Either I'm misunderstanding you, or you're misunderstanding the GP. The GP is getting at large language models being equivalent to very high order Markov models combined with calculating argmax over all possible outputs.
Huh, I suppose we're both right. Large language models are markov models since their transition probabilities are completely determined by the input. Consequently they cannot generate and recognize matching brackets correctly.
In practice however the state space is so humongously large that this barely comes up in any reasonable example.
This is a bit of a technicality, so forgive me for introducing some technical terms first.
I'm not sure how much you know about regular grammars, but basically they're the kind of thing that a regular expression can match. Now regular expressions can do a lot but they have their limitations, in particular they cannot distinguish a sequence of matched brackets '((())())' form one of unmatched brackets '(()(', or at least not with 100% accuracy.
It turns out that regular expressions are precisely the languages that can be recognized by finite state machines. Which is kind of equivalent to the possible outputs of a markov model.
Since large language models only have a finite number of states they must have the same limitations, which means it is fundamentally impossible to make them only generate balanced brackets. They get away with it by having a ridiculous number of states, so they might not be able to deal with arbitrarily deep nesting, but they can still get far enough that you won't generally notice.
No, it means that there is some input for which it will fail to properly balance brackets. The parameter count would have to be astronomical for this to fall outside the token window size.
ChatGPT Example:
> Add the correct number of closing parentheses to this string: (((((((((((((((((((((((((((((((
>> ))))))))))))))))))))))))))))
>> The correct number of closing parentheses to balance the opening parentheses is 21.
You could probably get it to generate code that does the correct operation, though, right? (Returns the correct number of parents.) It's kind of funny if that's the case.
It think the OP is getting at, a model can never be 100% accurate at this. Instead, the limit approaches 100% as the language model grows, but it never actually gets there. There will always be aliasing going on.
I think an analogy would be like saying that you can't represent pi as a floating point number. Precision can be increased by adding more bits, but there's a fundamental limitation because of the underlying storage mechanism.
I see. In any case, I don't think anything stops them from augmenting ChatGPT(-as-seen-by-the-user) so that it incorporates modules that aren't mere language models and thus allow richer behavior, as I suspected they were already doing:
Sipser[1] provides the clearest detailed description I've seen. You don't have to read anywhere near the whole thing. He covers the regular languages and (non)deterministic finite automata in the first few chapters.
Depending on your starting assumptions, Transformers, RNNs and LSTMS can either be
a) Turing-complete, in which case they can all match unbounded brackets, or
b) they are all not Turing-complete, LSTMs might be able to match unbounded brackets (if there is only one type of bracket), while RNNs and Transformers can't.
> For RNN/LSTM all you need is enough neurons to implement a counter.
For an arbitrary depth, that would need to be an infinitely sized counter. (I presume you know this, but this is why a push-down automaton can always close parens, but a finite state machine can only close parens up to a finite nesting depth.)
So, "all you need is enough neurons" for an RNN/LSTM is equivalent to just saying you just need to scale the LMM state large enough to handle your use case.
In reality, ignoring rdrand (and other quantum noise instructions) and ignoring using I/O for external storage, all of our computers are (gigantic) finite state machines. Technically, our programming languages might be Turing complete, but our near-infinite memory implementations are actually finite state machines, not Turing-complete. Though, you only run into the difference when you fill the whole machine's memory.
So, I think a more important question is how efficiently different finite state machines make use of their state sizes for a given problem. How many neurons would it take to match parens to a maximum depth of 2^40 for an RNN/LSTM vs. an LLM?
An RNN with infinite-precision rational weights can implement a counter with a bounded number of neurons. With finite precision the number of neurons scales linearly in your desired depth of matching brackets: https://arxiv.org/pdf/2010.07515.pdf
"LLMs are Markov Models"...
There's a reason we don't use Markov models anymore though (for language modeling - still used heavily in RL). The density of information and composability you get from MHA makes the problem far more tractable.
My prediction is that it will take Apple and Google ten years to replace or upgrade their installed base of conditional liars with an installed base of statistical liars.
Sorry to be pedantic, but Siri was released 2011 and Google Home 2016. With all the recent progress on LLMs, people forget that these “old” assistants are rather recent developments.
I've been following speech recognition, in particular, since the mid-90s. Around 2000, after many hours of training the best speech recognition software available commercially, with a slight speech impediment (which does not confuse people, for some reason) I personally concluded that even tailored speech recognition of general speech for a specific person was not viable yet. General purpose speech recognition of an arbitrary speaker perhaps with an accent that was even 80% accurate would be a long, long time away. If you had asked me to guess I'd probably have said after 2050.
I remember a presentation by Bill Gates, about the cutting edge statistical modelling based translation and speech recognition at Microsoft, similar to what Google was doing. The software was live-transcribing him, well enough that he could be understood. I was floored. Assuming this wasn't tailored to Bill specifically for the demo, it was revolutionary technology of the kind I had expected to take much longer to develop. That was 2008. At the time the notion that speech might become a common interface still seemed rather far-fetched to many. By 2018 such tech was everywhere. Deep learning based models have now closed much of the remaining gap in just the last couple years.
