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On the Training of Infinitely Deep and Wide ResNets

On the Training of Infinitely Deep and Wide ResNets

Talk at Optimization and Statistical Learning 2023

Gabriel Peyré

January 15, 2023
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  1. On the Training of
    Infinitely Deep and
    Wide ResNets
    Gabriel Peyré
    É C O L E N O R M A L E
    S U P É R I E U R E
    François-Xavier


    Vialard
    Raphaël


    Barboni

    View Slide

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    ResNet and
    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
    Neural-ODEs
    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
    Global and local
    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
    Polyak- Lojasiewicz
    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
    conditions
    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
    P- L condition
    AABE9XictVzbchTJES3WtzW+LOt99EuvtThYB4uFjC8RG45Y0AihRYBgRoJdBojpmZ5hoDU9zE3ArD7F4ReHw37yJ/g7/AGOsJ/8C85LVVf1THVntYzpkFRdXSczK7sqKzOrmnicDqezzc1/nHvvW9/+zne/9/73z//ghz/68QcXPvzJ0TSbT7rJYTdLs8mjuDNN0uEoOZwNZ2nyaDxJOsdxmjyMX27j84eLZDIdZqPW7M04eXLcGYyG/WG3M4OqZxc+asf9qJ9NorvJfNJJP7vX2Jk+u7CxeWWT/kXrhau6sKH0v4Psw4//qdqqpzLVVXN1rBI1UjMop6qjpnA9VlfVphpD3RO1hLoJlIb0PFGn6jxg59AqgRYdqH0Jvwdw91jXjuAeaU4J3QUuKfxMABmpi4DJoN0Eysgtoudzooy1ZbSXRBNlewN/Y03rGGpn6jnUSjjTMhSHfZmpvvod9WEIfRpTDfauq6nMSSsoeeT0agYUxlCH5R48n0C5S0ij54gwU+o76rZDz/9FLbEW77u67Vz9m6S8CFekmrr3WU6hoxZEP6K3OYdnLE8KnAdAIdF9xNIJ6fqYej+C9kuovwvXKZWMTmK4llR7WonchsuH3BaRu3D5kLsich8uH3JfRB7A5UMeaCRiJ6RzP74Jlw/fFDnfh8uHvC8iH8DlQz4QkUdw+ZBHIvJruHzIr0XkTbh8yJsi8jZcPuRtEdmCy4dsichDuHzIQxG5A5cPuaOR5TN1AldGdIbCrLwO5SIPtBQp1FwX5btB1tGHvREwp7slWHlWN+CvH9sI0GlSgt0JGHf9Eqw88nbBRvqxsi26RauJD3tLxO7BCPBj90Tsl+pFCfbLgJn2sgQrz7V9aOfHytb3Dtz5sXdE7F0o+bHyGnUPavzYewErxrgEeyBi76tXJdgQqz8pwcp2vwl2xY+V16kWtPdjQ6zpvAQr29Mj8GD8WHm1egi1fuxDEftIvS7BPhKxX4F192O/Clhh35ZgzRp7nlaQAfkjCczYKmqdfFZiaQzUOgL/NF9bUvKNY6iXMIMcMyDMsYjYzRG7gYj9HLEfLNc0t6NT8ndlLs0c0QxExPnahKWZ2L6Xt8dSGoBo5IjGCqLKI8V3bfqyIO/C1EjIWb5yYSmkT1luv7GU6PFQbXkN4l4BwWP7OY38yxQtYQSFmqqi9jxf4xkZ0X0V4oSiN9NLw0PGzXKr4KJei6jYg4pF1BsP6o2ImntQcxG18KAWIsrOfBfXDhgBVv/4LpZ0xyOAfeTyKwKv4DqsOrdgjkYwfg7AC3xANffgb5Nib+mqkgyjeVwnMcvxpGCJJ1Baqg2ot1Fhg+LrlGZYApJxy3s6xsc7zG0s9ZxjK3yar+RRnjEJpzMkeQY5HfQWI5pP9ejcpppT8u64VA9/K5/3plQPv0MaPyUvnkv18DMt/ewMsrc0tnUGbBNm01hr35br0uD8C9Mw5fO06qLFxbd6rMcM0ntdk/6efjN7Z3gv21Ri/dhyPRpTp3/TQv/q0LB6njp6rkcFvSf2ek0pqt2TkY57bbmuDBmtoiMth72r+2awTU+/GVOuR+MAPK5tirmXTrnu6B3nvbHlejSOFOc9T8mTN+V6NAZ0z/qw5Xo0MNvS0XG+Lde17KgBjp1tua5VH1EWGHNAPOa5xnpFE/KT5prakPyD6myN6/Ovr2OYs3maxwjVlKxvW04nzteyaomMv5CAVZvVlAP9i7njgxVpLNWWGF+xDLPC+r5Ox67xqPl90GIEs5/3AKSceQoSmpwEWu8UKF4Vo65izwxuS8ThKOmvoNq6diZ6i5YvZ42Kdc+oVorLbG+tHttkr6c09sbkE+6TZiU97Je+4TKKkob2CxqS6dXR3Vs9X4va3xRx4xXEOB9pXdoR4p206jjVp/Wmo+OLepdnBhfv+djxi9nmvrY2GPNkZItQliqebjuTR3LrcF29rGyOm59F9EbRXi3IagxpR2oqRqEmW8ze+JLuLe1D2pNDHkyjC+8x0lTGinfNMIuO+fSILKprbyXeqC+ToePylKyuscfV6IGDHnjQ9WOcbVgx7kKpBTHDIdy1AqKc87muMtL4RH2W745m9AarI/q0YCENDbY3ScFCVkXZzwtUTgCNo4Gj9HAaq3QMvr1GSY76ffLY2LVo+S/Szq3Z3+7QGC8fzeWZmB5x3SKuEc0a3tXlu1UOLMHS+2SL/NfqXiK/OhzRhkpcnzqcWS8j2vFPKIIdk2ec0myTZkextZufWn1iOB0os3eOu9kZWciI7F8E61NGYzKiH/fsgNlBZ4uQko0MsTvD3Lvx+TpDcYxZP26o+FSDHW8J2bI58Td03dk1pbHIEQOvA6crY9voZJ98wYS4TrR1t3O7evVBpD0n4Y4SpmjHyiXi/yn9Nj9mnGysjQjUML6BqbZ1vveRUcyCOurQKl9tg0xbV8pPchmeaqnt+mdl+qQgWYMiLpQHV+secO7SPfPCUTIhuadrbXgdrcrmIuXxih6xt32K4tnuD/QKjHJfplVyg+Zcm0bJAEbBLI8iTFspi7zKt5pXkXoY7en/hbrVdVFrSDFSNoPLGpLy+wlFa66UKYxqHr8vaTb5tT5ZaVXNZ0Rj8diZy99A7cfw28ht7sPoxAWrcIPGAFOwd1YjXBOttQjjdaPAy4xMQ8veW352TJpWbs1Z4mu2bjbGXtSmckCj5rXOWpjyWWi8cGi8CNRhi/YarRZNvbFEz8TYoqV3K0P51eHWqkF5LlKWPTKDGgZI6cZSYVR7IlU5xjeotyKtTZFWB2aruxvgzvkQpH+ur87ub/LVPVI3ybfpkgfG8UuPZumQfC5TWx2pMQXkfE3bV3f2t6kGucdkQZEyn+PEGcO7Tl26TnNJf65XtozsvLUI5tzSiW5jbGybyr9aQx7TnJjSvDSIa9Qi0fK7ckQrFumK43NElPnvkE/Ffkd1zOy2tu8kKvgTNt7kWWV5caQwIv1Lmbe9teh1z4lfI4oJ59q7joFW/TeMFBhjMgl+z3JKbwhXOd5JYI82Jvu5bqd4F2/kSHSFpF6q3wfYGI567Vh3x5bpsenbL6Alat2+dV8LmV8azFHid5YdvQ6tasfaR12u3J+NVkevcsX7Kj3MV/hafcypjRtZ2CiviGmrz4O5sET1uDAmhEu9XtSRv57kdWTm3alQyqa1oVzMNLCNeU7xknQOFBE+7+6S15v7VOhHvEYvJqxLjWskSpiNy3R+wLW0mJWKViIkt15ak1JnPSpbLywPd9WwdpwtZUJWMFVS7oZbu31oF6IVORvDFLqKT/aWxYkuzc/hwt+R8kWJhmNIDrEJfu51ta123sGpiFe6zJnNiGrQJvRWYvCO7mexRbWOXjnUXfohHMJ5DEHXkvRDWlHrys6UZcld6uH0T8gaTFQiSm9b1u+Dy0XuyTqnOv0ZkoWTezNU5pucun0xHEJ6UuQSzof3N6Re9JX5tqleHwx1uQdFDnV4mPMMYe/ctq7Py+VUra91LqE8eB0wOy8GhzuA5TGLbRdioSbOG3n3HNA69Cuom9Xif+2H4WM51ecVym1K35y9CHjr3C7RmVn0i+vPGcstZDSXcwznmeW9s16Tnx/7f1GtN5U5vXn39NEvtWPA8FoqzofK0jHeHUVW3lAquD/gkyFT/1F/Pyd/lfAqp1EmRx1KZr+inJppIVMzX176emeehchk6ZTJVKRm44kmnYzdVnvqJvxs5x5g3VOi/E0l/0Ws/zvaHtT2yXqYbDpnENpUl1AWxO6m9ejenqMtkxjP9PIZ3xbU4J74PtXied+71B7P/LYKfSv/koTn+h2VqV4hMlnd5bPzKoYeFHfgOBdkvveN6Ew9Z7P4BNpxwB4jn6PiSMl8/bwkRI/iwlVJl4Qwo6WKcuylHNOZpKSEdlzoW5dG+Fjv9OO+A57P7+TZpUj9kuo6enXAlVqS6sAj1WPKDMSk/02I0H6tLsPfy7rsl/RgTdIpvYOiRK+dZ9UnwU6948J+zXiR8mAmU7fQ7TKK6u3uYXUmtlHKhU+8V+MHFfiBI2WT3tZLirsnqjp3OK+gOdcyufu5I2XynqwHjGY7+fiojp8XFbwWAf2/XYq+7Ui6C7LElG2PaD9vQvRSrZsdkp7PVVbnbW9VSGu+2mSa9mSlHQfmjGT1nkCqx1357OdzkFKuJimh4851PpEpnRYZeinJ83MccBqiE9Bbua8hPZWozEVJ5gFfIi8CZFkE0OkL0vRFCgNREm0fnl3YuLr6f32sF462rlz9zZVr97c2vrih/x+Q99VP1c/UJVj7fqu+gPF/oA6B0xv1R/UX9dfGSeMPjT81/sxN3zunMR+pwr/G3/4LbbhG0g==
    for Neural-ODEs
    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    xi
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    RKHS Neural-ODEs

    View Slide

  3. ResNet-type Architectures [He et al’ 16]
    ResNet-34
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    image

    View Slide

  4. ResNet-type Architectures [He et al’ 16]
    ResNet-34
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    image
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    changes
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    skip-connexion
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    xs = xs 1 + v✓s
    (xs 1)

    View Slide

  5. ResNet-type Architectures [He et al’ 16]
    ResNet-34
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    image
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    ! Makes the “infinite depth” limit non-degenerate.
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    x0
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    x1
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    xT
    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
    ! Enable v✓ = 0 initialization, i.e. identity map.
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    x0
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    x1
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    x0
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    changes
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    skip-connexion
    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
    xs = xs 1 + v✓s
    (xs 1)

    View Slide

  6. Infinite Depth and Neural-ODEs
    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
    where
    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
    ResNet [He et al, 2016]
    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
    ✓(x0) , xT
    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
    xt+1 = xt + 1
    T
    v✓t
    (xt)
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    x0
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    x1
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    xT

