1969 ChatGPT 2022 Di ff usion 2021 SVMs 1995 BackProp 1986 ConvNets 1998 Birth of AI 1956 ADALINE 1959 Perceptron 1957 Turing test 1950 Arti fi cial Neuron 1943 Neocognitron 1980 Universality 1989 LSTM 1997 The revolutions of (deep) learning
b, log(a), p a . . . ) and their derivatives cost O(1). <latexit sha1_base64="XBU0O16nV93z/lhQgn5HZRGW7gQ=">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</latexit> Setup: E : Rd ! R computable in K operations. <latexit sha1_base64="BLbI91EqNObAlbI/2RJe4xs+gGo=">AAA92nictVtfc9u4EUeu/y7pv1z72JkOWyedu06asd1M27kbTy+xncQXX2JHspO7U5KhJFpmQokKSdlOdH7pW6ev/T596ZfoN2j70of2A3R3ARCgBHJBNzXGNgjht7tYAPsHoPrTJM6L1dW/XXrvG9/81re/8/7lK9/93vd/8MOrH/zoME9n2SA6GKRJmj3th3mUxJPooIiLJHo6zaJw3E+iJ/1Xm/j5k5Moy+N00i3eTKNn43A0iY/iQVhA04urz3tFdFb0j+b7syjHpo/PgyfHYRHEeVAcR8EgHU+T6Cwu3gTpET3NingyCq71JmE/CYPedhR8HPQeP34+DHpZPDouwixLT2XLtd+/uLqyenOVfoLlypqqrAj1s5d+8NN10RNDkYqBmImxiMREFFBPRChyKF+JNbEqptD2TMyhLYNaTJ9H4lxcAewMekXQI4TWV/B3BE9fqdYJPCPNnNAD4JLAbwbIQFwHTAr9Mqgjt4A+nxFlbK2jPSeaKNsb+N9XtMbQWohjaOVwuqcvDsdSiCPxOxpDDGOaUguObqCozEgrKHlgjaoAClNow/oQPs+gPiCk1nNAmJzGjroN6fO/U09sxeeB6jsT/yApr0MJREeNPi0phOKE6Ac0mzP4TMqTAOcRUIjUGLF2Sroe0+gn0H8O7Q+hnFNN66QPZU6t543ITSgu5CaLvAfFhbzHInehuJC7LHIPigu5p5CIzUjnbnwHigvfYTnvQ3Eh91nkYygu5GMWeQjFhTxkkV9CcSG/ZJF3obiQd1nkAygu5AMW2YXiQnZZ5AEUF/KARW5DcSG3FbJ+p2ZQUqITM7vyNtSrPNBSJNBym5XvDllHF/aOx54e1GD5Xb0F/93YLQ+dRjXYbY91d1SD5VfePbCRbixvi+6TN3Fh77PYHVgBbuwOi/1MvKzBfuax017VYPm9tgv93Fje+n4OT27s5yz2IdTcWN5HPYIWN/aRh8eY1mD3WOy+eF2D9bH6WQ2Wt/sdsCtuLO+nutDfjfWxprMaLG9PDyGCcWN5b/UEWt3YJyz2qTirwT5lsV+AdXdjv/DwsG9rsNrHXiEPMqJ4JIId20QtLHcl1qZALWT4J6VvSSg27kM7hxmVmBFhxiziXom454nYLRG73nLlpR3NKd7luXRKRMcT0S99E9YKtv+w7I+1xAOxVSK2FhBNESnOtR7LCUUXuoVDFqXnwprPmNLSfmMtUuuh2fJqxKMKQq7tY1r5NyhbwgwKNdVE7bj08RIZ0HMT4pSyNz1KzYPHFaVVsFFnLKrvQPVZ1BsH6g2LmjlQMxZ14kCdsCiz821cz2MFGP3jXMzpSa4AGSPXlwCigtvgde7DHg1g/exBFPiYWh7B/w7l3lxpkgyzefSTeMrxrGKJM6jNxQq0m6xwi/LrhHZYBJLJno9Ujo9PeLYxV3tOWuHz0pMH5YmJP52Y5BmVdDBaDGg/taPzgFrOKbqTtXb4++W+17V2+G3S+DlF8bLWDl8o6YsLyN5V2O4FsB3YTVOlfVNvS0Oev0gaun6FvC5aXJzVsVozSO+sJf0dNTM7F5iXTapJ/Zh6Oxq5Nb68Mr42NIyec0vP7ahg9CSjXl0LWo9kovJeU28rQ0pedKLkME9tZwb7DNXM6Ho7GnsQcW1Szj236m1X77Qcjam3o3Eo5LnnOUXyut6OxoiepT5MvR0NPG0JVZ5v6m0tO2pA5s6m3taqT+gUGM+A5JqXLSYqyihOmilqMcUHzac1dsy/7MfwzOZ5mSM0UzKxbT2dfunLmiXS8UIEVq1oKQfGFzMrBqvSmIt1Nr+SMhQV/75Mx/h41PwuaDGA3S/vALgz8wQk1GcSaL0ToLjGZl3VkWncOovDVXK0gOqp1oKNFg1feWpUbXtBrVxeZkZr9Ngje53T2ptSTLhLmuX0sFs7w3UUOQ3tVjTE02uju7dqv1a1v8ripguIabnSBnQjJG/SmvNUl9Y7lo6vq1ueAoq88zHrF0+bj5S1wZwnJVuEsjTxtPvpcyS7Df3qDWHOuOVnAc0o2qsTshox3UjlbBaqT4tlND6nZ0P7gO7kkIekMYB5DBSVqZC3ZniKjufpAVlU295yvFFf+oRO1nOyutoeN6NHFnrkQLfPcTbBYzyEWhdyhgN46npkOVdKXaWk8Uz8qrwdTWkGmzP6pGIhNQ1pb6KKhWzKso8rVE4BjatBZun+NBbpaHxviRKf9bvkMblr1fJfp5tbfb8d0hqvX831JzFD4rpOXAPaNfJWVz4tcpASzJ2frFP82jxK5NeGI9pQjutzi7PUy4Ru/CPKYKcUGSe027jdUe1tn08tfqI57Ql9d4632SlZyIDsXwD+KaU1GdCv/e6AvkGXFiEhG+ljd+IyunHFOjG7xkwcFwv5VoNZbxHZshnx13Tt3ZXTWpQZg/QD5wtrW+tkl2LBiLhmyrqbvd3sfRBp3pOwV4mkaNbKh8T/I/qrf/U6WVlaEahhnIFc2TrXfKSUs6COQvLyzTZI97WlvFbK8FxJbfyfkelaRbItyrhQHvTWQ+A8oGfJC1dJRnLnS32kH206zUXK0wU94miPKIuXdn+kPDDKfYO85ArtuR6tkhGsgqLMInRf7hR5kW8zryp1P9r5/4W60XVVa0gxEOYEV2qIO9+PKFuzpUxgVcv1+4p2k1vr2UKvZj4TWotjay9/Da0/g79abv3sR6dfsQp3aA1ICubJaES2BEs9/HjdqfDSK1PTMs+Gn1mTupfdcpH8Wlo3k2OftKayR6vmTJ1a6PpFaLy0aLz01GGX7hqNFnW7tkQv2Nyiq24rffm14dZtQXnGUuYjMo2KPaS0cyk/qkOWKp/ja9RbltYqSyuE3WrfBth73gfp3uuLu/vr0rsH4i7FNgOKwGT+MqRdGlPMpVubMzVJATnfUvbV3v09akHufbKgSFm+x4k7Rt46Daicl5L+Qnm2lOy8sQj6vaVT1Ufb2B7Vf72EHNOeyGlfasQt6hEp+W05ggWLdNOKOQI6+Q8pppJxR3PObPc2cxJU4gmTb8pdZXjJTGFC+udO3naWstcdK38NKCecqei6D7TazzBSkBh9kuCOLHOaIfRy8iZBRrR9sp/Ldkre4k0siW6S1HOx4WFjZNZr1rq9tvSI9dh+CT1R62bWXT14fok3R47fRW70QvJqYxWjzheeL0YrVF6u+tykh9kCX6OPGfWxMwuT5VUxPfGJNxcpUTsuEuPDpd0o2sjfTvI2MsvbKV/KuremXD1pkDbmmPIl7j1QRLiiuw+d0dxHzDj6S/T6hLWpyRaOEp7Gpep8wLa0eCp1eckPydbLjd4osTxRnafQ1G1vYey3tJARWb9EcGc2srcte6+SpfCnMJLCQMg3euvyQ5vmJ1DwbyBc2aHm6HN22IH49rbYFNvv4G2I16ouTzQDakFbMFzIvUM1zmqPZh29tqjb9H04+POIQdec9DF50rayS8q85DZ1f/qnZAUyEbHSm57tx2Bz4UeyzKnNeGKybPxoYqG/i9N2LJqDz0iqXPz5yHsNbhRHQn+nqd0YNHV+BFUObXjo9xj85tz0bs/L5tSsr2UuvjykF9A3LhqHN3/1uYrp52OhMmtG3j0HtA5HDdS1t/hfx6H5GE7teflyy+m7Zi89Zl32i9SJLMbD7feM4eazmus5+vNMy9GZaMnNT8Z9QauZSq3RvHv6GI+aNaB5zYU8B+Wlk3h7FRl5fangvYBLhlT8S/zlEv9thNcljTo52lDS9xT11HQPnpr+xqVrdPozH5kMnTqZqtRMHtGhN2I3xY64C7+bZQTY9u1Q+V1K+R+x7u/PDqH1iKyHPkWXJwc9aovo9MPcog3pWZ0xvri6srb4LeTlyuH6zbXf3Ly1v77y6R31DeX3xU/EzyEvWRO/FZ+K+zDeA5Dpr+Kf4t/iPxu9jT9s/HHjT7Lre5cU5sei8rPx5/8CFHT5UQ==</latexit> Question: What is the complexity of computing rE : Rd ! Rd? Finite di↵erences: <latexit sha1_base64="IJjbmZX1RxHFJ6LjH+Uz9oKFiHc=">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</latexit> rE(✓) ⇡ 1 " (E(✓ + " 1) E(✓), . . . E(✓ + " d) E(✓)) <latexit sha1_base64="elfmtYFgpa8JKGP5IFiZSMc3eME=">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</latexit> K(d + 1) operations, intractable for large d.
