Not sure you're wanting an explanation, but it comes down more to equivalent algorithms than rigid categories. For example there is a P algo to sort a list of numbers, but not to solve a sudoku (NP). However there is a polynomial algo to check sudoku (spaces ^ 2 if you check every space against every other space for rule violation).
However, the reason all NP algos are part of the same category is because you can solve any problem in NP by switching the problem into another problem in the same category and solving that. For example, you can turn sudoku into a graph coloring problem, which is also NP. You can turn sorting (P) into something like balancing a tree, which is also P.
The major question is "is there any algorithm that would allow us to change some NP problems into P problems, solve it, then use it for the original problem". E.g. could we take graph coloring and turn it into sorting a list of numbers?
So basically, if there is any way to bridge the two, then it might mean every NP problem is actually solvable by a P algorithm, under some transformation. This would be immense because it would completely change the way we solve those algorithms and greatly reduce compute costs.
While this seems far-fetched, realize that there are some problems that seem extremely expensive if done the naiive way, but are actually solvable in P. For example, you _could_ write an exponential sorting algo (try every element in every position), but clever people found a way to make it efficient (P). So its possible we just need the right algo to completely change the landscape of computing.
However, as you say, its almost self-evidently true that P != NP, but has never been proven so (to do so, we need to prove that no such algorithm can exist). But clearly, solving an exponentially complex problem using a O(log n) algo would be remarkable.
To take a concrete example, currently the best algos to exhaustively check a board game like chess or go are exponential (NP). Its easy to verify the winner, but its exponential to enumerate every possible move (e.g. 80^turns states). If we found a polynomial way to solve this (even by converting to something simplified), then it would mean we could exhaustively search chess polynomial to the number of moves (e.g. turns^100). This changes it from "cannot be done in the lifespan of universe" to "its possible with a powerful computer in measurable time". We already use heuristics and estimates to explore the exponential space in efficient time, so if we had a polynomial algo chess, markets, optimization, and other NP problems would be extremely efficient to solve.
Isn't the question at hand whether its bad for mathematics if "prove the circle has area 3" devolves into 500 lines of inscrutable lean code, vs just having `pi r^2 == 3`? Sure they both "proved" it true/false, but knowing an answer isn't as useful as knowing why its an answer. Knowing an answer does have some value, its just not as valuable. If I can't work it out myself, I just trust the oracle.
Now if you ask "does the area of unit circle equal 4?", I don't really know, but we can go back to the oracle and ask again (we haven't learned the general pattern).
Also, I'm not sure that assuming this 'area of circle' question was cutting edge math, that the oracle wouldn't say 'yes, to a certain level of tolerance'. Can't count how many times I've seen agent decide a test needs to be loosened or deleted because its an "edge case" or "blocking". If you don't understand the proof you might get back 'yes' for some versions of 'is the area of unit circle 3' (depending on complexity of that ask).
Its an inevitable state of any market system (especially if regulated). Eventually it will become more profitable to use the gains of capital to buy protection from regulators, instead of investing in ever smaller business improvements. Using money to defeat competition is ultimately inefficient and generates lower returns for investment. Unless regulators are totally insulated from the market, they will have a stake in selecting winners and will eventually construct moats that others can't cross, as that provides the highest returns to capital, and the greatest rewards to regulators.
Monopoly is the most market-efficient vehicle to deliver returns to capital, and the most natural state of the market; one player using advantages and gains eventually destroys all opponents. Smaller players can never gain a foothold due to the incumbents being so efficient and far ahead, and it makes more sense to merge with the front-runner, allies, or be destroyed (hence the competitor pool keeps shrinking).
These are features of the system that naturally emerge without counterveiling forces.
For example, AI companies will shortly find its cheaper to just get the government to constrain their competition. The alternative is many companies spending trillions to eek out profits, a poor state to be in. Regulators want money and power, so its in their interest to create this protected state, as the "free and open market" isn't buying elections or vacation homes. And of course, any unprotected competitors left behind will die, consolidate, or sell to the victors; so we will eventually have a "winner takes all" system where one or two big players dominate. Any startups will either be quickly destroyed as people ask "why use a worse product", or will sell to the monopoly when they realize they can't afford to spend $1T training models and building data centers, and complying with all the regulations.
