David Udell

Ex­plain­ing GPT-2-Small For­ward Passes with Edge-Level Au­toen­coder Circuits

• David UdellJun 11, 2025, 3:06 AM

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  on: David Udell’s Shortform

  An excerpt from Richard Hamming’s The Art of Doing Science and Engineering with some relevance to AI coding:

  In the beginning we programmed in absolute binary, meaning we wrote the actual address where things were in binary, and wrote the instruction part also in binary!

  [...]

  If, in fixing up an error, you wanted to insert some omitted instructions, then you took the immediately preceding instruction and replaced it by a transfer to some empty space. There you put in the instruction you just wrote over, added the instructions you wanted to insert, followed by a transfer back to the main program. Thus the program soon became a sequence of jumps of the control to strange places. When, as almost always happens, there were errors in the corrections, then you used the same trick again, using some other available space. As a result the control path of the program though storage soon took on the appearance of a can of spaghetti. Why not simply insert them in the run of instructions? Because then you would have to go over the entire program and change all the addresses which referred to any of the moved instructions! Anything but that!

  We very soon got the idea of reusable software, as it is now called. Indeed, Babbage had the idea. We wrote mathematical libraries to reuse blocks of code. But an absolute address library meant each time the library routine was used it had to occupy the same locations in storage. When the complete library became too large we had to go to relocatable programs.

  [...]

  The first published book devoted to programming was by Wilkes, Wheeler, and Gill, and applied to the Cambridge, England EDSAC (1951). I, among others, learned a lot from it, as you will see in a few minutes.

  Someone got the idea a short piece of program could be written which would read in the symbolic names of the operations (like ADD) and translate them at input time to the binary representations used inside the machine (say $01100101$). This was soon followed by the idea of using symbolic addresses—a real heresy for the old time programmers. You do not now see much of the old heroic absolute programming (unless you fool with a handheld programmable computer and try to get it to do more than the designer and builder ever intended).

  I once spent a full year, with the help of a lady programmer from Bell Telephone Laboratories, on one big problem coding in absolute binary for the IBM 701, which used all the 32K registers then available. After that experience I vowed never again would I ask anyone to do such labor. Having heard about a symbolic system from Poughkeepsie, IBM, I asked her to send for it and to use it on the next problem, which she did. As I expected, she reported it was much easier. So we told everyone about the new method, meaning about 100 people, who were also eating at the IBM cafeteria near where the machine was. About half were IBM people and half were, like us, outsiders renting time. To my knowledge only one person—yes, only one—of all the 100 showed any interest!

  Finally, a more complete, and more useful, Symbolic Assembly Program (SAP) was devised—after more years than you are apt to believe, during which time most programmers continued their heroic absolute binary programming. At the time SAP first appeared I would guess about 1% of the older programmers were interested in it—using SAP was “sissy stuff,” and a real programmer would not stoop to wasting machine capacity to do the assembly. Yes! Programmers wanted no part of it, though when pressed they had to admit their old methods used more machine time in locating and fixing up errors than the SAP program ever used. One of the main complaints was when using a symbolic system you didn’t know where anything was in storage—though in the early days we supplied a mapping of symbolic to actual storage, and believe it or not they later lovingly pored over such sheets rather than realize they did not need to know that information if they stuck to operating within the system—no! When correcting errors they preferred to do it in absolute binary addresses.

  FORTRAN, meaning FORmula TRANslation, was proposed by Backus and friends, and again was opposed by almost all programmers. First it was said it could not be done. Second, if it could be done, it would be too wasteful of machine time and capacity. Third, even if it did work, no respectable programmer would use it—it was only for sissies!

  [...]

  With FORTRAN available and running, I told my programmer to do the next problem in FORTRAN, get her errors out of it, let me test it to see it was doing the right problem, and then she could, if she wished, rewrite the inner loop in machine language to speed things up and save machine time. As a result we were able, with about the same amount of effort on our part, to produce almost ten times as much as the others were doing. But to them programming in FORTRAN was not for real programmers!