b, log(a), p a . . . ) and their derivatives cost O(1). <latexit sha1_base64="XBU0O16nV93z/lhQgn5HZRGW7gQ=">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</latexit> Setup: E : Rd ! R computable in K operations. <latexit sha1_base64="BLbI91EqNObAlbI/2RJe4xs+gGo=">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</latexit> Question: What is the complexity of computing rE : Rd ! Rd? Finite di↵erences: <latexit sha1_base64="IJjbmZX1RxHFJ6LjH+Uz9oKFiHc=">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</latexit> rE(✓) ⇡ 1 " (E(✓ + " 1) E(✓), . . . E(✓ + " d) E(✓)) <latexit sha1_base64="elfmtYFgpa8JKGP5IFiZSMc3eME=">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</latexit> K(d + 1) operations, intractable for large d. This algorithm is reverse mode automatic di↵erentiation [Seppo Linnainmaa, 1970] Theorem: there is an algorithm to compute rE in O(K) operations. Seppo Linnainmaa
= P k xk✓k x f(x) = 0 x y y = f(x) <latexit sha1_base64="+XMTGU2h84i8kefw5ntE/6bvDrk=">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</latexit> y = hx, ✓i <latexit sha1_base64="e28RrObc11sWn0kQ5h8O8+nwJLU=">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</latexit> x1 <latexit sha1_base64="8fJQ441uQeL54tkhtX/5TOvRTK0=">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</latexit> xd <latexit sha1_base64="fE3rdXmbVBpApvDfMbC5u6HdDmI=">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</latexit> ✓d <latexit sha1_base64="ki7nwGdAmEGxp6MgNOP55iKvCr8=">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</latexit> ✓1 <latexit sha1_base64="bndq4rqhHbqPw9mJu61gLB09r4Y=">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</latexit> . . . <latexit sha1_base64="bUJ02qeI41DxuTDiB2vInHl2EVQ=">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</latexit> Regression <latexit sha1_base64="OlDgU+OKIQz+ynHUitJ8TvkH7r8=">AAA9i3ictVv9chu3EYfTr1htGqf9szOdaxV3ko6rkRRP20mqmViULClWLNmkZCehreHHiTr7xKN5pGSb0ZP03/Y5+hx9g/avvkJ3F8ABR+JuAdUVRhIOxG93sQD2Azh2R2mST1ZX/3njvR/88Ec//sn7N5d++rMPfv7hrY9+cZxn03EvPuplaTZ+2u3kcZoM46NJMknjp6Nx3DnvpvGT7ssGfv7kIh7nSTZsTd6M4mfnncEwOU16nQk0ndz6sJF28rxo+Pzk1vLqyir9RIuVNVVZFurnMPvo1+uiLfoiEz0xFeciFkMxgXoqOiKH8p1YE6tiBG3PxAzaxlBL6PNYXIklwE6hVww9OtD6Ev4O4Ok71TqEZ6SZE7oHXFL4HQMyErcBk0G/MdSRW0SfT4kytlbRnhFNlO0N/O8qWufQOhFn0MrhdE9fHI5lIk7Fn2kMCYxpRC04up6iMiWtoOSRNaoJUBhBG9b78PkY6j1Caj1HhMlp7KjbDn3+L+qJrfjcU32n4t8k5W0okWiq0WcFhY64IPoRzeYUPpPypMB5ABRiNUasXZKuz2n0Q+g/g/aHUK6opnXShTKj1qtaZAOKC9lgkTtQXMgdFrkPxYXcZ5GHUFzIQ4VE7Jh07sY3objwTZbzIygu5CMW+RiKC/mYRR5DcSGPWeS3UFzIb1nkfSgu5H0W+QCKC/mARbaguJAtFnkExYU8YpHbUFzIbYWs3qljKBnRSZhdeQ/qZR5oKVJoucfKt0nW0YXd9NjTvQosv6u34L8bu+Wh07gCu+2x7k4rsPzK2wEb6cbytmiXvIkLu8ti92AFuLF7LPYr8aIC+5XHTntZgeX32j70c2N56/s1PLmxX7PYh1BzY3kfdQAtbuyBh8cYVWAPWewj8aoC62P1xxVY3u43wa64sbyfakF/N9bHmk4rsLw9PYYIxo3lvdUTaHVjn7DYp+J1BfYpi/0GrLsb+42Hh31bgdU+dok8yIDikRh2bB21TrErsTYCah2Gf1r4lpRi4y60c5hBgRkQ5pxF7BSIHU/EfoHY95YrL+xoTvEuz6VZIJqeiG7hm7A2Yfv3i/5YSz0QWwViaw5RF5HiXOuxXFB0oVs45KTwXFjzGVNW2G+sxWo91FtejTgoIeTaPqOVf4eyJcygUFN11M4KHy+RET3XIS4pe9Oj1Dx43KSwCjbqNYvqOlBdFvXGgXrDoqYO1JRFXThQFyzK7Hwb1/ZYAUb/OBczepIrQMbI1SWCqOAeeJ1d2KMRrJ9DiAIfU8sB/G9S7s2VOskwm0c/iaccz0qWeAy1mViGdpMVblF+ndIOi0Ey2fNA5fj4hGcbM7XnpBW+Kjx5VJyY+NNJSJ5BQQejxYj2UxidB9RyRdGdrIXhd4t9r2th+G3S+BVF8bIWhp8o6SfXkL2lsK1rYJuwm0ZK+6YeSkOev0gaur5EXhctLs7quVozSO91IP09NTN715iXBtWkfkw9jEZujS8vjS+EhtFzbuk5jApGTzLq1bUoeCRDlfeaeqgMGXnRoZLDPIXODPbpq5nR9TAahxBxNSjnnln10NU7KkZj6mE0joU897yiSF7Xw2gM6Fnqw9TDaOBpS0fl+aYeatlRAzJ3NvVQqz6kU2A8A5JrXraYqGhMcdJUUUsoPqg/rbFj/kU/hmc2z4scoZ6SiW2r6XQLX1YvkY4XYrBqk0A5ML6YWjFYmcZMrLP5lZRhUvLvi3SMj0fN74MWI9j98g6AOzNPQUJ9JoHWOwWKa2zWVR6Zxq2zOFwlp3OotmqdsNGi4StPjcptJ9TK5WVmtEaPbbLXOa29EcWE+6RZTg/7lTNcRZHT0H5JQzy9EN29Vfu1rP1VFjeaQ4yKldajGyF5k1afp7q03rR0fFvd8kygyDsfs37xtPlUWRvMeTKyRShLHU+7nz5HstvQr94R5oxbfhbRjKK9uiCrkdCNVM5mofq0WEbjM3o2tI/oTg55SBo9mMdIURkJeWuGp+h4nh6RRbXtLccb9aVP6GQ9J6ur7XE9emChBw50eI7TAI/xEGotyBmO4KnlkeUsFbrKSONj8YfidjSjGazP6NOShdQ0pL2JSxayLss+K1G5BDSuBpml+9OYp6Px7QVKfNbvksfkrmXLf5tubvX9dofWePVqrj6J6RPXdeIa0a6Rt7ryaZ6DlGDm/GSd4tf6USK/EI5oQzmuzy3OUi9DuvGPKYMdUWSc0m7jdke5t30+Nf+J5nQo9N053mZnZCEjsn8R+KeM1mREv/a7A/oGXVqElGykj91JiujGFesk7BozcVwi5FsNZr3FZMumxF/TtXdXTmtRZgzSD1zNrW2tk32KBWPiOlbW3ezteu+DSPOehL1KJEWzVj4h/p/SX/2r18nywopADeMM5MrWueYjo5wFddQhL19vg3RfW8qPCxmeK6mN/zMyfVySbIsyLpQHvXUfOPfoWfLCVTImufOFPtKP1p3mIuXRnB5xtKeUxUu7P1AeGOW+Q15ymfZcm1bJAFbBpMgidF/uFHmebz2vMnU/2vn/hbrRdVlrSDES5gRXaog7348pW7OlTGFVy/X7knaTW+vjuV71fIa0Fs+tvfw9tP4G/mq59bMfnW7JKmzSGpAUzJPRiGyJFnr48dos8dIrU9Myz4afWZO6l91ynfxaWjeTY18EUzmkVfNanVro+nVovLBovPDUYYvuGo0Wdbu2RCdsbtFSt5W+/EK4tQIoT1nKfESmUYmHlHYu5Ue1z1Llc3yNesvSWmVpdWC32rcB9p73Qbr3+vzu/r7w7pG4T7FNjyIwmb/0aZcmFHPp1vpMTVJAzneVfbV3f5takHuXLChSlu9x4o6Rt049KleFpL9Tni0jO28sgn5v6VL10Ta2TfXPFpDntCdy2pcacZd6xEp+W45oziKtWDFHRCf/HYqpZNxRnzPbvc2cRKV4wuSbclcZXjJTGJL+uZO3vYXsdc/KXyPKCacquu4CrfAZRgoSo08S3JFlTjOEXk7eJMiItkv2c9FOyVu8oSXRCkk9ExseNkZmvWat22tLj1iP7ffQE7VuZt3Vg+eXenPk+F3nRq9DXu1cxaizuefr0eooL1d+rtPDdI6v0ceU+tiZhcnyypi2+MKbi5QojIvE+HAJG0WI/GGSh8gsb6d8KevemnL5pEHamDPKl7j3QBHhiu4+cUZznzLj6C7Q6xLWpiZbOEp4Gpep8wHb0uKp1M0FPyRbb9Z6o9TyRFWeQlO3vYWx39JCxmT9UsGd2cjetuztUpbCn8JICj0h3+ityg9tml9Awb+RcGWHmqPP2WET4tt7oiG238HbEK9UXZ5oRtSCtqA/l3t31DjLPep19MqibtP34eDPIwFdc9In5ElDZZeUeclt6v70L8kKjEXMSm96ho/B5sKPZJFTyHgSsmz8aBKhv4sTOhbNwWckZS7+fOS9BjeKU6G/0xQ2Bk2dH0GZQwgP/R6D35yb3uG8bE71+lrk4stDegF946JxePNXnauYfj4WamzNyLvngNbhtIa69hb/6zg0H8MpnJcvt5y+a/bCY9Zlv1idyGI8HL5nDDef1VzN0Z9nVozOREtufjLui4JmKrNG8+7pYzxq1oDmNRPyHJSXTuLtVWTk9aWC9wIuGTLxH/GPG/y3EV4VNKrkCKGk7ymqqekePDX9jUvX6PRnPjIZOlUylamZPKJJb8Q2xJ64D7+NIgIMfTtUfpdS/kes+/uzfWg9JeuhT9HlyUGb2mI6/TC3aH16VmeMJ7eW1+a/hbxYOV5fWfvjyt1H68tfbqpvKL8vfiV+C3nJmviT+FLswniPBH5T+a/ib+LvGx9sfLbx+cZfZNf3bijML0XpZ2P7v8Qf2jo=</latexit> Classification: <latexit sha1_base64="oZtLSn/RQ6q3EYWRSzhaZE3zewI=">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</latexit> min ✓ , 1 n n X i=1 `(hxi, ✓i i, yi) <latexit sha1_base64="PvseIPRi4Nf4IH/9H8AceNGnDTM=">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</latexit> Convex optimization:
= P k xk✓k <latexit sha1_base64="5ovuZPU8dBWGm61iCoXPGu2QOzU=">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</latexit> Deep learning methods: learn '(x)! <latexit sha1_base64="1XeLXevO/37cS+xzOgmDhuoA57o=">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</latexit> Kernel methods: replace x by '(x) 2 RD <latexit sha1_base64="tiWppV9cOnzGLrlROqmigub8TPo=">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</latexit> (D d, even D = 1!) x f(x) = 0 x y y = f(x) <latexit sha1_base64="+XMTGU2h84i8kefw5ntE/6bvDrk=">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</latexit> y = hx, ✓i <latexit sha1_base64="e28RrObc11sWn0kQ5h8O8+nwJLU=">AAA9fXictVvrchu3FYbTS2L15rQ/O9PZVlEnybgaSfE0nUk1E+tiSbFiySYlOwltDS8rau0Vl+aSkmxGj9C/7eP0OfoG7a8+QnvOAbDAktg9gOoKIwkL4jvn4AA4F2DZGaZJPl5Z+cet937wwx/9+P0Pbi/85Kc/+/kv7nz4y+M8m4y68VE3S7PRs047j9NkEB+Nk3EaPxuO4vZ5J42fdl5t4udPL+JRnmSD5vjNMH5+3u4PktOk2x5DU+PqZPXkzuLK8gr9RPOVVVVZFOrnMPvwN2uiJXoiE10xEeciFgMxhnoq2iKH8p1YFStiCG3PxRTaRlBL6PNYXIsFwE6gVww92tD6Cv724ek71TqAZ6SZE7oLXFL4HQEyEkuAyaDfCOrILaLPJ0QZW6toT4kmyvYG/ncUrXNoHYszaOVwuqcvDscyFqfiTzSGBMY0pBYcXVdRmZBWUPLIGtUYKAyhDes9+HwE9S4htZ4jwuQ0dtRtmz7/J/XEVnzuqr4T8S+ScglKJBpq9FlBoS0uiH5EszmBz6Q8KXDuA4VYjRFrl6Trcxr9APpPof0RlGuqaZ10oEyp9boWuQnFhdxkkTtQXMgdFrkPxYXcZ5GHUFzIQ4VE7Ih07sY3oLjwDZbzYygu5GMW+QSKC/mERR5DcSGPWeS3UFzIb1nkAygu5AMW+RCKC/mQRTahuJBNFnkExYU8YpHbUFzIbYWs3qkjKBnRSZhdeR/qZR5oKVJouc/Kt0HW0YXd8NjT3Qosv6u34L8bu+Wh07gCu+2x7k4rsPzK2wEb6cbytmiXvIkLu8ti92AFuLF7LPYr8bIC+5XHTntVgeX32j70c2N56/s1PLmxX7PYR1BzY3kfdQAtbuyBh8cYVmAPWexj8boC62P1RxVY3u43wK64sbyfakJ/N9bHmk4qsLw9PYYIxo3lvdVTaHVjn7LYZ+KqAvuMxX4D1t2N/cbDw76twGofu0AepE/xSAw7to5au9iVWBsCtTbDPy18S0qxcQfaOUy/wPQJc84idgrEjidiv0Dse8uVF3Y0p3iX59IoEA1PRKfwTVgbs/17RX+spR6IrQKxNYOoi0hxrvVYLii60C0cclx4Lqz5jCkr7DfWYrUe6i2vRhyUEHJtn9HKv0vZEmZQqKk6ameFj5fIiJ7rEJeUvelRah48blxYBRt1xaI6DlSHRb1xoN6wqIkDNWFRFw7UBYsyO9/GtTxWgNE/zsWUnuQKkDFydYkgKrgPXmcX9mgE6+cQosAn1HIA/xuUe3OlTjLM5tFP4inH85IlHkFtKhah3WSFW5Rfp7TDYpBM9jxQOT4+4dnGVO05aYWvC08eFScm/nQSkqdf0MFoMaL9FEbnIbVcU3Qna2H43WLf61oYfps0fk1RvKyF4cdK+vENZG8qbPMG2AbspqHSvqmH0pDnL