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7uplycLvraw | you know that we that we that doesn't have that we cannot to solve the small sir okay that's it so that's a sorry complex see that show so the kinds of things I want to do is circuits I is I want to analyze them so I'm going to talk about computational problems that take a circuit encode it in some way as an input and compute something on that circuit so the circuit analysis problem | 1,378 | 1,403 | https://www.youtube.com/watch?v=7uplycLvraw&t=1378s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | is a problem where the input is a circuit so here we have some logical circuit written down in some encoding the P that our program can read and we want to output some property of the function computed by this circuit so we want to know something about what function is it computing in you know inside this little description so the canonical example of this is a circuit | 1,403 | 1,428 | https://www.youtube.com/watch?v=7uplycLvraw&t=1403s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | satisfiability problem also known as circuit set okay it's really like the simplest circuit analysis problem in a particular sense here you're given a logical circuit see so you wrote you've written down some description of some circuits got wired together in some funky way and you want to know is it computing the all zeroes function is it the case that no matter what input I | 1,428 | 1,451 | https://www.youtube.com/watch?v=7uplycLvraw&t=1428s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | give it is always going to print zero or is there some input which will make it print one okay that would usually when something makes it print one we call it a satisfying assignment and that's the origin of satisfiability but really want to know Jesus is it computing a trivial function or not so just tell me that okay so a circuit set is a so-called np-complete problem and so it's very | 1,451 | 1,477 | https://www.youtube.com/watch?v=7uplycLvraw&t=1451s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | unlikely to be solvable efficiently okay unless P equals NP okay like this so probably we're not going to be able to solve this circuit analysis problem very well but we could ask still if there is some way to solve it faster than the obvious self what is the obvious algorithm just try every possible input to the circuit okay so here we're leveraging the fact that there's a | 1,477 | 1,500 | https://www.youtube.com/watch?v=7uplycLvraw&t=1477s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | finite number of inputs so the circuit has a finite number of bits coming in so you could just if it's got n bits coming in there to the impossibility is just try them all see if any of them make this thing print one okay so we can answer this something faster this obvious brute-force search our okay we and maybe this is an interesting question maybe it isn't I always thought it was a | 1,500 | 1,524 | https://www.youtube.com/watch?v=7uplycLvraw&t=1500s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | very interesting question turns out it actually is interesting for other reasons it actually is connected to circuit complexity but just the question of it you have us you have a silly algorithm you have a obvious algorithm is it the best you can do this is just a very fundamental question by itself all right so that's a quick introduction to circuits okay now I want to talk about | 1,524 | 1,549 | https://www.youtube.com/watch?v=7uplycLvraw&t=1524s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | how circuits compare to algorithms so in the usual everything model where you think of you know writing a single program it's going to solve a problem you have some finite description of some program and this program can take an arbitrarily long inputs and still solve the problem okay if you give it an input of length 10 no problem input of length of thousand no problem a million no | 1,549 | 1,575 | https://www.youtube.com/watch?v=7uplycLvraw&t=1549s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | problem 100 million no problem this thing always solves the problem single thing okay that is in contrast with the circuit model where we only allow you to take in fixed length inputs okay so so if we're thinking about how our circuits can relate to one another we've got this sort of correctness type mismatch where algorithms can take an arbitrarily long input and circuits can | 1,575 | 1,601 | https://www.youtube.com/watch?v=7uplycLvraw&t=1575s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | only take in the fixed length inputs and there's a very easy way that complexity theorist came up with sort of unifying the two and the idea is to talk about a computational model called a circuit family the circuit family has is an infinite collection of circuits infinitely many and you have a circuit on one bit of input a circuit on two bits of input circuit on ten bits of | 1,601 | 1,627 | https://www.youtube.com/watch?v=7uplycLvraw&t=1601s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | input for every possible size of input you've got a circuit with that many inputs okay so for each end you have a circuit C sub n that's going to bring you on on inputs of lengths in and so it's obvious what I'm going to do and I want to compute something I'm you give me an input I measure its length I feed it to whatever the circuit is in the collection that matches that length as I | 1,627 | 1,649 | https://www.youtube.com/watch?v=7uplycLvraw&t=1627s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | run it it gives me some answer okay that's how the circuit family would compute on on some problem that would normally be solved by now okay all right so in this model the circuit family model programs have infinitely long descriptions a priori okay there is nothing bounding what these circuits could be you get a separate program every single time here input changes so it's possible that you | 1,649 | 1,678 | https://www.youtube.com/watch?v=7uplycLvraw&t=1649s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | know if your input if your input is you know a thousand there's something really clever you can do just when in facility two thousand one thousand and one you gotta restart everything do something