  —Hamming (1996), pp. 45–8

• David UdellMay 1, 2025, 12:12 AM

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  on: David Udell’s Shortform

  Epistemic status: Just a confusion I once had, and how I eventually resolved it to my satisfaction.

  In ordinary differential equations, separability is a deductive rule stating that whenever you have a differential equation of the form

  $f\left(x\right)=g\left(y\right)\frac{dy}{dx}$

  you can then reason that

  $f\left(x\right)dx=g\left(y\right)dy$

  and then than

  $\int f\left(x\right)dx=\int g\left(y\right)dy$

  From the very first time I saw that, I was immediately off-put by that middle equation. What the hell does an expression like $f\left(x\right)dx$ (by itself) even mean? Until I saw this, I had figured that, apart from their weird notation, differentiation and integration were just plain-old multivariate functions. I had made sense of their notation by just ignoring it, basically. And when I held that point of view, the above deduction is just nonsensical.

  I also remember not getting good clarificatory answers about this at the time! I mostly recall being told to just ignore the middle equation and take the whole conditional on faith, as something that has been separately proven.

  Eventually, I learned that there was this idea in math called differential forms which gave a precise-and-everywhere-valid interpretation to the stand-alone expression $dx$. But you don’t quite need that machinery to resolve the above thing that bothered me.

  ---

  Did you know that “calculus,” is an abridgment of the original term “the infinitesimal calculus”? “The rules for soundly manipulating infinitesimal quantities,” basically. I did not know this when I first encountered this separability thing. There’s a whole saga, maybe even the main story in mathematics, about why that interpretation and corresponding terminology fell out of favor.

  The basic infinitesimal calculus idea (which is only sometimes, not always, a valid interpretation of the symbols) is that

  $\underset{\text{sum of their products over a range}}{\underset{}{\int }}\stackrel{\text{function value}}{\stackrel{}{f\left(x\right)}}\underset{\text{infintesimal quantity}}{\underset{}{dx}}$

  (I very vividly remember the moment when I discovered that the integral sign was just a stylized “S”, for “sum”!) Now you cannot everywhere use the above separability reasoning on the strength of the infinitesimal interpretation. Again, it’s not an everywhere-valid interpretation!

  Once you’re using any everywhere-valid interpretation, using any way of giving $dx$ and $\int$ their own independent meanings as symbols, though, the separability deduction just falls out! If two things are equal, you can multiply both by any mathematical object and get a true equation. It doesn’t matter what kind of mathematical object $dx$ is. If two things are equal, you can apply the same operation to both and get a true equation. It doesn’t matter what the integration summation operation amounts to, precisely.

Why Can’t We Hy­poth­e­size After the Fact?

• David UdellJul 10, 2024, 11:58 PM

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  in reply to: RogerDearnaley’s comment on: Causal Graphs of GPT-2-Small’s Resi­d­ual Stream

  I sampled hundreds of short context snippets from openwebtext, and measured ablation effects averaged over those sampled forward-passes. Averaged over those hundreds of passes, I didn’t see any real signal in the logit effects, just a layer of noise due to the ablations.

  More could definitely be done on this front. I just tried something relatively quickly that fit inside of GPU memory and wanted to report it here.

• David UdellJul 10, 2024, 11:02 PM

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  in reply to: RogerDearnaley’s comment on: Causal Graphs of GPT-2-Small’s Resi­d­ual Stream

  Could you hotlink the boxes on the diagrams to that, or add the resulting content as a hover text to areas, in them or something? This might be hard to do on LW: I suspect some Javascript code might be required to do this sort of thing, but perhaps a library exists for this?

  My workaround was to have the dimension links laid out below each figure.

  3: [14555]

  4: [5030]

  5: [10603]

  6: [3290]

  7: [4330]

  My current “print to flat .png” approach wouldn’t support hyperlinks, and I don’t think LW supports .svg images.