5KGri+Q10WLi7N6rtYM0rsKpL+nZmbvBvOySTWpH1MPo5Fb48tL4wuhYfScW3oOo4LRk4x6dS0KHslA5b2mHipDRl50oOQwT6Ezg316amZ0PYzGIURcm5RzT6166OodFqMx9TAax0Kee15TJK/rYTT69Cz1YephNPC0pa3yfFMPteyoAZk7m3qoVR/QKTCeAck1L1tMVDSiOGmiqCUUH9Sf1tgx/7wfwzObF0WOUE/JxLbVdDqFL6uXSMcLMVi1caAcGF9MrBisTGMq1tj8SsowLvn3eTrGx6Pm90GLEex+eQfAnZmnIKE+k0DrnQLFVTbrKo9M49ZYHK6S0xlUS7WO2WjR8JWnRuW2E2rl8jIzWqPHFtnrnNbekGLCfdIsp4f9yhmuoshpaL+kIZ5eiO7eqv1a1v4KixvOIIbFSuvSjZC8SavPU11ab1g6XlK3PGMo8s7HrF88bT5V1gZznoxsEcpSx9Pup8+R7Db0q3eFOeOWn0U0o2ivLshqJHQjlbNZqD4tltH4lJ4N7SO6k0MekkYX5jFSVIZC3prhKTqep0dkUW17y/FGfekTOlnPyepqe1yP7lvovgMdnuNsgsd4BLUm5AxH8NT0yHIWCl1lpPGR+ENxO5rRDNZn9GnJQmoa0t7EJQtZl2WflahcAhpXg8zS/WnM0tH41hwlPut3yWNy17LlX6KbW32/3aY1Xr2aq09iesR1jbhGtGvkra58muUgJZg6P1mj+LV+lMgvhCPaUI7rC4uz1MuAbvxjymCHFBmntNu43VHubZ9PzX6iOR0KfXeOt9kZWciI7F8E/imjNRnRr/3ugL5BlxYhJRvpY3eSIrpxxToJu8ZMHJcI+VaDWW8x2bIJ8dd07d2V01qUGYP0A9cza1vrZJ9iwZi4jpR1N3u73vsg0rwnYa8SSdGslY+J/yf0V//qdbI4tyJQwzgDubJ1rvnIKGdBHbXJy9fbIN3XlvKjQoYXSmrj/4xMH5Uk26KMC+VBb90Dzl16lrxwlYxI7nyuj/Sjdae5SHk4o0cc7Sll8dLu95UHRrnvkpdcpD3XolXSh1UwLrII3Zc7RZ7lW8+rTN2Pdv5/oW50XdYaUoyEOcGVGuLO92PK1mwpU1jVcv2+ot3k1vpoplc9nwGtxXNrL38Prb+Fv1pu/exHp1OyChu0BiQF82Q0IluiuR5+vDZKvPTK1LTMs+Fn1qTuZbfcJL+W1s3k2BfBVA5p1VypUwtdvwmNlxaNl546bNJdo9GibteW6ITNLZrqttKXXwi3ZgDlCUuZj8g0KvGQ0s6l/Kj2WKp8jq9Rb1laKyytNuxW+zbA3vM+SPden93d3xfePRIPKLbpUgQm85ce7dKEYi7dWp+pSQrI+Z6yr/bub1ELcu+QBUXK8j1O3DHy1qlL5bqQ9PfKs2Vk541F0O8tXao+2sa2qP7ZHPKc9kRO+1Ij7lGPWMlvyxHNWKRlK+aI6OS/TTGVjDvqc2a7t5mTqBRPmHxT7irDS2YKA9I/d/K2N5e97ln5a0Q54URF1x2gFT7DSEFi9EmCO7LMaYbQy8mbBBnRdsh+ztspeYs3sCRaJqmnYt3Dxsis16x1e23pEeuxfQo9Uetm1l09eH6pN0eO301u9Nrk1c5VjDqdeb4ZrbbycuXnOj1MZvgafUyoj51ZmCyvjGmJL7y5SInCuEiMD5ewUYTIHyZ5iMzydsqXsu6tKZdPGqSNOaN8iXsPFBGu6O5jZzT3CTOOzhy9DmFtarKFo4SncZk6H7AtLZ5K3Z7zQ7L1dq03Si1PVOUpNHXbWxj7LS1kTNYvFdyZjexty94qZSn8KYyk0BXyjd6q/NCm+QUU/BsJV3aoOfqcHTYgvr0vNsX2O3gb4rWqyxPNiFrQFvRmcu+2Gme5R72OXlvUbfo+HPx5JKBrTvqEPGmo7JIyL7lN3Z/+JVmBkYhZ6U3P8DHYXPiRzHMKGU9Clo0fTSL0d3FCx6I5+IykzMWfj7zX4EZxKvR3msLGoKnzIyhzCOGh32Pwm3PTO5yXzaleX/NcfHlIL6BvXDQOb/6qcxXTz8dCjawZefcc0Dqc1lDX3uJ/HYfmYziF8/LlltN3zV56zLrsF6sTWYyHw/eM4eazmqs5+vPMitGZaMnNT8Z9UdBMZdZo3j19jEfNGtC8pkKeg/LSSby9ioy8vlTwXsAlQyb+Lf5+i/82wuuCRpUcIZT0PUU1Nd2Dp6a/cekanf7MRyZDp0qmMjWTRzTojdhNsScewO9mEQGGvh0qv0sp/yPW/f3ZHrSekvXQp+jy5KBFbTGdfphbtB49qzPGkzuLq7PfQp6vHK8tr/5x+d7je4tfbqhvKH8gfi1+B3nJqvhcfCl2YbxHIFNf/EX8Vfztz/9ZX1q/u74su753S2F+JUo/65//Fyag1bQ=</latexit> x1 <latexit sha1_base64="8fJQ441uQeL54tkhtX/5TOvRTK0=">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</latexit> xd <latexit sha1_base64="fE3rdXmbVBpApvDfMbC5u6HdDmI=">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</latexit> ✓d <latexit sha1_base64="ki7nwGdAmEGxp6MgNOP55iKvCr8=">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</latexit> ✓1 <latexit sha1_base64="bndq4rqhHbqPw9mJu61gLB09r4Y=">AAA9gHictVvpchu5EYada61c3uRnqlKTaJ3yphxFUlxJKluqWuuwpLXWkk1K9u7SdvEYUSMPOTSHlGxz9Q75m7xMniNvkPzKK6S7AQwwJGYaUByhJGFAfN2NBtAHMOyM0iSfrK7+88bN73z3e9//wUe3ln74ox//5Ke3P/7ZSZ5Nx934uJul2fh5p53HaTKMjyfJJI2fj8Zxe9BJ42ed11v4+bOLeJwn2bA5eTeKXwza/WFymnTbE2g6aaW9bJK/ur28urJKP9FiZU1VloX6Oco+/uW6aImeyERXTMVAxGIoJlBPRVvkUL4Ra2JVjKDthZhB2xhqCX0eiyuxBNgp9IqhRxtaX8PfPjx9o1qH8Iw0c0J3gUsKv2NARuIOYDLoN4Y6covo8ylRxtYq2jOiibK9g/8dRWsArRNxBq0cTvf0xeFYJuJU/JnGkMCYRtSCo+sqKlPSCkoeWaOaAIURtGG9B5+Pod4lpNZzRJicxo66bdPn/6Ke2IrPXdV3Kv5NUt6BEomGGn1WUGiLC6If0WxO4TMpTwqc+0AhVmPE2iXpekCjH0L/GbQ/hnJFNa2TDpQZtV7VIreguJBbLHIXigu5yyIPoLiQByzyCIoLeaSQiB2Tzt34BhQXvsFyfgLFhXzCIp9CcSGfssgTKC7kCYv8GooL+TWLfAjFhXzIIh9BcSEfscgmFBeyySKPobiQxyxyB4oLuaOQ1Tt1DCUjOgmzKx9AvcwDLUUKLQ9Y+TbJOrqwmx57uluB5Xf1Nvx3Y7c9dBpXYHc81t1pBZZfebtgI91Y3hbtkTdxYfdY7D6sADd2n8V+Ic4rsF947LTXFVh+rx1APzeWt75fwpMb+yWLfQw1N5b3UYfQ4sYeeniMUQX2iMU+EW8qsD5Wf1yB5e1+A+yKG8v7qSb0d2N9rOm0Asvb0xOIYNxY3ls9g1Y39hmLfS7eVmCfs9ivwLq7sV95eNj3FVjtY5fIg/QpHolhx9ZRaxe7EmsjoNZm+KeFb0kpNu5AO4fpF5g+YQYsYrdA7HoiDgrEgbdceWFHc4p3eS6NAtHwRHQK34S1Cdu/V/THWuqB2C4Q23OIuogU51qP5YKiC93CISeF58Kaz5iywn5jLVbrod7yasRhCSHX9hmt/HuULWEGhZqqo3ZW+HiJjOi5DnFJ2ZsepebB4yaFVbBRb1lUx4HqsKh3DtQ7FjV1oKYs6sKBumBRZufbuJbHCjD6x7mY0ZNcATJGri4RRAUPwOvswR6NYP0cQRT4lFoO4X+Dcm+u1EmG2Tz6STzleFGyxGOozcQytJuscJvy65R2WAySyZ6HKsfHJzzbmKk9J63wVeHJo+LExJ9OQvL0CzoYLUa0n8LoPKKWK4ruZC0Mv1fse10Lw++Qxq8oipe1MPxEST+5huxNhW1eA9uA3TRS2jf1UBry/EXS0PUl8rpocXFWB2rNIL23gfT31czsX2Netqgm9WPqYTRya3x5aXwhNIyec0vPYVQwepJRr65FwSMZqrzX1ENlyMiLDpUc5il0ZrBPT82MrofROIKIa4ty7plVD129o2I0ph5G40TIc88riuR1PYxGn56lPkw9jAaetrRVnm/qoZYdNSBzZ1MPtepDOgXGMyC55mWLiYrGFCdNFbWE4oP60xo75l/0Y3hm87LIEeopmdi2mk6n8GX1Eul4IQarNgmUA+OLqRWDlWnMxDqbX0kZJiX/vkjH+HjU/AFoMYLdL+8AuDPzFCTUZxJovVOguMZmXeWRadw6i8NVcjqHaqnWCRstGr7y1Kjc9opaubzMjNbosUX2Oqe1N6KY8IA0y+nhoHKGqyhyGjooaYinF6K792q/lrW/yuJGc4hRsdK6dCMkb9Lq81SX1huWju+oW54JFHnnY9YvnjafKmuDOU9GtghlqeNp99PnSHYb+tV7wpxxy88imlG0VxdkNRK6kcrZLFSfFstofEbPhvYx3ckhD0mjC/MYKSojIW/N8BQdz9Mjsqi2veV4o770CZ2s52R1tT2uR/ctdN+BDs9xtsBjPIZaE3KGY3hqemQ5S4WuMtL4WPyuuB3NaAbrM/q0ZCE1DWlv4pKFrMuyz0pULgGNq0Fm6f405ulofGuBEp/1u+QxuWvZ8t+hm1t9v92mNV69mqtPYnrEdZ24RrRr5K2ufJrnICWYOT9Zp/i1fpTIL4Qj2lCO60uLs9TLkG78Y8pgRxQZp7TbuN1R7m2fT81/ojkdCX13jrfZGVnIiOxfBP4pozUZ0a/97oC+QZcWISUb6WN3kiK6ccU6CbvGTByXCPlWg1lvMdmyKfHXdO3dldNalBmD9ANXc2tb6+SAYsGYuI6VdTd7u977INK8J2GvEknRrJW7xP9T+qt/9TpZXlgRqGGcgVzZOtd8ZJSzoI7a5OXrbZDua0v5SSHDSyW18X9Gpk9Kkm1TxoXyoLfuAecuPUteuErGJHe+0Ef60brTXKQ8mtMjjvaUsnhp9/vKA6Pc98hLLtOea9Eq6cMqmBRZhO7LnSLP863nVabuRzv/v1A3ui5rDSlGwpzgSg1x5/sxZWu2lCmsarl+X9Nucmt9PNerns+Q1uLA2svfQuuv4K+WWz/70emUrMImrQFJwTwZjciWaKGHH6/NEi+9MjUt82z4mTWpe9kt18mvpXUzOfZFMJUjWjVv1amFrl+HxrlF49xTh026azRa1O3aEr1ic4umuq305RfCrRlAecpS5iMyjUo8pLRzKT+qPZYqn+Nr1HuW1ipLqw271b4NsPe8D9K91+d397eFd4/EQ4ptuhSByfylR7s0oZhLt9ZnapICcr6v7Ku9+1vUgtw7ZEGRsnyPE3eMvHXqUrkqJP2N8mwZ2XljEfR7S5eqj7axLar/YQE5oD2R077UiPvUI1by23JEcxZpxYo5Ijr5b1NMJeOO+pzZ7m3mJCrFEybflLvK8JKZwpD0z5287S9kr/tW/hpRTjhV0XUHaIXPMFKQGH2S4I4sc5oh9HLyJkFGtB2yn4t2St7iDS2JVkjqmdjwsDEy6zVr3V5besR6bL+Fnqh1M+uuHjy/1Jsjx+86N3pt8moDFaPO5p6vR6utvFz5uU4P0zm+Rh9T6mNnFibLK2Na4jNvLlKiMC4S48MlbBQh8odJHiKzvJ3ypax7a8rlkwZpY84oX+LeA0WEK7q764zmPmXG0Vmg1yGsTU22cJTwNC5T5wO2pcVTqVsLfki23qr1Rqnliao8haZuewtjv6WFjMn6pYI7s5G9bdlbpSyFP4WRFLpCvtFblR/aND+Dgn8j4coONUefs8MGxLcPxJbY+QBvQ7xRdXmiGVEL2oLeXO7dVuMs96jX0RuLuk3fh4M/jwR0zUmfkCcNlV1S5iW3qfvTvyQrMBYxK73pGT4Gmws/kkVOIeNJyLLxo0mE/i5O6Fg0B5+RlLn485H3GtwoToX+TlPYGDR1fgRlDiE89HsMfnNueofzsjnV62uRiy8P6QX0jYvG4c1fda5i+vlYqLE1Ix+eA1qH0xrq2lv8r+PQfAyncF6+3HL6rtm5x6zLfrE6kcV4OHzPGG4+q7maoz/PrBidiZbc/GTcFwXNVGaN5sPTx3jUrAHNaybkOSgvncTbq8jI60sF7wVcMmTiP+IfN/hvI7wpaFTJEUJJ31NUU9M9eGr6G5eu0enPfGQydKpkKlMzeUSD3ojdEvviIfxuFRFg6Nuh8ruU8j9i3d+f7UHrKVkPfYouTw5a1BbT6Ye5RevRszpjfHV7eW3+W8iLlZP1lbU/rtx/cn/58031DeWPxC/EryEvWRN/Ep+LPRjvMch0Lv4q/ib+vnFz4+7G7zfWZNebNxTm56L0s/GX/wJfNdZN</latexit> . . . <latexit sha1_base64="bUJ02qeI41DxuTDiB2vInHl2EVQ=">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</latexit> Regression <latexit sha1_base64="OlDgU+OKIQz+ynHUitJ8TvkH7r8=">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</latexit> Classification: <latexit sha1_base64="oZtLSn/RQ6q3EYWRSzhaZE3zewI=">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</latexit> min ✓ , 1 n n X i=1 `(hxi, ✓i i, yi) <latexit sha1_base64="PvseIPRi4Nf4IH/9H8AceNGnDTM=">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</latexit> Convex optimization:
<latexit sha1_base64="4q707XOseaJG4SEM7kRUBlKiggY=">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</latexit> w1 <latexit sha1_base64="dTEPGRjwpObKto22Pdj89jMy0R4=">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</latexit> a1 p = 6 neurons p = 30 neurons p = 100 neurons <latexit sha1_base64="v5o5dJsoyPefg3wihB9aJpDhTXc=">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</latexit> Input y = f(x) <latexit sha1_base64="ttgglA5lmQEZUY9EO2WF1erSv+8=">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</latexit> ! sum of “ridge” functions (hx, wi + b) <latexit sha1_base64="ZUzFyuvUCbPFlo/gmg9KYP4mygc=">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</latexit> f✓(x) , p X s=1 as (hx, ws i + bs) <latexit sha1_base64="ax7LaFmi/3bdYTxeFckx/E70i7o=">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</latexit> wp <latexit sha1_base64="Tb21R6PdEthdsl9c3KfkRE3g53s=">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</latexit> ap George Cybenko Andrew Barron
