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.
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
Time to first detected slop in this article is <1s. Claudisms per paragraph is also very high.
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...
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.
For the first time ever in my life, I consider the fact that English is not my first language and that I never had any formal education in it as an advantage.
Nobody is going to consider my weird and barbarian prose with the well polished product of a SOTA model.
English as a 2nd language speakers often have better grammar than natives in my experience! I wouldn't be surprised if the average native english speaker doesn't know the different between there and their.
> A validation set is one you consult repeatedly while building the model — to compare candidates, tune hyperparameters, and decide what to try next.
The validation can be done like that but it is better to do a cross-fold validation or selecting a random subset. These are equally valid. Keeping the validation like a hold-out set can end up creating biases if the statistics don't match. Honestly, this is true about the test set too. Though I've found that most people really don't think about this much. It's mundane, boring, hard to do, but deceptively important.
"The more your listener already knows, the shorter the message you need to send. An expert ML engineer needs only a few sentences; a newcomer needs the whole manual."
Literally from the first words on the page. 1st sentence passed barely. 2nd sentence ending "a newcomer needs the whole manual" and it's Claude.
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.
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.
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.
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.
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.)
PAC isn't asymptotic in general. It gives finite estimates for finite sizes of training data.
If you say, and I think you are indeed saying so, that PAC is ridiculously pessimistic, I would be in violently agreement with you. That's one reason why for practical training data sizes and practical (infinite version space) hypothesis classes PAC gives bound such as -- probability of error is less than 41K. This isn't exactly incorrect but not very useful or informative.
A far more useful formulation is PAC-Bayesian where you get error bounds less than 1 guaranteed and usually less than 0.5 on reasonable sized training data sets.
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.
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.
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.
This is provably not true, and you can use the marginal likelihood / PAC-Bayes to prove it (or any other framework for measuring model quality). Increase the number of parameters in a linear model way beyond the point of interpolation, and concentrate the likelihood around the zero loss set. Then reduce the variance on a Gaussian prior. You can balance the two temperatures at exactly the right rate so that any measure of model quality will monotonically increase with model size and achieve a maximum at infinite model size.
Even easier, just take a limit of polynomial regression to a Gaussian process while optimizing the marginal likelihood over the prior temperature.
In all of these cases, the model with the least parameters is not the simplest in principle and does not have the best chance of not overfitting. The reality is significantly more nuanced.
You are saying something interesting, but talking like Grok and skipping a lot of the details, without any references to common check-in points like terminology or specific studies.
> and concentrate the likelihood around the zero loss set. Then reduce the variance on a Gaussian prior.
Those phrases could mean a lot of different things. What are you proposing?
> so that any measure of model quality will monotonically increase with model size and achieve a maximum at infinite model size.
any measure of model quality? You must have some bounds of any measure, since trivially that's false because "fewer parameters is better" is a measure of model quality, even if dumb.
It's hard to even engage when you're being so imprecise, and not even giving one specific example.
Apologies, I'm skipping details, because that's how I speak with my colleagues, but I realize this is an external environment without context. No references since this is folklore (you can look at Hastie et al's Surprises in High-Dimensional Ridgeless Regression paper for the non-Bayesian version, Bruno Loureiro or Andrew Gordon Wilson probably have a paper with something similar).
Concentrating a density around a zero set means that I raise it to the power of 1/gamma (appropriately normalizing) and then take gamma to zero. If the likelihood was Gaussian, this would be equivalent to taking the variance to zero (yielding a point mass). But in overparameterized settings, this concentrates on a submanifold describing the set of interpolating solutions. In least-squares linear regression, that is the solution space. Reducing the variance on a Gaussian prior is treated as an asymptotic expansion by Laplace's method. If you choose the variance to decrease (inversely proportional to the parameter size, for example), then the marginal likelihood will increase monotonically with model size.
By any measure of model size, I mean that you can pick your favourite among the common ones, such as information metrics (e.g. mutual information / KL), statistical metrics (e.g. marginal likelihood), test error. You should be able to show the same phenomenon happening for all of them, so it isn't a quirk of marginal likelihood. It is concentration of measure working in your favor to reduce the variance in the estimator.