My point is that protectionism (in any form) isn't something to bring down over time to encourage competition -- the system can't naturally function that way, as it would require each player to go against their own interests. Instead, protectionism is a natural ever-increasing good that will be cultivated for the controlling capital and regulators in the system. We only see the "free market" operations during a time before market / regulator capture, as that's the time when there aren't yet dominant players who can guarantee power and money to the regulators, and there isn't enough consolidation of capital to immediately destroy all competition, but its an unstable market state.
"approaching" is doing some work there. $30K today will get you 90-144GB usable VRAM with solid system RAM and disk and CPU. A single B200 chip at 180GB is $40K. Unfortunately that is nowhere close to being able to run a 750B param model. For something like that, we're getting closer to 1TB VRAM (8+ H200/B200), and then 1M context KV cache is many more GBs on top of that.
That's a $500K-$1M+ rig as of now. That's a lot of $200 subscriptions to break even, but reasonable if you are paying Anthropic $25/M tokens. Then of course there's the power, cooling, and maintenance to consider...
But yeah, I can see if the prices come down 10x in a few years, or crater after the bubble, $30-40k might get you a decent machine.
What's crazy is the prompt must be something like "pro-AI but still believable and measured", since its "fixed my iOS app albeit with back and forth". Interesting, they know the HN crowd for sure.
hey that's perfectly understandable, and yeah, definitely there is a group that wants you to "do the work for them". I was reacting more to a kind of question/chat shaming I've seen -- where engineers act like they're optimizing 99% of their precious time and mental energy and can't be bothered to make a humanized workplace experience for others.
honestly a sad state. Obviously there is a reasonable threshold, but trying not to speak to anyone until you've done a ton of work / research when they know the answer is just sad. Like what's wrong with asking a question? We've entered this anti-human hellscape where asking a question in slack (async) is somehow a crime, like posting an opinion without a double-blind study to back it up (burn him!).
And the same people who are complaining about time wasting of having to ask/answer a question from a coworker which might create a modicum of civility and connection in this bitter cruel world are the same shit-posting on social media and doom watching youtube all day. "My flow can't be interrupted, I need all my energy to refactor this column from VARCHAR to TEXT, and to update this button from onClick inline to using a named closure".
Please, the reality is that we sold human connection for an illusion of productivity and the bitter pill of isolation where we all now feel guilt and shame for wanting to talk with other people (through an albeit disconnected and disembodied asynchronous channel).
If anyone responds with "I don't have time to respond I'm so busy", please realize you are proving my point. You are literally doom scrolling YC for no reason and alienating / pushing away coworkers to argue with internet strangers, sad.
I think he meant "show me a true linked list / node graph in rust that isn't unsafe". The reason being its not possible using c-style pointer following (or without just putting everything auto-pointers). What you've shown is exactly the tradeoff they were referring to. In rust, the answer is: make sure lifetime of all memory is explicitly managed, then use integers for the 'links' between nodes.
His point was that for his programming, he wants to be able to make real pointers and real linked lists with memory unsafe, which Rust makes difficult or opaque. For example with linked list, you could simulate (to avoid unsafe), by either boxing everything (so all refs are actually smart pointers), or you can use a container with scoped memory lifetime, and have integers in an array that are the "next" pointer. In addition to extra complexity, the "integers as edges" doesn't actually solve the complexity, it just means you can't get a bad memory error (you can still have 'pointers' that point to the wrong index if you're rolling your own).
Same with your graph code. Using a COO representation for a graph does in theory make it "memory safe" (albeit more clumsy to use if you are doing pointer-following logic), and it also introduces other subtle bugs if your logic is wrong (e.g. you have edge 100 but actually those nodes were removed, so now you're pointing at the wrong node).
I think the point (which I agree with for things like linked list, graph, compiler) is that depending on your usecase, the "safety" guarantees of rust are just making it harder to write the simplest most understandable code. Now instead of: `Node* next` I have lifetimes, integer references, two collections (nodes and edges) to keep in sync, smart pointers, etc. Previously my complexity was to make sure `next != null`, now its a ton of boilerplate and abstractions, performance hits, or more subtle bugs (like 'next' indices getting out of sync with the array of 'nodes').
If there was a way to explicitly track the lifetime of an arbitrary graph/tree of pointers at compile time, we wouldn't need garbage collection -- its not solvable at compile time, and the complexity has to live somewhere.
Yeah the usual mott and bailey. Monday -- AI is taking over the world, tremble in fear! Tuesday -- sure it did a boneheaded thing, its just a tool, no better than an intern, actually its _your_ fault, all the data in the entire world isn't enough to train this system not to delete prod!
