I always get annoyed when people misinterpret Occam’s razor. It’s not that the simplest is more likely to be correct, it’s that you should prefer it, because it’s simple.
It’s just like the Hopper quote. She said it’s better to ask for forgiveness during the fog of war, doing something you thought was right, not to do something you knew they were going to say no to and now you are trying to get away with something.
Another useful link [0], page 91. Effectively, the more complex the solution, the heavier is the upper bound on true risk. It doesn't mean a simpler model is necessarily better. But the complexity brings its own larger support for mistakes to live in. The _likelihood_ of being _more correct_ is probably related to larger sample required to learn a more complex model.
And I like the bayesian interpretation too. Murphy's "Probabilistic machine learning" has an occam's razor section.
The idea is that a complex model explains many more configurations (datasets) than a simple one. So its (prior) probability distribution is lower on the data seen (to compensate for the other possibilities it might explain). So the (marginal) likelihood that the simple model is correct is higher if it fits the data well enough.
This is a longstanding principle in model-fitting. More parameters, almost always, improves the ability of the model to fit to any particular data, in-sample. The model with the least parameters is both the simplest in principle and has the best chance of not overfitting.
The notion of "simplicity" can be completely arbitrary, though. It's enough that there are only finitely many hypotheses simpler than the best hypothesis (assuming there's such a thing as a best hypothesis). So as you eliminate hypotheses incompatible with the data, at some point you'll have eliminated all simpler hypotheses, and the simplest hypothesis left will also be the best hypothesis. If simpler hypotheses are also more likely to be correct, you get there faster, but it's not required.
It doesn't have to be arbitrary. The Kolmogorov/Solomonoff definition, that the simpler models are the shortest programs that can generate what we know about a domain, measured in bits, have a solid mathematical foundation, based on information entropy and even thermodynamic entropy if you cross over into computer hardware.
Entropy is a metric targeted in LLM training which is likely why LLMs are overfitting less and less as they improve and why they subjectively seem to obey Occam's razor.
There is some art to it, especially in model architecture choices.
But your smarter data scientists will try to get the best information density on test data to approximate generalization. MDL, as championed here, or AIC/BIC if working with more established and acceptable methods.
Except for the fact that eventually we are all dead.
So it is kind of important to get there faster.
For complicated hypotheses, where complicated is defined appropriately, it takes many many examples to realize that it was a wrong hypothesis all along. There lies the rub.
For a particular instance of a learning problem we can't tell much, however using a Occams razor over many instances, one would be correct more often than not. Provided, of course, the PAC assumptions are true or they are not very far from being true.
How far is not very far ? That gets very hairy to quantify.
To be clear, I was doing a reductio ad absurdum. PAC is precisely the kind of theoretical framework that concerns itself with asymptotic long-run behavior. An appropriate definition of simplicity certainly gets you to the goal much faster than the worst-case bound. For example, you could order hypotheses from most to less likely. But that would render the claim that simpler hypotheses are more likely rather tautological.
More typical definitions of simplicity, e.g. using the bit length of some kind of natural encoding, aren't guaranteed to offer any special advantages in terms of likelihood. So if you have prior knowledge that a particular hypothesis is more likely than another, but the less likely one is simpler in an intuitive sense, you shouldn't let that override you, but still prefer the more likely option. (And you don't need to take the circuitous route of coming up with a new encoding where the more likely hypothesis has a shorter bit length, either.)
There are also various metaphysical theories that posit that the universe is algorithmically generated in some sense or the other, and from many of those theories it follows that simplicity is a fundamental feature of reality, which yields an even stronger version of Occam’s Razor.
Not sure about Hopper, as I recall biographers of Lawrence of Arabia certainly made it seem like he was using the fog of war to do things he knew his superiors may object to.
Regardless, even if its misinterpreted it still has a kernal of truth and separate utility than your version, that is: the people in the field closest to the action have an operational awareness that may result in better decisions in times of urgency.
That's not true. It's pretty clear that she meant "do something you knew they were going to say no to and now you are trying to get away with something."
> So I want to tell something to all the young people here on many many occasions you'll find it is much easier to apologize than it is to get permission.
You do it then when somebody comes after you and say are you supposed to do that, "oh gee I didn't know I wasn't supposed
to do that" ...
so just remember it's frequently much easier to apologize than it is to get permission do it
She goes on further, explaining how to deceive your superiors to manipulate them to get what you want.