“The first wearable computer was conceived in 1955 by the author to predict roulette, culminating in a joint effort at M.I.T. with Claude Shannon in 1960-61. The final operating version was tested in Shannon’s basement home lab in June of 1961. […]
The Shannons and Thorps tested the computer in Las Vegas in the summer of 1961.”
It was just an idea before they jointly developed it.
Also, there is J. Doyne Farmer [1], who was part of a group that used computers in their shoes, early 1980s, to "game" roulette tables in Los Vegas. Story is told in Thomas Bass's interesting book, "The Eudaemonic Pie". [2]
What's funny about this is as we get better at text prediction, we revise our entropy estimations downward. The last I heard was 2016, at around 6 bits/word of EU-produced English. I'm sure it's lower now.
I couldn't resist asking it about the word entropy of its training corpus and quite predictably it wasn't able to understand my question and instead answered similar questions. However, it stuck quite firmly to a figure of 10--12 bits per word! I'm fairly sure that refers to the vocabulary entropy and not word entropy of English.
This is a good point, it happens because newer models are able to use larger and larger context - long range correlations in text. This amounts to finding more redundancy in the source text, driving down the estimated entropy.
Language models are related to text compression, except that the compression is lossy, not trying to be able to recreate the source text exactly but rather to be able to recreate something that is statistically similar.
For what it's worth, GPT-2 got PTB perplexity of around 20, which translates to about 4.3 bits/word. The later language models are presumably better but they report bits-per-character or bits-per-token which doesn't convert straightforwardly into bits per word.
Kind of neither, but it's more like the entropy of its output than its input. LLM's can be used to generate text but fundamentally what they do is calculate probabilities of a token given previous tokens. Given a context like "I saw a", the LLM gives a probability to each token in its vocabulary within that context. It's really a probability distribution p(token | context). You can sample from that distribution to generate text, or you can use it to get the probability of some fixed text that you feed into it, which is the probability that the model would have generated that text (at temperature 1).
The PTB perplexity numbers are based on the probabilities assigned to some text from the Wall Street Journal that used to be used as a standard test set in language modeling. It's 2 to the power of the average log probability of each word in the text under the model. So perplexity of 20 corresponds to around 4.3 bits of log probability per word, or another way of thinking of it is that the model will guess the correct following word in 1/20 cases.
The reason I say this isn't exactly the output entropy is that, since perplexity is evaluated on a fixed text, it might not correspond to the kinds of texts that the model would generate purely on its own. In other words when you're looking at some fixed txt, the contexts you get in p(token | context) might not be anything like a context that the LM would generate itself. This was a problem people pointed out a few years ago---back then it looked like LM generations were somewhat higher-entropy than what you measured looking at a fixed text. I don't know if the modern huge LMs have this same problem.
It seems plausible that the entry of written English is decreasing over time. As it becomes cheaper to 'publish' the median effort spent in writing is decreasing.
My introduction to Shannon and information theory through this book [1], which talks briefly about language entropy, is what set me on the path to my career.
It's incredible how Shannon published "A Mathematical Theory of Communication", while actually working on the "Communication Theory of Secrecy Systems":
What an absolute genius who disrupted two fields in two years.
I was exposed to Shannon's channel capacity theorem of a binary erasure channel in a grad comms theory course, and totally fell in love with the beauty and elegance of his mathematical formulations. Since that day, teaching Information Theory has been my most favorite hobby--which also used to a career. I love to see students' eyes pop when you eventually show how elegantly simple it is to express disorder (entropy) and to find fundamental limits on source and channel codes using this expression.
Heh, I think I'm going to start bringing up this paper whenever somebody tells me they majored in communications. This stuff is fascinating! Shannon really was a genius.
Yeah, I just re-encountered Shannon while reading about the board game Hex. The Shannon Switching game is the base case of Hex. Guy was firing on all cylinders ;)
I read Gleick's The Information[0] a few years ago and was riveted. Do you have any suggestions for further reading if I wanted to take a hobbyist interest?
I would read "Lifespan" by David Sinclair, who used Shannon's information theory to model epigenetic changes that cause us to age. Fascinating read and goes to show how far reaching impacts a foundational mathematical theory can have.
In EE we of course learned about the Shannon capacity of a channel, but when I read his proof using higher dimensional sphere packing I was amazed. Inspired me to attempt to look further into the math we see in engineering. I highly recommend anyone interested read his paper.
Claude Shannon also had early ideas about machine learning. AT&T has a 1950s video of the maestro himself demonstrating a maze solver with physical output. A true genius. In those days, geeks were dressed in suit.
Since we are on the topic, does anyone know what Shannon was up to after disrupting 3 fields?
...
He got into ball juggling and built the mathematical theory that led to creation of an automated juggling machine: https://cs.stanford.edu/people/eroberts/courses/soco/project....
He actually showed that ball juggling is one of the most complex cognitive tasks that a human can undertake:
"The physical constraints that affect mastery and limit the number of objects juggled arise from gravity - more specifically, Newtonian mechanics (h=1/2gt2). Each ball must be thrown sufficiently high to allow the juggler time to deal with the other balls. The need for either speed or height increases rapidly with the number of objects juggled."
What else? Well, one thing was making a lot of money as an investor. I don't remember quite what Fortune's Formula said about his overall rate of return over many decades, but iirc he made less than Warren Buffett mainly because he started with much less. (That book is about information theory and betting.)