Yeah I think there are two definitions of determinism people are using which is causing confusion. In a strict sense, LLMs can be deterministic meaning same input can generate same output (or as close as desired to same output). However, I think what people mean is that for slight changes to the input, it can behave in unpredictable ways (e.g. its output is not easily predicted by the user based on input alone). People mean "I told it don't do X, then it did X", which indicates a kind of randomness or non-determinism, the output isn't strictly constrained by the input in the way a reasonable person would expect.
Kind of crazy they are posting statuses to reddit. Thought the complaints about "why not status page and email?" are very valid -- seems kind of unprofessional. If I'm paying $200 per month per user for a service, an email or a message from the claude interface itself would be nice, so I don't have to stumble on this in random forums.
Photoshop is a good example -- not that I agree with everything in the app, but just to design all the interactions properly in photoshop would take hundreds of hours (not to mention testing and figuring out the edges). If your goal is a 1-to-1 clone why not use Krita or photoshop? With LLM you'll get "mostly there" with many many hours of work, and lots of sharp edges. If all you need is paint bucket, basic brush / pencil, and save/load, ok maybe you can one-shot it in a few hours... or just use paint / aesprite...
In this case, I see the author's point. The DJ isn't being advertised as "a narrow tool to select some random pop tunes". If an average person is told this is AI, has a full text interface and responds with "sure I'll do what you asked" and appears to understand, then they expect it to do what it is asked.
We're told its better than people at selecting songs (e.g. has the combined wisdom of all music and music experts), basic requests like "play the first movement of Beethoven's 7th" don't sound hard for an average person with limited / no musical expertise. If I said "please play the entire 7th symphony", and the tool responds with "sure, I'll play the whole thing", then proceeds to play the Beatles, I'd say that's a fair thing to point out as a shortcoming.
Its only obvious to tech people that understand that the technology has extreme limits and only works well on areas with abundant high quality data and labels, and can't be expected to reason like a person at all in many cases, that those limits seem as obvious as hammer / screw-driver. And that given how spotify developed these models, they probably didn't really intend classical or test that area -- so it fails despite sounding confident.
But maybe we should stop advertising screwdrivers as universal intelligence? There's a lot of mott and bailey going on. When AI makes mistakes its "just tools, stop expecting intelligence." However, when people question the AI hype its "humans make mistakes too, LLMs are truly reasoning and better most humans already." And "the entire labor economy will be replaced, human DJs will cease to exist.".
There's a simple solution. If a medical malpractice happens, law suit against the LLM company. If their license is revoked as part of that finding, unfortunately that applies to the "doctor" (e.g. ChatGPT).
Same for self-driving. Just hold each car like a normal driver, the owning AI company has liability. So after ~20 tickets and accidents in a week, a few ambulances being blocked, the only option is to revoke the driver's license (of which, all the cars share one, as they have the same brain).
This would make AI companies more cautious and only advertise capabilities they actually have and can verify. They would be held to the standard of a human. I think that's reasonable (why replace humans if the outcome is worse, and why reduce protections for individuals).
To make the analogy more clear: even if a telemedicine doc sees 10,000 patients a day all over the world, they would be held liable for any medical malpractice. Bad enough, and their license would be revoked, regardless of the fact that they see many patients all over the world. Same deal with AI / LLM -- if ChatGPT is making medical advice and it hurts someone, that's the same as a human doing so -- its malpractice and lawsuits can happen.
If they are somehow licensed, well then that license can be revoked. We would revoke a human's license for a single offense in some cases, the same should occur with AI.
they can be continuously updated, assuming you re-run representative samples of the training set through them continuously. Unlike a mammal brain which preserves the function of neurons unless they activate in a situation which causes a training signal, deep nets have catastrophic forgetting because signals get scattered everywhere. If you had a model continuously learning about you in your pocket, without tons of cycles spent "remembering" old examples. In fact, this is a major stumbling block in standard training, sampling is a huge problem. If you just iterate through the training corpus, you'll have forgotten most of the english stuff by the time you finish with chinese or spanish. You have to constantly mix and balance training info due to this limitation.
The fundamental difference is that physical neurons have a discrete on/off activation, while digital "neurons" in a network are merely continuous differentiable operations. They also don't have a notion of "spike timining dependency" to avoid overwriting activations that weren't related to an outcome. There are things like reward-decay over time, but this applies to the signal at a very coarse level, updates are still scattered to almost the entire system with every training example.
