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+"nc-nd license. (c) mit press.contents vii 20 why does deep learning work? 401 20.1 the case against deep learning . . . . . . . . . . . . . . . . . . . . . . . . 401 20.2 factors that influence fitting performance . . . . . . . . . . . . . . . . . 402 20.3 properties of loss functions . . . . . . . . . . . . . . . . . . . . . . . . . . 406 20.4 factors that determine generalization . . . . . . . . . . . . . . . . . . . . 410 20.5 do we need so many parameters? . . . . . . . . . . . . . . . . . . . . . . 414 20.6 do networks have to be deep? . . . . . . . . . . . . . . . . . . . . . . . . 417 20.7 summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 21 deep learning and ethics 420 21.1 value alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 21.2 intentional misuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 21.3 other social, ethical, and professional issues . . . . . . . . . . . . . . . . 428 21.4 case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 21.5 the value-free ideal of science . . . . . . . . . . . . . . . . . . . . . . . . 431 21.6 responsible ai research as a collective action problem . . . . . . . . . . 432 21.7 ways forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 21.8 summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 a notation 436 b mathematics 439 b.1 functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 b.2 binomial coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 b.3 vector, matrices, and tensors. . . . . . . . . . . . . . . . . . . . . . . . . 442 b.4 special types of matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 b.5 matrix calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 c probability 448 c.1 random variables and probability distributions . . . . . . . . . . . . . . 448 c.2 expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 c.3 normal probability distribution . . . . . . . . . . . . . . . . . . . . . . . 456 c.4 sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 c.5 distances between probability distributions. . . . . . . . . . . . . . . . . 459 bibliography 462 index 513 draft: please send errata to [email protected] the history of deep learning is unusual in science. the perseverance of a small cabal of scientists,workingovertwenty-fiveyearsinaseeminglyunpromisingarea,hasrevolution- ized a field"