* Strange to see see citations as footnotes, not a references section. (Nash's thesis was kind enough to include two cites in its references.) Was this typical?
There was no computer involved when publishing at the time. It certainly just took time and money for a professional typesetter to painstakingly set symbol after symbol on his manual typesetting machine.
It's called professional typesetting. The manuscript sent to BSTJ would have been typed, probably double-spaced, and I assume with hand-drawn equations. Once editing was finished, it would go to the typesetter.
Answers on this Stackexchange thread go into some detail: https://tex.stackexchange.com/questions/244082/typesetting-b...
On page 290 of a linked source you can see an example of typed/handwritten copy that the typesetter (a person) would have been working from: https://gwern.net/doc/design/typography/2003-matrix-typeandt...
As a liberal, am gonzo for diversity.
As a capitalist, I recognize that talent is very rare and I think it is foolish to reject talent based on irrelevant personal details.
As an intellectual, I am for focus and clarity.
This kind of activism isn't the only source of distraction.
But it's a big one right now.
Feel free to disagree, but that's how I feel, and my feelings aren't nonsense.
There's so much condescension in that sentence alone.
They say 'LatinX', where the correct term is Latin. They specifically list black students because the constant message in the liberal USA is that black people aren't capable and need to be called out by skin color in all contexts so they can be helped across the line by virtuous white people who recognize their weakness.
But keep reading the lesson plans and it goes on and on.
Chapter 1 is "Dismantling Racism in Mathematics Instruction", and it claims that "White supremacy culture infiltrates math classrooms [...] perpetuate educational harm on Black, Latinx, [...]"
- "greater focus on getting the 'right' answer ..."
- "required to 'show their work' in standardized, prescribed ways."
- "Independent practice is valued over teamwork or collaboration."
God forbid individual minority students are given the ability to personally succeed without being forced into a group identity, or that they be taught how to use math to communicate with others.
- "It also presupposes that “good” math teaching is about a Eurocentric type of mathematics, devoid of cultural ways of being."
Yes, of course, because math is about the numbers! You can apply it to your personal cultural way of being after learning how to get correct answers.
It's actual racism is to assume that all black people need to have a social-justice framework put in front of their academics to "help" them. Not help them to success, but to a white-constructed pseudo-success of wrong but "culturally correct" answers that is somehow the best they can be expected to achieve.
- "study ethnomathematics and incorporate into all classrooms."
In other words, don't try to help everyone achieve a common goal, create race-based targets and replace all education with them.
"the practice of school mathematics in the US regulates the child by privileging:"
- "algebra/calculus over geometry/topology/spatial reasoning;"
- "rule following over rule breaking;"
- "Western mathematics (culture free) over ethnomathematics"
- "logic over intuition"
Calculus encompasses geometry and spatial reasoning, so that's just wrong.
They attack "Rule following" - like the rules that get you correct answers. Western mathematics (which they've just identified as the type of math focused on correct answers). And logic, damned logic, getting in the way of the "lessers" just doing what they culturally know is right rather than applying critical thought like white people.
There's nothing in that course, or any of the rest, or in the critical theory that it came from, which is capable of helping, or even intended to help, any minority student.
It only prioritizes raising students uneducated and with a bunch of misplaced racial baggage.
If you don't believe me, or want to write it off as "what a white supremacist would say", read this:
"After the tragic killing of George Floyd in 2020, much of the virtue-signalling that followed focused on an unexpected target: admissions processes. Activists claimed children “of colour” weren’t getting their fair share of places at good schools — or, to be precise, black and Hispanic children weren’t. The same couldn’t be said of Asian children. And so Asian students became a convenient scapegoat for “anti-racists”. [...] in the months when America was rocked by race riots, self-described “equity warriors” described the Asian, mostly immigrant families of TJ as “white-adjacent” and “resource hoarders”. The white principal, Ann Bonitatibus, told us to check our “privileges”, ...
You've been on this site 8 months and yet you haven't read the guidelines:
Be kind. Don't be snarky. Converse curiously; don't cross-examine. Edit out swipes. Comments should get more thoughtful and substantive, not less, as a topic gets more divisive.
> Are we on a submission about language? Why are you guys talking about race-based admissions
My mistake. I'm also discussing the anti SAT/ACT and anti-MCAT movement on parenting forums and I open posts in new tabs to respond to them and forgot which thread was which.
The reasons being given for dropping the standardized tests are to help minorities despite that tests generally end up being a positive for disadvantaged people, not a burden. That's exactly where I was going with that "anti"-racist racist teaching guidance - rules that are claimed to help minorities which are in fact the worst things you could do.
> You know what you're doing
You read that post and you think I want minorities to fail? That I want racist school policies?
I was railing against the assumption that minority (it's always racial minorities they mean) students are failing to begin with, and then that they were failing because white courses and white standards are too hard for them.
That sort of racial framing goes against decades of psych research into things like stereotype threat and is known to be harmful to students' success.
Since my other comment was seeminglyf downvoted to hell - everything you write is projection. This is a random website that one person sent. This is not governement enforced - it's actually just some guidelines and propositions that are voluntary. So everything you write is basically irrelevant.
Even if you were actually reading what's in the recommendations - what's the point? Why are we talking about this?