    View Slide

  7. Infinite Depth and Neural-ODEs
    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
    where
    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
    ResNet [He et al, 2016]
    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
    ✓(x0) , xT
    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
    xt+1 = xt + 1
    T
    v✓t
    (xt)
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    x0
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    x1
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    x(1)
    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
    Neural ODE [Chen et al, 2018]
    AABE6HictVzbchTJES3WtzW+sfajX3qtxcE6WCwwvkRsOGJBI4SWWRDMSLDLADE90xoNtKZHcxMwq39w+MXhsJ/8I/4Of4Aj7Cf/gvNS1VU9U91ZLWM6JFVX18nMyq7KysyqJh6nw+lsc/MfF977xje/9e3vvP/di9/7/g9++KNLH/z4YJrNJ71kv5el2eRJ3J0m6XCU7M+GszR5Mp4k3eM4TR7Hr7bw+eNFMpkOs1F79macPDvuDkbDw2GvO4OqJ52T06Nkkpy8uLSxeW2T/kXrheu6sKH0v73sgw//qTqqrzLVU3N1rBI1UjMop6qrpnA9VdfVphpD3TO1hLoJlIb0PFFn6iJg59AqgRZdqH0Fvwdw91TXjuAeaU4J3QMuKfxMABmpy4DJoN0Eysgtoudzooy1ZbSXRBNlewN/Y03rGGpn6ghqJZxpGYrDvszUofod9WEIfRpTDfaup6nMSSsoeeT0agYUxlCH5T48n0C5R0ij54gwU+o76rZLz/9FLbEW73u67Vz9m6S8DFekWrr3WU6hqxZEP6K3OYdnLE8KnAdAIdF9xNIp6fqYej+C9kuovw/XGZWMTmK4llR7VoncgsuH3BKRO3D5kDsisgmXD9kUkXtw+ZB7GonYCencj2/B5cO3RM4P4fIhH4rIR3D5kI9E5AFcPuSBiPwKLh/yKxF5By4f8o6IvAeXD3lPRLbh8iHbInIfLh9yX0Ruw+VDbmtk+UydwJURnaEwK29BucgDLUUKNbdE+W6TdfRhbwfM6V4JVp7VDfjrxzYCdJqUYLcDxt1hCVYeeTtgI/1Y2RbdpdXEh70rYndhBPixuyL2c/WyBPt5wEx7VYKV51oT2vmxsvX9Au782C9E7H0o+bHyGvUAavzYBwErxrgEuydiH6qTEmyI1Z+UYGW73wK74sfK61Qb2vuxIdZ0XoKV7ekBeDB+rLxaPYZaP/axiH2iXpdgn4jYL8G6+7FfBqywb0uwZo29SCvIgPyRBGZsFbVuPiuxNAZqXYF/mq8tKfnGMdRLmEGOGRDmWETs5IidQEQzRzSD5ZrmdnRK/q7MpZUjWoGIOF+bsDQT2/fz9lhKAxCNHNFYQVR5pPiuTV8W5F2YGgk5y1cuLIX0KcvtN5YSPR6qLa9BPCggeGwf0ci/StESRlCoqSpqR/kaz8iI7qsQpxS9mV4aHjJullsFF/VaRMUeVCyi3nhQb0TU3IOai6iFB7UQUXbmu7hOwAiw+sd3saQ7HgHsI5dfEXgFt2DVuQtzNILxswde4COqeQB/WxR7S1eVZBjN4zqJWY5nBUs8gdJSbUC9jQobFF+nNMMSkIxbPtAxPt5hbmOp5xxb4bN8JY/yjEk4nSHJM8jpoLcY0XyqR+ce1ZyRd8elevi7+bw3pXr4bdL4GXnxXKqHn2npZ+eQva2x7XNgWzCbxlr7tlyXBudfmIYpX6RVFy0uvtVjPWaQ3uua9Hf1m9k9x3vZohLrx5br0Zg6/ZsW+leHhtXz1NFzPSroPbHXa0pR7Z6MdNxry3VlyGgVHWk57F3dN4Nt+vrNmHI9GnvgcW1RzL10ynVH7zjvjS3Xo3GgOO95Rp68KdejMaB71oct16OB2ZaujvNtua5lRw1w7GzLda36iLLAmAPiMc811iuakJ8019SG5B9UZ2tcn399HcOczfM8RqimZH3bcjpxvpZVS2T8hQSs2qymHOhfzB0frEhjqW6I8RXLMCus7+t07BqPmm+CFiOY/bwHIOXMU5DQ5CTQeqdA8boYdRV7ZnA3RByOksMVVEfXzkRv0fLlrFGx7gXVSnGZ7a3VY4fs9ZTG3ph8wiZpVtJDs/QNl1GUNNQsaEimV0d3b/V8LWp/U8SNVxDjfKT1aEeId9Kq41Sf1luOji/rXZ4ZXLznY8cvZpsPtbXBmCcjW4SyVPF025k8kluH6+pVZXPc/CyiN4r2akFWY0g7UlMxCjXZYvbGl3Rvae/TnhzyYBo9eI+RpjJWvGuGWXTMp0dkUV17K/FGfZkMHZenZHWNPa5GDxz0wIOuH+NswYpxH0ptiBn24a4dEOVczHWVkcYn6pN8dzSjN1gd0acFC2losL1JChayKso+KlA5BTSOBo7Sw2ms0jH4zholOer3yWNj16Llv0w7t2Z/u0tjvHw0l2di+sT1BnGNaNbwri7frXJgCZbeJzfIf63uJfKrwxFtqMT1ucOZ9TKiHf+EItgxecYpzTZpdhRbu/mp1SeG054ye+e4m52RhYzI/kWwPmU0JiP6cc8OmB10tggp2cgQuzPMvRufrzMUx5j144aKTzXY8ZaQLZsTf0PXnV1TGoscMfA6cLYyto1OmuQLJsR1oq27ndvVqw8i7TkJd5QwRTtWrhD/j+m3+THjZGNtRKCG8Q1Mta3zvY+MYhbUUZdW+WobZNq6Un6Uy/BcS23XPyvTRwXJGhRxoTy4WveBc4/umReOkgnJPV1rw+toVTYXKY9X9Ii9PaQonu3+QK/AKPdVWiU3aM51aJQMYBTM8ijCtJWyyKt8q3kVqYfRnv5fqFtdF7WGFCNlM7isISm/n1C05kqZwqjm8fuKZpNf65OVVtV8RjQWj525/DXUfgi/jdzmPoxOXLAKt2kMMAV7ZzXCNdFaizBetwu8zMg0tOy95WfHpGnl1pwnvmbrZmPsRW0qezRqXuushSmfh8ZLh8bLQB22aa/RatHUG0v0Qowt2nq3MpRfHW7tGpTnImXZIzOoYYCUbiwVRrUvUpVjfIN6K9LaFGl1Yba6uwHunA9B+uf66uz+Ol/dI3WHfJseeWAcv/Rplg7J5zK11ZEaU0DON7V9dWd/h2qQe0wWFCnzOU6cMbzr1KPrLJf053ply8jOW4tgzi2d6jbGxnao/Ks15DHNiSnNS4O4SS0SLb8rR7Rika45PkdEmf8u+VTsd1THzG5r+06igj9h402eVZYXRwoj0r+Uedtdi153nfg1ophwrr3rGGjVf8NIgTEmk+D3LKf0hnCV450E9mhjsp/rdop38UaORNdI6qX6fYCN4ajXjnV3bJkem779Alqi1u1b97WQ+aXBHCV+59nR69Kqdqx91OXK/flodfUqV7yv0sN8ha/Vx5zauJGFjfKKmI76NJgLS1SPC2NCuNTrRR3560leR2benQqlbFobysVMA9uYI4qXpHOgiPB5d1e83tzHQj/iNXoxYV1qXCNRwmxcpvMDrqXFrFS0EiG59dKalDrrUdl6YXm4q4a142wpE7KCqZJyN9za7UOnEK3I2Rim0FN8srcsTnRpfgoX/o6UL0o0HENyiC3wc2+pLbX9Dk5FnOgyZzYjqkGb0F+Jwbu6n8UW1To6cai79EM4hPMYgq4l6Ye0otaVnSnLkrvUw+mfkjWYqESU3ras3weXi9yTdU51+jMkCyf3ZqjMNzl1+2I4hPSkyCWcD+9vSL04VObbpnp9MNTlHhQ51OFhzjOEvXPbuj4vl1O1vta5hPLgdcDsvBgc7gCWxyy2XYiFmjhv5N1zQOtwWEHdrBb/az8MH8upPq9QblP65uxlwFvndonOzKJfXH/OWG4ho7mcYzjPLO+d9Zr8/Nj/i2q9qczpzbunj36pHQOG11JxPlSWjvHuKLLyhlLB/QGfDJn6j/r7BfmrhJOcRpkcdSiZ/YpyaqaFTM18eenrnXkWIpOlUyZTkZqNJ1p0MnZL7ao78LOVe4B1T4nyN5X8F7H+72j7UHtI1sNk0zmD0KG6hLIgdjetT/f2HG2ZxHiml8/4tqEG98SbVIvnfe9Tezzz2y70rfxLEp7rX6hM9QuRyeoun51XMfSguAPHuSDzvW9EZ+o5m8Un0I4D9hj5HBVHSubr5yUh+hQXrkq6JIQZLVWUYy/lmM4kJSW040LfejTCx3qnH/cd8Hx+N88uReqXVNfVqwOu1JJUex6pnlJmICb9b0KE9mt1Ff5e1WW/pHtrkk7pHRQleu08qz4JduYdF/ZrxsuUBzOZuoVul1FUb3cPqzOxjVIufOK9Gj+owA8cKVv0tl5R3D1R1bnDeQXNuZbJ3c8dKZP3ZD1gNNvNx0d1/Lyo4LUI6P+9UvQ9R9IdkCWmbHtE+3kTopdq3WyT9Hyusjpve7dCWvPVJtO0JyvtODBnJKv3BFI97spnP5+DlHI1SQkdd67ziUzptMjQS0men+OA0xDdgN7KfQ3pqURlLkoyD/gSeREgyyKAzqEgzaFIYSBKou3Di0sb11f/r4/1wsGNa9d/c+3mw5sbn93W/w/I++qn6mfqCqx9v1WfwfjfU/vkM/xR/UX9tfGy8YfGnxp/5qbvXdCYn6jCv8bf/guSMUME
    where
    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
    T ! +1
    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
    dx(t)
    dt
    = v✓(t)
    (x(t))
    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
    ✓(x(0)) , x(1)

    View Slide

  8. Infinite Depth and Neural-ODEs
    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
    where
    AABE+XictVzbchu5EYU3t41z8yYPecjLbLROebcUR1KcTaq2UrW2KEtayzZtUrJ3LdvFy4imPeLQHJK+cPUxqbykUslTPiDfkQ9IVfKUX0hfgAGGxExjFEdTEjEgTnejB2h0NzDqjpNhNt3Y+MeF977xzW99+zvvf/fi977/gx/+6NIHPz7K0tmkFx/20iSdPOx2sjgZjuLD6XCaxA/Hk7hz2k3iB90X2/j9g3k8yYbpqD19M44fn3YGo+HJsNeZQtXTSz+9H2d34mn0aC+O4KOTrEdbG5ufPn56aW3j6gb9RKuFTV1YU/qnmX7w4T/VseqrVPXUTJ2qWI3UFMqJ6qgMrkdqU22oMdQ9Vguom0BpSN/H6kxdBOwMWsXQogO1L+DvAO4e6doR3CPNjNA94JLA7wSQkboMmBTaTaCM3CL6fkaUsbaM9oJoomxv4LOraZ1C7VQ9g1oJZ1qG4rAvU3Wifkd9GEKfxlSDvetpKjPSCkoeOb2aAoUx1GG5D99PoNwjpNFzRJiM+o667dD3/6KWWIv3Pd12pv5NUl6GK1It3fs0p9BRc6If0dOcwXcsTwKcB0Ah1n3E0ivS9Sn1fgTtF1B/B64zKhmddOFaUO1ZJXIbLh9yW0TuwuVD7orIA7h8yAMR2YTLh2xqJGInpHM/vgWXD98SOd+Dy4e8JyLvw+VD3heRR3D5kEci8iu4fMivRORNuHzImyLyFlw+5C0R2YbLh2yLyEO4fMhDEbkDlw+5o5HlM3UCV0p0hsKsvA7lIg+0FAnUXBflu0HW0Ye9ETCneyVYeVY34NOPbQToNC7B7gSMu5MSrDzydsFG+rGyLdqj1cSH3ROx+zAC/Nh9EfuFel6C/SJgpr0owcpz7QDa+bGy9b0Nd37sbRF7B0p+rLxG3YUaP/ZuwIoxLsE2Rew99bIEG2L1JyVY2e63wK74sfI61Yb2fmyINZ2VYGV7egQejB8rr1YPoNaPfSBiH6rXJdiHIvZLsO5+7JcBK+zbEqxZYy/SCjIgfySGGVtFrZPPSiyNgVpH4J/ka0tCvnEX6iXMIMcMCHMqInZzxG4g4iBHHATLleV2NCN/V+bSyhGtQEQ3X5uwNBXb9/P2WEoCEI0c0VhCVHmk+KxNX+bkXZgaCTnNVy4shfQpze03lmI9Hqotr0HcLSB4bD+jkb9O0RJGUKipKmrP8jWekRHdVyFeUfRmeml4yLhpbhVc1GsR1fWguiLqjQf1RkTNPKiZiJp7UHMRZWe+izsOGAFW//gsFnTHI4B95PIrAq/gOqw6ezBHIxg/TfAC71PNXfhsUewtXVWSYTSP6yRmOR4XLPEESgu1BvU2KmxQfJ3QDItBMm55V8f4eIe5jYWec2yFz/KVPMozJuF0hiTPIKeD3mJE86kenVtUc0beHZfq4ffyeW9K9fA7pPEz8uK5VA8/1dJPzyF7W2Pb58C2YDaNtfZtuS4Nzr8wDVO+SKsuWlx8qqd6zCC91zXp7+sns3+O57JNJdaPLdejkTn9ywr9q0PD6jlz9FyPCnpP7PWaUlS7JyMd99pyXRlSWkVHWg57V/fJYJu+fjKmXI9GEzyubYq5F0657ugd572x5Xo0jhTnPc/IkzflejQGdM/6sOV6NDDb0tFxvi3XteyoAY6dbbmuVR9RFhhzQDzmucZ6RRPyk2aa2pD8g+psjevzr65jmLN5kscI1ZSsb1tOp5uvZdUSGX8hBqs2rSkH+hczxwcr0lioLTG+YhmmhfV9lY5d41HzB6DFCGY/7wFIOfMEJDQ5CbTeCVDcFKOuYs8MbkvE4Sg5WUId69qp6C1avpw1KtY9pVopLrO9tXo8Jnud0dgbk094QJqV9HBQ+oTLKEoaOihoSKZXR3dv9Xwtan9DxI2XEON8pPVoR4h30qrjVJ/WW46OL+tdnilcvOdjxy9mm0+0tcGYJyVbhLJU8XTbmTySW4fr6rqyOW7+LqInivZqTlZjSDtSmRiFmmwxe+MLure0D2lPDnkwjR48x0hTGSveNcMsOubTI7Korr2VeKO+TIaOyxlZXWOPq9EDBz3woOvHONuwYtyBUhtihkO4awdEORdzXaWk8Yn6Zb47mtITrI7ok4KFNDTY3sQFC1kVZT8rUHkFaBwNHKWH01imY/DHK5TkqN8nj41di5b/Mu3cmv3tDo3x8tFcnonpE9ct4hrRrOFdXb5b5sASLLzfbJH/Wt1L5FeHI9pQiesThzPrZUQ7/jFFsGPyjBOabdLsKLZ281PL3xhOTWX2znE3OyULGZH9i2B9SmlMRvTrnh0wO+hsERKykSF2Z5h7Nz5fZyiOMevHDRWfarDjLSZbNiP+hq47uzIaixwx8DpwtjS2jU4OyBeMietEW3c7t6tXH0TacxLuKGGKdqxcIf4f01/za8bJ2sqIQA3jE8i0rfM9j5RiFtRRh1b5ahtk2rpSfpTL8ERLbdc/K9NHBckaFHGhPLha94Fzj+6ZF46SCcmdrbThdbQqm4uUx0t6xN6eUBTPdn+gV2CUe51WyTWac8c0SgYwCqZ5FGHaSlnkZb7VvIrUw2hn/xfqVtdFrSHFSNkMLmtIyu/HFK25UiYwqnn8vqDZ5Nf6ZKlVNZ8RjcVTZy5/DbUfwl8jt7kPo9MtWIUbNAaYgr2zGuGaaKVFGK8bBV5mZBpa9t7ys2PStHJrzhNfs3WzMfa8NpUmjZrXOmthyueh8dyh8TxQh23aa7RaNPXGEj0VY4u23q0M5VeHW7sG5ZlIWfbIDGoYIKUbS4VR7YtU5RjfoN6KtDZEWh2Yre5ugDvnQ5D+ub48u7/OV/dI3STfpkceGMcvfZqlQ/K5TG11pMYUkPM1bV/d2X9MNci9SxYUKfM5TpwxvOvUo+ssl/QXemVLyc5bi2DOLb3SbYyNPabyr1eQpzQnMpqXBnGNWsRafleOaMkiXXV8jogy/x3yqdjvqI6Z3db2mUQFf8LGmzyrLC+OFEakfynztr8Sve478WtEMeFMe9ddoFX/CSMFxphMgt+zzOgJ4SrHOwns0XbJfq7aKd7FGzkSXSWpF+r3ATaGo1471t2xZXps+vYJtESt26fuayHzS4I5SvzOs6PXoVXtVPuoi6X789Hq6FWueF+lh9kSX6uPGbVxIwsb5RUxx+qzYC4sUT0ujAnhUq8XdeSvJ3kdmXl3KpSyaW0oFzMNbGOeUbwknQNFhM+7u+L15j4W+tFdodclrEuNayRKmI1LdX7AtbSYlYqWIiS3XlqTEmc9KlsvLA931bB2nC1lTFYwUVLuhlu7fTguRCtyNoYp9BSf7C2LE12an8GFfyPlixINx5AcYgv83OtqW+28g1MRL3WZM5sR1aBN6C/F4B3dz2KLah29dKi79EM4hPMYgq4l6Ye0otaVnSnLkrvUw+m/ImswUbEovW1Zvw8uF7knq5zq9GdIFk7uzVCZd3Lq9sVwCOlJkUs4H97fkHpxosy7TfX6YKjLPShyqMPDnGcIe+a2dX1eLqdqfa1yCeXB64DZeTE43AEsj1lsuxALNXGeyLvngNbhpIK6WS3+134YPpZTfV6h3DJ65+x5wFPndrHOzKJfXH/OWG4ho7mcYzjPNO+d9Zr8/Nj/i2o9qdTpzbunj36pHQOG10JxPlSWjvHuKLLyhlLB/QGfDKn6j/r7BfmthJc5jTI56lAy+xXl1EwLmZp589LXO/NdiEyWTplMRWo2nmjRydhtta9uwu927gHWPSXK71TyJ2L979H2ofaErIfJpnMG4ZjqYsqC2N20Pt3bc7RlEuOZXj7j24Ya3BM/oFo873uH2uOZ33ahb+VvkvBcv61S1S9EJsu7fHZedaEHxR04zgWZ930jOlPP2Sw+gXYasMfI56g4UjJvPy8I0ae4cFnSBSHMaKmi3PVS7tKZpLiEdrfQtx6N8LHe6cd9Bzyf38mzS5H6FdV19OqAK7UkVdMj1SPKDHRJ/xsQof1GrcPnui77JW2uSJrRMyhK9Nr5rvok2Jl3XNi3GS9THsxk6ua6XUpRvd09rM7ENkq58In3avygAj9wpGzR03pBcfdEVecOZxU0Z1omdz93pEzek/WA0WwnHx/V8fO8gtc8oP+3StG3HEl3QZYuZdsj2s+bEL1E62aHpOdzldV5270Kac1bm0zTnqy048CckazeE0j0uCuf/XwOUsrVxCV03LnOJzKl0yJDLyV5fo4DTkN0Anor9zWkpxKVmSjJLOBN5HmALPMAOieCNCcihYEoibYPTy+tbS7/r4/VwtHW1c1Pr167t7X2+Q39f0DeVz9TP1dXYO37rfocxn9THZKX8Uf1F/XXxqLxh8afGn/mpu9d0JifqMJP42//BSU0R0E=
    ResNet [He et al, 2016]
    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
    ✓(x0) , xT
    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
    xt+1 = xt + 1
    T
    v✓t
    (xt)
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    x0
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    x1
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    x(1)
    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
    Neural ODE [Chen et al, 2018]
    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
    where
    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
    T ! +1
    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
    dx(t)
    dt
    = v✓(t)
    (x(t))
    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
    ✓(x(0)) , x(1)
    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
    T ! +1 is a singular limit (✓ can “explodes” during training)
    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
    Trajectories cannot cross: ✓ defines a di↵eomorphism.

    View Slide

  9. Training Dynamic
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    Training:
    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
    Gradient descent: 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
    ✓(k+1) = ✓(k) ⌧rf(✓(k))
    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
    min

    f(✓) , 1
    N
    PN
    i=1
    ||B ✓(Axi) yi||2

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    A +
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    v✓1
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    B
    +
    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
    v✓2
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    A
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    xi
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    B
    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
    ˙
    x(t) = v✓(t)
    (x(t))
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    ! No explicit regularization!

