ᴘᴇᴛᴇʀ ɢ. ᴄʜᴀɴɢ

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@petergchang

PhD Student | @MIT EECS (with @m_sendhil) | AI for Scientific Understanding

Cambridge, MA petergchang.github.io Joined May 2022

864 Following 256 Followers 73 Posts

Latest posts 5

ᴘᴇᴛᴇʀ ɢ. ᴄʜᴀɴɢ @petergchang Oct 13

Relatedly, this is how basically every jazz musician trains, by transcribing old masters (i.e., listening to solos over and over again, often writing down the notes, until you can play along).

When first learning to transcribe, students often mistakenly think that the point of transcriptions is to learn to play the notes. Especially students who’ve already had some classical music training often make this mistake, myself included. But the point of transcriptions is to imitate the mental process that resulted in the notes being produced, and not to merely imitate the notes themselves. (As Rich Sutton likes to point out) This is a crucial distinction, as learning to play the notes requires a completely different mental process from one required to improvise the notes in real time.

Clearly, there is no hope in you ever being able to imitate in full fidelity the entire thought process of Miles Davis as he blows through a nasty solo. There are infinitely many mental processes that could improvise the notes that he plays (Rashomon effect). But that is the entire point of transcriptions! You learn your own digested version that is compatible with your own sensibilities, and the accumulation of these “world models” is what comes to define your own artistry and style.

Joshua Achiam Verified account @jachiam0 Oct 13

I was talking with someone earlier today about the process of becoming a stronger writer and what it takes to get better at clearly explaining ideas - I forgot to mention one really helpful tip, and thought it would be good to share broadly. Try to write style imitations of writers you like! Spend time trying to work out how they structure their arguments and how to replicate that argument structure. Do special effects tests where you try to write like them and see if what you produce can inspire the same feelings in you as the original author's writing. The old masters in many other domains of art learned by imitation; writing is not so different in this respect.
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ᴘᴇᴛᴇʀ ɢ. ᴄʜᴀɴɢ @petergchang Oct 6

This reminds me of the time I sought advice from my academic advisor (a very famous theoretical physicist) as a starry-eyed junior about potentially applying for graduate school in theoretical physics. He asked me why I wanted to pursue physics; I muttered some grandiosity about wanting to make a significant contribution. He ended our meeting by confessing that he strongly believes that even if Einstein hadn’t existed, progress in physics would have been delayed by at most five years.

Now, if a young, ambitious student seriously believed this thesis (that scientific progress cannot be meaningfully perturbed by any individual scientist), then what path should they take?

First is to go into a field which brings them great personal joy. Second is to go into engineering. The apparent determinism in the sciences is not so apparent in fields like computer science; TeX wouldn’t exist if Donald Knuth hadn’t invented it, the Transformer architecture in its current state, arguably, would not exist if not for the several individuals that engineered it to existence. The third option is to go into a scientific field where expedition of a discovery even by a few months or even days has a significant tangible impact; I would put medical research in this category.

To end on a more optimistic note: at the time, I was dejected and struck by his apparent cynicism. But looking back I realize he told me just what I needed to hear at the time. AI for Science, the field that I’ve ended up in somehow via a series of serendipities, is an extremely compelling path, certainly for me and I’m sure for many others.

Noah Smith 🐇🇺🇸🇺🇦🇹🇼 Verified account @Noahpinion Oct 6

Grigori Perelman and Andrew Wiles could have just taken it easy and worked mid-level marketing jobs, and we'd have gotten the solutions to the Poincare Conjecture and Fermat's Last Theorem before 2030 anyway
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ᴘᴇᴛᴇʀ ɢ. ᴄʜᴀɴɢ @petergchang Oct 5

Taste is a judgment about aesthetics. It’s easy to think that taste applies exclusively to the final artifact, but in fact it is more often a judgment on the creation process itself.

This is why a banana taped to a wall can sell for millions of dollars. It is also why OpenAI’s approach to solving Navier Stokes is widely regarded as low taste. People are judging the process of creation (deploy 10k agents) even before looking at the outcome.

It is also why the bitter lesson is so hard to swallow; there is beauty to the simplicity of the idea of the bitter lesson, but the lesson applied to any particular domain feels distinctively low-taste.