And great example ofs anecdotal evidence. How hard is it to make a HN handle with antiracist in the name? If you give me a few minutes I can get you a bunch of comments that show the inverse.
Please argue things that are factual or matter OR at least are on subject.
The only effect your long comment has is to further radicalize people into believing that nothing should be done to support minorities. Think twice before writing reactionary nonsense.
Edit: btw, the source you quote here, Unherd, has this article at the top of their website "Why lesbian women should sleep with men". Laughable.
Why here? Because, as I said below, I posted that in response to this specific thread somewhat by mistake. I was discussing racially motivated changes in university acceptance criteria on a parenting forum and pretty much the same example was being used as an example of the thinking of those calling for the changes.
> And great example of anecdotal evidence.
Is anecdotal the new dismissal word of 2023 or something? "Oh, sure that happens and you see it near you, but that's just an anecdote - if you can't show it happening worldwide it doesn't count!"
Racialized teaching is in schools, rarely with justification this blatant though. They're using this rhetoric to justify getting rid of advanced classes and push groups of people entirely out of academics sometimes. If you don't follow schools and local politics I can imagine why you don't hear about it though.
> The only effect your long comment has is to further radicalize people into believing
Oh, I thought you were using the actual meaning of radicalize - you know. Violence instead of speech, etc.
> that nothing should be done to support minorities
No... That what should be done to support minorities is the same thing that should be done to support the majority - full and proper academic standards.
You should never need to talk about a student's race, or even take it into account. If a specific group of students really need extra help, use class analysis (ie, poverty) instead of racial analysis.
> Think twice before writing reactionary nonsense
Is this like calling me fascist, or do you actually mean something by this label?
> btw, the source you quote here, Unherd, has this article at the top of their website "Why lesbian women should sleep with men". Laughable.
I don't pick and choose source sites by their overall ideology so I didn't check the rest of their site before sharing the opinion piece.
But, yeah .... That is laughable. Can you believe that homophobes are literally attacking lesbian at pride parades and dyke marches for saying things such as "Lesbianism is female."
Note the Benford question mark in the headline though, it's sarcastic - the content says lesbians should not sleep with men. Sadly though, the article is in response to very real calls for violence against lesbians.
Using anecdotal evidence is what you do when you don't have factual evidence. Like a study that proves your point.
Feel free to use a dictionary or google to look up the meaning of "to radicalize" - I get "cause (someone) to adopt radical positions on political or social issues.".
What do you think reactionary mean? You have no further point other than reaction to what some activists do. You don't work for schools to have actual policy, you just flail your arms.
Vetting media outlet by general editorial quality is a good idea to not read nonsense.
You don't understand evidence. When our school boards are getting rid of advanced classes they're referencing race based reasoning like that example. Also, these specific recommendations are adopted in many schools - Stride Equitable Math - it's one of the more common.
> "cause (someone) to adopt radical positions on political or social issues".
That's circular reasoning though. What about the positions I would encourage someone to adopt is "radical"?
So far you're just using it as an insult.
> What do you think reactionary mean? You have no further point other than reaction to what some activists do. You don't work for schools to have actual policy, you just flail your arms.
That's probably the dumbest standard because by nobody has a plan when they first discover a problem. As you're using it, it's just an insult, and an empty one at that.
> "You don't work for schools to have actual policy"
Also, um, yeah. We do. A policy which bans using racial identifiers in all policy and policy discussions. Mandates that the same curriculum be available to any student gated only by skill.
> Vetting media outlet by general editorial quality is a good idea to not read nonsense.
I said I don't check for ideology. The quality is just fine - a mom had a complaint and they published her opinion piece as an editorial.
You pointed to a headline you didn't understand about lesbians but that's on you, not the paper. The headline was fine and references real events.
> Good job not using HN for ideological battles
Ironically, here you are flailing with insults and wildly reacting to my comments about a radical new movement to shove racism into schools.
Only one of us is having a battle.
You got freaked out because you saw something you didn't understand, refused to read deeply and engage, and now you've accused me of all this crypto-racism because I'm trying to remove racist policies from schools. Slow down. Not everyone uses your dog whistles, and not everyone on the other side is a bad guy.
Do you actually have any problem with my stance on this, that "what should be done to support minorities is the same thing that should be done to support the majority - full and proper academic standards."
Yes, but you haven't explained why this is a problem though.
Let's say a black man gets beaten by the police. It's just "anecdotal" in that he hasn't performed a study showing that it's a global issue, but it is irrefutable proof that police do beat up at least some black men.
In this case, let's say that only our school was enacting these policies and that we the parents discovered it only by our personal observation of policy updates, why would that matter? We'd still want to change it.
"The high school, [the parents] argued, should reinstate honors English classes that were eliminated because they didn’t enroll enough Black and Latino students. The district earlier this school year replaced the honors classes at Culver City High School with uniform courses that officials say will ensure students of all races receive an equal, rigorous education."
> "no ideological battles"
You're the one having a battle, and over an ideology. Walk away or engage with the issue, either is fine, but you're attacking me directly, using labels (radical, reactionary, etc) and saying that I "know what I'm doing".
You don't say what you'd do instead. You don't say why you support the policies, or would/wouldn't if they existed.