    View Slide

  10. Training Dynamic
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    Training:
    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
    Gradient descent: 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
    ✓(k+1) = ✓(k) ⌧rf(✓(k))
    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
    Question: convergence of ✓k toward global minimum?
    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
    min

    f(✓) , 1
    N
    PN
    i=1
    ||B ✓(Axi) yi||2

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    A +
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    v✓1
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    B
    +
    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
    v✓2
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    A
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    xi
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    B
    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
    ˙
    x(t) = v✓(t)
    (x(t))
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
    Polyak- Lojasiewicz inequality [Liu, Zhu, Belkin 2021]:
    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
    ! conditionning might explodes as T ! +1.
    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
    ! find a suitable limit model and show “implicit” regularization e↵ect.
    AABFCXictVzbchxJES0vt8XcvPDISy9as94NYyRhYIMNItbWyLJsrT32jGTvWrajZ6Y1Hqs1PZ6bL7P6AoKPIXghCAge+Ao+gAh44hfIS1VX9Ux1Z7Uw7pBUXV0nMyu7Kiszq9qdUTqYTNfX/3Huna99/Rvf/Na73z7/ne9+7/s/uPDeDw8m2WzcTfa7WZqNH3biSZIOhsn+dDBNk4ejcRKfdNLkQed4C58/mCfjySAbtqevR8njk7g/HBwNuvEUqp5e+PBOMhvHaTSNh/1kOI2Ok/EwSaNHt+JuNo2SaRSnH2588vg3Ty+srV9Zp3/RamFDF9aU/tfM3nv/n+pQ9VSmumqmTlSihmoK5VTFagLXI7Wh1tUI6h6rBdSNoTSg54k6VecBO4NWCbSIofYYfvfh7pGuHcI90pwQugtcUvgZAzJSFwGTQbsxlJFbRM9nRBlry2gviCbK9hr+djStE6idqmdQK+FMy1Ac9mWqjtQn1IcB9GlENdi7rqYyI62g5JHTqylQGEEdlnvwfAzlLiGNniPCTKjvqNuYnv+LWmIt3nd125n6N0l5Ea5ItXTvs5xCrOZEP6K3OYNnLE8KnPtAIdF9xNJL0vUJ9X4I7RdQfweuUyoZnXTgWlDtaSVyCy4fcktE7sDlQ+6IyD24fMg9EdmEy4dsaiRix6RzP74Flw/fEjnfg8uHvCci78PlQ94XkQdw+ZAHIvJLuHzIL0XkDbh8yBsi8jZcPuRtEdmGy4dsi8h9uHzIfRG5DZcPua2R5TN1DFdGdAbCrLwG5SIPtBQp1FwT5btO1tGHvR4wp7slWHlWN+CvH9sI0GlSgt0OGHdHJVh55O2AjfRjZVt0k1YTH/amiN2FEeDH7orYW+p5CfZWwEw7LsHKc20P2vmxsvX9HO782M9F7B0o+bHyGnUXavzYuwErxqgE2xSx99SLEmyI1R+XYGW73wK74sfK61Qb2vuxIdZ0VoKV7ekBeDB+rLxaPYBaP/aBiH2oXpVgH4rYL8C6+7FfBKywb0qwZo09TytIn/yRBGZsFbU4n5VYGgG1WOCf5mtLSr5xB+olTD/H9AlzIiJ2csROIGIvR+wFyzXJ7eiE/F2ZSytHtAIRnXxtwtJUbN/L22MpDUA0ckRjCVHlkeK7Nn2Zk3dhaiTkNF+5sBTSpyy331hK9HiotrwGcbeA4LH9jEb+ZYqWMIJCTVVRe5av8YyM6L4K8ZKiN9NLw0PGTXOr4KJeiaiOB9URUa89qNciauZBzUTU3IOaiyg7813cYcAIsPrHd7GgOx4B7COXXxF4Bddg1bkJczSC8dMEL/A+1dyFvy2KvaWrSjKM5nGdxCzH44IlHkNpodag3kaFDYqvU5phCUjGLe/qGB/vMLex0HOOrfBpvpJHecYknM6A5OnndNBbjGg+1aNzm2pOybvjUj38zXzem1I9/DZp/JS8eC7Vw0+19NMzyN7W2PYZsC2YTSOtfVuuS4PzL0zDlM/TqosWF9/qiR4zSO9VTfq7+s3snuG9bFGJ9WPL9WhMnP5NCv2rQ8PqeeLouR4V9J7Y6zWlqHZPhjruteW6MmS0ig61HPau7pvBNj39Zky5Ho0meFxbFHMvnHLd0TvKe2PL9WgcKM57npInb8r1aPTpnvVhy/VoYLYl1nG+Lde17KgBjp1tua5VH1IWGHNAPOa5xnpFY/KTZpragPyD6myN6/OvrmOYs3mSxwjVlKxvW06nk69l1RIZfyEBqzatKQf6FzPHByvSWKhNMb5iGaaF9X2Vjl3jUfN7oMUIZj/vAUg58xQkNDkJtN4pUNwQo65izwxuU8ThKDlaQh3q2qnoLVq+nDUq1j2lWikus721ejwkez2hsTcin3CPNCvpYa/0DZdRlDS0V9CQTK+O7t7o+VrU/rqIGy0hRvlI69KOEO+kVcepPq23HB1f1Ls8U7h4z8eOX8w2H2lrgzFPRrYIZani6bYzeSS3DtfVy8rmuPlZRG8U7dWcrMaAdqQmYhRqssXsjS/o3tLepz055ME0uvAeI01lpHjXDLPomE+PyKK69lbijfoyGTouT8jqGntcje476L4HXT/G2YIV4w6U2hAz7MNdOyDKOZ/rKiONj9XP8t3RjN5gdUSfFiykocH2JilYyKoo+1mByktA42jgKD2cxjIdgz9coSRH/T55bOxatPwXaefW7G/HNMbLR3N5JqZHXDeJa0Szhnd1+W6ZA0uw8D7ZJP+1upfIrw5HtKES1ycOZ9bLkHb8E4pgR+QZpzTbpNlRbO3mp5afGE5NZfbOcTc7IwsZkf2LYH3KaExG9OOeHTA76GwRUrKRIXZnkHs3Pl9nII4x68cNFJ9qsOMtIVs2I/6Grju7JjQWOWLgdeB0aWwbneyRL5gQ17G27nZuV68+iLTnJNxRwhTtWLlE/D+i3+bHjJO1lRGBGsY3MNG2zvc+MopZUEcxrfLVNsi0daX8IJfhiZbarn9Wpg8KkjUo4kJ5cLXuAecu3TMvHCVjknuy0obX0apsLlIeLekRe3tEUTzb/b5egVHuy7RKrtGcO6RR0odRMM2jCNNWyiIv863mVaQeRnvyf6FudV3UGlKMlM3gsoak/H5C0ZorZQqjmsfvMc0mv9bHS62q+QxpLJ44c/krqH0ffhu5zX0YnU7BKlynMcAU7J3VCNdEKy3CeF0v8DIj09Cy95afHZOmlVtzlviarZuNsee1qTRp1LzSWQtTPguN5w6N54E6bNNeo9WiqTeW6KkYW7T1bmUovzrc2jUoz0TKskdmUIMAKd1YKoxqT6Qqx/gG9UaktS7SimG2ursB7pwPQfrn+vLs/ipf3SN1g3ybLnlgHL/0aJYOyOcytdWRGlNAzle1fXVn/yHVIPcOWVCkzOc4ccbwrlOXrtNc0p/qlS0jO28tgjm39FK3MTb2kMq/WEGe0JyY0Lw0iKvUItHyu3JESxbpiuNzRJT5j8mnYr+jOmZ2W9t3EhX8CRtv8qyyvDhSGJL+pczb7kr0uuvErxHFhDPtXXeAVv03jBQYYzIJfs9yQm8IVzneSWCPtkP2c9VO8S7e0JHoCkm9UL8NsDEc9dqx7o4t02PTt4+hJWrdvnVfC5lfGsxR4neWHb2YVrUT7aMulu7PRivWq1zxvkoPsyW+Vh8zauNGFjbKK2IO1afBXFiielwYE8KlXi/qyF9P8joy8+5UKGXT2lAuZhrYxjyjeEk6B4oIn3d3yevNfST0o7NCr0NYlxrXSJQwG5fp/IBraTErFS1FSG69tCalznpUtl5YHu6qYe04W8qErGCqpNwNt3b7cFiIVuRsDFPoKj7ZWxYnujQ/hQt/R8oXJRqOITnEFvi519SW2n4LpyJe6DJnNiOqQZvQW4rBY93PYotqHb1wqLv0QziE8xiAriXpB7Si1pWdKcuSu9TD6b8kazBWiSi9bVm/Dy4XuSernOr0Z0AWTu7NQJlvcur2xXAI6UmRSzgf3t+QenGkzLdN9fpgqMs9KHKow8OcZwh757Z1fV4up2p9rXIJ5cHrgNl5MTjcASyPWWy7EAs1dt7I2+eA1uGogrpZLf7Xfhg+llN9XqHcJvTN2fOAt87tEp2ZRb+4/pyx3EJGcznHcJ5Z3jvrNfn5sf8X1XpTmdObt08f/VI7BgyvheJ8qCwd491RZOUNpYL7Az4ZMvUf9bdz8lcJL3IaZXLUoWT2K8qpmRYyNfPlpa935lmITJZOmUxFajaeaNHJ2C21q27Az1buAdY9JcrfVPJfxPq/o+1B7RFZD5NN5wzCIdUllAWxu2k9urfnaMskxjO9fMa3DTW4J75HtXje9w61xzO/7ULfyr8k4bn+ucpUrxCZLO/y2XnVgR4Ud+A4F2S+943oTD1ns/gE2knAHiOfo+JIyXz9vCBEj+LCZUkXhDCjpYpyx0u5Q2eSkhLanULfujTCR3qnH/cd8Hx+nGeXIvVzqov16oArtSRV0yPVI8oMdEj/6xCh/VJdhr+XddkvaXNF0gm9g6JEr5xn1SfBTr3jwn7NeJHyYCZTN9ftMorq7e5hdSa2UcqFT7xX4/sV+L4jZYve1jHF3WNVnTucVdCcaZnc/dyhMnlP1gNGs3E+Pqrj53kFr3lA/2+Xom87ku6ALB3Ktke0nzcmeqnWzTZJz+cqq/O2NyukNV9tMk17stKOA3NGsnpPINXjrnz28zlIKVeTlNBx5zqfyJROiwy8lOT5OQo4DREH9Fbua0hPJSozUZJZwJfI8wBZ5gF0jgRpjkQKfVESbR+eXljbWP6/PlYLB5tXNn515eq9zbXPruv/B+Rd9WP1E3UJ1r5fq89g/DfVPnD6vfqj+ov6a+N3jT80/tT4Mzd955zG/EgV/jX+/l8UA06i
    Neural tangent kernel [Jacot et al’18]: 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
    local linear expansion.
    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
    ! No explicit regularization!

    View Slide

  11. Training Dynamic
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    Training:
    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
    Gradient descent: 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
    ✓(k+1) = ✓(k) ⌧rf(✓(k))
    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
    Question: convergence of ✓k toward global minimum?
    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
    min