Are you sure that this is valid and does not suffer from the equivalent of peeking-into-the-test-set problem ? There are ways to address the peeking problem but that requires additional machinery.
I don't dispute your broad claim but the first counterexample you quote seems problematic.
You can choose the prior according to any selection rule that does not see the data (actually, you can do more, but justifying this is the realm of empirical Bayes and requires some more precise arguments). In this case, you can choose it according to the model size and provided that your Jacobian is full rank, you will get increasing marginal likelihood.
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.
Absolutely not. This link is a reference on PAC learning, which is thoroughly misleading in the land of deep learning and inevitably leads to vacuous bounds. This is common knowledge in deep learning. I would not recommend that any student learn any part of this theory at this point, since we have far better alternatives in terms of simplicity, accuracy, and generality.
PAC-Bayes is genuinely superior, for example. Instead of a uniform weighting over all hypotheses (effectively encoded in the supremum), you get to weight the hypothesis class in virtually any way that you want. This is critical to ensure that you exclude absurd hypotheses that you have almost nil chance of reaching. If you do consider a uniform weighting, then you can just easily reduce to PAC anyway, but you do so in a cleaner package.
"Can be misleading" is an accurate characterization.
It is an uniform bound and will have problems with very large hypothesis classes but its statement isnt wrong (just that the tool is a little heavy handed). For simpler models they are adequately useful.
Real world isn't the adversarial/ worst-case that these models of generalization assume. So the generalization performance you experience is usually a better than what PAC indicates, but estimating that experience was not PAC's charter. It's charter was to quantify a adversarial/legal guarantee, the minimum (infimum) guaranteed program.
I too like PAC-Bayes a lot (see my other comments) but it does have a cop out in that by definition you do not know how good your prior is, yet the quantitative estimate of generalization error depends on how good it was.
Nevertheless, PAC-Bayesian and statistical physics based bounds are closer to what we experience.
I agree that this is a good nuanced take. However, I find that students who have learned PAC (which usually takes quite some time) often have to unlearn certain principles to do PAC-Bayes, so my comments come from a fair amount of frustration with the topic. On the other hand, I find that teaching students PAC-Bayes from the get-go is easier, it still works for simpler models (you can derive the same PAC bounds, so you can't do any worse), and they get the full story. Obviously for those of us who learned both, it is good to know both. But I am skeptical for the next generation coming through whether it is worth teaching PAC at all.
“You should prefer it, because it’s simple” is just restating Occam’s razor, not giving any explanation. “The simplest is more likely to be accurate” is a much better interpretation than yours.
I think the most accessible example of Occam’s razor is fitting a line to some points; you can always use a high enough order polynomial to fit the seen points exactly, but a straight line is likely closer to representing the underlying distribution.
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.
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 think that the ratio of work done by priors and search is the interesting question at this point. We aren't quite at the point where reading off the most likely hypothesis decompressed from a transformer is sufficient, but it's a lot closer than I originally suspected when we were ~solving chess. I think AlphaGo was kind of the watershed moment that prior-guided search was so much better than either alone.
I think the adversarial policies against Go AIs directly show the gap between intelligence and compression/priors.
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?
If anything, the latest generation of AI models, Astra and Fable, are prime example of overfitting—whereas benchmarks suggest they’re AGI-tier, users (including myself) report the same old gaslighting, hallucination, context rot, cheating, incomprehensibility patterns as with prior models, sometimes even more pronounced.
Fable and Opus 5, I suspect, will become textbook examples of RL collapse.
71 comments
[ 0.22 ms ] story [ 74.9 ms ] threadWell they memorize the patterns.
memorization doesnt mean rote learning.
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.
Nobody is going to consider my weird and barbarian prose with the well polished product of a SOTA model.
Literally from the first words on the page. 1st sentence passed barely. 2nd sentence ending "a newcomer needs the whole manual" and it's Claude.
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.
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.
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.