Please read the first paragraph of the wikipedia article, it'll clarify the issue.
Please chat with your representative with all this wonderful evidence I'm sure you'll change their mind or they will gladly answer all your questions - I'm not a civil servant, I'll let them do it
> Please read the first paragraph of the wikipedia article, it'll clarify the issue.
No. It doesn't. Because we have the school boards saying this in this in their own words and publishing them in their policy updates. All the "limited in value" stuff in the Wiki article is about ad-hoc and poorly collected evidence and that doesn't apply here. We're pointing to their own words.
> chat with your representative with all this wonderful evidence
It's perfect evidence. It's their own policy statements with their own justification.
A lot of people are like you initially but when they actually read the policies they come around - race-based rules are something most people feel icky about.
I've seen people rudely dismiss a pamphlet about this from a white parent only to happily read and engage when approached by an asian parent only moments later. That's racist, but I understand because all the news pumps out is a constant stream of partisan race-baiting and it takes many people a while to turn off that defensiveness.
> or they will gladly answer all your questions
No, usually they refuse to let us even get on the agenda for meetings.
> I'm sure you'll change their mind
Thankfully we don't have to talk to our representatives when they're this dismissive, we can simply vote them out and we have been.
But usually we find that at least half of them felt railroaded into these blatantly racist policies by a bunch of small frog-boiling policies and they're grateful for an opportunity to put things back in order.
That's what I thought! Go chat with your reptesentative - or keep wasting your time here, I'm sure you don't have anything else better to do for this very important issue !
If I may, I understand your first remark but I think you’re ascribing the wrong cause. Papers written by geniuses tend to be quite clear. Papers written by very smart people are a trainwreck.
Always a regressive bringing up identity politics. What is it with you guys being so sensitive? Be an individual, dont think so much about what others think.
What's the difference between not caring what other people think and sociopathy?
There are two error modes: Listening too much to people and not listening to them enough. Maybe it is some sort of mental or personality failing on my part that I cannot choose to completely disregard unjustified hate. It's still hate and it still hurts. And I'm not entirely convinced that that's bad.
I get a vibe as well, though I don't share your theory of it. Older math/CS papers have a more conversational feel to them, and tend to assume that the reader shares a kind of philosophical disposition. Today, research papers often have a very corporate feel, and are bristling with "motivation". But I don't think it's at all difficult to write such papers without referencing race or gender. Many people do it every day, successfully. I'm curious why you think that race and gender have invaded math/CS.
The Idea Factory is a great book describing the magical period at Bell Labs where they invented the future. It's just mind boggling how much of today's world was discovered and invented there - from the transistor to information theory.
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[ 4.2 ms ] story [ 159 ms ] threadIn practice however the state space is so humongously large that this barely comes up in any reasonable example.
Can you expand on this? Not quite following.
I'm not sure how much you know about regular grammars, but basically they're the kind of thing that a regular expression can match. Now regular expressions can do a lot but they have their limitations, in particular they cannot distinguish a sequence of matched brackets '((())())' form one of unmatched brackets '(()(', or at least not with 100% accuracy.
It turns out that regular expressions are precisely the languages that can be recognized by finite state machines. Which is kind of equivalent to the possible outputs of a markov model.
Since large language models only have a finite number of states they must have the same limitations, which means it is fundamentally impossible to make them only generate balanced brackets. They get away with it by having a ridiculous number of states, so they might not be able to deal with arbitrarily deep nesting, but they can still get far enough that you won't generally notice.
ChatGPT Example:
> Add the correct number of closing parentheses to this string: (((((((((((((((((((((((((((((((
>> ))))))))))))))))))))))))))))
>> The correct number of closing parentheses to balance the opening parentheses is 21.
which is not correct
I think an analogy would be like saying that you can't represent pi as a floating point number. Precision can be increased by adding more bits, but there's a fundamental limitation because of the underlying storage mechanism.
https://news.ycombinator.com/item?id=35472089
[1] https://www.goodreads.com/en/book/show/400716
a) Turing-complete, in which case they can all match unbounded brackets, or
b) they are all not Turing-complete, LSTMs might be able to match unbounded brackets (if there is only one type of bracket), while RNNs and Transformers can't.
For RNN/LSTM all you need is enough neurons to implement a counter.
For an arbitrary depth, that would need to be an infinitely sized counter. (I presume you know this, but this is why a push-down automaton can always close parens, but a finite state machine can only close parens up to a finite nesting depth.)
So, "all you need is enough neurons" for an RNN/LSTM is equivalent to just saying you just need to scale the LMM state large enough to handle your use case.
In reality, ignoring rdrand (and other quantum noise instructions) and ignoring using I/O for external storage, all of our computers are (gigantic) finite state machines. Technically, our programming languages might be Turing complete, but our near-infinite memory implementations are actually finite state machines, not Turing-complete. Though, you only run into the difference when you fill the whole machine's memory.
So, I think a more important question is how efficiently different finite state machines make use of their state sizes for a given problem. How many neurons would it take to match parens to a maximum depth of 2^40 for an RNN/LSTM vs. an LLM?
For a Transformer you need to add a new layer of self-attention to increase bracket matching depth by 1. https://direct.mit.edu/tacl/article/doi/10.1162/tacl_a_00306...