Dean W. Ball Verified account @deanwball Oct 5

Research taste in particular may be trickier than it looks. Say the next generation of AI really does have an interesting, high-taste set of research directions to pursue. Well presumably find those fast, after which the fruit will have been plucked, and the ideas will no longer be high taste (because they’ve been explored en masse). This is a similar dynamic to the ever-moving target of “slop.” *Any* output that is recognizably of the agents becomes slop, or at least commodified, in a sense, once that output is sufficiently promulgated in bulk. Certain styles of math paper will become (are becoming) slop. Certain styles of web design already are. On and on it will go. It’s unclear if any kind of media/intellectual output proliferated at such scale can remain high taste, even if we’d have considered it genius from a human just a few years ago.

The bar will continually be raised. The world will get smarter as what was once brilliance becomes commodified, but *what was once brilliance will nevertheless be commodified.* And so the definition of brilliant will change. The wedge for continued value creation by humans lies here, I would guess.
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ᴘᴇᴛᴇʀ ɢ. ᴄʜᴀɴɢ @petergchang Sep 30

I found this to be a deeply confused view of what writing is.

The professor identifies the two utilities of writing as: 1) a process of “achieving thought”; and 2) a summary of thought already achieved, and he claims that writing is useful as 2) but overrated as 1).

His evidence? When he teaches, he doesn’t prepare scripts and instead engages in conversations. Also, his students demonstrated more clarity of thought during oral exams than in their final essays.

His mistake is that he believes that the process of “achieving thought” exclusively lies in the response to whatever question posed by an external agent (his students during his lecture, himself during the oral exam). It is ironic that he brings up Socrates as a defender of his argument, since Socrates’ writing is the ultimate example of how clarity of thought is achieved through writing down the back-and-forth that is required to develop and mature an idea.

What writing allows is for the writer to play both parts: once the words are externalized, they are no longer the writer’s; this allows the writer to examine them and interrogate them. Thus, writing allows the writer to engage in the oral exam through oneself without relying on an audience.

Probing and asking questions that motivate development and movement of ideas is arguably the most important component in the process of achieving thought. The distinct lack of deep interrogation within the opinion piece perhaps is the biggest indictment of his thesis.

Steve McGuire Verified account @sfmcguire79 Sep 29

The head of the philosophy department at Williams College downplays the pedagogical value of writing:

“What if we are mistaken in treating writing as the highest cultivation of thought? The evidence that supports this belief is thin at best. Writing can be useful cognitive scaffolding for memory and self-regulated learning, but the notion that it is the best process for developing thinking skills is a fairly recent idea, traceable to the 1970s writing-across-the-curriculum movement.”

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ᴘᴇᴛᴇʀ ɢ. ᴄʜᴀɴɢ @petergchang Sep 26

I'm noticing a disproportionate level of hostility towards this project.

Are all theorems with long, incompressible proofs interesting? Of course not. But I would argue that "easy to state, hard to prove" is at least a defensible proxy for what is ultimately a subjective judgment, though “length of proof” as a proxy for “hard to prove” is perhaps a less defensible one. Overall I think it's a timely (perhaps too timely...) and very well-executed paper, and I hope to see more active academic research in the direction of explicitly training models to solve more ambitious scientific problems, as opposed to the current paradigm of setting up elaborate agentic frameworks and waiting for the frontier models to become “smarter”.

People’s reactions make more sense when considering the sudden loss of value of “length” as a proxy for insight, as evidenced by the deluge of hundred-page proofs that no one wants to read. There is a deep confusion in the field as to whether a theorem can be unconditionally interesting, i.e., whether a problem previously thought to be interesting can be retroactively made uninteresting by the existence of a slop proof (see the ambivalent reaction towards Navier Stokes).

Niket Patel Verified account @niketnpatel Sep 25

“An accumulation of facts is no more a science than a heap of stones is a house.” - Poincaré

LLMs are now proving results that have resisted mathematicians for decades. Finding interesting theorems without human guidance is a new bottleneck. We show that we can teach an LLM to do it!

TL;DR:
→ a quantitative notion of interestingness
→ 4.3× higher interestingness
→ a self-expanding discovery loop
[1/5]

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