completely different and get something you know very good okay so that there's this infinite description can be really really powerful okay but our notion of efficiency here is this class P poly so | 1,678 | 1,702 | https://www.youtube.com/watch?v=7uplycLvraw&t=1678s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | efficiency for algorithms is just the class P P poly is a set of problems solvable with one of these infinite circuit families so separate circuits ease of in for each input length where for every end the size of the in circuit is some polynomial in it this polynomial is fixed once and for all let's say it's N squared and so this circuit sees up a thousand be a thousand | 1,702 | 1,725 | https://www.youtube.com/watch?v=7uplycLvraw&t=1702s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | squared sighs okay so this is our notion of efficiency here for this or infinite model okay and the idea is that each circuit here it's going to be small relative to its input but you get a separate circuit for each input length that's sort of the extra thing you get you get this infinite description okay so this circuit family right here alright that's a notion of P poly so you | 1,725 | 1,752 | https://www.youtube.com/watch?v=7uplycLvraw&t=1725s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | anything programs have infinite link descriptions huh excuse me why study this model okay Theory dork that's all fine and good but why don't you go play off in theory land well all the rest of us go change the world okay okay well I have an answer for you all right okay so so proving limitations on what circuit families can compute is a step towards a non asymptotic complexity theory a | 1,752 | 1,784 | https://www.youtube.com/watch?v=7uplycLvraw&t=1752s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | complexity it doesn't talk about polynomials or Exponential's or whatever when have you talked about numbers how big does the computation get if I want to run it and if I want to run it on inputs of length a million can I fit it inside the known universe so so concrete limitations on computing within the known universe is would be is the the thing you would like to have that's sort | 1,784 | 1,810 | https://www.youtube.com/watch?v=7uplycLvraw&t=1784s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | of the ideal thing you would like to have something not as I'm sorry we don't care about polynomials exploration we just want to know how big is the computation gonna get so think something like any computer solving most instances might tend to for a bit problem these at least 10 to the 125 bits to be described so if you've got you know this kind of statement then your problem is just | 1,810 | 1,831 | https://www.youtube.com/watch?v=7uplycLvraw&t=1810s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | simply not solvable period okay so actually such a statement was proved by Meyer and stockmeyer in the 70s for a particular logic problem and they derived it we by reverse engineering a circuit lure about because circuit lower bounds are actually explicitly considering the trade-offs between the size of an input and the size of the computation you got a throw at the input to solve whereas | 1,831 | 1,854 | https://www.youtube.com/watch?v=7uplycLvraw&t=1831s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | Peters MP is actually not talking about this time at a fixed algorithm that's gonna work on all inputs okay and so the universe turns out stores a less than 10 to the 125 bits this is the this is the famous bekenstein bound in 1970s let's derive from that and so what you're saying is that any computer solving most instance my problem just won't fit within the known universe okay | 1,854 | 1,877 | https://www.youtube.com/watch?v=7uplycLvraw&t=1854s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | that's a pretty good lower bound okay so that's the kind of thing we would like to have and so the circuit family is just some stepping stone to getting some non asymptotic things were just talking about numbers that is the ultimate goal we are really this is des soon okay all right so a lot of algorithms compared to circuit families okay so we define this thing how does it compare to the uniform | 1,877 | 1,904 | https://www.youtube.com/watch?v=7uplycLvraw&t=1877s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | one program during low so if you got a program that runs and say T of n time when inputs of length n so in the squared time then it's well-known that you can always get a circuit family that will do the same thing and it has about TN in size as well there's some extra little factors don't see it in size so you can simulate efficient albums with efficient circuit families okay so time | 1,904 | 1,931 | https://www.youtube.com/watch?v=7uplycLvraw&t=1904s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | will scale the size all right so so that's all fine good in fact if you flip random coins in your algorithm and it gives you the right answer with high probability you will still be able to get infinite family no circuits has about the same size so in a sense you can remove the RAM this when you allow for an infinite circuit fan this is nothing more than the statement okay in | 1,931 | 1,957 | https://www.youtube.com/watch?v=7uplycLvraw&t=1931s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | complexity theory terms that bvp is in P Polly randomized phone real-time as efficient bonafide circuit changes okay suppose I'm just looking at circuit families I want to know can they be simulated by algorithms well turns out there is a family we in fact every circuit has size about in some linear size circuits so there's definitely in ppalli there's only a linear size as so | 1,957 | 1,983 | https://www.youtube.com/watch?v=7uplycLvraw&t=1957s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | as the input gross it's only just grows linearly in the transit slice however that family has no algorithm at all okay there is just simply no algorithm that will solve the problem that is solved by the circuit family okay so you you can't like hope to make them equivalent okay the main key here is that the circuit family gets an infinite description you get a different circuit for every input | 1,983 | 2,010 | https://www.youtube.com/watch?v=7uplycLvraw&t=1983s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | link and here you have a finite description a single element right and this is just a statement of some undecidable problems in fact many of them are in P poly okay so undecidable meaning there's no our at all that's just technical so finally I want to talk about okay suppose you've got a really complicated algorithm what what can you say about the size of the | 2,010 | 2,037 | https://www.youtube.com/watch?v=7uplycLvraw&t=2010s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | circuit family solving it so let's suppose I have some album running in exponential time so to the in step so given an in bit input it takes to the in step so like something just solving the trivial rm4 circuit set so I'm just going through all possibilities through the the inputs and just seeing what happens okay so it's actually open it's an open question whether every | 2,037 | 2,061 | https://www.youtube.com/watch?v=7uplycLvraw&t=2037s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | exponential time algorithm I'm saying extraordinary amount of time can be solved by circuits with a circuit family with N squared size every circuit has this is this is a really really remarkably open question so is it somehow possible that extremely long time consuming computation can be split up into implementing tiny little you know chunks we're on every single | 2,061 | 2,089 | https://www.youtube.com/watch?v=7uplycLvraw&t=2061s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | input length when I solve that problem optimally I actually get only N squared amount of computation this is possible it's actually possible we don't believe it's true but it's still a possibility we cannot rule it out and this is saying in complexity terms that X in ppalli is an open question so exponential time being in poly size there is the open question okay so just to give you | 2,089 | 2,117 | https://www.youtube.com/watch?v=7uplycLvraw&t=2089s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | just a even more crazy way in which we still don't know how like the power circuit families talk about exponential time versus shallowness some of you might have attended ms or a workshop on neural net okay this is also we don't want shallow Nets here so this is a very very shallow neural networks so suppose you've got an algorithm and this algorithm is solving a problem that | 2,117 | 2,147 | https://www.youtube.com/watch?v=7uplycLvraw&t=2117s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | solvable in so-called non-deterministic exponential time so this is like some just gigantic unfathomable class so this is problems where the solution takes exponentially many bits to describe and then verifying the solution is exponentially so this is just some gigantic class of problems ok the solutions themselves are gigantic and then verifying them takes a gigantic | 2,147 | 2,172 | https://www.youtube.com/watch?v=7uplycLvraw&t=2147s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | amount of time ok so this is a huge class of problems so it's actually possible this is gigantic class problems every single problem in this class could be again simulated by an infinite family of circuits one for every input length with the following property so this is zooming in ok so every circuit looks like the following very very simple object okay we've got N squared neurons | 2,172 | 2,199 | https://www.youtube.com/watch?v=7uplycLvraw&t=2172s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | here and so in some layer we've got n inputs so this is the amp circuit so it's going to take n inputs and output a bit and then from those n squared neurons they're gonna give me a 0 or 1 and they want to take one more neuron some function of those and output 0 1 ok so if each neuron we're just computing some linear form of the input so there's some weights here | 2,199 | 2,222 | https://www.youtube.com/watch?v=7uplycLvraw&t=2199s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | being some real weights being multiplied to 0 one values we're checking whether that exceeds some particular threshold value let's say T part if it does we we fire it doesn't you know what if it doesn't we fire as you just this very simple activation function okay so these are neural networks with one hidden layer small neural networks with one hidden layer there should be a very very | 2,222 | 2,244 | https://www.youtube.com/watch?v=7uplycLvraw&t=2222s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | weak class ok in fact if the weights are really small the weights are like minus 1 1 we do have very strong Louisville but if we allow the weights to be anything we want this is still possible it's a gigantic gap in our knowledge so we don't yet understand very simple neural networks okay just even things like just one hidden layer just one hidden layer with | 2,244 | 2,271 | https://www.youtube.com/watch?v=7uplycLvraw&t=2244s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | a simple activation function it's so so I like to just give an analogy here of an alien brain versus implementing for libraries okay so so think of this not as a central time thing is as you got some super advanced you know alien brain no no think of it is like something times 100 that okay something just just some brains and solving problems unfathomable to you okay okay but it's | 2,271 | 2,304 | https://www.youtube.com/watch?v=7uplycLvraw&t=2271s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | one brain it's just one of them okay and that you want to know if there are any mini little fly brains you know just just one just two layers of depth you know anslee many of them though which will also solve the problem no matter what this no matter what the the big alien brain okay so this so the only advantage you have is that there are implementing our brains and there's a different for | 2,304 | 2,330 | https://www.youtube.com/watch?v=7uplycLvraw&t=2304s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | each input length is that enough almost certainly not but it's the implementing that's that trips us up alright okay so now I want to talk and remaining turn about how certain analysis algorithms can actually imply circuit limitations so circuit islands algorithms