Transformers are formally a lot weaker than RNNs/LSTMs.
In the 80s-90s, Shannon’s predict the next token idea gave us spell check.
In 2000-2010 it gave us Siri & Google Home.
In 2020 it gave us ChatGPT.
I remember a presentation by Bill Gates, about the cutting edge statistical modelling based translation and speech recognition at Microsoft, similar to what Google was doing. The software was live-transcribing him, well enough that he could be understood. I was floored. Assuming this wasn't tailored to Bill specifically for the demo, it was revolutionary technology of the kind I had expected to take much longer to develop. That was 2008. At the time the notion that speech might become a common interface still seemed rather far-fetched to many. By 2018 such tech was everywhere. Deep learning based models have now closed much of the remaining gap in just the last couple years.
http://languagelog.ldc.upenn.edu/myl/Shannon1950.pdf
Btw Shannon also invented wearable computers. He did it to cheat at roulette.
https://www.cs.virginia.edu/~evans/thorp.pdf
It was just an idea before they jointly developed it.
[1] https://en.wikipedia.org/wiki/J._Doyne_Farmer [2] https://en.wikipedia.org/wiki/The_Eudaemonic_Pie
Highly recommended!
You’ll be lucky to get anything reasonable at all.
Language models are related to text compression, except that the compression is lossy, not trying to be able to recreate the source text exactly but rather to be able to recreate something that is statistically similar.
The PTB perplexity numbers are based on the probabilities assigned to some text from the Wall Street Journal that used to be used as a standard test set in language modeling. It's 2 to the power of the average log probability of each word in the text under the model. So perplexity of 20 corresponds to around 4.3 bits of log probability per word, or another way of thinking of it is that the model will guess the correct following word in 1/20 cases.
The reason I say this isn't exactly the output entropy is that, since perplexity is evaluated on a fixed text, it might not correspond to the kinds of texts that the model would generate purely on its own. In other words when you're looking at some fixed txt, the contexts you get in p(token | context) might not be anything like a context that the LM would generate itself. This was a problem people pointed out a few years ago---back then it looked like LM generations were somewhat higher-entropy than what you measured looking at a fixed text. I don't know if the modern huge LMs have this same problem.
https://archive.org/details/bstj30-1-50/mode/2up
[1]. An Introduction to Information Theory, Symbols, Signals & Noise By John Robinson Pierce · 1980 https://www.google.com/books/edition/An_Introduction_to_Info...
https://pages.cs.wisc.edu/~rist/642-spring-2014/shannon-secr...
https://pure.mpg.de/rest/items/item_2383164/component/file_2...
What an absolute genius who disrupted two fields in two years.
I was exposed to Shannon's channel capacity theorem of a binary erasure channel in a grad comms theory course, and totally fell in love with the beauty and elegance of his mathematical formulations. Since that day, teaching Information Theory has been my most favorite hobby--which also used to a career. I love to see students' eyes pop when you eventually show how elegantly simple it is to express disorder (entropy) and to find fundamental limits on source and channel codes using this expression.
Wish we had more MS theses today that at least attempted something as ambitious as this one, instead of just checking a box :(
[0]https://en.wikipedia.org/wiki/The_Information:_A_History,_a_...
0: https://techchannel.att.com/play-video.cfm/2010/3/16/In-Thei...
He actually showed that ball juggling is one of the most complex cognitive tasks that a human can undertake: "The physical constraints that affect mastery and limit the number of objects juggled arise from gravity - more specifically, Newtonian mechanics (h=1/2gt2). Each ball must be thrown sufficiently high to allow the juggler time to deal with the other balls. The need for either speed or height increases rapidly with the number of objects juggled."
* How did Shannon get nice looking math before LaTeX? John Nash's thesis in 1950 (only 32 pages long!) had handwritten math: https://library.princeton.edu/special-collections/sites/defa...
* Strange to see see citations as footnotes, not a references section. (Nash's thesis was kind enough to include two cites in its references.) Was this typical?
As a liberal, am gonzo for diversity. As a capitalist, I recognize that talent is very rare and I think it is foolish to reject talent based on irrelevant personal details. As an intellectual, I am for focus and clarity.
This kind of activism isn't the only source of distraction. But it's a big one right now.
Feel free to disagree, but that's how I feel, and my feelings aren't nonsense.
Literally the first line of your source
Laughable
Those who can't do teach.
Those who can't teach administer.
They say 'LatinX', where the correct term is Latin. They specifically list black students because the constant message in the liberal USA is that black people aren't capable and need to be called out by skin color in all contexts so they can be helped across the line by virtuous white people who recognize their weakness.
But keep reading the lesson plans and it goes on and on.
Chapter 1 is "Dismantling Racism in Mathematics Instruction", and it claims that "White supremacy culture infiltrates math classrooms [...] perpetuate educational harm on Black, Latinx, [...]"
- "greater focus on getting the 'right' answer ..."
- "required to 'show their work' in standardized, prescribed ways."
- "Independent practice is valued over teamwork or collaboration."
God forbid individual minority students are given the ability to personally succeed without being forced into a group identity, or that they be taught how to use math to communicate with others.
- "It also presupposes that “good” math teaching is about a Eurocentric type of mathematics, devoid of cultural ways of being."