• David UdellJul 9, 2024, 11:41 PM

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  in reply to: the gears to ascension’s comment on: Causal Graphs of GPT-2-Small’s Resi­d­ual Stream

  That line was indeed quite poorly phrased. It now reads:

  At the bottom of the box, blue or red token boxes show the tokens most promoted (blue) and most suppressed (red) by that dimension.

  That is, you’re right. Interpretability data on an autoencoder dimension comes from seeing which token probabilities are most promoted and suppressed when that dimension is ablated, relative to leaving its activation value alone. That’s an ablation effect sign, so the implied, plotted promotion effect signs are flipped.

Causal Graphs of GPT-2-Small’s Resi­d­ual Stream

• David UdellApr 23, 2024, 10:15 PM

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  on: David Udell’s Shortform

  The main thing I got out of reading Bostrom’s Deep Utopia is a better appreciation of this “meaning of life” thing. I had never really understood what people meant by this, and always just rounded it off to people using lofty words for their given projects in life.

  The book’s premise is that, after the aligned singularity, the robots will not just be better at doing all your work but also be better at doing all your leisure for you. E.g., you’d never study for fun in posthuman utopia, because you could instead just ask the local benevolent god to painlessly, seamlessly put all that wisdom in your head. In that regime, studying with books and problems for the purpose of learning and accomplishment is just masochism. If you’re into learning, just ask! And similarly for any psychological state you’re thinking of working towards.

  So, in that regime, it’s effortless to get a hedonically optimal world, without any unendorsed suffering and with all the happiness anyone could want. Those things can just be put into everyone and everything’s heads directly—again, by the local benevolent-god authority. The only challenging values to satisfy are those that deal with being practically useful. If you think it’s important to be the first to discover a major theorem or be the individual who counterfactually helped someone, living in a posthuman utopia could make things harder in these respects, not easier. The robots can always leave you a preserve of unexplored math or unresolved evil… but this defeats the purpose of those values. It’s not practical benevolence if you had to ask for the danger to be left in place; it’s not a pioneering scientific discovery if the AI had to carefully avoid spoiling it for you.

  Meaning is supposed to be one of these values: not a purely hedonic value, and not a value dealing only in your psychological states. A further value about the objective state of the world and your place in relation to it, wherein you do something practically significant by your lights. If that last bit can be construed as something having to do with your local patch of posthuman culture, then there can be plenty of meaning in the postinstrumental utopia! If that last bit is inextricably about your global, counterfactual practical importance by your lights, then you’ll have to live with all your “localistic” values satisfied but meaning mostly absent.

  It helps to see this meaning thing if you frame it alongside all the other objectivistic “stretch goal” values you might have. Above and beyond your hedonic values, you might also think it good for you and others to have objectively interesting lives, accomplished and fulfilled lives, and consumingly purposeful lives. Meaning is one of these values, where above and beyond the joyful, rich experiences of posthuman life, you also want to play a significant practical role in the world. We might or might not be able to have lots of objective meaning in the AI utopia, depending on how objectivistic meaningfulness by your lights ends up being.

  Considerations that in today’s world are rightly dismissed as frivolous may well, once more pressing problems have been resolved, emerge as increasingly important [remaining] lodestars… We could and should then allow ourselves to become sensitized to fainter, subtler, less tangible and less determinate moral and quasi-moral demands, aesthetic impingings, and meaning-related desirables. Such recalibration will, I believe, enable us to discern a lush normative structure in the new realm that we will find ourselves in—revealing a universe iridescent with values that are insensible to us in our current numb and stupefied condition (pp. 318-9).

• David UdellMar 29, 2024, 1:00 AM

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  in reply to: Scott Garrabrant’s comment on: The Cog­ni­tive-The­o­retic Model of the Uni­verse: A Par­tial Sum­mary and Review

  I believe I and others here probably have a lot to learn from Chris, and arguments of the form “Chris confidently believes false thing X,” are not really a crux for me about this.

