works the same way, and the math overlaps with what physicists already know. Those tools, he adds, also differ from theoretical computer science and theoretical machine learning.

Grady points to Roberts’s essay *Black Holes and the Intelligence Explosion*, which distinguishes a microscopic view from a system-level view, and asks how physics trains people for the latter. Roberts starts with something he says goes further than an analogy. Around the Industrial Revolution, engineers built steam engines first. Thermodynamics arrived later as a high-level theory: the ideal gas law relates pressure, volume, and temperature—macro quantities you can measure with a thermometer, a barometer, or the volume of a room. Underneath are air molecules bouncing around, which nobody sees day to day.

Later, statistical physics derived the ideal gas law from those molecules, then derived the corrections, because the ideal gas law is wrong: it is a toy model. The microscopic picture is invisible; the macroscopic quantities are stable, measurable, and predictive. Roberts thinks something similar is going on with deep learning. He wrote a book with Sho Yaida and Boris Hanin—*The Principles of Deep Learning Theory*—to start applying those methods. The micro perspective is neurons, weights, and biases: a simple set of equations, not many lines of code, but an astronomical number of parameters. The macro perspective is what the system *did*: it wrote a poem, it solved a math problem.

For statistical physics, that derivation is complete. For neural nets, it is the open project: how does the underlying micro statistical behavior of the model lead to the system-level behavior we actually care about? That gap, in Roberts’s framing, is the missing thermodynamics of deep learning. The weights are the molecules; the poem is the temperature. Until the field can derive one from the other, scaling and engineering will keep outrunning theory.

Huang cites Andrej Karpathy at Sequoia’s AI Ascent: current AI systems look five or six orders of magnitude less efficient than biological neural nets. Roberts splits that into two questions. The first is human learning efficiency. His toddler is already speaking in sentences and has been exposed to far fewer tokens than a typical large language model. Humans and models are designed differently and learn differently, so some gap is expected—but the gap also means there is room to bridge. The second question is the one he thinks actually belongs to scaling laws: what is the final GPT?

GPT-4 exists now. Will it be six, or seven? If we have to keep scaling, something breaks: economic limits, if a training run exceeds world GDP; production limits, if we cannot make enough GPUs; physical limits, if compute covers the surface of the Earth. “Probably the economic one happens first.” The practical question is how many more iterations we get before we cannot scale, and where that gets us. You cannot fully disentangle scale from efficiency, because everyone is making models more efficient at the same time. Still, he asks a cleaner thought experiment: take GPT-2, the first big model, and keep scaling it. Does that get us to the economically interesting end state of AI?

The general scaling hypothesis says it is just the scaling, and the ideas do not matter. Getting to human-like efficiency, Roberts thinks, requires non-trivial ideas. That is why he is excited to join OpenAI: there is high leverage in going beyond scaling, and the field will need that for the next steps. He has no idea what he will be working on—when the episode airs, he jokes, he will know. The bet is not that scale is unimportant. It is that scale alone will not close the efficiency gap Karpathy named.

Grady asks whether the field has a pendulum: Transformers were a great idea, then came a race to scale, and now, as scaling starts to asymptote, is the currency swinging back toward architectural breakthroughs? Roberts cites Richard Sutton’s essay *The Bitter Lesson*, which he summarizes as the claim that ideas are not important and scale always trumps them. There is a grain of truth. Interesting ideas from the 1980s and 1990s lacked the scale to be explored; after AlphaGo, people at DeepMind rediscovered old papers and reimplemented them in deep learning. Even now, researchers try architectures other than Transformers, including simpler ones, on the theory that scaling laws come from the data process rather than from a special idea—so long as the architecture “isn’t sick.”

His own answer is a balance. Scale is hugely important, and that importance was underappreciated; the field also lacked the resources to scale. GPUs and models have co-evolved, and Transformers were a good idea in part because they were designed to train well on the hardware of the time. Other architectures might work at an ideal scientific level, but practically you needed something that could reach scale. Deep learning itself was an idea: McCulloch and Pitts proposed a neuron, Rosenblatt built the perceptron, and eighty years of discoveries sit underneath today’s clusters. When people are bottlenecked, they think about ideas; when a new capacity of scale unlocks, results explode and scale looks like everything. He calls it a synergy, not a swing.

Huang then asks whether the race to scale requires a Manhattan Project at the nation-state or international level. Roberts tells a story from the process that led him to OpenAI. Talking with Sequoia partner Shaun Maguire about whether a startup made sense, Maguire said that in the 1940s, physicists went to the Manhattan Project even if they were doing other things—“that was the place to be.” Now AI is the same thing, and OpenAI is that place. Roberts is careful about the analogy: not the negative impact of the original project, but the scale and organization. Maybe the field does not need a public-sector Manhattan Project. It can be OpenAI. Grady loves the line and immediately flags that it should not be taken out of context; they settle on a metaphorical Manhattan Project of scale and ambition.