I don't know what Occam meant, but if you accept the formalism of PAC learning, it is more likely to be correct
http://www.cse.buffalo.edu/~hungngo/classes/2008/694/papers/...
http://cs.ecs.baylor.edu/~hamerly/courses/5325_10s/papers/le...
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.
Removing them at effectively zero cost is extremely valuable.
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.)
If you say, and I think you are indeed saying so, that PAC is ridiculously pessimistic, I would be in violently agreement with you. That's one reason why for practical training data sizes and practical (infinite version space) hypothesis classes PAC gives bound such as -- probability of error is less than 41K. This isn't exactly incorrect but not very useful or informative.
A far more useful formulation is PAC-Bayesian where you get error bounds less than 1 guaranteed and usually less than 0.5 on reasonable sized training data sets.
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.
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
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.
Even easier, just take a limit of polynomial regression to a Gaussian process while optimizing the marginal likelihood over the prior temperature.
In all of these cases, the model with the least parameters is not the simplest in principle and does not have the best chance of not overfitting. The reality is significantly more nuanced.
> and concentrate the likelihood around the zero loss set. Then reduce the variance on a Gaussian prior.
Those phrases could mean a lot of different things. What are you proposing?
> so that any measure of model quality will monotonically increase with model size and achieve a maximum at infinite model size.
any measure of model quality? You must have some bounds of any measure, since trivially that's false because "fewer parameters is better" is a measure of model quality, even if dumb.
It's hard to even engage when you're being so imprecise, and not even giving one specific example.
Concentrating a density around a zero set means that I raise it to the power of 1/gamma (appropriately normalizing) and then take gamma to zero. If the likelihood was Gaussian, this would be equivalent to taking the variance to zero (yielding a point mass). But in overparameterized settings, this concentrates on a submanifold describing the set of interpolating solutions. In least-squares linear regression, that is the solution space. Reducing the variance on a Gaussian prior is treated as an asymptotic expansion by Laplace's method. If you choose the variance to decrease (inversely proportional to the parameter size, for example), then the marginal likelihood will increase monotonically with model size.
By any measure of model size, I mean that you can pick your favourite among the common ones, such as information metrics (e.g. mutual information / KL), statistical metrics (e.g. marginal likelihood), test error. You should be able to show the same phenomenon happening for all of them, so it isn't a quirk of marginal likelihood. It is concentration of measure working in your favor to reduce the variance in the estimator.
Are you sure that this is valid and does not suffer from the equivalent of peeking-into-the-test-set problem ? There are ways to address the peeking problem but that requires additional machinery.
I don't dispute your broad claim but the first counterexample you quote seems problematic.
[0]: https://www.cs.huji.ac.il/~shais/UnderstandingMachineLearnin...
PAC-Bayes is genuinely superior, for example. Instead of a uniform weighting over all hypotheses (effectively encoded in the supremum), you get to weight the hypothesis class in virtually any way that you want. This is critical to ensure that you exclude absurd hypotheses that you have almost nil chance of reaching. If you do consider a uniform weighting, then you can just easily reduce to PAC anyway, but you do so in a cleaner package.
It is an uniform bound and will have problems with very large hypothesis classes but its statement isnt wrong (just that the tool is a little heavy handed). For simpler models they are adequately useful.
Real world isn't the adversarial/ worst-case that these models of generalization assume. So the generalization performance you experience is usually a better than what PAC indicates, but estimating that experience was not PAC's charter. It's charter was to quantify a adversarial/legal guarantee, the minimum (infimum) guaranteed program.
I too like PAC-Bayes a lot (see my other comments) but it does have a cop out in that by definition you do not know how good your prior is, yet the quantitative estimate of generalization error depends on how good it was.
Nevertheless, PAC-Bayesian and statistical physics based bounds are closer to what we experience.
I think the most accessible example of Occam’s razor is fitting a line to some points; you can always use a high enough order polynomial to fit the seen points exactly, but a straight line is likely closer to representing the underlying distribution.
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
they do.
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.
Then why don't you ?
I think the adversarial policies against Go AIs directly show the gap between intelligence and compression/priors.
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.
Fable and Opus 5, I suspect, will become textbook examples of RL collapse.