But I still don’t think that means eat all the cookies in the cookie jar and then apologize after because nobody would have given permission. That’s still about doing what you believe to be right. She even frames the fallout as “where you supposed to do that?” and not “you shouldn’t have done that”.
It's partly because of disagreement about what "complexity" and "simplicity" actually are. Many simple statements are in fact backed by massively complex, unstated assumptions. In attempting to deal with assumptions, scientists necessarily end up having to deal with the complexity involved in that. But the problem is if you don't engage with that, how do you know what is really more conformant with Occam's razor, as opposed to just satisfying what is readily expressed in common language?
Likewise in software development a C developer will say abstractions are not simple, a java programmer will argue that dealing with low levels details is not simple. They're both kinda right but will resort to framings which back their world view.
Ah, over-the-top larger-than-life LLM-isms, they are really funny when you see them in a company blog, but they are vomitive when it's your coworker copy-pasting it and insisting you on reading it.
These models are trained on human language, which belongs to us, we shouldn’t surrender it to them. Keep the em-dashes. IMO don’t overuse negative parallelisms though, they were always bad and lazy.
Why is this being published as a blog post and not as a peer-reviewed submission? If it's going to be a blog post, why isn't there a corresponding scientific version for me to look at?
Compression in this modern day and age is so slop.
Yes, I'm familiar with keystone results such as Solomonoff induction. It's a direct counterexample to compression - your intensional algorithm can completely outrun reality. I can literally specify a huge mega-algorithm that just searches over all possible Turing machines and evaluates them, and it's an optimal compressor. It's completely vacuous though. You can always hide the "heavy work" in your mappings and descriptions. It's ironic that a kolomogorov complexity minimizer is so loaded that it's vacuous.
This is pretty much why I roll my eyes at this point at all the compression is intelligence memes.
I wonder when intervention and causality will hit the mainstream. These tools were designed specifically to counteract purely predictive theories. But your average compression dude will hold tight to their paradigms and slogans, not realize their internal contradictions (that their own field has brought up), and then whenever a new paradigm suddenly becomes visible and mainstream, they'll latch onto that. It's not principled at all.
And to be clear - I do think intelligence is some amount of compression, and I am well aware of formal results such as the arithmetic decoding theoretical and empricial result. Just annoyed. It's literally no different than the whole Bayesianism meme. If you're not actually practicing that type of intelligence as a basis, then you don't get to go around beating the drum about how it's the ultimate reality. You're just spouting dogma to feel like part of an in-group.
I’m guessing your downvotes were for tone? You’re correct though regarding Solomonoff induction, as the choice of reference universal partial recursive function gives drastically different results for predictions based on finite data (even with access to a halting oracle). Asymptotically, any choice eventually converges to the same predictions, but that’s no help when there are infinitely many choices for U and no obvious natural prior over universal functions. And I don’t find the argument that our natural environment “implements some choice of U” particularly convincing. There’s definitely an open mystery there.
I don't take issue with that. Attempting memorized pattern generalization through holdout / validation strategies is a big part of ML that you would not typically see with econometrics / psychometrics / possibly sabermetrics / most other -metrics. Philosophically the explain versus predict divide. https://www.stat.berkeley.edu/~aldous/157/Papers/shmueli.pdf
That's a bit pedantic no. Memorization in ML refers to the model having the wrong level of capacity such that it's too hard to optimise it such that it doesn't memorize the _training examples_ themselves.
It’s just like the Hopper quote. She said it’s better to ask for forgiveness during the fog of war, doing something you thought was right, not to do something you knew they were going to say no to and now you are trying to get away with something.
> It’s not that the simplest is more likely to be correct, it’s that you should prefer it, because it’s simple.
I don't know what Occam meant, but if you accept the formalism of PAC learning, it is more likely to be correct
https://web.archive.org/web/20170428225156/http://www.cse.bu...
https://web.archive.org/web/20130412062821/http://cs.ecs.bay...
[0]: https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearnin...
The idea is that a complex model explains many more configurations (datasets) than a simple one. So its (prior) probability distribution is lower on the data seen (to compensate for the other possibilities it might explain). So the (marginal) likelihood that the simple model is correct is higher if it fits the data well enough.