<latexit sha1_base64="4q707XOseaJG4SEM7kRUBlKiggY=">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</latexit> w1 <latexit sha1_base64="dTEPGRjwpObKto22Pdj89jMy0R4=">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</latexit> a1 p = 6 neurons p = 30 neurons p = 100 neurons <latexit sha1_base64="v5o5dJsoyPefg3wihB9aJpDhTXc=">AABB0XictVzdchPJFW42fwv5WTa5zM0khhSkCDEOlaRqa6vW2MZ4EWCQbNhdAaWfsRCMNEIjGRutq1K5zSPkNnmOPEfeILnKK+T8dE/3SD1zehxCl+2eVn/nnD7Tffqc0y26k2SYzdbX/3nho+9893vf/8HHFy/98Ec//sknlz/96WGWzqe9+KCXJun0WbeTxclwHB/MhrMkfjaZxp1RN4mfdt9s4edPj+NpNkzHrdnpJH4+6gzGw6NhrzODppeXP9kbT+az6Mrp50fXTq5fiV5eXlu/uU7/otXKLV1ZU/rffvppdKDaqq9S1VNzNVKxGqsZ1BPVURmUb9Qtta4m0PZcLaBtCrUhfR6rM3UJsHPoFUOPDrS+gd8DePpGt47hGWlmhO4BlwR+poCM1FXApNBvCnXkFtHnc6KMrWW0F0QTZTuFv11NawStM/UKWiWc6RmKw7HM1JH6I41hCGOaUAuOrqepzEkrKHnkjGoGFCbQhvU+fD6Feo+QRs8RYTIaO+q2Q5//i3piKz73dN+5+jdJeRVKpJp69GlOoaOOiX5Eb3MOn7E8CXAeAIVYjxFr70jXIxr9GPovoP0hlDOqGZ10oSyo9awSuQXFh9wSkbtQfMhdEdmA4kM2ROQ+FB9yXyMROyWd+/FNKD58U+T8GIoP+VhEPoHiQz4RkYdQfMhDEfk1FB/yaxF5F4oPeVdE3ofiQ94XkS0oPmRLRB5A8SEPROQOFB9yRyPLV+oUSkp0hsKq3IR6kQdaigRaNkX57pB19GHvBKzpXglWXtXb8NeP3Q7QaVyC3QmYd0clWHnm7YKN9GNlW3SPdhMf9p6I3YMZ4Mfuidgv1esS7JcBK+1NCVZeaw3o58fK1vcBPPmxD0TsQ6j5sfIe9Qha/NhHATvGpAS7L2Ifq7cl2BCrPy3Byna/CXbFj5X3qRb092NDrOm8BCvb00PwYPxYebd6Cq1+7FMR+0ydlGCfidivwLr7sV8F7LDvS7Bmj71EO8iA/JEYVmwVtU6+KrE2AWodgX+S7y0J+cZdaJcwgxwzIMxIROzmiN1ARCNHNILlynI7mpG/K3Np5ohmIKKb701Ym4n9+3l/rCUBiO0csb2EqPJI8V2bsRyTd2FaJOQs37mwFjKmNLffWIv1fKi2vAbxqIDguf2KZv4NipYwgkJNVVF7le/xjIzouQrxjqI3M0rDQ8bNcqvgok5EVNeD6oqoUw/qVETNPai5iDr2oI5FlF35Lq4dMAOs/vFdLOiJZwD7yOUlAq9gE3ade7BGI5g/++AFPqGWR/C3SbG3VKokw2ge90nMcjwvWOIp1BZqDdptVLhN8XVCKywGybjnIx3j4xPmNhZ6zbEVPst38ijPmITTGZI8g5wOeosRrad6dO5Tyxl5d1yrh7+Xr3tTq4ffIY2fkRfPtXr4mZZ+dg7ZWxrbOge2CatporVv63VpcP6FaZj6Jdp10eLiWx3pOYP0TmrS39NvZu8c72WLaqwfW69HI3PGlxXGV4eG1XPm6LkeFfSe2Os1taj2SMY67rX1ujKktIuOtRz2qe6bwT59/WZMvR6NffC4tijmXjj1urN3ko/G1uvROFSc9zwjT97U69EY0DPrw9br0cBsS0fH+bZe17KjBjh2tvW6Vn1MWWDMAfGc5xbrFU3JT5prakPyD6qzNa7Pv7qPYc7mRR4jVFOyvm05nW6+l1VLZPyFGKzarKYc6F/MHR+sSGOhNsT4imWYFfb3VTp2j0fNN0CLEax+PgOQcuYJSGhyEmi9E6B4S4y6iiMzuA0Rh7PkaAnV1q0z0Vu0fDlrVGx7Sa1SXGZHa/XYJnud0dybkE/YIM1KemiUvuEyipKGGgUNyfTq6O69Xq9F7a+LuMkSYpLPtB6dCPFJWnWc6tN609HxVX3KM4PCZz52/mK2+UhbG4x5UrJFKEsVT7efySO5bbiv3lA2x82fRfRG0V4dk9UY0olUJkahJlvM3viCni3tAzqTQx5MowfvMdJUJopPzTCLjvn0iCyqa28l3qgvk6HjekZW19jjavTAQQ886PoxzhbsGA+h1oKY4QCeWgFRzqVcVylpfKp+k5+OpvQGqyP6pGAhDQ22N3HBQlZF2a8KVN4BGmcDR+nhNJbpGHx7hZIc9fvksbFr0fJfpZNbc77doTlePpvLMzF94rpBXCNaNXyqy0/LHFiChfeTDfJfq0eJ/OpwRBsqcX3hcGa9jOnEP6YIdkKecUKrTVodxd5ufmr5E8NpX5mzczzNTslCRmT/ItifUpqTEf24dwfMCTpbhIRsZIjdGebejc/XGYpzzPpxQ8W3Gux8i8mWzYm/oeuurozmIkcMvA+cLc1to5MG+YIxcZ1q627XdvXug0h7T8KdJUzRzpVrxP86/TY/Zp6srcwI1DC+gUzbOt/7SClmQR11aJevtkGmryvllVyGF1pqu/9Zma4UJNumiAvlwd26D5x79My8cJZMSe5spQ/vo1XZXKQ8WdIjjvaIoni2+wO9A6PcN2iXXKM116ZZMoBZMMujCNNXyiIv863mVaQeRjv7v1C3ui5qDSlGymZwWUNSfj+maM2VMoFZzfP3Da0mv9anS72q+YxpLo6ctfwttP4Cfhu5zXMYnW7BKtyhOcAU7JPVCLdEKz3CeN0p8DIz09Cyz5afnZOml9tynviarZuNsY9rU9mnWXOisxamfh4arx0arwN12KKzRqtF024s0Usxtmjp08pQfnW4tWpQnouUZY/MoIYBUrqxVBjVvkhVjvEN6r1Ia12k1YHV6p4GuGs+BOlf68ur+9t8d4/UXfJteuSBcfzSp1U6JJ/LtFZHakwBOd/W9tVd/W1qQe5dsqBIme9x4orhU6celbNc0l/pnS0lO28tgrm39E73MTa2TfXfrSBHtCYyWpcGcZt6xFp+V45oySLddHyOiDL/HfKp2O+ojpnd3vadRAV/wsabvKosL44UxqR/KfO2txK97jnxa0Qx4Vx7112gVf8NIwXGmEyC37PM6A3hLscnCezRdsl+rtopPsUbOxLdJKkX6vMAG8NRr53r7twyIzZj+zX0RK3bt+7rIfNLgjlK/M5zotehXW2kfdTF0vP5aHX0Lld8rtLDfImv1cec+riRhY3yipi2+iyYC0tUjwtjQrjUG0Ud+etJXkdmPp0KpWx6G8rFTAPbmFcUL0n3QBHh8+6ueb2568I4uiv0uoR1qXGLRAmzcanOD7iWFrNSF1f2IW69WLkbJc5OVLZTGOrubmHtN1vImKxfoqScDfd2ZW8XohQ5C8MUeopv9JbFhy7Nz6Dg70j5okPDMSR32AT/dlNtqZ0PcBvira5zRjOiFrQF/aXYu6PHWexRraO3DnWXfgiHcB5D0LUk/ZB20rqyM2VZcpd6OP13ZAWmKhaltz3rj8HlIo9klVOd8QzJssmjGSrzXZy6YzEcQkZS5BLOh881pFEcKfOdpnpjMNTlERQ51OFh7jGEvXPbuz4vl1O1vla5hPLgXcCcuBgcnvyVxyq2X4iFmjpv5MNzQOtwVEHd7Bb/6zgMH8upPq9Qbhl91+x1wFvnfrHOyKI/XH/NWG4hs7mcYzjPNB+d9Zb8/Njvi2q9qdQZzYenj/6onQOG10JxHlSWjvHuLLLyhlLBcwGfDKn6j/rHBfnbCG9zGmVy1KFkzinKqZkeMjXzjUvf6MxnITJZOmUyFanZOKJJN2K31J66Cz9buQdY93Yof5eS/yLW//3ZPrQekfUwWXTOHLSpLabshz1F69OzvT9bJjHe5eW7vS1owbPwBrXiPd+H1B/v+rYKYyv/Bgmv9QcqVf1CRLJ8umfXVRdGUDx54xyQ+Z5vRHfpOYvFN89GAWeL5v7UskQL+kS+WdAtxXcdKXs0Vyf6rB5PDvCGfSfPD0Xqt9TW0XYe91yJ834p5/0lzhlpp8jhxPms+m5WGZcth0s/z50d634pxdn2PK86N7pdyoXvoFfjBxX4gSNlk7T/hiLhqarO5s0raM61TO4J61iZTCTrAePMTv6+qyPb4wpexwHjv1+Kvu9IuguydCn/HdEJ25ToJVo3OyQ933SszqTeq5BWf4/y5eW1W8v/l8Fq5XDj5q3f37z9eGPtizv6/zn4WP1c/VJdgzX+B/UFUNtXBwr/v4O/qr+pv282N083/7T5Z+760QWN+Zkq/Nv8y38BeaelZQ==</latexit> Input y = f(x) <latexit sha1_base64="ttgglA5lmQEZUY9EO2WF1erSv+8=">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</latexit> ! sum of “ridge” functions (hx, wi + b) <latexit sha1_base64="ZUzFyuvUCbPFlo/gmg9KYP4mygc=">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</latexit> f✓(x) , p X s=1 as (hx, ws i + bs) <latexit sha1_base64="ax7LaFmi/3bdYTxeFckx/E70i7o=">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</latexit> wp <latexit sha1_base64="Tb21R6PdEthdsl9c3KfkRE3g53s=">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</latexit> ap George Cybenko Andrew Barron