Yes, of course, because math is about the numbers! You can apply it to your personal cultural way of being after learning how to get correct answers.
It's actual racism is to assume that all black people need to have a social-justice framework put in front of their academics to "help" them. Not help them to success, but to a white-constructed pseudo-success of wrong but "culturally correct" answers that is somehow the best they can be expected to achieve.
- "study ethnomathematics and incorporate into all classrooms."
In other words, don't try to help everyone achieve a common goal, create race-based targets and replace all education with them.
"the practice of school mathematics in the US regulates the child by privileging:"
- "algebra/calculus over geometry/topology/spatial reasoning;"
- "rule following over rule breaking;"
- "Western mathematics (culture free) over ethnomathematics"
- "logic over intuition"
Calculus encompasses geometry and spatial reasoning, so that's just wrong.
They attack "Rule following" - like the rules that get you correct answers. Western mathematics (which they've just identified as the type of math focused on correct answers). And logic, damned logic, getting in the way of the "lessers" just doing what they culturally know is right rather than applying critical thought like white people.
There's nothing in that course, or any of the rest, or in the critical theory that it came from, which is capable of helping, or even intended to help, any minority student.
It only prioritizes raising students uneducated and with a bunch of misplaced racial baggage.
If you don't believe me, or want to write it off as "what a white supremacist would say", read this:
https://unherd.com/2022/02/anti-racism-betrays-asian-student...
"After the tragic killing of George Floyd in 2020, much of the virtue-signalling that followed focused on an unexpected target: admissions processes. Activists claimed children “of colour” weren’t getting their fair share of places at good schools — or, to be precise, black and Hispanic children weren’t. The same couldn’t be said of Asian children. And so Asian students became a convenient scapegoat for “anti-racists”. [...] in the months when America was rocked by race riots, self-described “equity warriors” described the Asian, mostly immigrant families of TJ as “white-adjacent” and “resource hoarders”. The white principal, Ann Bonitatibus, told us to check our “privileges”, ...
Be kind. Don't be snarky. Converse curiously; don't cross-examine. Edit out swipes. Comments should get more thoughtful and substantive, not less, as a topic gets more divisive.
https://news.ycombinator.com/newsguidelines.html
Please don't use Hacker News for political or ideological battle. That tramples curiosity.
Are we on a submission about language? Why are you guys talking about race-based admissions and the quality of papers going down?
You know what you're doing and it doesn't deserve respectful discourse
My mistake. I'm also discussing the anti SAT/ACT and anti-MCAT movement on parenting forums and I open posts in new tabs to respond to them and forgot which thread was which.
The reasons being given for dropping the standardized tests are to help minorities despite that tests generally end up being a positive for disadvantaged people, not a burden. That's exactly where I was going with that "anti"-racist racist teaching guidance - rules that are claimed to help minorities which are in fact the worst things you could do.
> You know what you're doing
You read that post and you think I want minorities to fail? That I want racist school policies?
I was railing against the assumption that minority (it's always racial minorities they mean) students are failing to begin with, and then that they were failing because white courses and white standards are too hard for them.
That sort of racial framing goes against decades of psych research into things like stereotype threat and is known to be harmful to students' success.
Even if you were actually reading what's in the recommendations - what's the point? Why are we talking about this?
And great example ofs anecdotal evidence. How hard is it to make a HN handle with antiracist in the name? If you give me a few minutes I can get you a bunch of comments that show the inverse.
Please argue things that are factual or matter OR at least are on subject.
The only effect your long comment has is to further radicalize people into believing that nothing should be done to support minorities. Think twice before writing reactionary nonsense.
Edit: btw, the source you quote here, Unherd, has this article at the top of their website "Why lesbian women should sleep with men". Laughable.
Why here? Because, as I said below, I posted that in response to this specific thread somewhat by mistake. I was discussing racially motivated changes in university acceptance criteria on a parenting forum and pretty much the same example was being used as an example of the thinking of those calling for the changes.
> And great example of anecdotal evidence.
Is anecdotal the new dismissal word of 2023 or something? "Oh, sure that happens and you see it near you, but that's just an anecdote - if you can't show it happening worldwide it doesn't count!"
Racialized teaching is in schools, rarely with justification this blatant though. They're using this rhetoric to justify getting rid of advanced classes and push groups of people entirely out of academics sometimes. If you don't follow schools and local politics I can imagine why you don't hear about it though.
> The only effect your long comment has is to further radicalize people into believing
Oh, I thought you were using the actual meaning of radicalize - you know. Violence instead of speech, etc.
> that nothing should be done to support minorities
No... That what should be done to support minorities is the same thing that should be done to support the majority - full and proper academic standards.
You should never need to talk about a student's race, or even take it into account. If a specific group of students really need extra help, use class analysis (ie, poverty) instead of racial analysis.
> Think twice before writing reactionary nonsense
Is this like calling me fascist, or do you actually mean something by this label?
> btw, the source you quote here, Unherd, has this article at the top of their website "Why lesbian women should sleep with men". Laughable.
I don't pick and choose source sites by their overall ideology so I didn't check the rest of their site before sharing the opinion piece.
But, yeah .... That is laughable. Can you believe that homophobes are literally attacking lesbian at pride parades and dyke marches for saying things such as "Lesbianism is female."