can imply cellular balance and particular situations and in a particular sense this was well known a long time ago | 2,330 | 2,360 | https://www.youtube.com/watch?v=7uplycLvraw&t=2330s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | there's a theorem of car flipping and Meyer from 1980 which says suppose we had extremely efficient circuit now serums like basically perfect sureños arms okay so then there are problems solvable by hours in exponential time say to the end time long enough time that cannot be solved the polynomial size circuit family so this would resolve this X and P poly question we were talking about really | 2,360 | 2,383 | https://www.youtube.com/watch?v=7uplycLvraw&t=2360s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | okay so just a notation if P equals empty say circuit side is in P that is a good circuit an office algorithm then we would have it this class X was not in people okay this is a very interesting implication very interesting that that an algorithm analysis could even the other P would be okay that's part not gonna be there but some error analysis can actually prove a lower bound can | 2,383 | 2,409 | https://www.youtube.com/watch?v=7uplycLvraw&t=2383s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | actually lead to a lower bound at all okay but the thing is we don't believe that hypothesis is true so it's kind of like saying if pigs can fly then pigs can wink I mean like we we don't believe I bought is this we expect the conclusion to happen okay so so it's it's you know it's it could be useful but it seems to be a limited utility it seems like we have to assume you've got | 2,409 | 2,434 | https://www.youtube.com/watch?v=7uplycLvraw&t=2409s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | like this amazing like circuit analysis algorithm let's go study that I mean okay maybe extra people not in people ollie happens but okay this is you know by far the more interesting of the of the tooth to me okay so so what we want to do this you know take the wings off this i'll just dude and you know bring him back down to earth and like maybe maybe he can like you know like a lot no | 2,434 | 2,459 | https://www.youtube.com/watch?v=7uplycLvraw&t=2434s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | you know something that is actually possible and then you know we can prove something that we expect anyway yeah so a lower a circuit lower about that that's what we would like to do alright and so we were able to do this in particularly restricted situations so this is work of myself and many others who are working on this too and and a very high level what we can say is it a | 2,459 | 2,485 | https://www.youtube.com/watch?v=7uplycLvraw&t=2459s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | slightly faster algorithm for the circuit set problem just slightly faster than exhaustive search already implies lower balanced against circuits solving these problems gigantic class non-deterministic exponential time this class were which like it's possible that even neural Nets is one hidden layer could just solve the class so in pictures what we're saying is that | 2,485 | 2,510 | https://www.youtube.com/watch?v=7uplycLvraw&t=2485s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | suppose you know I'll give you just some arbitrary circuit well and there's some way to inspect this circuit and you can find an input which makes it print one whenever it exists yeah and the one extra thing I want to say is instead of taking say the exponential cost of two to the end time as you would have exhaustively you take to the end over end of the ten time okay and you do | 2,510 | 2,533 | https://www.youtube.com/watch?v=7uplycLvraw&t=2510s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | this for all polynomial size circuits so let's just say you do this for every circuit in particular s you shave off some polynomial into the tenth is enough okay for for our purposes suppose you can do that just a tiny sliver off exhaustive search then you'll be able to prove for the same circuit class that there it that it cannot compute sorry in X cannot be so so X is not in people | 2,533 | 2,559 | https://www.youtube.com/watch?v=7uplycLvraw&t=2533s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | okay so so what's the intuition behind this the there's two part the basic intuitions what is it faster circuit set algorithms uncover a weakness in and what circuits can do so in particular it says it high-level that small circuits can't offer you skate the all zeros function they can't hide it from you so I suppose this where a black box okay and you can't actually appear inside the | 2,559 | 2,589 | https://www.youtube.com/watch?v=7uplycLvraw&t=2559s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | circuit and look at what's going on the only thing you can do is take inputs stick them in and get outputs that's why that's the only thing you could do and now you want to solve this a problem you want to know there's an input which makes the circuit print one right then you can prove that you you would need to call this black box at least to the end times to know for sure by there ways you | 2,589 | 2,612 | https://www.youtube.com/watch?v=7uplycLvraw&t=2589s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | could trip up any particular strategy for querying this black box getting inputs and outputs without looking in it so that you've got to take to the end time so if we can solve the problem into the end over a ten time then there is some fundamental way in which we are opening up the guts of this circuit and getting some advantage over a black box and turns out this little advantage this | 2,612 | 2,635 | https://www.youtube.com/watch?v=7uplycLvraw&t=2612s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | weakness in circuits of the algorithm is uncovered is already enough to start proving the lower bounds alright so that's it that's the first intuition for why is such an implication should even hold the second intuition is that faster circuits set algorithms show a strength of faster than to the N algorithm so they saw some tasks that you didn't think could be done namely find an input | 2,635 | 2,663 | https://www.youtube.com/watch?v=7uplycLvraw&t=2635s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | which makes the circuit print one it does it faster than to the end so there's some nice algorithm that can efficiently tell us when a given circuit computes the all zeroes function so so given these two intuitions you can think of this problem in general as some kind of gain between ours and in circuits there's a circuit set problem that algorithms would like to solve and there | 2,663 | 2,686 | https://www.youtube.com/watch?v=7uplycLvraw&t=2663s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | are circuits that are you know inherently devious and try you know trying to fool any given algorithm and wired in some way to keep the algorithms from telling whether it's and when we can be exhaustive search we are winning the game the algorithm is winning the game and no matter what circuits given it can somehow drill down through the back black box and and get the answer | 2,686 | 2,709 | https://www.youtube.com/watch?v=7uplycLvraw&t=2686s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | okay so with the algorithm winning the game we running a lesson to the end time we hope to say circuits or a week less than to the entire albums are strong and somehow we're going to turn this into some function in non interesting exponential time that doesn't have your smallest area so now the circuits algorithm is showing that circuits are weak and this theorem is more less | 2,709 | 2,731 | https://www.youtube.com/watch?v=7uplycLvraw&t=2709s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | making that formal ok so we can actually apply this kind of theorem to prove lower bounds for restricted classes of circuits see fancy see ok I won't go into what the definitions of these things are but the the way in which they're proof lays out exactly as you might expect we show that faster circuits at algorithms for this for particular classes can imply circuit | 2,731 | 2,757 | https://www.youtube.com/watch?v=7uplycLvraw&t=2731s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | lower bounds for that particular class ok so just some generic kind of theorem if see circuits sat on circuits with n inputs can be solved and to the N over in ten steps then this class in X or some function this big class in X it doesn't have circuits all that kind whatever it is that we prove this circuit settling for okay and the second step is just design | 2,757 | 2,779 | https://www.youtube.com/watch?v=7uplycLvraw&t=2757s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | the element now this is just an in conditional sort of thing so just we can prove for many interesting certain classes ones will renew no lower bounds whatsoever we can solve the SAP problem faster than exhaustive search and then plugging that into the above connection you get lower bounds for them so you can improve over exhaustive search in some cases and so far this is kind of the | 2,779 | 2,801 | https://www.youtube.com/watch?v=7uplycLvraw&t=2779s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | only way we know how to prove certain lower balance is through the design of the right kind of set over all right so I'd like to conclude with the following challenge so how do we become smarter about computation so the outsiders it may seem that we already know maybe too much about computation like computers are getting smarter and smarter than us all the time yet from the theory level | 2,801 | 2,832 | https://www.youtube.com/watch?v=7uplycLvraw&t=2801s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | we actually don't know precisely how powerful that we are understanding this is really coarse so the dirty secret we still don't know too much about the limits of computers so how can algorithms help prove lower bounds so this is just in general a direction I would like people to think more about what kinds of algorithms could help to lower bounds because if we can set | 2,832 | 2,859 | https://www.youtube.com/watch?v=7uplycLvraw&t=2832s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | things up in this way then the lower bound problem does not become so intimidating anymore it just becomes the problem of designing the right kind of our something that we have done as computer scientists for many years and then how can lower bounds help design algorithms I didn't have time at all here to talk about how that how the connections of that form but there are | 2,859 | 2,879 | https://www.youtube.com/watch?v=7uplycLvraw&t=2859s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | there are many such connections namely in this thing I briefly mentioned about how lower bounds can imply D randomization removing the roundness from algorithms and making them fully deterministic there are many more connections to be film I'm sure so just earlier this year my student Brin more Chapman and I showed that lower bound circuit lower bounds can in a particular | 2,879 | 2,901 | https://www.youtube.com/watch?v=7uplycLvraw&t=2879s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | sense be equivalent to a particular design problem so you prove a lower bound circuit lower bound if and only if you desire test data for testing whether a given function of given circuit computes a particular function okay so trying to minimize the test data you need to test whether a circuit computes of function is actually equivalent to proving a lower bound so this is very nice in the | 2,901 | 2,926 | https://www.youtube.com/watch?v=7uplycLvraw&t=2901s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | sense that that it gives a very constructive way of thinking about how you prove an impossibility result a very algorithmic way how you do and so in general I think we will make serious progress by studying alguns and complexity as a whole and not as competing fields for anything we're really doing I really think we're doing a lot of the same thing more than we | 2,926 | 2,951 | https://www.youtube.com/watch?v=7uplycLvraw&t=2926s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | think okay that's all I have to say thank you sorry can you repeat it again right here oh so like the work of prasada you know yeah I mean so I think what's going on there is they're explaining the fact that I'm at least to me is that improving something is np-hard is actually an algorithms problem and so it's like from my understanding