3⇥3, 512 3⇥3, 512 ⇥3 4 1⇥1, 512 3⇥3, 512 1⇥1, 2048 5 ⇥3 4 1⇥1, 512 3⇥3, 512 1⇥1, 2048 5 ⇥3 4 1⇥1, 512 3⇥3, 512 1⇥1, 2048 5 ⇥3 1⇥1 average pool, 1000-d fc, softmax FLOPs 1.8⇥109 3.6⇥109 3.8⇥109 7.6⇥109 11.3⇥109 1. Architectures for ImageNet. Building blocks are shown in brackets (see also Fig. 5), with the numbers of blocks stacked. Down- ing is performed by conv3 1, conv4 1, and conv5 1 with a stride of 2. 0 10 20 30 40 50 20 30 40 50 60 iter. (1e4) error (%) plain-18 plain-34 0 10 20 30 40 50 20 30 40 50 60 iter. (1e4) error (%) ResNet-18 ResNet-34 18-layer 34-layer 18-layer 34-layer e 4. Training on ImageNet. Thin curves denote training error, and bold curves denote validation error of the center crops. Left: plain rks of 18 and 34 layers. Right: ResNets of 18 and 34 layers. In this plot, the residual networks have no extra parameter compared to plain counterparts. Standard Neural Networks Residual Neural Networks (ResNets) xn+1 = f(xn , θN n ) xn+1 = xn + 1 N f(xn , θN n ) The deeper, the better
e⟨Qxi ,Kxℓ ⟩ Vxj Transformers and attention mechanism … + <latexit sha1_base64="aTL0Qvb1dLhAur6wfZM9PGylzLY=">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</latexit> x1 <latexit sha1_base64="7Z/IumRXp79HdyogVfnC2DA+LeM=">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</latexit> x2 <latexit sha1_base64="Fgw+vWgPriclgLxpVoHDEicBDLw=">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</latexit> {xi }i Points cloud Positional encoding Token encoding Tokenize Le groupe thématique SMAI- S I G M A ( S i g n a l - I m a g e - Géométrie-Modélisation- Approximation) est issu de l ’A s s o c i a t i o n F r a n ç a i s e d ’A p p r o x i m a t i o n ( A FA ) , association créée en 1989 et intégrée en tant que groupe au sein de la SMAI en 2000. Le groupe thématique SMAI- S I G M A ( S i g n a l - I m a g e - G é o m é t r i e - M o d é l i s a t i o n - Approximation) est issu de l ’ A s s o c i a t i o n F r a n ç a i s e d ’ A p p ro x i m a t i o n ( A FA ) , association créée en 1989 et intégrée en tant que groupe au sein de la SMAI en 2000. xi xj (Unmasked) Attention layer … next token probabilities Attention Norm MLP Classif N × … Ashish Vaswani
e⟨Qxi ,Kxℓ ⟩ Vxj Transformers and attention mechanism … + <latexit sha1_base64="aTL0Qvb1dLhAur6wfZM9PGylzLY=">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</latexit> x1 <latexit sha1_base64="7Z/IumRXp79HdyogVfnC2DA+LeM=">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</latexit> x2 <latexit sha1_base64="Fgw+vWgPriclgLxpVoHDEicBDLw=">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</latexit> {xi }i Points cloud Positional encoding Token encoding Tokenize Le groupe thématique SMAI- S I G M A ( S i g n a l - I m a g e - Géométrie-Modélisation- Approximation) est issu de l ’A s s o c i a t i o n F r a n ç a i s e d ’A p p r o x i m a t i o n ( A FA ) , association créée en 1989 et intégrée en tant que groupe au sein de la SMAI en 2000. Le groupe thématique SMAI- S I G M A ( S i g n a l - I m a g e - G é o m é t r i e - M o d é l i s a t i o n - Approximation) est issu de l ’ A s s o c i a t i o n F r a n ç a i s e d ’ A p p ro x i m a t i o n ( A FA ) , association créée en 1989 et intégrée en tant que groupe au sein de la SMAI en 2000. xi xj (Unmasked) Attention layer Arbitrary number of tokens Arbitrary number of layers Expressivity Understanding … next token probabilities Attention Norm MLP Classif N × … Ashish Vaswani
en mathématiques en train de présenter l’IA générative devant un large auditoire. Raconte de façon rigolotte l'histoire d'un chercheur CNRS qui présente l’IA générative devant un large auditoire. Le professeur Jacques Leclair, célèbre directeur de l’Institut de Mathématiques du CNRS, monte sur scène avec l’enthousiasme d’un enfant qui vient de découvrir que son yaourt préféré a un nouveau goût. Devant lui, un large auditoire aux regards curieux. “Aujourd’hui, mes amis,” commence-t-il avec un clin d’œil complice, “je vais vous prouver que les mathématiques peuvent être aussi sexy qu’un chaton jouant avec une pelote de laine… et je parle bien sûr de l’IA générative!”. D’un geste dramatique, il appuie sur sa télécommande, et l’écran derrière lui se remplit d’équations complexes qui dansent comme des notes de musique sur un karaoké.