    f(✓) , 1
    N
    PN
    i=1
    ||B ✓(Axi) yi||2

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    A +
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    v✓1
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    B
    +
    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
    v✓2
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    A
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    xi
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    B
    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
    ˙
    x(t) = v✓(t)
    (x(t))
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
    Polyak- Lojasiewicz inequality [Liu, Zhu, Belkin 2021]:
    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
    ! conditionning might explodes as T ! +1.
    AABFOHictVxtb9vIEd5c367pW6792C+8OunlDqnruOkLcChwieUkvvgSJ5Kd3EVJjpIomQklKqQkJ9H5jxUF+jv6rShQtIcWKNBf0NmZXe5SWnKWbhrC9nK5z8zscHd2ZnaZ3jSJ89nW1p/PvfONb37r299597vnv/f9H/zwRxfe+/FRns6zfnTYT5M0e9QL8yiJJ9HhLJ4l0aNpFoXjXhI97L3Ykc8fLqIsj9NJZ/Z6Gj0Zh6NJPIz74Qyqnl04utjN4tHxLMyy9ORiMIwngyAM8nk8C4FEkMTjeBaM00GUBCE8yo/Tk+DLL+MxyNaPZx98EGTRaJ6EWfwGCQbRcBj1Z5vPLmxsbW7hv2C9cFUVNoT6d5C+9/7fRFcMRCr6Yi7GIhITMYNyIkKRw/VYXBVbYgp1T8QS6jIoxfg8EqfiPGDn0CqCFiHUvoDfI7h7rGoncC9p5ojuA5cEfjJABuISYFJol0FZcgvw+Rwpy9oq2kukKWV7DX97itYYamfiGGo5nG7pi5N9mYmh+B32IYY+TbFG9q6vqMxRK1LywOrVDChMoU6WB/A8g3IfkVrPAWJy7LvUbYjP/4EtZa2876u2c/E1SnkJrkC0Ve/TgkIoFkg/wLc5h2ckTwKcR0AhUn2UpRPU9Rh7P4H2S6i/C9cplrROenAtsfa0FrkDlwu5wyJvweVC3mKR+3C5kPss8gAuF/JAISU2Q5278W24XPg2y/k+XC7kfRb5AC4X8gGLPILLhTxikV/A5UJ+wSJvwuVC3mSRd+ByIe+wyA5cLmSHRR7C5UIesshduFzIXYWsnqkZXCnSiZlZeR3KZR7SUiRQc52V7wZaRxf2hsec7ldg+Vndgr9ubMtDp1EFdtdj3A0rsPzIuwU20o3lbdFtXE1c2Nssdg9GgBu7x2I/Fc8rsJ96zLQXFVh+ru1DOzeWt76fwZ0b+xmLvQslN5Zfo+5BjRt7z2PFmFZgD1jsffGyAutj9bMKLG/322BX3Fh+nepAezfWx5rOK7C8PT0CD8aN5Verh1Drxj5ksY/EqwrsIxb7OVh3N/ZzjxX2TQVWr7HncQUZoT8SwYytoxYWs1KWpkAtZPgnxdqSoG/cg3oOMyowI8SMWcStAnHLE7FfIPa95coLO5qjv8tzaReItieiV6xNsjRj2w+K9rKUeCBaBaK1gqjzSOW71n1ZoHehazjkrFi5ZMmnT2lhv2UpUuOh3vJqxL0Sgsb2MY78KxgtyQhKaqqO2nGxxhMywPs6xAlGb7qXmgePmxVWwUa9YlE9B6rHol47UK9Z1NyBmrOohQO1YFFm5tu4rscIMPqX72KJdzQCyEeuvgLwCq7DqnMb5mgA4+cAvMAHWHMP/rYx9uauOslkNC/XSZnleFKyxBmUlmID6k1U2ML4OsEZFoFk1PKeivHlncxtLNWcIyt8WqzkQZEx8acTozyjgo70FgOcT83o3MGaU/TuqNQMf7uY97rUDL+LGj9FL55KzfAzJf3sDLJ3FLZzBmwbZtNUad+Um9Kg/AvR0OXzuOpKiyvf6liNGUnvVUP6e+rN7J3hvexgifRjys1o5Fb/8lL/mtAwes4tPTejIr0n8np1KWjck4mKe025qQwprqITJYe5a/pmZJuBejO63IzGAXhcOxhzL61y09E7LXpjys1oHAnKe56iJ6/LzWiM8J70YcrNaMhsS6jifFNuatmlBih2NuWmVn2CWWCZA6IxTzXGK8rQT5orajH6B/XZGtvnX1/HZM7maREj1FMyvm01nV6xltVLpP2FCKzarKEc0r+YWz5YmcZSbLPxFckwK63v63TMGi81vw9aDGD20x4AlzNPQEKdk5DWOwGKV9moq9wzjdtmcXKUDFdQXVU7Y71Fw5eyRuW6Z1jLxWWmt0aPXbTXOY69KfqE+6hZTg/7lW+4iiKnof2Shnh6TXT3Rs3Xsva3WNx0BTEtRlofd4RoJ60+TnVpvW3p+JLa5ZnBRXs+ZvzKbPNQWRsZ86Roi6QsdTztdjqPZNfJdfWKMDluehbgG5X2aoFWI8YdqZyNQnW2mLzxJd4b2oe4Jyd5EI0+vMdAUZkK2jWTWXSZTw/Qotr2luMt9aUzdFTO0epqe1yPHlnokQPdPMbZgRXjLpQ6EDMcwl3HI8o5X+gqRY1n4hfF7miKb7A+ok9KFlLTIHsTlSxkXZR9XKJyAmg5GihK96exSkfju2uU+KjfJY+JXcuW/xLu3Or97RDHePVors7EDJDrNnINcNbQri7drXIgCZbOJ9vov9b3UvJrwlHaUI7rU4sz6WWCO/4RRrBT9IwTnG3c7Ci3tvNTq080pwOh987lbnaKFjJA+xfA+pTimAzwxz47oHfQySIkaCN97E5ceDcuXydmx5jx42JBpxrMeIvQls2Rv6Zrz64cxyJFDLQOnK6Mba2TffQFI+SaKetu5nb96iOR5pyEPUqIohkrl5H/h/hb/+hxsrE2IqSG5RvIla1zvY8UYxapoxBX+XobpNvaUl4sZHiqpDbrn5HpYkmyFkZcUh65Wg+Acx/viZccJRnKna+1oXW0LpsrKU9X9Ch7O8Qonuz+SK3AUu4ruEpu4Jzr4igZwSiYFVGEbstlkVf51vMqU/ejnf9fqBtdl7UmKQbCZHBJQ1x+P8JozZYygVFN4/cFzia31rOVVvV8JjgWx9Zc/gpq34ffWm5970enV7IKN3AMEAVzZzRCNcFaCz9eN0q89MjUtMy94WfGpG5l15wlvibrZmLsRWMqBzhqXqmshS6fhcZzi8ZzTx12cK/RaFHXa0v0jI0tOmq30pdfE26dBpTnLGXeI9Oo2ENKO5byozpgqfIxvka9YWltsbRCmK32boA9532Q7rm+Oru/Klb3QNxE36aPHhjFLwOcpTH6XLq2PlIjCpLzNWVf7dnfxRrJvYcWVFKmc5xyxtCuUx+v00LSn6uVLUU7byyCPrd0otpoG9vF8q/WkGOcEznOS424hi0iJb8tR7BikTYtnyPAzH+IPhX5HfUxs93avJOg5E+YeJNmleFFkcIE9c9l3vbWotc9K34NMCacK++6B7Sav2FJgTA6k+D2LHN8Q3KVo50E8mh7aD/X7RTt4k0siTZR6qX4vYeNoajXjHV7bOke6759BC2l1s1bd7Xg+SXeHDl+Z9nRC3FVGysfdblyfzZaoVrlyvd1epiv8DX6mGMbO7IwUV4Z0xUfe3MhiZpxIYwPl2a9aCJ/M8mbyEy7U76UdWtNuZxpIBtzjPESdw5UIlze3WWnN/ch04/eGr0eYm1qVMNRktm4VOUHbEsrs1LBSoRk13NrUmKtR1XrheFhrxrGjpOljNAKJoLL3VBruw/dUrTCZ2OIQl/Qyd6qONGm+TFc8ncgXFGi5uiTQ2yDn3td7Ijdt3Aq4qUqU2YzwBppEwYrMXio+lluUa+jlxZ1m74PB38eMeiakz7GFbWp7ESZl9ym7k//BK1BJiJWetOyeR9sLnxP1jk16U+MFo7vTSz0NzlN+6I5+PSkzMWfD+1vcL0YCv1tU7M+aOp8D8ocmvDQ5xn83rlp3ZyXzaleX+tcfHnQOqB3XjRO7gBWxyymnY+Fyqw38vY5SOswrKGuV4v/tR+aj+HUnJcvtxy/OXvu8dapXaQys9Ivbj5nDDef0VzN0Z9nWvTOeE1ufuT/BY3eVGr15u3Tl36pGQOa11JQPpSXjvD2KDLy+lKR+wMuGVLxb/Gnc/xXCS8LGlVyNKGk9yuqqekWPDX95aWrd/qZj0yGTpVMZWomnmjjydgdsSduws9O4QE2PSVK31TSX4l1f0c7gNohWg+dTacMQhfrIsyCmN20Ad6bc7RVEsszvXTGtwM1ck98H2vled+72F6e+e2U+lb9JQnN9c9EKgalyGR1l8/Mqx70oLwDR7kg/b1vgGfqKZtFJ9DGHnuMdI6KIiX99fMSEQOMC1clXSJCj5Y6yj0n5R6eSYoqaPdKfevjCJ+qnX657yDP54dFdikQv8S6UK0OcqXmpDpwSPUYMwM91P8WRGi/Flfg7xVVdkt6sCZpju+gLNEr61n9SbBT57gwXzNewjyYztQtVLsUo3qze1ifiW1VcqET7/X4UQ1+ZEnZxrf1AuPuTNTnDuc1NOdKJns/dyJ03pP0IKPZsBgf9fHzoobXwqP/dyrRdyxJb4EsPcy2B7iflyG9ROlmF6Wnc5X1edvbNdLqrzaJpjlZacaBPiNZvyeQqHFXPfvpHCSXq4kq6NhznU5kcqdFYiclfn5OPU5DhB695fvq01OOypyVZO7xJfLCQ5aFB50hI82QpTBiJVH24dmFjaur/9fHeuFoe/Pqbzav3d/e+OSG+n9A3hU/FT8Tl2Ht+634BMb/gTgETn8UfxX/FP9q/aH1l9bfW19T03fOKcxPROlf6z//BTkEYoY=
    ! find a suitable limit model and show “implicit” regularization e↵ect.
    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
    Neural tangent kernel [Jacot et al’18]: 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
    local linear expansion.
    AABFGHictVxfc9y2EYfTf6n7J0772BemijtOx3El1U0zzXQmls6WFcu27DvJTizbQ97xTrSp45m8O/+56It0+l3a6Uun0z71rR+gM+1Tv0J3FwAB3oFcUHXNkQSC+O0ulsBidwE6mqRJMV1f/8e5d77xzW99+zvvfvf8977/gx++d+H9Hx0W2Szvxwf9LM3yh1FYxGkyjg+myTSNH07yODyJ0vhB9Hwbnz+Yx3mRZOPe9PUkfnwSjsbJMOmHU6h6euGT23E4DoZJnA6CYZYHm0Eavob2wSQGBpNpno2DR9vHyZtw+vFW2D8ONtc3Pn38m6cX1tavrNO/YLWwoQprQv3bz97/4J/iSAxEJvpiJk5ELMZiCuVUhKKA65HYEOtiAnWPxQLqcigl9DwWp+I8YGfQKoYWIdQ+h98juHukasdwjzQLQveBSwo/OSADcREwGbTLoYzcAno+I8pYW0d7QTRRttfwN1K0TqB2Ko6hlsPplr447MtUDMWn1IcE+jShGuxdX1GZkVZQ8sDq1RQoTKAOywN4nkO5T0it54AwBfUddRvS839RS6zF+75qOxP/JikvwhWIrup9VlIIxZzoB/Q2Z/BMypMC5xFQiFUfsfSSdH1CvR9D+wXU34HrlEpaJxFcC6o9bURuw+VCbrPIHbhcyB0WuQeXC7nHIvfhciH3FRKxOencje/C5cJ3Wc734HIh77HI+3C5kPdZ5CFcLuQhi/wKLhfyKxZ5Ay4X8gaLvAWXC3mLRfbgciF7LPIALhfygEVeh8uFvK6Q9TM1hysjOgkzK69BucoDLUUKNddY+bbIOrqwWx5zul+D5Wd1B/66sR0PncY12Ose425Yg+VH3g7YSDeWt0U3aTVxYW+y2F0YAW7sLov9QjyrwX7hMdOe12D5ubYH7dxY3vrehjs39jaLvQMlN5Zfo+5CjRt712PFmNRg91nsPfGiButj9fMaLG/3u2BX3Fh+nepBezfWx5rOarC8PT0ED8aN5VerB1Drxj5gsQ/FqxrsQxb7JVh3N/ZLjxX2TQ1Wr7HnaQUZkT8Sw4xtohaWsxJLE6AWMvzTcm1JyTeOoJ7DjErMiDAnLGKnROx4IvZKxJ63XEVpRwvyd3ku3RLR9URE5dqEpSnbflC2x1LqgeiUiM4SoskjxXet+zIn70LXcMhpuXJhyadPWWm/sRSr8dBseTXibgUhx/YxjfzLFC1hBIWaaqJ2XK7xEhnQfRPiJUVvupeaB4+bllbBRr1iUZEDFbGo1w7UaxY1c6BmLGruQM1ZlJn5Nu7IYwQY/eO7WNCdHAHSR66/AvAKrsGqcxPmaADjZx+8wPtUcxf+din25q4myTCax3USsxyPK5Y4h9JCrEG9iQo7FF+nNMNikEy2vKtifLzD3MZCzTlphU/LlTwoMyb+dBKSZ1TSQW8xoPnUjs4tqjkl706W2uFvlvNel9rhr5PGT8mLl6V2+KmSfnoG2XsK2zsDtguzaaK0b8ptacj8i6Shy+dp1UWLi2/1RI0ZpPeqJf1d9WZ2z/Betqkk9WPK7WgUVv+KSv/a0DB6Liw9t6OC3pP0enUpaN2TsYp7TbmtDBmtomMlh7lr+2awzUC9GV1uR2MfPK5tirkXVrnt6J2UvTHldjQOhcx7npInr8vtaIzoXurDlNvRwGxLqOJ8U25r2VEDMnY25bZWfUxZYMwByTEva4xXlJOfNFPUEvIPmrM1ts+/uo5hzuZJGSM0UzK+bT2dqFzLmiXS/kIMVm3aUg70L2aWD1alsRCbbHwlZZhW1vdVOmaNR83vgRYDmP1yD4DLmacgoc5JoPVOgeIGG3VVe6ZxmywOR8lwCXWkaqest2j4yqxRte4p1XJxmemt0eMR2euCxt6EfMI90iynh73aN1xHkdPQXkVDPL02unuj5mtV++ssbrKEmJQjrU87QnInrTlOdWm9a+n4otrlmcIl93zM+MVs81BZG4x5MrJFKEsTT7udziPZdbiuXhYmxy2fBfRG0V7NyWoktCNVsFGozhZLb3xB94b2Ae3JIQ9Jow/vMVBUJkLummEWHfPpAVlU295yvFFfOkMnywVZXW2Pm9EjCz1yoNvHONuwYtyBUg9ihgO463lEOedLXWWk8Vx8XO6OZvQGmyP6tGIhNQ1pb+KKhWyKso8rVF4CGkeDjNL9aSzT0fijFUp81O+Sx8SuVct/kXZu9f52SGO8fjTXZ2IGxHWTuAY0a+Surrxb5iAlWDifbJL/2txL5NeGI9pQjusTi7PUy5h2/GOKYCfkGac027jZUW1t56eWn2hO+0LvneNudkYWMiD7F8D6lNGYDOjHPjugd9ClRUjJRvrYnaT0bly+TsKOMePHJUKeajDjLSZbNiP+mq49uwoaizJikOvA6dLY1jrZI18wJq65su5mbjevPog05yTsUSIpmrFyifh/RL/1jx4naysjAjWMb6BQts71PjKKWVBHIa3yzTZIt7Wl/LCU4YmS2qx/RqYPK5J1KOJCeXC1HgDnPt1LXjhKcpK7WGkj19GmbC5SnizpEXs7pChe2v2RWoFR7su0Sq7RnDuiUTKCUTAtowjdlssiL/Nt5lWl7ke7+L9QN7quag0pBsJkcKWGuPx+TNGaLWUKo1qO3+c0m9xaz5daNfMZ01g8seby11D7AfzWcut7PzpRxSps0RiQFMyd0YisCVZa+PHaqvDSI1PTMveGnxmTupVdc5b4Wlo3E2PPW1PZp1HzSmUtdPksNJ5ZNJ556rBHe41Gi7peW6KnbGzRU7uVvvzacOu1oDxjKfMemUYlHlLasZQf1QFLlY/xNeoNS2udpRXCbLV3A+w574N0z/Xl2f11uboH4gb5Nn3ywGT8MqBZmpDPpWubIzVJATlfVfbVnv1HVIPcI7KgSFme48QZI3ed+nSdlpL+TK1sGdl5YxH0uaWXqo22sUdU/uUK8oTmREHzUiOuUotYyW/LESxZpCuWzxFQ5j8kn0r6Hc0xs93avJOg4k+YeFPOKsNLRgpj0j+XedtdiV53rfg1oJhwprzrCGi1f8NIQWJ0JsHtWRb0hnCVkzsJ0qONyH6u2im5ize2JLpCUi/Ebz1sjIx6zVi3x5buse7bz6Elat28dVcLnl/qzZHjd5YdvZBWtRPloy6W7s9GK1SrXPW+SQ+zJb5GHzNqY0cWJsqrYo7EZ95cpETtuEiMD5d2vWgjfzvJ28gsd6d8KevWmnI10yBtzDHFS9w5UES4vLtLTm/uI6Yf0Qq9iLA2NVnDUcJsXKbyA7alxaxUsBQh2fXcmpRa61HdemF42KuGsePSUsZkBVPB5W5ka7sPR5Vohc/GSAp9IU/21sWJNs3P4MLfgXBFiZqjTw6xC37uNbEtrr+FUxEvVFlmNgOqQZswWIrBQ9XPaotmHb2wqNv0fTj480hA15z0Ca2obWWXlHnJber+9F+SNchFzEpvWrbvg82F78kqpzb9ScjC8b1JhP4mp21fNAefnlS5+POR+xtcL4ZCf9vUrg+aOt+DKoc2PPR5Br93blq352VzatbXKhdfHnId0DsvGoc7gPUxi2nnY6Fy6428fQ5oHYYN1PVq8b/2Q/MxnNrz8uVW0DdnzzzeumwXq8ws+sXt54zh5jOa6zn688zK3hmvyc1P+n9BqzeVWb15+/TRLzVjQPNaCJkP5aWTeHsUGXl9qeD+gEuGTPxH/OEc/1XCi5JGnRxtKOn9inpqugVPTX956eqdfuYjk6FTJ1OVmoknunQydlvsihvws116gG1PicpvKuVfxLq/ox1A7ZCsh86mywzCEdXFlAUxu2kDujfnaOskxjO98oxvD2pwT3yPavG87x1qj2d+e5W+1X9JIuf6bZGJQSUyWd7lM/Mqgh5Ud+BkLkh/7xvQmXqZzZIn0E489hjlOSoZKemvnxeEGFBcuCzpghB6tDRRjpyUIzqTFNfQjip969MIn6idftx3wPP5YZldCsQvqC5UqwOu1JxU+w6pHlFmICL9r0OE9itxGf5eVmW3pPsrkhb0DqoSvbKeNZ8EO3WOC/M140XKg+lM3Vy1yyiqN7uHzZnYTi0XeeK9GT9qwI8sKbv0tp5T3J2L5tzhrIHmTMlk7+eOhc57Sj1gNBuW46M5fp438Jp79P9WLfqWJekOyBJRtj2g/byc6KVKN9dJenmusjlve7NBWv3VpqRpTlaacaDPSDbvCaRq3NXPfnkOksvVxDV07LkuT2Ryp0USJyV+fk48TkOEHr3l++rTU47KjJVk5vEl8txDlrkHnSEjzZClMGIlUfbh6YW1jeX/62O1cLh5ZeOTK1fvba59vqX+H5B3xU/ET8UlWPt+LT6H8b8vDoDT78WfxF/F3zq/6/yx8+fOX2TTd84pzI9F5V/n7/8FLc9UEQ==
    Mean field for 2 layers perceptron [Chizat-Bach 2018]: 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
    global convergence.
    AABFD3ictVxtc9TIER4ubxfyxiUf80XEOMWlOGIc8lJ1laoDrzE+DBh2bbhjgZJ2tWuBvFq0Lzbs+Uek8mNS+ZKkkk/5CfkBqUo+5S+ku2dGM9odqUcOQWV7NJqnu6c109PdMyIap8lkurHxjwsffO3r3/jmtz789sXvfPd73//BpY9+eDjJZnkvPuhlaZY/jcJJnCaj+GCaTNP46TiPw+MojZ9Er7fw+ZN5nE+SbNSZvh3Hz4/D4SgZJL1wClUvL31ypZsnw6NpmOfZyZWgGw2CB1kQnwLvXjIN8ng4S8M8eUfNL7+8tLZxfYP+BauFG6qwJtS//eyjy/8UXdEXmeiJmTgWsRiJKZRTEYoJXM/EDbEhxlD3XCygLodSQs9jcSYuAnYGrWJoEULta/g9hLtnqnYE90hzQugecEnhJwdkINYBk0G7HMrILaDnM6KMtVW0F0QTZXsLfyNF6xhqp+IIajmcbumLw75MxUD8hvqQQJ/GVIO96ykqM9IKSh5YvZoChTHUYbkPz3Mo9wip9RwQZkJ9R92G9Pxf1BJr8b6n2s7Ev0nKdbgC0Va9zwoKoZgT/YDe5gyeSXlS4DwECrHqI5ZOSNfH1PsRtF9A/QO4zqikdRLBtaDas1rkFlwu5BaL3IHLhdxhkXtwuZB7LHIfLhdyXyERm5PO3fg2XC58m+X8CC4X8hGLfAyXC/mYRR7C5UIessgv4XIhv2SRd+ByIe+wyHtwuZD3WGQHLheywyIP4HIhD1jkNlwu5LZCVs/UHK6M6CTMrLwF5TIPtBQp1Nxi5btN1tGFve0xp3sVWH5Wt+CvG9vy0Glcgd32GHeDCiw/8nbARrqxvC26S6uJC3uXxe7CCHBjd1ns5+JVBfZzj5n2ugLLz7U9aOfG8tb3Pty5sfdZ7AMoubH8GvUQatzYhx4rxrgCu89iH4k3FVgfq59XYHm73wa74sby61QH2ruxPtZ0VoHl7ekheDBuLL9aPYFaN/YJi30qTiuwT1nsF2Dd3dgvPFbYdxVYvcZepBVkSP5IDDO2jlpYzEosjYFayPBPi7UlJd84gnoOMywwQ8Ics4idArHjidgrEHveck0KOzohf5fn0i4QbU9EVKxNWJqy7ftFeyylHohWgWgtIeo8UnzXui9z8i50DYecFisXlnz6lBX2G0uxGg/1llcjHpYQcmwf0ci/RtESRlCoqTpqR8UaL5EB3dchTih6073UPHjctLAKNuqURUUOVMSi3jpQb1nUzIGasai5AzVnUWbm27iuxwgw+sd3saA7OQKkj1x9BeAV3IJV5y7M0QDGzz54gY+p5iH8bVPszV11kmE0j+skZjmelyxxDqWFWIN6ExW2KL5OaYbFIJls+VDF+HiHuY2FmnPSCp8VK3lQZEz86SQkz7Cgg95iQPOpGZ17VHNG3p0sNcPfLea9LjXDb5PGz8iLl6Vm+KmSfnoO2TsK2zkHtg2zaay0b8pNacj8i6Shyxdp1UWLi2/1WI0ZpHfakP6uejO753gvW1SS+jHlZjQmVv8mpf41oWH0PLH03IwKek/S69WloHFPRiruNeWmMmS0io6UHOau6ZvBNn31ZnS5GY198Li2KOZeWOWmo3dc9MaUm9E4FDLveUaevC43ozGke6kPU25GA7MtoYrzTbmpZUcNyNjZlJta9RFlgTEHJMe8rDFeUU5+0kxRS8g/qM/W2D7/6jqGOZsXRYxQT8n4ttV0omItq5dI+wsxWLVpQznQv5hZPliZxkJssvGVlGFaWt9X6Zg1HjW/B1oMYPbLPQAuZ56ChDongdY7BYo32Kir3DON22RxOEoGS6iuqp2y3qLhK7NG5bqXVMvFZaa3Ro9dstcTGntj8gn3SLOcHvYq33AVRU5DeyUN8fSa6O6dmq9l7W+wuPESYlyMtB7tCMmdtPo41aX1tqXjdbXLM4VL7vmY8YvZ5oGyNhjzZGSLUJY6nnY7nUey63BdvSZMjls+C+iNor2ak9VIaEdqwkahOlssvfEF3RvaB7QnhzwkjR68x0BRGQu5a4ZZdMynB2RRbXvL8UZ96QydLE/I6mp7XI8eWuihA908xtmCFeMBlDoQMxzAXccjyrlY6Cojjefik2J3NKM3WB/RpyULqWlIexOXLGRdlH1UonICaBwNMkr3p7FMR+O7K5T4qN8lj4ldy5Z/nXZu9f52SGO8ejRXZ2L6xHWTuAY0a+Surrxb5iAlWDifbJL/Wt9L5NeEI9pQjusLi7PUy4h2/GOKYMfkGac027jZUW5t56eWn2hO+0LvneNudkYWMiD7F8D6lNGYDOjHPjugd9ClRUjJRvrYnaTwbly+TsKOMePHJUKeajDjLSZbNiP+mq49uyY0FmXEINeBs6WxrXWyR75gTFxzZd3N3K5ffRBpzknYo0RSNGPlKvH/mH7rHz1O1lZGBGoY38BE2TrX+8goZkEdhbTK19sg3daW8kohwwsltVn/jExXSpK1KOJCeXC17gPnHt1LXjhKcpJ7stJGrqN12VykPF7SI/Z2QFG8tPtDtQKj3NdolVyjOdelUTKEUTAtogjdlssiL/Ot51Wm7kd78n+hbnRd1hpSDITJ4EoNcfn9mKI1W8oURrUcv69pNrm1ni+1quczorF4bM3lr6D2MvzWcut7PzpRySrcpjEgKZg7oxFZE6y08ON1u8RLj0xNy9wbfmZM6lZ2zXnia2ndTIw9b0xln0bNqcpa6PJ5aLyyaLzy1GGH9hqNFnW9tkQv2diio3Yrffk14dZpQHnGUuY9Mo1KPKS0Yyk/qn2WKh/ja9Q7ltYGSyuE2WrvBthz3gfpnuvLs/urYnUPxB3ybXrkgcn4pU+zNCGfS9fWR2qSAnK+qeyrPfu7VIPcI7KgSFme48QZI3edenSdFZL+VK1sGdl5YxH0uaUT1Ubb2C6Vf7GCPKY5MaF5qRE3qUWs5LflCJYs0nXL5wgo8x+STyX9jvqY2W5t3klQ8idMvClnleElI4UR6Z/LvO2uRK+7VvwaUEw4U951BLSav2GkIDE6k+D2LCf0hnCVkzsJ0qONyH6u2im5izeyJLpOUi/Ebz1sjIx6zVi3x5buse7bz6Alat28dVcLnl/qzZHjd54dvZBWtWPloy6W7s9HK1SrXPm+Tg+zJb5GHzNqY0cWJsorY7riU28uUqJmXCTGh0uzXjSRv5nkTWSWu1O+lHVrTbmcaZA25ojiJe4cKCJc3t1Vpzf3MdOPaIVeRFibmqzhKGE2LlP5AdvSYlYqWIqQ7HpuTUqt9ahqvTA87FXD2HFpKWOygqngcjeytd2Hbila4bMxkkJPyJO9VXGiTfNTuPB3IFxRoubok0Nsg597S2yJ7fdwKuKNKsvMZkA1aBP6SzF4qPpZblGvozcWdZu+Dwd/HgnompM+oRW1qeySMi+5Td2f/glZg1zErPSmZfM+2Fz4nqxyatKfhCwc35tE6G9ymvZFc/DpSZmLPx+5v8H1YiD0t03N+qCp8z0oc2jCQ59n8HvnpnVzXjanen2tcvHlIdcBvfOicbgDWB2zmHY+Fiq33sj754DWYVBDXa8W/2s/NB/DqTkvX24T+ubslcdbl+1ilZlFv7j5nDHcfEZzNUd/nlnRO+M1uflJ/y9o9KYyqzfvnz76pWYMaF4LIfOhvHQSb48iI68vFdwfcMmQif+IP1/gv0p4U9CokqMJJb1fUU1Nt+Cp6S8vXb3Tz3xkMnSqZCpTM/FEm07GboldcQd+tgoPsOkpUflNpfyLWPd3tH2oHZD10Nl0mUHoUl1MWRCzm9ane3OOtkpiPNMrz/h2oAb3xPeoFs/7PqD2eOa3U+pb9Zckcq7fF5nolyKT5V0+M68i6EF5B07mgvT3vgGdqZfZLHkC7dhjj1Geo5KRkv76eUGIPsWFy5IuCKFHSx3lyEk5ojNJcQXtqNS3Ho3wsdrpx30HPJ8fFtmlQPyc6kK1OuBKzUm175DqGWUGItL/BkRovxTX4O81VXZLur8i6YTeQVmiU+tZ/UmwM+e4MF8zrlMeTGfq5qpdRlG92T2sz8S2KrnIE+/1+GENfmhJ2aa39Zri7lzU5w5nNTRnSiZ7P3ckdN5T6gGj2bAYH/Xx87yG19yj//cq0fcsSXdAloiy7QHt5+VEL1W62Sbp5bnK+rzt3Rpp9VebkqY5WWnGgT4jWb8nkKpxVz375TlILlcTV9Cx57o8kcmdFkmclPj5OfY4DRF69Jbvq09POSozVpKZx5fIcw9Z5h50Bow0A5bCkJVE2YeXl9ZuLP9fH6uFw83rN351/eajzbXPbqv/B+RD8WPxE3EV1r5fi89g/O+LA+D0e/FH8Vfxt9bvWn9o/an1F9n0gwsK8yNR+tf6+38B84FSDQ==
    ! No explicit regularization!