Can we ever understand deep neural nets, or are they a hopeless black box? Roberts offers this as his contrarian position inside AI communities: we can really understand these systems. Physics systems are extremely complicated, and humans have made huge progress on them; neural nets sit in the same framework. A principle he and Yaida discuss in their book is that extreme simplicity often appears at very large scales, from statistical averaging—more technically, the central limit theorem. He is not claiming that this is exactly what happens in large language models. He does think the methods transfer, and that AI tools (not autonomous intelligences running on their own) can help apply them. At the extreme, this will not stay an art. The science will catch up.

What can AI teach physics? He is optimistic, but he ranks math as easier than physics—which, he notes, betrays that he is a physicist, not a mathematician. Friends still in physics describe a growing sense approaching dread: if what you care about is the answer to your physics question, the highest-leverage move might be to work on AI and wait for it to solve the physics. He does not know how seriously anyone takes that, but in the theoretical physics community he comes from, it gets discussed. On the object level, he points to Noam Brown’s long-standing argument about inference-time compute. In a hard game position you sit and think rather than playing on intuition; games have a clear win/loss signal, so you can simulate ahead. Some math problems are less constrained than games but still have a notion of the next *move* in a proof. Doing well at games, he thinks, is a reason to expect progress on certain kinds of mathematical discovery. Brown likes the Riemann hypothesis as the example.

Physics questions have a different flavor. There is a Millennium Prize problem related to the Yang–Mills mass gap, but Roberts thinks what physicists care about often does not look like a proof. Physicists are informal and hand-wavy, saved by the interplay with experiment and by explanations that actually account for things. Engineers invent the machines, physicists clean up the theory, mathematicians formalize it later. The interesting questions are less “solve this model” than “what is the right model, does it capture the thing you care about, what insights should you draw?” Those do not look like “start generating tokens.” What is quantum gravity? What happens when something goes into a black hole? In a physics department people hang out at the blackboard, chat, and sketch. The useful data might look like Slack conversations, emails, and scratch work. Short-term, AI is an accelerator: help me understand this paper so I do not spend two weeks on it—the way Mathematica does integrals, and, he apologizes to Stephen Wolfram, a lot more than integrals.

Huang asks why people go after the hardest school subjects—physics, math—instead of other unsolved domains. Roberts pushes back: these may be the *easy* domains. Biology makes no sense to him; his girlfriend works in bioengineering and biotech, and he cannot understand any of it. Math is unembodied and self-sufficient, close to how language models generate text and how reinforcement learning plays games. The further you go from that, the messier it gets, and the harder it is to get the right data. A self-sustaining AI biologist would need robotics, experimental design, and the right data formats, or humans in the loop. Along the way there will be artifacts like AlphaFold 3, which DeepMind is trying to use for drug discovery. Hard for a human is not the same as hard for a machine. As for whether it all coalesces into one big model, the big labs seem to be going that way; mixture-of-experts was originally meant to be that and is not, in practice. Speculation in this field, he warns, is dangerous, because everything you say is wrong, usually sooner than people will hold you to it.

In a lightning round, Grady asks what Roberts is most optimistic about at five months, five years, and five decades. Roberts starts at five years. Five years ago was around GPT-2, after Transformers; the last five years have been about scaling. He imagines that within the next five, scaling will terminate. Maybe it terminates in a utopia, everyone post-economic, Sequoia shutting down its funds and returning Monopoly money because money will not matter. Or we discover we need lots of ideas, and maybe there is another AI winter. Something interestingly different will be true of AI within five years, he thinks—even if that difference is that AI is over and capital has moved on.

On the five-month scale he wants the delta between the next generation of models. Scaling laws relate to loss, which is hard to translate into capabilities. What will it feel like to talk to the next model, and will it have a huge economic impact? Estimating velocity takes more than one data point. GPT-3 to GPT-4 gave a first interval; the next delta will show what model-to-model progress actually feels like. He jokes that in physics there are only three numbers that matter—zero, one, and infinity—and that venture capitalists are as hand-wavy as physicists. Five months from now he may have a better prediction, and he probably will not be able to tell them.

Grady also asks about Roberts’s accessible, funny technical writing. It is deliberate. At lunch as an IAS postdoc, he argued with professor Nathan Seiberg about titles and jokes. Roberts insisted that the reason to write a paper is the jokes: you package them inside the science so people who want the science are forced to suffer through them. Seiberg did not get it—why not just write for the science? A roommate, now a linguistics professor at UT Austin, later taught him which rules he could break and where the rules come from. The ultimate test is whether the reader will read, understand, and enjoy it. You do not want to compromise comprehension, but if it is more enjoyable, people are more likely to take the point, and it is more fun to write. That is the same instinct he is taking into an AI lab: make the system-level story readable, then let the science catch up.