is you know either something can be done or it can't be | 2,951 | 3,030 | https://www.youtube.com/watch?v=7uplycLvraw&t=2951s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | done you get and you get a hardness reduction so it's so I mean in one case you get an algorithm or you get a hard introduction I mean in both cases you get some kind of algorithm but but I don't know I mean or any of them unconditional I don't know I need a lower bound you get unconditional yeah yeah I think it's a different kind of instance it's very interesting kind | 3,030 | 3,071 | https://www.youtube.com/watch?v=7uplycLvraw&t=3030s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | of instance but yeah I think I think it's different from what I'm trying to say but that's I didn't think I thought you still need unique games are or P not equal NP or something like this so I mean I would like to say something stronger than this so it's not just algorithm or hardness reduction yeah yes yes yes yeah yeah yeah yeah yeah so that's what makes the problem so | 3,071 | 3,136 | https://www.youtube.com/watch?v=7uplycLvraw&t=3071s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | immensely difficult is that it could just be anything in you know in and the hardest case is where each one is sort of incompressible by itself yeah if they're uniform if there's an algorithm generating those then you know this kind of dichotomy I was talking about becomes a completely different picture it was a very different picture I mean there's still interesting questions I mean the | 3,136 | 3,159 | https://www.youtube.com/watch?v=7uplycLvraw&t=3136s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | open questions around it but the picture is very different see I thought it was very careful not to say that I'm not trying a equals not hmm oh so yeah I mean even at the undergrad automata Theory level like when I teach them my hole in the road theorem I say well this means that for every language either it's got a fire automaton it's regular or there's this weird infinite | 3,159 | 3,219 | https://www.youtube.com/watch?v=7uplycLvraw&t=3159s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | object called distinguishing set and this proves that there's no final total and so in that case it is some sort of constructive way in which you're showing that something is not regular something does not have a DFA so yeah it does come up elsewhere I just yeah I only have so much time yeah yeah there's a whole community of people that would disagree with I mean that solving | 3,219 | 3,261 | https://www.youtube.com/watch?v=7uplycLvraw&t=3219s | Thinking Algorithmically About Impossibility | |
7uplycLvraw | is quite an enterprise actually yeah yeah oh well I mean there are things like this so-called exponential time hypothesis is false so then for example counting independent sets if it's in sub exponential time you can prove nonlinear circuit size lower bounds that that connection actually carries over in that kind so if you could count independent sets in sub exponential time you would | 3,261 | 3,299 | https://www.youtube.com/watch?v=7uplycLvraw&t=3261s | Thinking Algorithmically About Impossibility | |
hDQNCWR3HLQ | on April 21st jurgen schmidhuber tweeted out stop crediting the wrong people for inventions made by others at least in science the facts will always win at the end as long as the facts have not yet won it is not yet the end no fancy award can ever change that hashtag it self-correcting science hashtag plagiarism and links to an article of his own website where he | 0 | 29 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=0s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | wrote critique of Honda Prize for dr. Hinton so this is on Schmidt Hoover's own website and it's by himself and don't you love this how to pronounce his name jurgen schmidhuber you again sorry this is this is absolutely great so both actually Schmid over and Hinton are on Twitter you can tweet at them and follow them this article here is a basically a critique of the press release of Honda | 29 | 61 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=29s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | when they awarded geoff hinton for his achievements and it goes through it step by step and we won't look at the whole thing but just two for you to get the flavor so here honda says dr. Hinton has created a number of technologies that have enabled the broader application of AI including the backpropagation algorithm that forms the basis of deep learning approach to AI and schmidhuber | 61 | 89 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=61s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | just goes off its he basically claims him while Hinton and his co-workers have made certain significant contributions to deep learning he claimed above is plain wrong right he did not invent back propagation the person who invented back propagation was settled in linear MA and the many papers he says basically many papers failed to cite linin MA and this who was the original inventor of back | 89 | 123 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=89s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | prop and so on and he go kind of goes through a history of this and how it's even earlier I always have a bit of a trouble with claims like who invented what because when it is an algo them really the same thing right and when he when is it a variation on another algorithm and when is it something completely new it's never entirely clear but the the points here | 123 | 143 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=123s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | made that the things the backpropagation algorithm existed before Hinton and also that some of the papers some of the seminal papers did not cite the correct origin statement to in 2002 he introduced the a fast learning algorithm for restricted Boltzmann machines that allowed them to learn a single layer of distributor representation without requiring any labeled data these methods | 143 | 174 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=143s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | allow deep learning to work better and they led to the current deep learning revolution and he