    View Slide

  12. 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
    ResNet and
    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
    Neural-ODEs
    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
    Global and local
    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
    Polyak- Lojasiewicz
    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
    conditions
    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
    P- L condition
    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
    for Neural-ODEs
    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    xi
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    RKHS Neural-ODEs

    View Slide

  13. Polyak-Łojasiewicz Condition
    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
    Polyak- Lojasiewicz inequality:
    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
    ! no spurious stationary points.
    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
    Example: f strongly convex.
    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
    mf(✓) 6 ||rf(✓)||2

    View Slide

  14. Polyak-Łojasiewicz Condition
    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
    Polyak- Lojasiewicz inequality:
    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
    ! no spurious stationary points.
    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
    Example: f strongly convex.
    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
    mf(✓) 6 ||rf(✓)||2

    View Slide

  15. Polyak-Łojasiewicz Condition
    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
    Polyak- Lojasiewicz inequality:
    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
    ! no spurious stationary points.
    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
    [Polyak 1963]
    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
    Theorem:
    AABFIHictVzdc9u4EUeuX9f043LtY194ddJxOrnUdtOPmZt2LrEcxxdf4kSyk7soyZASJSumREWUlA+d/plO/4++dvrS6bQv7Xtn2qf+C91dAAQogVzQTcOxDYL47S6WwGJ3ASYaJ4NsurX19wvvfe3r3/jmt97/9sXvfPd73//g0oc/OMnS2aQTH3fSJJ08jsIsTgaj+Hg6mCbx4/EkDodREj+Kznbx+aN5PMkG6ag1fTOOnw7D/mjQG3TCKVQ9v/Tby73N9vT02WLz7OryatBO4pdBOxr0N7c/bvcmYWcxXC52oCZeYu3VZ2eBbr8F7S8/v7SxdX2L/gXrhW1V2BDq31H64Uf/FG3RFanoiJkYiliMxBTKiQhFBtcTsS22xBjqnooF1E2gNKDnsViKi4CdQasYWoRQewa/+3D3RNWO4B5pZoTuAJcEfiaADMQVwKTQbgJl5BbQ8xlRxtoy2guiibK9gb+RojWE2qk4hVoOp1v64rAvU9ETv6Y+DKBPY6rB3nUUlRlpBSUPrF5NgcIY6rDchecTKHcIqfUcECajvqNuQ3r+L2qJtXjfUW1n4t8k5RW4AtFUvU9zCqGYE/2A3uYMnkl5EuDcBwqx6iOWXpGuh9T7EbRfQP09uJZU0jqJ4FpQ7bISuQuXC7nLIvfhciH3WeQhXC7kIYs8gsuFPFJIxE5I5258Ey4XvslyfgCXC/mART6Ey4V8yCJP4HIhT1jkl3C5kF+yyNtwuZC3WeRduFzIuyyyBZcL2WKRx3C5kMcscg8uF3JPIctn6gSulOgMmFl5E8pFHmgpEqi5ycp3i6yjC3vLY053SrD8rG7AXze24aHTuAS75zHueiVYfuTtg410Y3lbdIdWExf2Dos9gBHgxh6w2M/EixLsZx4z7awEy8+1Q2jnxvLW93O4c2M/Z7H3oOTG8mvUfahxY+97rBjjEuwRi30gXpZgfaz+pATL2/0m2BU3ll+nWtDejfWxprMSLG9PT8CDcWP51eoR1Lqxj1jsY/G6BPuYxX4B1t2N/cJjhX1bgtVr7EVaQfrkj8QwY6uohfmsxNIYqIUM/yRfWxLyjSOo5zD9HNMnzJBF7OeIfU/EYY449JYry+1oRv4uz6WZI5qeiChfm7A0Zdt38/ZYSjwQjRzRWEFUeaT4rnVf5uRd6BoOOc1XLiz59CnN7TeWYjUeqi2vRtwvIOTYPqWRf42iJYygUFNV1E7zNV4iA7qvQryi6E33UvPgcdPcKtio1ywqcqAiFvXGgXrDomYO1IxFzR2oOYsyM9/GtT1GgNE/vosF3ckRIH3k8isAr+AmrDp3YI4GMH6OwAt8SDX34W+TYm/uqpIMo3lcJzHL8bRgiSdQWogNqDdRYYPi64RmWAySyZb3VYyPd5jbWKg5J63wMl/Jgzxj4k9nQPL0czroLQY0n+rRuUs1S/LuZKke/k4+73WpHn6PNL4kL16W6uGnSvrpOWRvKWzrHNgmzKax0r4p16Uh8y+Shi5fpFUXLS6+1aEaM0jvdU36B+rNHJzjvexSSerHlOvRyKz+ZYX+1aFh9JxZeq5HBb0n6fXqUlC7JyMV95pyXRlSWkVHSg5zV/fNYJuuejO6XI/GEXhcuxRzL6xy3dE7zntjyvVonAiZ91ySJ6/L9Wj06V7qw5Tr0cBsS6jifFOua9lRAzJ2NuW6Vn1EWWDMAckxL2uMVzQhP2mmqA3IP6jO1tg+//o6hjmbZ3mMUE3J+LbldKJ8LauWSPsLMVi1aU050L+YWT5YkcZC7LDxlZRhWljf1+mYNR41fwhaDGD2yz0ALmeegIQ6J4HWOwGK22zUVeyZxu2wOBwlvRVUW9VOWW/R8JVZo2Ldc6rl4jLTW6PHNtnrjMbemHzCQ9Isp4fD0jdcRpHT0GFBQzy9Orp7q+ZrUftbLG68ghjnI61DO0JyJ606TnVpvWnp+Ira5ZnCJfd8zPjFbHNPWRuMeVKyRShLFU+7nc4j2XW4rl4TJsctnwX0RtFezclqDGhHKmOjUJ0tlt74gu4N7WPak0MekkYH3mOgqIyF3DXDLDrm0wOyqLa95XijvnSGTpYzsrraHlej+xa670DXj3F2YcW4B6UWxAzHcNfyiHIu5rpKSeMT8XG+O5rSG6yO6JOChdQ0pL2JCxayKso+LVB5BWgcDTJK96exSkfj22uU+KjfJY+JXYuW/wrt3Or97ZDGePloLs/EdInrDnENaNbIXV15t8pBSrBwPtkh/7W6l8ivDke0oRzXZxZnqZcR7fjHFMGOyTNOaLZxs6PY2s5PrT7RnI6E3jvH3eyULGRA9i+A9SmlMRnQj312QO+gS4uQkI30sTuD3Ltx+ToDdowZP24g5KkGM95ismUz4q/p2rMro7EoIwa5DixXxrbWySH5gjFxnSjrbuZ29eqDSHNOwh4lkqIZK5vE/yr91j96nGysjQjUML6BTNk61/tIKWZBHYW0ylfbIN3WlvJyLsMzJbVZ/4xMlwuSNSjiQnlwte4C5w7dS144SiYkd7bWRq6jVdlcpDxe0SP2tkdRvLT7fbUCo9zXaJXcoDnXplHSh1EwzaMI3ZbLIq/yreZVpO5HO/u/UDe6LmoNKQbCZHClhrj8fkzRmi1lAqNajt8zmk1urU9WWlXzGdFYHFpz+Suo/Qh+a7n1vR+dqGAVbtEYkBTMndGIrAnWWvjxulXgpUempmXuDT8zJnUru+Y88bW0bibGntemckSj5rXKWujyeWi8sGi88NRhi/YajRZ1vbZEz9nYoqV2K3351eHWqkF5xlLmPTKNGnhIacdSflS7LFU+xteotyytLZZWCLPV3g2w57wP0j3XV2f3V/nqHojb5Nt0yAOT8UuXZumAfC5dWx2pSQrI+Yayr/bsb1MNco/IgiJleY4TZ4zcderQtcwl/Yla2VKy88Yi6HNLr1QbbWPbVP75GnJIcyKjeakRN6hFrOS35QhWLNJ1y+cIKPMfkk8l/Y7qmNlubd5JUPAnTLwpZ5XhJSOFEemfy7wdrEWvB1b8GlBMOFPedQS06r9hpCAxOpPg9iwzekO4ysmdBOnRRmQ/1+2U3MUbWRJdJ6kX4jceNkZGvWas22NL91j37afQErVu3rqrBc8v8ebI8TvPjl5Iq9pQ+aiLlfvz0QrVKle8r9LDbIWv0ceM2tiRhYnyipi2+MSbi5SoHheJ8eFSrxd15K8neR2Z5e6UL2XdWlMuZhqkjTmleIk7B4oIl3e36fTmrjL9iNboRYS1qckajhJm41KVH7AtLWalgpUIya7n1qTEWo/K1gvDw141jB2XljImK5gILncjW9t9aBeiFT4bIyl0hDzZWxYn2jQ/gQt/B8IVJWqOPjnEJvi5N8Wu2HsHpyJeqrLMbAZUgzahuxKDh6qfxRbVOnppUbfp+3Dw5zEAXXPSD2hFrSu7pMxLblP3p/+KrMFExKz0pmX9Pthc+J6sc6rTnwFZOL43A6G/yanbF83BpydFLv585P4G14ue0N821euDps73oMihDg99nsHvnZvW9XnZnKr1tc7Fl4dcB/TOi8bhDmB5zGLa+VioifVG3j0HtA69Cup6tfhf+6H5GE71eflyy+ibsxceb122i1VmFv3i+nPGcPMZzeUc/Xmmee+M1+TmJ/2/oNabSq3evHv66JeaMaB5LYTMh/LSSbw9ioy8vlRwf8AlQyr+I/5wgf8q4WVOo0yOOpT0fkU5Nd2Cp6a/vHT1Tj/zkcnQKZOpSM3EE006GbsrDsRt+NnNPcC6p0TlN5XyL2Ld39F2obZH1kNn02UGoU11MWVBzG5al+7NOdoyifFMrzzj24Ia3BM/pFo873uP2uOZ31ahb+Vfksi5/rlIRbcQmazu8pl5FUEPijtwMhekv/cN6Ey9zGbJE2hDjz1GeY5KRkr66+cFIboUF65KuiCEHi1VlCMn5YjOJMUltKNC3zo0wsdqpx/3HfB8fphnlwLxM6oL1eqAKzUn1ZFDqieUGYhI/1sQof1CXIO/11TZLenRmqQZvYOiRK+tZ9UnwZbOcWG+ZrxCeTCdqZurdilF9Wb3sDoT2yjlIk+8V+P7Ffi+JWWT3tYZxd0TUZ07nFXQnCmZ7P3ckdB5T6kHjGbDfHxUx8/zCl5zj/7fLUXftSTdB1kiyrYHtJ83IXqJ0s0eSS/PVVbnbe9USKu/2pQ0zclKMw70GcnqPYFEjbvy2S/PQXK5mriEjj3X5YlM7rTIwEmJn59jj9MQoUdv+b769JSjMmMlmXl8iTz3kGXuQafHSNNjKfRZSZR9eH5pY3v1//pYL5zsXN/+5fUbD3Y2Pr2l/h+Q98WPxI/FJqx9vxKfwvg/EsfA6ffiT+Kv4m+N3zX+2Phz4y+y6XsXFOaHovCv8Y//Au51VmE=
    f(✓(k)) 6 1 m
    2
    k
    f(✓(0))
    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
    ✓(k+1) = ✓(k)
    1
    rf(✓(k))
    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
    If rf is -Lipschitz:
    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
    Gradient descent:
    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
    Example: f strongly convex.
    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
    mf(✓) 6 ||rf(✓)||2