Note the Benford question mark in the headline though, it's sarcastic - the content says lesbians should not sleep with men. Sadly though, the article is in response to very real calls for violence against lesbians.
Feel free to use a dictionary or google to look up the meaning of "to radicalize" - I get "cause (someone) to adopt radical positions on political or social issues.".
What do you think reactionary mean? You have no further point other than reaction to what some activists do. You don't work for schools to have actual policy, you just flail your arms.
Vetting media outlet by general editorial quality is a good idea to not read nonsense.
Good job not using HN for ideological battles
You don't understand evidence. When our school boards are getting rid of advanced classes they're referencing race based reasoning like that example. Also, these specific recommendations are adopted in many schools - Stride Equitable Math - it's one of the more common.
> "cause (someone) to adopt radical positions on political or social issues".
That's circular reasoning though. What about the positions I would encourage someone to adopt is "radical"?
So far you're just using it as an insult.
> What do you think reactionary mean? You have no further point other than reaction to what some activists do. You don't work for schools to have actual policy, you just flail your arms.
That's probably the dumbest standard because by nobody has a plan when they first discover a problem. As you're using it, it's just an insult, and an empty one at that.
> "You don't work for schools to have actual policy"
Also, um, yeah. We do. A policy which bans using racial identifiers in all policy and policy discussions. Mandates that the same curriculum be available to any student gated only by skill.
> Vetting media outlet by general editorial quality is a good idea to not read nonsense.
I said I don't check for ideology. The quality is just fine - a mom had a complaint and they published her opinion piece as an editorial.
You pointed to a headline you didn't understand about lesbians but that's on you, not the paper. The headline was fine and references real events.
> Good job not using HN for ideological battles
Ironically, here you are flailing with insults and wildly reacting to my comments about a radical new movement to shove racism into schools.
Only one of us is having a battle.
You got freaked out because you saw something you didn't understand, refused to read deeply and engage, and now you've accused me of all this crypto-racism because I'm trying to remove racist policies from schools. Slow down. Not everyone uses your dog whistles, and not everyone on the other side is a bad guy.
Do you actually have any problem with my stance on this, that "what should be done to support minorities is the same thing that should be done to support the majority - full and proper academic standards."
Go read the HN guidelines buddy
And you piggybacked on a racebaiting comment on an unrelated subject. Come on.
Yes, but you haven't explained why this is a problem though.
Let's say a black man gets beaten by the police. It's just "anecdotal" in that he hasn't performed a study showing that it's a global issue, but it is irrefutable proof that police do beat up at least some black men.
In this case, let's say that only our school was enacting these policies and that we the parents discovered it only by our personal observation of policy updates, why would that matter? We'd still want to change it.
But in this case it actually is a widespread issue: https://archive.is/bZcXu
"The high school, [the parents] argued, should reinstate honors English classes that were eliminated because they didn’t enroll enough Black and Latino students. The district earlier this school year replaced the honors classes at Culver City High School with uniform courses that officials say will ensure students of all races receive an equal, rigorous education."
> "no ideological battles"
You're the one having a battle, and over an ideology. Walk away or engage with the issue, either is fine, but you're attacking me directly, using labels (radical, reactionary, etc) and saying that I "know what I'm doing".
You don't say what you'd do instead. You don't say why you support the policies, or would/wouldn't if they existed.
Please chat with your representative with all this wonderful evidence I'm sure you'll change their mind or they will gladly answer all your questions - I'm not a civil servant, I'll let them do it
No. It doesn't. Because we have the school boards saying this in this in their own words and publishing them in their policy updates. All the "limited in value" stuff in the Wiki article is about ad-hoc and poorly collected evidence and that doesn't apply here. We're pointing to their own words.
> chat with your representative with all this wonderful evidence
It's perfect evidence. It's their own policy statements with their own justification.
A lot of people are like you initially but when they actually read the policies they come around - race-based rules are something most people feel icky about.
I've seen people rudely dismiss a pamphlet about this from a white parent only to happily read and engage when approached by an asian parent only moments later. That's racist, but I understand because all the news pumps out is a constant stream of partisan race-baiting and it takes many people a while to turn off that defensiveness.
> or they will gladly answer all your questions
No, usually they refuse to let us even get on the agenda for meetings.
> I'm sure you'll change their mind
Thankfully we don't have to talk to our representatives when they're this dismissive, we can simply vote them out and we have been.
But usually we find that at least half of them felt railroaded into these blatantly racist policies by a bunch of small frog-boiling policies and they're grateful for an opportunity to put things back in order.
And why does it matter? I'm part of a multi-racial group of parents. What does it matter if I'm the asian one or the white one or the black one?
There are two error modes: Listening too much to people and not listening to them enough. Maybe it is some sort of mental or personality failing on my part that I cannot choose to completely disregard unjustified hate. It's still hate and it still hurts. And I'm not entirely convinced that that's bad.
https://www.youtube.com/watch?v=z2Whj_nL-x8
Shouldn't that be U instead of V? Or am I missing something.
https://www.amazon.com/Idea-Factory-Great-American-Innovatio...
https://www.lesswrong.com/posts/htrZrxduciZ5QaCjw/language-m...