I think one major draw to human-like for factors is the reuse of existing ecosystems and tools. If you have human-like grasping, you can reuse tools and utensils for human hands, otherwise, you need custom attachments. If you have human-like legs you can navigate stairs, wear pants for customization, and possibly operate a car or bike.
Its a bit like choosing JS / python -- of course performance is inferior to a compiled language with highly tailored code, but they are flexible and have an ecosystem that might do 99% of the lifting for you.
But in isolation, I agree with your idea that specialized robots with form fitted specifically to task will likely outperform a more generalized solution in a specific domain of behavior, the more generalized will likely outperform in flexibility and reusability (e.g. capable of reusing the human ecosystem).
Wrote this elsewhere, but I think its worth thinking about a scenario like the book "daemon", rather than a "super-intelligence explosion" type scenario (which may be more like curing the cold or fusion than building a faster car).
All it really takes to do some kind of crazy world-dominating thing is some simple mechanisms and base intelligence, which the machines already possess. Using basic tactics like coercion, spoofing, threats, financial leverage, an unsophisticated attacker could cause major damage.
For example, that Meta exec who had their email deleted. Imagine instead one email had a malicious prompt which the bot obeyed. That prompt simply emailed everyone in her contacts list telling them to do something urgently (and possibly prompting other bots who are reading those emails). You could pretty quickly do something like cause a market crash, a nationwide panic, or maybe even an international conflict with no "super intelligence" needed, just human negligence, short-sightedness, and laziness.
Examples would be things like saying there is a threat incoming, a CIA source said so. Another would be that everyone will be fired, Meta is going bankrupt, etc. Its very easy to craft a prompt like that and fire it off to all the execs you can find (or just fire off random emails with plausible sounding emails). Then you just need to hit one and might set off a cascade.
The book daemon explored an interesting concept. It explored the idea that an AI could dominate and cause problems, not through super-intelligence, but through simple mechanisms that already exist.
Like the executive who deleted all her emails -- humans giving tons of control and access, and being extremely compliant to digital systems is all it takes. Give agent control of bank and your social media, and it already has all the movie scripts and mobster movie themes to exploit and blackmail you effectively with very rudimentary methods (threats, coercion, blackmail, etc.).
Just spoofing a simple email with the account it gained access too at the Meta exec's email (had it hit an email with an attack prompt), could have been enough to initiate some kind of thing like this. For example, by emailing everyone at the company and in contacts with commands that would be caught by other bots. No super-intelligence needed, just a good prompt and some human negligence.
However, the reason all NP algos are part of the same category is because you can solve any problem in NP by switching the problem into another problem in the same category and solving that. For example, you can turn sudoku into a graph coloring problem, which is also NP. You can turn sorting (P) into something like balancing a tree, which is also P.
The major question is "is there any algorithm that would allow us to change some NP problems into P problems, solve it, then use it for the original problem". E.g. could we take graph coloring and turn it into sorting a list of numbers?
So basically, if there is any way to bridge the two, then it might mean every NP problem is actually solvable by a P algorithm, under some transformation. This would be immense because it would completely change the way we solve those algorithms and greatly reduce compute costs.
While this seems far-fetched, realize that there are some problems that seem extremely expensive if done the naiive way, but are actually solvable in P. For example, you _could_ write an exponential sorting algo (try every element in every position), but clever people found a way to make it efficient (P). So its possible we just need the right algo to completely change the landscape of computing.
However, as you say, its almost self-evidently true that P != NP, but has never been proven so (to do so, we need to prove that no such algorithm can exist). But clearly, solving an exponentially complex problem using a O(log n) algo would be remarkable.
To take a concrete example, currently the best algos to exhaustively check a board game like chess or go are exponential (NP). Its easy to verify the winner, but its exponential to enumerate every possible move (e.g. 80^turns states). If we found a polynomial way to solve this (even by converting to something simplified), then it would mean we could exhaustively search chess polynomial to the number of moves (e.g. turns^100). This changes it from "cannot be done in the lifespan of universe" to "its possible with a powerful computer in measurable time". We already use heuristics and estimates to explore the exponential space in efficient time, so if we had a polynomial algo chess, markets, optimization, and other NP problems would be extremely efficient to solve.