    View Slide

  16. Obstruction for P-Ł for Neural ODE
    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
    Linear ResNet, time-independant weights: 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
    ˙
    x = ✓x 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
    ✓(x) = e✓x
    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
    For yj = xi, i.e. learning Id:
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    f(✓) , ||e✓ + Id||2
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    ✓(k+1) = ✓(k)
    1
    rf(✓(k))

    View Slide

  17. Obstruction for P-Ł for Neural ODE
    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
    Linear ResNet, time-independant weights: 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
    ˙
    x = ✓x 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
    ✓(x) = e✓x
    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
    For yj = xi, i.e. learning Id:
    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
    f(✓) , ||e✓ + Id||2
    AABE93ictVxbcxPJFW42tw25sUnlKS+z8ZJitwgxDrlUtlK1YBnjxYBAsmEXAaXLWAjGGqGRhEHr35LKSyqVPOUX5HfkB6QqecpfyLl0T/dIPXN6HMKU7Z6e/s45fab79Dmne+hNklE229z8x7n3vvb1b3zzW+9/+/x3vvu97//gwgc/PMzS+bQfH/TTJJ0+6nWzOBmN44PZaJbEjybTuHvcS+KHvZfb+PzhIp5mo3Tcnr2ZxE+Ou8Px6GjU786g6tmFH3dm8Qngls1pOkmzEdb+7vTZhY3NK5v0L1ovXNWFDaX/NdMPPvyn6qiBSlVfzdWxitVYzaCcqK7K4HqsrqpNNYG6J2oJdVMojeh5rE7VecDOoVUMLbpQ+xJ+D+Husa4dwz3SzAjdBy4J/EwBGamLgEmh3RTKyC2i53OijLVltJdEE2V7A397mtYx1M7Uc6iVcKZlKA77MlNH6rfUhxH0aUI12Lu+pjInraDkkdOrGVCYQB2WB/B8CuU+IY2eI8Jk1HfUbZee/4taYi3e93Xbufo3SXkRrki1dO/TnEJXLYh+RG9zDs9YngQ4D4FCrPuIpdek62Pq/RjaL6H+LlynVDI66cG1pNrTSuQ2XD7ktojchcuH3BWR+3D5kPsisgmXD9nUSMROSed+fAsuH74lcr4Plw95X0Q+gMuHfCAiD+HyIQ9F5Jdw+ZBfisibcPmQN0Xkbbh8yNsisg2XD9kWkQdw+ZAHInIHLh9yRyPLZ+oUrpTojIRZeR3KRR5oKRKouS7Kd4Osow97I2BO90uw8qxuwF8/thGg07gEuxMw7o5KsPLI2wUb6cfKtugWrSY+7C0RuwcjwI/dE7Gfqxcl2M8DZtrLEqw81/ahnR8rW987cOfH3hGxd6Hkx8pr1D2o8WPvBawYkxJsU8TeV69KsCFWf1qCle1+C+yKHyuvU21o78eGWNN5CVa2p4fgwfix8mr1EGr92Ici9pE6KcE+ErFfgHX3Y78IWGHflmDNGnueVpAh+SMxzNgqat18VmJpAtS6Av8kX1sS8o17UC9hhjlmSJhjEbGbI3YDEfs5Yj9Yriy3oxn5uzKXVo5oBSJ6+dqEpZnYfpC3x1ISgGjkiMYKosojxXdt+rIg78LUSMhZvnJhKaRPaW6/sRTr8VBteQ3iXgHBY/s5jfzLFC1hBIWaqqL2PF/jGRnRfRXiNUVvppeGh4yb5VbBRZ2IqJ4H1RNRbzyoNyJq7kHNRdTCg1qIKDvzXVwnYARY/eO7WNIdjwD2kcuvCLyC67Dq3II5GsH4aYIX+IBq7sHfFsXe0lUlGUbzuE5iluNJwRJPobRUG1Bvo8IGxdcJzbAYJOOW93SMj3eY21jqOcdW+DRfyaM8YxJOZ0TyDHM66C1GNJ/q0blNNafk3XGpHv5WPu9NqR5+hzR+Sl48l+rhZ1r62Rlkb2ts+wzYFsymida+LdelwfkXpmHK52nVRYuLb/VYjxmkd1KT/p5+M3tneC/bVGL92HI9GpnTv6zQvzo0rJ4zR8/1qKD3xF6vKUW1ezLWca8t15UhpVV0rOWwd3XfDLYZ6DdjyvVoNMHj2qaYe+mU647eSd4bW65H41Bx3vOUPHlTrkdjSPesD1uuRwOzLV0d59tyXcuOGuDY2ZbrWvUxZYExB8RjnmusVzQlP2muqY3IP6jO1rg+//o6hjmbp3mMUE3J+rbldHr5WlYtkfEXYrBqs5pyoH8xd3ywIo2l2hLjK5ZhVljf1+nYNR41vw9ajGD28x6AlDNPQEKTk0DrnQDFq2LUVeyZwW2JOBwlRyuojq6did6i5ctZo2LdM6qV4jLbW6vHDtnrjMbehHzCfdKspIf90jdcRlHS0H5BQzK9Orp7q+drUfubIm6ygpjkI61PO0K8k1Ydp/q03nJ0fFHv8szg4j0fO34x23ykrQ3GPCnZIpSliqfbzuSR3DpcVy8rm+PmZxG9UbRXC7IaI9qRysQo1GSL2Rtf0r2lfUB7csiDafThPUaaykTxrhlm0TGfHpFFde2txBv1ZTJ0XM7I6hp7XI0eOuihB10/xtmGFeMulNoQMxzAXTsgyjmf6yoljU/Vz/Pd0ZTeYHVEnxQspKHB9iYuWMiqKPt5gcprQONo4Cg9nMYqHYPvrFGSo36fPDZ2LVr+i7Rza/a3uzTGy0dzeSZmQFy3iGtEs4Z3dflulQNLsPQ+2SL/tbqXyK8OR7ShEtenDmfWy5h2/GOKYCfkGSc026TZUWzt5qdWnxhOTWX2znE3OyULGZH9i2B9SmlMRvTjnh0wO+hsERKykSF2Z5R7Nz5fZySOMevHjRSfarDjLSZbNif+hq47uzIaixwx8DpwujK2jU72yReMietUW3c7t6tXH0TacxLuKGGKdqxcIv4f02/zY8bJxtqIQA3jG8i0rfO9j5RiFtRRl1b5ahtk2rpSfpTL8FRLbdc/K9NHBckaFHGhPLhaD4Bzn+6ZF46SKcmdrbXhdbQqm4uUJyt6xN4eURTPdn+oV2CU+zKtkhs05zo0SoYwCmZ5FGHaSlnkVb7VvIrUw2hn/xfqVtdFrSHFSNkMLmtIyu/HFK25UiYwqnn8vqTZ5Nf6dKVVNZ8xjcVjZy5/BbUfwm8jt7kPo9MrWIUbNAaYgr2zGuGaaK1FGK8bBV5mZBpa9t7ys2PStHJrzhJfs3WzMfaiNpUmjZoTnbUw5bPQeOHQeBGowzbtNVotmnpjiZ6JsUVb71aG8qvDrV2D8lykLHtkBjUKkNKNpcKoDkSqcoxvUG9FWpsirS7MVnc3wJ3zIUj/XF+d3V/lq3ukbpJv0ycPjOOXAc3SEflcprY6UmMKyPmatq/u7O9QDXLvkQVFynyOE2cM7zr16TrNJf2ZXtlSsvPWIphzS691G2NjO1T+5RrymOZERvPSIK5Ri1jL78oRrVikK47PEVHmv0s+Ffsd1TGz29q+k6jgT9h4k2eV5cWRwpj0L2Xe9tai1z0nfo0oJpxr77oHtOq/YaTAGJNJ8HuWGb0hXOV4J4E92h7Zz3U7xbt4Y0eiKyT1Uv0+wMZw1GvHuju2TI9N3z6Blqh1+9Z9LWR+STBHid9ZdvS6tKodax91uXJ/NlpdvcoV76v0MF/ha/UxpzZuZGGjvCKmoz4N5sIS1ePCmBAu9XpRR/56kteRmXenQimb1oZyMdPANuY5xUvSOVBE+Ly7S15v7mOhH701ej3CutS4RqKE2bhU5wdcS4tZqWglQnLrpTUpcdajsvXC8nBXDWvH2VLGZAUTJeVuuLXbh04hWpGzMUyhr/hkb1mc6NL8FC78HSlflGg4huQQW+DnXlfbaucdnIp4pcuc2YyoBm3CYCUG7+p+FltU6+iVQ92lH8IhnMcIdC1JP6IVta7sTFmW3KUeTv81WYOpikXpbcv6fXC5yD1Z51SnPyOycHJvRsp8k1O3L4ZDSE+KXML58P6G1IsjZb5tqtcHQ13uQZFDHR7mPEPYO7et6/NyOVXra51LKA9eB8zOi8HhDmB5zGLbhVioqfNG3j0HtA5HFdTNavG/9sPwsZzq8wrlltE3Zy8C3jq3i3VmFv3i+nPGcgsZzeUcw3mmee+s1+Tnx/5fVOtNpU5v3j199EvtGDC8lorzobJ0jHdHkZU3lAruD/hkSNV/1N/PyV8lvMpplMlRh5LZryinZlrI1MyXl77emWchMlk6ZTIVqdl4okUnY7fVnroJP9u5B1j3lCh/U8l/Eev/jnYAtUdkPUw2nTMIHaqLKQtid9MGdG/P0ZZJjGd6+YxvG2pwT3yfavG8711qj2d+24W+lX9JwnP9jkrVoBCZrO7y2XnVgx4Ud+A4F2S+943oTD1ns/gE2nHAHiOfo+JIyXz9vCTEgOLCVUmXhDCjpYpyz0u5R2eS4hLavULf+jTCJ3qnH/cd8Hx+N88uReoXVNfVqwOu1JJUTY9Ujykz0CP9b0KE9it1Gf5e1mW/pM01STN6B0WJTpxn1SfBTr3jwn7NeJHyYCZTt9DtUorq7e5hdSa2UcqFT7xX44cV+KEjZYve1kuKu6eqOnc4r6A51zK5+7ljZfKerAeMZrv5+KiOnxcVvBYB/b9dir7tSLoLsvQo2x7Rft6U6CVaNzskPZ+rrM7b3qqQ1ny1yTTtyUo7DswZyeo9gUSPu/LZz+cgpVxNXELHnet8IlM6LTLyUpLn5yTgNEQ3oLdyX0N6KlGZi5LMA75EXgTIsgigcyRIcyRSGIqSaPvw7MLG1dX/62O9cLh15eqvr1y7v7Xx2Q39/4C8r36ifqouwdr3G/UZjP+mOlB4KuSP6i/qr403jT80/tT4Mzd975zG/EgV/jX+9l+0Jkky
    Proposition:
    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
    ˜
    f(z) , |ez + 1|2
    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
    If ✓(0) = U diag(z(0)
    1
    , . . . , z(0)
    d
    )U⇤,
    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
    then ✓(k) = U diag(z(k)
    1
    , . . . , z(k)
    d
    )U⇤
    AABFFXictVxfc9u4EUeu/67pv1z72BdenXSSTpo6vvTPzE1nLrEcxxcncSLZyV2UeEiJkhnToiJKchKdP0enH6ZzL51O+9TnfoDOtE/9Ct1dAAQogVzQTc2xBUL47S6WwGJ3AToap0k+XV//x4UPvvHNb337Ox9+9+L3vv+DH/7o0kc/Psiz2aQX7/eyNJs8i8I8TpNRvD9Npmn8bDyJw5MojZ9Gx5v4/dN5PMmTbNSZvh3HL07C4SgZJL1wClWHlz45PYoncXD53WHycnH1+NpZ0E1GQXdz83KQ5EEYDCdhP4lH06Af5z38zAbB4aW19Rvr9BOsFm6qwppQP3vZRx//U3RFX2SiJ2biRMRiJKZQTkUocriei5tiXYyh7oVYQN0ESgl9H4szcRGwM2gVQ4sQao/h7xDunqvaEdwjzZzQPeCSwu8EkIG4ApgM2k2gjNwC+n5GlLG2ivaCaKJsb+EzUrROoHYqjqCWw+mWvjjsy1QMxO+oDwn0aUw12LueojIjraDkgdWrKVAYQx2W+/D9BMo9Qmo9B4TJqe+o25C+/xe1xFq876m2M/FvkvIKXIFoq95nBYVQzIl+QE9zBt9JeVLgPAQKseojlk5J1yfU+xG0X0D9Q7jOqKR1EsG1oNqzWuQmXC7kJovchsuF3GaRu3C5kLsscg8uF3JPIRE7IZ278W24XPg2y/kxXC7kYxb5BC4X8gmLPIDLhTxgkV/C5UJ+ySLvwuVC3mWR9+FyIe+zyA5cLmSHRe7D5ULus8gtuFzILYWsnqkTuDKikzCz8jaUyzzQUqRQc5uV7w5ZRxf2jsec7lVg+Vndgk83tuWh07gCu+Ux7gYVWH7kbYONdGN5W3SPVhMX9h6L3YER4MbusNjPxasK7OceM+24AsvPtV1o58by1vcB3LmxD1jsQyi5sfwa9Qhq3NhHHivGuAK7x2Ifi9cVWB+rP6nA8na/DXbFjeXXqQ60d2N9rOmsAsvb0wPwYNxYfrV6CrVu7FMW+0y8qcA+Y7FfgHV3Y7/wWGHfVWD1GnuRVpAh+SMxzNg6amExK7E0Bmohwz8t1paUfOMI6jnMsMAMCXPCIrYLxLYnYrdA7HrLlRd2NCd/l+fSLhBtT0RUrE1YmrLt+0V7LKUeiFaBaC0h6jxSfNa6L3PyLnQNh5wWKxeWfPqUFfYbS7EaD/WWVyMelRBybB/RyL9O0RJGUKipOmpHxRovkQHd1yFOKXrTvdQ8eNy0sAo26g2LihyoiEW9daDesqiZAzVjUXMHas6izMy3cV2PEWD0j89iQXdyBEgfufoKwCu4DavOPZijAYyfPfACn1DNI/hsU+zNXXWSYTSP6yRmOV6ULPEESguxBvUmKmxRfJ3SDItBMtnykYrx8Q5zGws156QVPitW8qDImPjTSUieYUEHvcWA5lMzOvep5oy8O1lqhr9XzHtdaobfIo2fkRcvS83wUyX99ByydxS2cw5sG2bTWGnflJvSkPkXSUOXL9KqixYXn+qJGjNI701D+jvqyeyc47lsUknqx5Sb0cit/uWl/jWhYfScW3puRgW9J+n16lLQuCcjFfeaclMZMlpFR0oOc9f0yWCbvnoyutyMxh54XJsUcy+sctPROy56Y8rNaBwImfc8I09el5vRGNK91IcpN6OB2ZZQxfmm3NSyowZk7GzKTa36iLLAmAOSY17WGK9oQn7STFFLyD+oz9bYPv/qOoY5m5dFjFBPyfi21XSiYi2rl0j7CzFYtWlDOdC/mFk+WJnGQmyw8ZWUYVpa31fpmDUeNb8LWgxg9ss9AC5nnoKEOieB1jsFijfZqKvcM43bYHE4SgZLqK6qnbLeouErs0blukOq5eIy01ujxy7Z65zG3ph8wl3SLKeH3conXEWR09BuSUM8vSa6e6fma1n76yxuvIQYFyOtRztCcietPk51ab1t6fiK2uWZwiX3fMz4xWzzQFkbjHkyskUoSx1Pu53OI9l1uK5eFybHLb8L6ImivZqT1UhoRypno1CdLZbe+ILuDe192pNDHpJGD55joKiMhdw1wyw65tMDsqi2veV4o750hk6Wc7K62h7Xo4cWeuhAN49xNmHFeAilDsQM+3DX8YhyLha6ykjjE/HLYnc0oydYH9GnJQupaUh7E5csZF2UfVSicgpoHA0ySvensUxH47srlPio3yWPiV3Llv8K7dzq/e2Qxnj1aK7OxPSJ6wZxDWjWyF1debfMQUqwcH6zQf5rfS+RXxOOaEM5ri8tzlIvI9rxjymCHZNnnNJs42ZHubWdn1r+RnPaE3rvHHezM7KQAdm/ANanjMZkQL/22QG9gy4tQko20sfuJIV34/J1EnaMGT8uEfJUgxlvMdmyGfHXdO3ZldNYlBGDXAfOlsa21sku+YIxcZ0o627mdv3qg0hzTsIeJZKiGStXif81+qt/9ThZWxkRqGF8Armyda7nkVHMgjoKaZWvt0G6rS3l5UKGl0pqs/4ZmS6XJGtRxIXy4GrdB849upe8cJRMSO58pY1cR+uyuUh5vKRH7O2Aonhp94dqBUa5r9MquUZzrkujZAijYFpEEbotl0Ve5lvPq0zdj3b+f6FudF3WGlIMhMngSg1x+f2YojVbyhRGtRy/xzSb3FqfLLWq5zOisXhizeWvoPZj+Kvl1vd+dKKSVbhDY0BSMHdGI7ImWGnhx+tOiZcemZqWuTf8zJjUreya88TX0rqZGHvemMoejZo3Kmuhy+eh8cqi8cpThx3aazRa1PXaEh2ysUVH7Vb68mvCrdOA8oylzHtkGpV4SGnHUn5U+yxVPsbXqHcsrXWWVgiz1d4NsOe8D9I915dn91fF6h6Iu+Tb9MgDk/FLn2ZpQj6Xrq2P1CQF5HxL2Vd79nepBrlHZEGRsjzHiTNG7jr16DorJP25WtkysvPGIuhzS6eqjbaxXSp/soI8oTmR07zUiFvUIlby23IESxbphuVzBJT5D8mnkn5HfcxstzbPJCj5EybelLPK8JKRwoj0z2Xedlai1x0rfg0oJpwp7zoCWs2fMFKQGJ1JcHuWOT0hXOXkToL0aCOyn6t2Su7ijSyJbpDUC/F7Dxsjo14z1u2xpXus+/YLaIlaN0/d1YLnl3pz5PidZ0cvpFXtRPmoi6X789EK1SpXvq/Tw2yJr9HHjNrYkYWJ8sqYrvjUm4uUqBkXifHh0qwXTeRvJnkTmeXulC9l3VpTLmcapI05oniJOweKCJd3d9XpzV1j+hGt0IsIa1OTNRwlzMZlKj9gW1rMSgVLEZJdz61JqbUeVa0Xhoe9ahg7Li1lTFYwFVzuRra2+9AtRSt8NkZS6Al5srcqTrRpfgoX/g2EK0rUHH1yiG3wc2+LTbH1Hk5FvFZlmdkMqAZtQn8pBg9VP8st6nX02qJu0/fh4M8jAV1z0ie0ojaVXVLmJbep+9M/JWswETErvWnZvA82F74nq5ya9CchC8f3JhH6nZymfdEcfHpS5uLPR+5vcL0YCP1uU7M+aOp8D8ocmvDQ5xn8nrlp3ZyXzaleX6tcfHnIdUDvvGgc7gBWxyymnY+FmlhP5P1zQOswqKGuV4v/tR+aj+HUnJcvt5zeOXvl8dRlu1hlZtEvbj5nDDef0VzN0Z9nVvTOeE1uftL/Cxo9qczqzfunj36pGQOa10LIfCgvncTbo8jI60sF9wdcMmTiP+LrC/xbCa8LGlVyNKGk9yuqqekWPDX95qWrd/o7H5kMnSqZytRMPNGmk7GbYkfchd/NwgNsekpUvlMpPxHrfo+2D7UDsh46my4zCF2qiykLYnbT+nRvztFWSYxneuUZ3w7U4J74LtXied+H1B7P/HZKfat+k0TO9QciE/1SZLK8y2fmVQQ9KO/AyVyQft83oDP1MpslT6CdeOwxynNUMlLSbz8vCNGnuHBZ0gUh9Gipoxw5KUd0JimuoB2V+tajET5WO/2474Dn88MiuxSIX1FdqFYHXKk5qfYcUj2nzEBE+l+HCO3X4jp8Xldlt6R7K5Lm9AzKEr2xvqs/CXbmHBfmbcYrlAfTmbq5apdRVG92D+szsa1KLvLEez1+WIMfWlK26WkdU9w9EfW5w1kNzZmSyd7PHQmd95R6wGg2LMZHffw8r+E19+j//Ur0fUvSbZAlomx7QPt5E6KXKt1skfTyXGV93vZejbT6rU1J05ysNONAn5Gs3xNI1birnv3yHCSXq4kr6NhzXZ7I5E6LJE5K/Pwce5yGCD16y/fVp6cclRkryczjTeS5hyxzDzoDRpoBS2HISqLsw+GltZvL/+tjtXCwcePmb27ceryx9tkd9X9APhQ/FT8TV2Ht+634DMb/ntgHTn8UX4u/ir+1/tD6U+vPrb/Iph9cUJifiNJP6+//BebeUro=
    where z(k)
    i
    2 C is a gradient descent of
    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
    ✓(k+1) = ✓(k)
    1
    rf(✓(k))
    AABE7XictVxZcxTJES7Wx67xxdqPfum1wAEOFgstPiI2HLGgEUKLAMGMBLsMEHP0DA2t6WEujln9DIdfHA77yT/Dv8M/wBH2k/+C86jqqp6p7qyWMR2Sqqvry8zKrsrKzKqmO06T6Wxz8x9nPvjWt7/z3Q8/+t7Z7//ghz/68bmPf3I0zeaTXnzYy9Js8qjbmcZpMooPZ8ksjR+NJ3HnuJvGD7svt/H5w0U8mSbZqDV7O46fHHeGo2SQ9DozqHpyvj1L0n4cDS6+u3T+2bmNzSub9C9aL1zVhQ2l/x1kH3/yT9VWfZWpnpqrYxWrkZpBOVUdNYXrsbqqNtUY6p6oJdRNoJTQ81idqLOAnUOrGFp0oPYl/B7C3WNdO4J7pDkldA+4pPAzAWSkLgAmg3YTKCO3iJ7PiTLWltFeEk2U7S387Wpax1A7U8+hVsKZlqE47MtMDdTvqA8J9GlMNdi7nqYyJ62g5JHTqxlQGEMdlvvwfALlHiGNniPCTKnvqNsOPf8XtcRavO/ptnP1b5LyAlyRaureZzmFjloQ/Yje5hyesTwpcB4ChVj3EUuvSdfH1PsRtF9C/V24TqhkdNKFa0m1J5XIbbh8yG0RuQuXD7krIvfh8iH3ReQBXD7kgUYidkI69+ObcPnwTZHzfbh8yPsi8gFcPuQDEXkElw95JCK/hsuH/FpE3oTLh7wpIm/D5UPeFpEtuHzIlog8hMuHPBSRO3D5kDsaWT5TJ3BlRCcRZuV1KBd5oKVIoea6KN8Nso4+7I2AOd0rwcqzugF//dhGgE7jEuxOwLgblGDlkbcLNtKPlW3RLVpNfNhbInYPRoAfuydiv1QvSrBfBsy0lyVYea7tQzs/Vra+d+DOj70jYu9CyY+V16h7UOPH3gtYMcYl2AMRe1+9KsGGWP1JCVa2+02wK36svE61oL0fG2JN5yVY2Z4egQfjx8qr1UOo9WMfithH6k0J9pGI/Qqsux/7VcAK+64Ea9bYs7SCDMkfiWHGVlHr5LMSS2Og1hH4p/nakpJv3IV6CTPMMUPCHIuI3RyxG4jYzxH7wXJNczs6JX9X5tLMEc1ARDdfm7A0E9v38/ZYSgMQjRzRWEFUeaT4rk1fFuRdmBoJOctXLiyF9CnL7TeWYj0eqi2vQdwrIHhsP6eRf5miJYygUFNV1J7nazwjI7qvQrym6M300vCQcbPcKrioNyKq60F1RdRbD+qtiJp7UHMRtfCgFiLKznwX1w4YAVb/+C6WdMcjgH3k8isCr+A6rDq3YI5GMH4OwAt8QDX34G+TYm/pqpIMo3lcJzHL8aRgiSdQWqoNqLdRYYPi65RmWAyScct7OsbHO8xtLPWcYyt8kq/kUZ4xCaeTkDzDnA56ixHNp3p0blPNCXl3XKqHv5XPe1Oqh98hjZ+QF8+leviZln52CtlbGts6BbYJs2mstW/LdWlw/oVpmPJZWnXR4uJbPdZjBum9qUl/T7+ZvVO8l20qsX5suR6NqdO/aaF/dWhYPU8dPdejgt4Te72mFNXuyUjHvbZcV4aMVtGRlsPe1X0z2Kav34wp16NxAB7XNsXcS6dcd/SO897Ycj0aR4rznifkyZtyPRpDumd92HI9Gpht6eg435brWnbUAMfOtlzXqo8oC4w5IB7zXGO9ogn5SXNNLSH/oDpb4/r86+sY5mye5jFCNSXr25bT6eZrWbVExl+IwarNasqB/sXc8cGKNJZqS4yvWIZZYX1fp2PXeNT8PmgxgtnPewBSzjwFCU1OAq13ChSvilFXsWcGtyXicJQMVlBtXTsTvUXLl7NGxbpnVCvFZba3Vo9tstdTGntj8gn3SbOSHvZL33AZRUlD+wUNyfTq6O6dnq9F7W+KuPEKYpyPtB7tCPFOWnWc6tN609HxBb3LM4OL93zs+MVs80BbG4x5MrJFKEsVT7edySO5dbiuXlY2x83PInqjaK8WZDUS2pGailGoyRazN76ke0v7kPbkkAfT6MF7jDSVseJdM8yiYz49Iovq2luJN+rLZOi4PCWra+xxNXrooIcedP0YZxtWjLtQakHMcAh3rYAo52yuq4w0PlGf5rujGb3B6og+LVhIQ4PtTVywkFVR9vMCldeAxtHAUXo4jVU6Bt9eoyRH/T55bOxatPwXaOfW7G93aIyXj+byTEyfuG4R14hmDe/q8t0qB5Zg6X2yRf5rdS+RXx2OaEMlrk8dzqyXEe34xxTBjskzTmm2SbOj2NrNT60+MZwOlNk7x93sjCxkRPYvgvUpozEZ0Y97dsDsoLNFSMlGhtidJPdufL5OIo4x68clik812PEWky2bE39D151dUxqLHDHwOnCyMraNTvbJF4yJ60Rbdzu3q1cfRNpzEu4oYYp2rFwk/pfot/kx42RjbUSghvENTLWt872PjGIW1FGHVvlqG2TaulKez2V4qqW265+V6XxBsgZFXCgPrtZ94Nyje+aFo2RCck/X2vA6WpXNRcrjFT1ibwcUxbPdH+oVGOW+TKvkBs25No2SIYyCWR5FmLZSFnmVbzWvIvUw2tP/C3Wr66LWkGKkbAaXNSTl92OK1lwpUxjVPH5f0mzya32y0qqaz4jG4rEzl7+B2k/gt5Hb3IfR6Raswg0aA0zB3lmNcE201iKM140CLzMyDS17b/nZMWlauTWnia/ZutkYe1GbygGNmjc6a2HKp6HxwqHxIlCHLdprtFo09cYSPRNji5berQzlV4dbqwbluUhZ9sgMKgmQ0o2lwqj2RapyjG9Q70RamyKtDsxWdzfAnfMhSP9cX53d3+Sre6Rukm/TIw+M45c+zdKEfC5TWx2pMQXkfE3bV3f2t6kGuXfJgiJlPseJM4Z3nXp0neSS/kKvbBnZeWsRzLml17qNsbFtKn+2hjymOTGleWkQ16hFrOV35YhWLNIVx+eIKPPfIZ+K/Y7qmNltbd9JVPAnbLzJs8ry4khhRPqXMm97a9HrnhO/RhQTzrV33QVa9d8wUmCMyST4PcspvSFc5XgngT3aLtnPdTvFu3gjR6IrJPVS/T7AxnDUa8e6O7ZMj03ffgktUev2rftayPzSYI4Sv9Ps6HVoVTvWPupy5f50tDp6lSveV+lhvsLX6mNObdzIwkZ5RUxbfR7MhSWqx4UxIVzq9aKO/PUkryMz706FUjatDeVipoFtzHOKl6RzoIjweXcXvd7cJaEf3TV6XcK61LhGooTZuEznB1xLi1mpaCVCcuulNSl11qOy9cLycFcNa8fZUsZkBVMl5W64tduHdiFakbMxTKGn+GRvWZzo0vwcLvwdKV+UaDiG5BCb4OdeV9tq5z2cinily5zZjKgGbUJ/JQbv6H4WW1Tr6JVD3aUfwiGcRwK6lqRPaEWtKztTliV3qYfTf03WYKJiUXrbsn4fXC5yT9Y51elPQhZO7k2izDc5dftiOIT0pMglnA/vb0i9GCjzbVO9Phjqcg+KHOrwMOcZwt65bV2fl8upWl/rXEJ58Dpgdl4MDncAy2MW2y7EQk2cN/L+OaB1GFRQN6vF/9oPw8dyqs8rlNuUvjl7EfDWuV2sM7PoF9efM5ZbyGgu5xjOM8t7Z70mPz/2/6JabypzevP+6aNfaseA4bVUnA+VpWO8O4qsvKFUcH/AJ0Om/qP+fkb+KuFVTqNMjjqUzH5FOTXTQqZmvrz09c48C5HJ0imTqUjNxhNNOhm7rfbUTfjZzj3AuqdE+ZtK/otY/3e0fagdkPUw2XTOILSpLqYsiN1N69O9PUdbJjGe6eUzvi2owT3xfarF8753qT2e+W0V+lb+JQnP9TsqU/1CZLK6y2fnVRd6UNyB41yQ+d43ojP1nM3iE2jHAXuMfI6KIyXz9fOSEH2KC1clXRLCjJYqyl0v5S6dSYpLaHcLfevRCB/rnX7cd8Dz+Z08uxSpX1FdR68OuFJLUh14pHpMmYEu6X8TIrRfq8vw97Iu+yU9WJN0Su+gKNEb51n1SbAT77iwXzNeoDyYydQtdLuMonq7e1idiW2UcuET79X4YQV+6EjZpLf1kuLuiarOHc4raM61TO5+7kiZvCfrAaPZTj4+quPnRQWvRUD/b5eibzuS7oIsXcq2R7SfNyF6qdbNDknP5yqr87a3KqQ1X20yTXuy0o4Dc0ayek8g1eOufPbzOUgpVxOX0HHnOp/IlE6LJF5K8vwcB5yG6AT0Vu5rSE8lKnNRknnAl8iLAFkWAXQGgjQDkcJQlETbh2fnNq6u/l8f64WjrStXf3Pl2v2tjS9u6P8H5CP1M/VzdRHWvt+qL2D8H6hD8kP+qP6i/trIGn9o/KnxZ276wRmN+akq/Gv87b83oEPi
    ˜
    f(z)
    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
    Problem: ˜
    f does not satisfies P- L
    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
    For Im(z(0)) = 0 mod 2⇡ , |z(k)| ! +1.