lattent space to image space . X Y Earlier attempts: VAE, GANs, Normalizing flows, … X Y generation noising X Y Y de-noising Denoising models Synthesis by inverting the noising (diffusion) Learning the denoiser (score matching) [Valentin de Bortoli]
(Pre)-trained for data generation Can be « tuned » easily (LORA, etc) Large Language Model ⟺ Pour prouver que le produit scalaire matriciel peut s'écrire sous la forme , considérons les définitions suivantes : le produit scalaire entre deux matrices et de taille est donné par . La trace du produit est définie comme . En développant l'élément diagonal, nous avons , ce qui donne . Ainsi, . ⟨S, T⟩ tr(STt) S T n × n ⟨S, T⟩ = ∑n i=1 ∑n j=1 sij tij STt tr(STt) = ∑n i=1 (STt)ii (STt)ii = ∑n j=1 sij tij tr(STt) = ∑n i=1 ∑n j=1 sij tij = ⟨S, T⟩ ⟨S, T⟩ = tr(STt) Prouve que le produit scalaire matriciel peut s'écrire tr . ⟨S, T⟩ (STt) … but used to solve (unseen?) problems! Foundation models Frontier models ⟺
(Pre)-trained for data generation Can be « tuned » easily (LORA, etc) Large Language Model ⟺ Pour prouver que le produit scalaire matriciel peut s'écrire sous la forme , considérons les définitions suivantes : le produit scalaire entre deux matrices et de taille est donné par . La trace du produit est définie comme . En développant l'élément diagonal, nous avons , ce qui donne . Ainsi, . ⟨S, T⟩ tr(STt) S T n × n ⟨S, T⟩ = ∑n i=1 ∑n j=1 sij tij STt tr(STt) = ∑n i=1 (STt)ii (STt)ii = ∑n j=1 sij tij tr(STt) = ∑n i=1 ∑n j=1 sij tij = ⟨S, T⟩ ⟨S, T⟩ = tr(STt) Prouve que le produit scalaire matriciel peut s'écrire tr . ⟨S, T⟩ (STt) … but used to solve (unseen?) problems! Genomics? What is the equivalent of next token prediction for science? How can these approaches be extended beyond images and text? Astrophysics ? Chemistry? Materials? … Maths ? Foundation models Frontier models ⟺
the program can come up with a non-obvious construction like this is very impressive, and well beyond what I thought was state of the art. » Prove that ∠KIL + ∠XPY = 180° Timothy Gowers AlphaProof and AlphaGeometry 2: silver medal level at the Olympiad. Toward gold medal? ? COQ Theoretically understanding the processes at work in transformers. Interoperability with formal proof languages. The evolution of the profession of mathematician. The industrial challenge of leveraging mathematics to train LLMs (reasoning, evaluation).
Model for Galaxies scPRINT: Large Cell Model for scRNAseq data Establishing connections between models from different disciplines. What is the equivalent of “next token prediction” in different scientific domains?
archival collections. • Historical, scientific, legislative texts… • Annotations, summaries, etc. From image to text: Handwritten text. Ancient texts. relatively reliable. very cheap.
(flash attention, triton…) Numerics The future ? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... [Mensch et al 2023]
(flash attention, triton…) Numerics The future ? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... Connect diffusion (continuous) and LLM (discrete) models Theory Understand the “in context learning” process. [Mensch et al 2023]
(flash attention, triton…) Numerics The future ? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... Connect diffusion (continuous) and LLM (discrete) models Theory Understand the “in context learning” process. [Mensch et al 2023] Applications AI for science: beyond next token prediction Towards multimodal (video, 3D, etc.). scGPT
(flash attention, triton…) Numerics The future ? Industry Business model (few qualified engineers + fine tuning)? Open weights vs. open source (training data?) Interface with daily life? Machine learning (AI) is changing at breakneck speed. Impossible to make 5 year predictions... Connect diffusion (continuous) and LLM (discrete) models Theory Understand the “in context learning” process. [Mensch et al 2023] Applications AI for science: beyond next token prediction Towards multimodal (video, 3D, etc.). scGPT