[1] https://probml.github.io/pml-book/book1.html
It so happens that one gets the best generalization error bounds when one combines PAC with Bayesian ideas -- the PAC-Bayesian bounds.
Entropy is a metric targeted in LLM training which is likely why LLMs are overfitting less and less as they improve and why they subjectively seem to obey Occam's razor.
There's lesson for software engineering in general behind that kind of simplicity. https://benoitessiambre.com/entropy.html
But your smarter data scientists will try to get the best information density on test data to approximate generalization. MDL, as championed here, or AIC/BIC if working with more established and acceptable methods.
For complicated hypotheses, where complicated is defined appropriately, it takes many many examples to realize that it was a wrong hypothesis all along. There lies the rub.
For a particular instance of a learning problem we can't tell much, however using a Occams razor over many instances, one would be correct more often than not. Provided, of course, the PAC assumptions are true or they are not very far from being true.
How far is not very far ? That gets very hairy to quantify.
More typical definitions of simplicity, e.g. using the bit length of some kind of natural encoding, aren't guaranteed to offer any special advantages in terms of likelihood. So if you have prior knowledge that a particular hypothesis is more likely than another, but the less likely one is simpler in an intuitive sense, you shouldn't let that override you, but still prefer the more likely option. (And you don't need to take the circuitous route of coming up with a new encoding where the more likely hypothesis has a shorter bit length, either.)
Fixed.
Not sure about Hopper, as I recall biographers of Lawrence of Arabia certainly made it seem like he was using the fog of war to do things he knew his superiors may object to.
Regardless, even if its misinterpreted it still has a kernal of truth and separate utility than your version, that is: the people in the field closest to the action have an operational awareness that may result in better decisions in times of urgency.
https://youtu.be/wHdHCoeUbU4?t=861s
> So I want to tell something to all the young people here on many many occasions you'll find it is much easier to apologize than it is to get permission. You do it then when somebody comes after you and say are you supposed to do that, "oh gee I didn't know I wasn't supposed to do that" ... so just remember it's frequently much easier to apologize than it is to get permission do it
She goes on further, explaining how to deceive your superiors to manipulate them to get what you want.
Likewise in software development a C developer will say abstractions are not simple, a java programmer will argue that dealing with low levels details is not simple. They're both kinda right but will resort to framings which back their world view.
Is it too much to ask from people to read their own article anymore?
If anyone read this at all, they would have had the ick, and would have fired off a prompt to get rid of the most popular AI slop tells...
I caught myself writing "And that matters because..." in a HN comment but had to edit myself. Also miss uising emdashes.
they do.
Someone else already found it. I don't understand why the link isn't in the blog post. https://arxiv.org/abs/2606.11045
Use of claude for writing it should be disclosed.
Yes, I'm familiar with keystone results such as Solomonoff induction. It's a direct counterexample to compression - your intensional algorithm can completely outrun reality. I can literally specify a huge mega-algorithm that just searches over all possible Turing machines and evaluates them, and it's an optimal compressor. It's completely vacuous though. You can always hide the "heavy work" in your mappings and descriptions. It's ironic that a kolomogorov complexity minimizer is so loaded that it's vacuous.
This is pretty much why I roll my eyes at this point at all the compression is intelligence memes.
I wonder when intervention and causality will hit the mainstream. These tools were designed specifically to counteract purely predictive theories. But your average compression dude will hold tight to their paradigms and slogans, not realize their internal contradictions (that their own field has brought up), and then whenever a new paradigm suddenly becomes visible and mainstream, they'll latch onto that. It's not principled at all.
And to be clear - I do think intelligence is some amount of compression, and I am well aware of formal results such as the arithmetic decoding theoretical and empricial result. Just annoyed. It's literally no different than the whole Bayesianism meme. If you're not actually practicing that type of intelligence as a basis, then you don't get to go around beating the drum about how it's the ultimate reality. You're just spouting dogma to feel like part of an in-group.
Then why don't you ? and did you mean all or those that halt ? I presume you have a way of separating those.
https://en.wikipedia.org/wiki/Double_descent
Do the submitters really not notice that this is AI slop? Do they like this? It is a complete pain to read.
We need to retvrn to rss feeds
Well they memorize the patterns.
memorization doesnt mean rote learning.