  Would you kindly explain this? Because you think some of his world-models independently throw out great predictions, even if other models of his are dead wrong?

• David UdellNov 1, 2023, 10:17 PM

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  on: David Udell’s Shortform

  Use your actual morals, not your model of your morals.

• David UdellSep 26, 2023, 12:47 AM

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  in reply to: Charlie Steiner’s comment on: Sparse Cod­ing, for Mechanis­tic In­ter­pretabil­ity and Ac­ti­va­tion Engineering

  I agree that stronger, more nuanced interpretability techniques should tell you more. But, when you see something like, e.g.,

  25132 ▁vs, ▁differently, ▁compared, ▁greater, all, ▁per
  25134 ▁I, ▁My, I, ▁personally

  isn’t it pretty obvious what those two autoencoder neurons were each doing?

• David UdellSep 23, 2023, 7:20 PM

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  in reply to: LawrenceC’s comment on: Sparse Cod­ing, for Mechanis­tic In­ter­pretabil­ity and Ac­ti­va­tion Engineering

  No, towards an $L^0$ value.$L^1$ is the training proxy for that, though.

Sparse Cod­ing, for Mechanis­tic In­ter­pretabil­ity and Ac­ti­va­tion Engineering

Ac­tAdd: Steer­ing Lan­guage Models with­out Optimization

• David UdellJul 24, 2023, 10:58 PM

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  on: David Udell’s Shortform

  Epistemic status: Half-baked thought.
  
  Say you wanted to formalize the concepts of “inside and outside views” to some degree. You might say that your inside view is a Bayes net or joint conditional probability distribution—this mathematical object formalizes your prior.

  Unlike your inside view, your outside view consists of forms of deferring to outside experts. The Bayes nets that inform their thinking are sealed away, and you can’t inspect these. You can ask outside experts to explain their arguments, but there’s an interaction cost associated with inspecting the experts’ views. Realistically, you never fully internalize an outside expert’s Bayes net.

  Crucially, this means you can’t update their Bayes net after conditioning on a new observation! Model outside experts as observed assertions (claiming whatever). These assertions are potentially correlated with other observations you make. But because you have little of the prior that informs those assertions, you can’t update the prior when it’s right (or wrong).

  To the extent that it’s expensive to theorize about outside experts’ reasoning, the above model explains why you want to use and strengthen your inside view (instead of just deferring to outside really smart people). It’s because your inside view will grow stronger with use, but your outside view won’t.

• David UdellJun 7, 2023, 12:43 AM

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  in reply to: noggin-scratcher’s comment on: The Base Rate Times, news through pre­dic­tion markets

  (Great project!) I strongly second the RSS feed idea, if that’d be possible.

• David UdellJun 1, 2023, 10:06 PM

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  on: Work dumber not smarter

  I think that many (not all) of your above examples boil down to optimizing for legibility rather than optimizing for goodness. People who hobnob instead of working quietly will get along with their bosses better than their quieter counterparts, yes. But a company of brown nosers will be less productive than a competitor company of quiet hardworking employees! So there’s a cooperate/​defect-dilemma here.

  What that suggests, I think, is that you generally shouldn’t immediately defect as hard as possible, with regard to optimizing for appearances. Play the prevailing local balance between optimizing-for-appearances and optimizing-for-outcomes that everyone around does, and try to not incrementally lower the level of org-wide cooperation. Try to eke that level of cooperation up, and set up incentives accordingly.

• David UdellMay 26, 2023, 3:43 AM

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  in reply to: David Udell’s comment on: David Udell’s Shortform

  The ML models that now speak English, and are rapidly growing in world-transformative capability, happen to be called transformers.

  This is not a coincidence because nothing is a coincidence.

Steer­ing GPT-2-XL by adding an ac­ti­va­tion vector