is no dr. Hinton's interesting unsupervised pre training for deep neural networks was irrelevant for the current latif learning revolution in 2010 our team showed that the feed-forward networks can be trained by plain backprop do not at all require pre training and he basically again says | 174 | 201 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=174s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | apart from this Hinton's unsupervised pretending was conceptually a rehash of my unsupervised pre training for deep recurrent neural networks so he you know as you know she made Ober has done a lot of work in recurrent neural networks and he basically says it it was just a rehash of his algorithm now I I have to say I have so first look first of all he he makes a point here right that we | 201 | 227 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=201s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | don't really do unsupervised pre-training him or until now of course but you like for to train an amnesty law fighter you don't have to do that but it's also doubtful that this this was a step even though even if it wasn't on the exact path to the current situation it was a thing that got people excited maybe and so the critique is like half valid and also it doesn't help me to burn that | 227 | 258 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=227s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | he always compares it to his own things like it just it just like either criticized them for you know in general things but then avoid bringing your own things in because it just sounds like I did this before and also I read some papers from from these times people just wrote papers sometimes I haven't read this specific one but sometimes people just wrote papers writing down their ideas | 258 | 285 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=258s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | like one could do this and this and this never doing any experiments or actually specifying exactly what they mean they just kind of wrote down a bunch of ideas and that got published especially like there's some some reinforcement learning papers where people are just like oh one I imagine agents doing this and learning from that so it is again it is never really clear in ideas or just had by | 285 | 315 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=285s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | everyone I think people people mistake this that think that the ideas are unique it's not ideas that are unique many people have the same ideas but some there's also execution and exact formalization and so on and exact level of specificity this all of this is really hard and then the honda says in 2009 dr. Hinton and two of his students used multi-layer neural nets to make major | 315 | 341 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=315s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | breakthrough and speech recognition that led directly to greatly improved and this of course Schrader who goes off by this because speech recognition is of course prime LS TM territory so you don't want to go near this and the Honda further says revolutionized computer vision by showing that deep learning worked far better than existing state of the art and again he says the basic | 341 | 369 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=341s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | ingredients were already there and so on and the our team in Switzerland already used his first superior award-winning GPU based CNN and so on that's what it's called dan net was produced by his group and again this seems correct right this seems when he lays it out like this but it doesn't change the fact that Alex net1 imagenet in 2012 and that was like the start of | 369 | 400 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=369s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | the deep learning revolution it was like wow you can cut the learn like the error rate by something like 30% simply by doing this deep learning stuff so again even if Dan that he says it blew away the competition it just seems it it always seems like Schmidt Hooper's kinda right but then also he's not he's like a cadet exact academic work and and the idea being | 400 | 435 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=400s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | there on a paper isn't the only thing that drives progress and says to achieve their dramatic results dr. Hinton also invented a widely used new method called dropout which reduces overfitting no like no and like no just no like randomly dropping parts in order to make something more robust that is surely not a new thing and he also says much early it is there's this stochastic Delta rule | 435 | 470 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=435s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | and so on and he also critiques that this paper did not cite this they just gave it the name right this is an idea that is kind of so simple that you you wouldn't even necessarily think about researching whether that has existed already I think they just did it and then because it's a natural idea and then they gave it a name and the name stuck right it's not about the idea | 470 | 497 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=470s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | itself and then lastly they say of the countless AI based technological services across the world it is no exaggeration to say that few would have been possible without the results dr. Hinton created I love this name one that would not have been possible and he just gives a list of their own group and that are basically possible without Hinton's contributions and this is just it's a | 497 | 527 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=497s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | bit of a cheap shot right clearly honda if they're not saying it would have been you know physically him possible without his contributions its but certainly Hinton has has if even if he hadn't invented any of those things he certainly has created like a spark and his these things created a splash got people excited people thinking about