Timeline for What advantage humans have over computers in mathematics?
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| Nov 12, 2017 at 3:37 | comment | added | yters | @DouglasZare, this is a related question I asked. Most of the answers tend to agree with you that NNs are not overfitting, but they cannot really say why, and seem to assume good accuracy on datasets implies the models are not overfitting, which I've explained is not a valid deduction. cs.stackexchange.com/questions/75327/… | |
| Nov 12, 2017 at 3:34 | comment | added | yters | @DouglasZare overfitting does not necessarily mean they perform poorly on a particular dataset. If all the training data has the same source of noise, then an overfitting model will learn the noise and the underlying true function, which means it gives good accuracy results on that dataset, but when the source of noise is removed it will perform badly. A famous example is a NN trained to recognize felons, but it was trained on prison mugshots, and learned to recognize the white background. This is precisely the issue we see with DNNs and adversarial examples. | |
| Nov 11, 2017 at 20:00 | comment | added | Douglas Zare | @yters: Again, this is not the place for a discussion, nor does it appear you are willing to discuss this as opposed to simply repeating your poorly-informed opinions. Good-bye. | |
| Nov 11, 2017 at 19:57 | comment | added | Douglas Zare | @yters: Oh, if the neural networks are just memorizing using their high VC dimensions, does that mean they performed poorly and should return all of the prizes they have been winning? It sounds like you have heard of overfitting, but you don't realize that other people have heard of it, too, and have very standard techniques for avoiding memorization. Some of these don't reduce the VC dimension but do avoid overfitting whether you are convinced or not. Moves like the famous "ear-reddening move" are more likely to be found by computers even if people are prejudiced against computer creativity. | |
| Nov 11, 2017 at 19:41 | comment | added | yters | @DouglasZare, neural networks have high VC dimension, which means they need tremendous amounts of data to guarantee they do not memorize. This requirement is almost always not met, and so they do memorize. Memorization makes ML models very brittle, from a sensitivity analysis point of view, so we would expect things like adversarial examples where small amounts of noise produce dramatic misclassifications. We see this sort of thing happen with the first AlphaGo and its bad lines of play, so most likely something similar happens with AlphaGo Zero. All this to say, ML is not creative. | |
| Nov 11, 2017 at 19:22 | comment | added | Douglas Zare | @yters: Are you claiming people can't be fooled? They definitely can. I have seen authors of excellent backgammon books filled with insightful analysis make horrible blunders over the board because they misanalyzed a position in ways that are similar to the way artificial neural networks fail on adversarial examples. I don't think this is the right place to have such a discussion, though, and I'm not convinced you are adding more than your uninformed feelings. You keep going on about nets memorizing, which is not what they do as I pointed out earlier, but you refuse to accept this fact. | |
| Nov 6, 2017 at 7:52 | comment | added | yters | @DouglasZare to give further explanation why I say these algorithms do not learn principles, is the ease that DNNs can be fooled with adversarial examples. From a principled approach, a little noise does not obscure the human's ability to recognize a principle. However, when memorizing, a little noise can completely confuse a memorizer. Adversarial examples suggest DNNs are memorizing, not learning principles. | |
| Nov 6, 2017 at 5:52 | comment | added | yters | @DouglasZare where are the principles in an AlphaGo neural net? | |
| Nov 6, 2017 at 3:26 | comment | added | Douglas Zare | @yters: That is a poor description of AlphaGo and many strong chess engines. Computers do not play stronger than humans by memorizing what human experts do in the tiny sample of positions we can get from human play. It was learned decades ago, in simpler games, that computers can do much better by deriving principles from playing and using the principles to determine the best moves, just as you say humans do. If you don't realize this, you should look into the literature on game AI from the past 30 years. | |
| Nov 5, 2017 at 11:37 | comment | added | yters | @DouglasZare neither AlphaGo nor the chess programs are creative in the same way as humans. These programs either require massive move databases from best human players, or play an enormous number of games. They essentially memorize a giant lookup table of moves to make, similar to the Chinese room thought experiment. Humans, on the other hand, can derive principles from playing and use the principles to infer the best moves. If we would more carefully analyze the "how" of computers and humans the difference would be much more apparent, instead of using a reductive functional analysis. | |
| Mar 17, 2016 at 21:36 | comment | added | Douglas Zare | How are you sure the creativity in mathematics is real and beyond computers (even in the future, when computers can model a human brain) when the creativity in chess turned out to be easily within reach of computers? | |
| Mar 15, 2016 at 20:31 | comment | added | Robert Israel | I don't know if you can infer a "fundamental difference" from the fact that this generation of neural networks can be fooled. People can also be fooled (although maybe not in the same ways). We just don't know as much about people's wiring. | |
| Mar 15, 2016 at 15:13 | comment | added | logicute | @Piyush Grover Self-rewriting programs are nothing new, even if the techniques have clearly vastly improved. Weizenbaum argued that the fact that you don't understand the whole of the algorithm doesn't make it "intelligent" (Chinese room again). The fact that neural networks can be fooled by meaningless images (arxiv.org/abs/1412.1897) while pigeons can learn human aesthetic criteria show that there is a fundamental difference between human intelligence and good algorithms. | |
| Mar 15, 2016 at 14:58 | comment | added | logicute | @Gil Kalai Thank you. Do you know some mathematical notions that capture the notion of creativity? It's a genuine question, if it exists it should be interesting to read about it. | |
| Mar 15, 2016 at 14:41 | comment | added | Gil Kalai | This is an interesting answer, but it is not clear that computers will be weaker "on creativity." | |
| Mar 13, 2016 at 13:53 | comment | added | Piyush Grover | I disagree with the comment 'Beating a human at go is the same kind of work that had been done on chess'. There is a fundamental difference since the latest advance has been made by a pattern-discovering neural network based framework, which is precisely what gives it the creativity that chess playing computers lacked. We haven't discovered the 'Go' analogue of the grandmaster-defeating Chess algorithms, rather we now have a computer program which discovers those algorithms automatically if fed enough data from 'Go' games. | |
| S Mar 13, 2016 at 12:44 | history | answered | logicute | CC BY-SA 3.0 | |
| S Mar 13, 2016 at 12:44 | history | made wiki | Post Made Community Wiki by logicute |