new ways of applying things even you | 527 | 559 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=527s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | know if this is all true so right and but but I would like you to I'd like you to notice this is a critique of what Honda says about Hinton and if I read through the statements of Schmidt who were most of them are technically correct right and you know that so that was that and then I thought okay cool but then someone posted II didn't read it and then Hinton replies and this is | 559 | 592 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=559s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | okay don't you love this so Hinton says having a public debate with schmidhuber about academic credit is not at advisable because it just encourages him and there is no limit to the time and effort that he is willing to put into trying to discredit his perceived Arrivals he is even escorted to tricks like having multiple aliases in Wikipedia to make it look as if other | 592 | 619 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=592s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | people agree the patient on his website about Alan Turing is a nice example of how he goes on trying to these are like these are shots fired and he says I'm going to respond once and only once I have never claimed that I invented backpropagation David Romo hard invented it independently after other after other people in other fields had invented it it's true when you first published we | 619 | 650 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=619s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | did not know the history so he basically says okay we did forget decided when we first published about rock crop but he doesn't say he invented it what I've claimed is that I was the person to clearly demonstrate that back prop could learn interesting in turn represent and that that this is what made it popular right so this goes into into the direction schmidhuber is very much on | 650 | 675 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=650s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | academic contributions idea was there before and hint and basically says no what we did is kind of we showed that it works in this particular way and we can have got people excited about it I did is by forcing that blah blah blah and it is he says it is true that many people in the press have said I invented back prop and I've spent a lot of time correcting them here's an excerpt from | 675 | 703 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=675s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | 2018 where this is I guess a quote from this book that quotes Hinton where he says lots of people invented different versions of back prop before day with normal heart they were mainly independent inventions something I feel I've got too much credit for it's one of these rare cases where an academic feels he has got too much credit for something my main contribution was to sure you can | 703 | 728 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=703s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | use it for learning distributed representations so I'd like to set the record straight on that and then he said maybe Jurgen would like to set the record straight on who invented LST M's boom boom crazy shot shots fired by Hinton here this is I mean this is just great but again look at what Hinton says Hinton basically says yes I have not invented that I have corrected this on | 728 | 761 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=728s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | public record in the past and yeah so so that's what Hinton says and I mean the the the comments here are just gold I really invite you to read it and then schmidhuber of course being Schmidt who replies again down here he has a a response to the reply and I don't expect Hinton to reply again so I waited for a bit but but I I believe him when he says he does it only once so he goes into | 761 | 794 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=761s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | this summary the facts presented in sections 1 2 3 4 5 are still valid so he goes what kind of statement by statements is having a public debate blah blah blah and he says this is an ad hominem attack which is true right this is true and he says he even has multiple aliases in Wikipedia and he just says another ad hominem attack and then he goes into that schmidhuber tries to discredit Alan | 794 | 829 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=794s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | Turing and then shmita goes into this big long big long basically claim that Alan Turing wasn't as important as people made him out to be and people invented this kind of Turing machine equivalents before that again it's kind of showing tubers take that the idea basically was already there and these people don't get the correct credit and also he's correct that this is a this is a true it's an ad | 829 | 864 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=829s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | hominem attack right so you know be it as it may this is correct and then when when Hinton goes that he doesn't stay and invent backdrop and me to persist this is finally response related to my post which is true right however he does not at all contradict what I wrote and it is true that he credited his co-author Rommel Hart with the invention but but neither cited alanine MA and | 864 | 893 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=864s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton | |
hDQNCWR3HLQ | also the statement lots of people he says it wasn't created by lots of different people but exactly one person so this I find como like can you really say now this is the exact time when backprop was invented even though it probably wasn't in the current exact current formulation and it probably existed someone like this so but again and he his main claim is dr. | 893 | 925 | https://www.youtube.com/watch?v=hDQNCWR3HLQ&t=893s | [Drama] Schmidhuber: Critique of Honda Prize for Dr. Hinton |
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