    View Slide

  18. AABFFXictVxfc9u4EUeu/67pv1z72Bde7XRyvTR1fOmfmZvOXGIlji9O4kSyk7soyVASJTOhRIWU5CQ6f45OP0znXjqd9qnP/QCdaZ/6FbrYBQhQArmgm4ZjGwTx210sgcXuAkxvmsT5bGvrH+fe+8Y3v/Xt77z/3fPf+/4PfvijCx/8+ChP51k/OuynSZo97oV5lMST6HAWz5Lo8TSLwnEviR71Xu7I548WUZbH6aQzezONno7D0SQexv1wBlXPL3yy2c3i0fEszLL0ZDPIouk8yaM8yKfzLE7neTCOJ/E4DMJZsPlxN54MZ282n1/Y2Lqyhf+C9cJVVdgQ6t9B+sGH/xRdMRCp6Iu5GItITMQMyokIRQ7XE3FVbIkp1D0VS6jLoBTj80icivOAnUOrCFqEUPsSfo/g7omqncC9pJkjug9cEvjJABmIi4BJoV0GZcktwOdzpCxrq2gvkaaU7Q387SlaY6idiWOo5XC6pS9O9mUmhuJ32IcY+jTFGtm7vqIyR61IyQOrVzOgMIU6WR7A8wzKfURqPQeIybHvUrchPv8XtpS18r6v2s7Fv1HKi3AFoq16nxYUQrFA+gG+zTk8I3kS4DwCCpHqoyydoK7H2PsJtF9C/T24TrGkddKDa4m1p7XIHbhcyB0WuQuXC7nLIvfhciH3WeQBXC7kgUJKbIY6d+PbcLnwbZbzA7hcyAcs8iFcLuRDFnkElwt5xCK/hMuF/JJF3oLLhbzFIu/A5ULeYZEduFzIDos8hMuFPGSRN+FyIW8qZPVMzeBKkU7MzMrrUC7zkJYigZrrrHw30Dq6sDc85nS/AsvP6hb8dWNbHjqNKrA3PcbdsALLj7xdsJFuLG+LbuNq4sLeZrF7MALc2D0W+7l4UYH93GOmvazA8nNtH9q5sbz1vQt3buxdFnsPSm4sv0bdhxo39r7HijGtwB6w2AfiVQXWx+pnFVje7rfBrrix/DrVgfZurI81nVdgeXt6BB6MG8uvVo+g1o19xGIfi9cV2Mcs9guw7m7sFx4r7NsKrF5jz+MKMkJ/JIIZW0ctLGalLE2BWsjwT4q1JUHfuAf1HGZUYEaIGbOI3QKx64nYLxD73nLlhR3N0d/lubQLRNsT0SvWJlmase0HRXtZSjwQrQLRWkHUeaTyXeu+LNC70DUcclasXLLk06e0sN+yFKnxUG95NeJ+CUFj+xhH/mWMlmQEJTVVR+24WOMJGeB9HeIEozfdS82Dx80Kq2CjXrOongPVY1FvHKg3LGruQM1Z1MKBWrAoM/NtXNdjBBj9y3exxDsaAeQjV18BeAXXYdW5DXM0gPFzAF7gQ6y5D3/bGHtzV51kMpqX66TMcjwtWeIMSkuxAfUmKmxhfJ3gDItAMmp5X8X48k7mNpZqzpEVPi1W8qDImPjTiVGeUUFHeosBzqdmdO5gzSl6d1Rqhr9dzHtdaoa/iRo/RS+eSs3wMyX97AyydxS2cwZsG2bTVGnflJvSoPwL0dDl87jqSosr3+pYjRlJ73VD+nvqzeyd4b3sYIn0Y8rNaORW//JS/5rQMHrOLT03oyK9J/J6dSlo3JOJintNuakMKa6iEyWHuWv6ZmSbgXozutyMxgF4XDsYcy+tctPROy16Y8rNaBwJynueoievy81ojPCe9GHKzWjIbEuo4nxTbmrZpQYodjblplZ9gllgmQOiMU81xivK0E+aK2ox+gf12Rrb519fx2TO5lkRI9RTMr5tNZ1esZbVS6T9hQis2qyhHNK/mFs+WJnGUmyz8RXJMCut7+t0zBovNb8PWgxg9tMeAJczT0BCnZOQ1jsBilfZqKvcM43bZnFylAxXUF1VO2O9RcOXskbluudYy8VlprdGj1201zmOvSn6hPuoWU4P+5VvuIoip6H9koZ4ek1091bN17L2t1jcdAUxLUZaH3eEaCetPk51ab1t6fii2uWZwUV7Pmb8ymzzUFkbGfOkaIukLHU87XY6j2TXyXX1sjA5bnoW4BuV9mqBViPGHamcjUJ1tpi88SXeG9qHuCcneRCNPrzHQFGZCto1k1l0mU8P0KLa9pbjLfWlM3RUztHqantcjx5Z6JED3TzG2YEV4x6UOhAzHMJdxyPKOV/oKkWNZ+KXxe5oim+wPqJPShZS0yB7E5UsZF2UfVyicgJoORooSvensUpH47trlPio3yWPiV3Llv8i7tzq/e0Qx3j1aK7OxAyQ6zZyDXDW0K4u3a1yIAmWzifb6L/W91Lya8JR2lCO6zOLM+llgjv+EUawU/SME5xt3Owot7bzU6tPNKcDoffO5W52ihYyQPsXwPqU4pgM8Mc+O6B30MkiJGgjfexOXHg3Ll8nZseY8eNiQacazHiL0JbNkb+ma8+uHMciRQy0DpyujG2tk330BSPkminrbuZ2/eojkeachD1KiKIZK5eQ/0f4W//ocbKxNiKkhuUbyJWtc72PFGMWqaMQV/l6G6Tb2lJuFjI8U1Kb9c/ItFmSrIURl5RHrtYD4NzHe+IlR0mGcudrbWgdrcvmSsrTFT3K3g4xiie7P1IrsJT7Mq6SGzjnujhKRjAKZkUUodtyWeRVvvW8ytT9aOf/F+pG12WtSYqBMBlc0hCX348wWrOlTGBU0/h9ibPJrfVspVU9nwmOxbE1l7+C2g/ht5Zb3/vR6ZWswg0cA0TB3BmNUE2w1sKP140SLz0yNS1zb/iZMalb2TVnia/JupkYe9GYygGOmtcqa6HLZ6HxwqLxwlOHHdxrNFrU9doSPWdji47arfTl14RbpwHlOUuZ98g0KvaQ0o6l/KgOWKp8jK9Rb1laWyytEGarvRtgz3kfpHuur87ur4rVPRC30LfpowdG8csAZ2mMPpeurY/UiILkfE3ZV3v2d7FGcu+hBZWU6RynnDG069TH67SQ9OdqZUvRzhuLoM8tnag22sZ2sfzJGnKMcyLHeakR17BFpOS35QhWLNIVy+cIMPMfok9Ffkd9zGy3Nu8kKPkTJt6kWWV4UaQwQf1zmbe9teh1z4pfA4wJ58q77gGt5m9YUiCMziS4Pcsc35Bc5WgngTzaHtrPdTtFu3gTS6IrKPVS/N7DxlDUa8a6PbZ0j3XffgEtpdbNW3e14Pkl3hw5fmfZ0QtxVRsrH3W5cn82WqFa5cr3dXqYr/A1+phjGzuyMFFeGdMVn3pzIYmacSGMD5dmvWgifzPJm8hMu1O+lHVrTbmcaSAbc4zxEncOVCJc3t0lpzf3EdOP3hq9HmJtalTDUZLZuFTlB2xLK7NSwUqEZNdza1JirUdV64XhYa8axo6TpYzQCiaCy91Qa7sP3VK0wmdjiEJf0MneqjjRpvkpXPJ3IFxRoubok0Nsg597XeyIm+/gVMQrVabMZoA10iYMVmLwUPWz3KJeR68s6jZ9Hw7+PGLQNSd9jCtqU9mJMi+5Td2f/glag0xErPSmZfM+2Fz4nqxzatKfGC0c35tY6G9ymvZFc/DpSZmLPx/a3+B6MRT626ZmfdDU+R6UOTThoc8z+L1z07o5L5tTvb7WufjyoHVA77xonNwBrI5ZTDsfC5VZb+Tdc5DWYVhDXa8W/2s/NB/DqTkvX245fnP2wuOtU7tIZWalX9x8zhhuPqO5mqM/z7TonfGa3PzI/wsavanU6s27py/9UjMGNK+loHwoLx3h7VFk5PWlIvcHXDKk4j/i63P8VwmvChpVcjShpPcrqqnpFjw1/eWlq3f6mY9Mhk6VTGVqJp5o48nYHbEnbsHPTuEBNj0lSt9U0l+JdX9HO4DaIVoPnU2nDEIX6yLMgpjdtAHem3O0VRLLM710xrcDNXJPfB9r5Xnfe9henvntlPpW/SUJzfW7IhWDUmSyustn5lUPelDegaNckP7eN8Az9ZTNohNoY489RjpHRZGS/vp5iYgBxoWrki4RoUdLHeWek3IPzyRFFbR7pb71cYRP1U6/3HeQ5/PDIrsUiF9hXahWB7lSc1IdOKR6gpmBHup/CyK0X4vL8PeyKrslPViTNMd3UJbotfWs/iTYqXNcmK8ZL2IeTGfqFqpdilG92T2sz8S2KrnQifd6/KgGP7KkbOPbeolxdybqc4fzGppzJZO9nzsROu9JepDRbFiMj/r4eVHDa+HR/zuV6DuWpLsgSw+z7QHu52VIL1G6uYnS07nK+rzt7Rpp9VebRNOcrDTjQJ+RrN8TSNS4q579dA6Sy9VEFXTsuU4nMrnTIrGTEj8/px6nIUKP3vJ99ekpR2XOSjL3+BJ54SHLwoPOkJFmyFIYsZIo+/D8wsbV1f/rY71wtH3l6m+uXHuwvfHZDfX/gLwvfip+Ji7B2vdb8RmM/wNxCJz+KL4WfxV/a/2h9afWn1t/oabvnVOYn4jSv9bf/wuyk1Rb
    ! repulses spurious minima at +1
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    m(||✓||)f(✓) 6 ||rf(✓)||2
    AABFD3ictVxfc9u4EUeu/67pv1z72Bde7XRyvVzquOmfmZvOXGIlji9O4kSyk7soyVASJTOhRIWU5CQ6f4hOP0ynL22nfepH6AfoTPvUr9DFLkCAEsgF3TQc2yCI3+5iCSx2F2B60yTOZ1tb/zj33te+/o1vfuv9b5//zne/9/0fXPjgh0d5Os/60WE/TdLscS/MoySeRIezeJZEj6dZFI57SfSo93JHPn+0iLI8Tied2Ztp9HQcjibxMO6HM6h6fuGTzfFmMIhG0STKwlmUB2EebHZnx0E3i0fHszDL0pPg4248Gc7ebAbPL2xsXdnCf8F64aoqbAj17yD94MN/iq4YiFT0xVyMRSQmYgblRIQih+uJuCq2xBTqnool1GVQivF5JE7FecDOoVUELUKofQm/R3D3RNVO4F7SzBHdBy4J/GSADMRFwKTQLoOy5Bbg8zlSlrVVtJdIU8r2Bv72FK0x1M7EMdRyON3SFyf7MhND8RvsQwx9mmKN7F1fUZmjVqTkgdWrGVCYQp0sD+B5BuU+IrWeA8Tk2Hep2xCf/wtbylp531dt5+LfKOVFuALRVr1PCwqhWCD9AN/mHJ6RPAlwHgGFSPVRlk5Q12Ps/QTaL6H+HlynWNI66cG1xNrTWuQOXC7kDovchcuF3GWR+3C5kPss8gAuF/JAISU2Q5278W24XPg2y/kBXC7kAxb5EC4X8iGLPILLhTxikV/C5UJ+ySJvweVC3mKRd+ByIe+wyA5cLmSHRR7C5UIessibcLmQNxWyeqZmcKVIJ2Zm5XUol3lIS5FAzXVWvhtoHV3YGx5zul+B5Wd1C/66sS0PnUYV2Jse425YgeVH3i7YSDeWt0W3cTVxYW+z2D0YAW7sHov9XLyowH7uMdNeVmD5ubYP7dxY3vrehTs39i6LvQclN5Zfo+5DjRt732PFmFZgD1jsA/GqAutj9bMKLG/322BX3Fh+nepAezfWx5rOK7C8PT0CD8aN5VerR1Drxj5isY/F6wrsYxb7BVh3N/YLjxX2bQVWr7HncQUZoT8SwYytoxYWs1KWpkAtZPgnxdqSoG/cg3oOMyowI8SMWcRugdj1ROwXiH1vufLCjubo7/Jc2gWi7YnoFWuTLM3Y9oOivSwlHohWgWitIOo8UvmudV8W6F3oGg45K1YuWfLpU1rYb1mK1Hiot7wacb+EoLF9jCP/MkZLMoKSmqqjdlys8YQM8L4OcYLRm+6l5sHjZoVVsFGvWVTPgeqxqDcO1BsWNXeg5ixq4UAtWJSZ+Tau6zECjP7lu1jiHY0A8pGrrwC8guuw6tyGORrA+DkAL/Ah1tyHv22MvbmrTjIZzct1UmY5npYscQalpdiAehMVtjC+TnCGRSAZtbyvYnx5J3MbSzXnyAqfFit5UGRM/OnEKM+ooCO9xQDnUzM6d7DmFL07KjXD3y7mvS41w99EjZ+iF0+lZviZkn52Btk7Cts5A7YNs2mqtG/KTWlQ/oVo6PJ5XHWlxZVvdazGjKT3uiH9PfVm9s7wXnawRPox5WY0cqt/eal/TWgYPeeWnptRkd4Teb26FDTuyUTFvabcVIYUV9GJksPcNX0zss1AvRldbkbjADyuHYy5l1a56eidFr0x5WY0jgTlPU/Rk9flZjRGeE/6MOVmNGS2JVRxvik3texSAxQ7m3JTqz7BLLDMAdGYpxrjFWXoJ80VtRj9g/psje3zr69jMmfzrIgR6ikZ37aaTq9Yy+ol0v5CBFZt1lAO6V/MLR+sTGMpttn4imSYldb3dTpmjZea3wctBjD7aQ+Ay5knIKHOSUjrnQDFq2zUVe6Zxm2zODlKhiuorqqdsd6i4UtZo3Ldc6zl4jLTW6PHLtrrHMfeFH3CfdQsp4f9yjdcRZHT0H5JQzy9Jrp7q+ZrWftbLG66gpgWI62PO0K0k1Yfp7q03rZ0fFHt8szgoj0fM35ltnmorI2MeVK0RVKWOp52O51HsuvkunpZmBw3PQvwjUp7tUCrEeOOVM5GoTpbTN74Eu8N7UPck5M8iEYf3mOgqEwF7ZrJLLrMpwdoUW17y/GW+tIZOirnaHW1Pa5Hjyz0yIFuHuPswIpxD0odiBkO4a7jEeWcL3SVosYz8UmxO5riG6yP6JOShdQ0yN5EJQtZF2Ufl6icAFqOBorS/Wms0tH47holPup3yWNi17Llv4g7t3p/O8QxXj2aqzMxA+S6jVwDnDW0q0t3qxxIgqXzyTb6r/W9lPyacJQ2lOP6zOJMepngjn+EEewUPeMEZxs3O8qt7fzU6hPN6UDovXO5m52ihQzQ/gWwPqU4JgP8sc8O6B10sggJ2kgfuxMX3o3L14nZMWb8uFjQqQYz3iK0ZXPkr+nasyvHsUgRA60DpytjW+tkH33BCLlmyrqbuV2/+kikOSdhjxKiaMbKJeT/Ef7WP3qcbKyNCKlh+QZyZetc7yPFmEXqKMRVvt4G6ba2lJuFDM+U1Gb9MzJtliRrYcQl5ZGr9QA49/GeeMlRkqHc+VobWkfrsrmS8nRFj7K3Q4ziye6P1Aos5b6Mq+QGzrkujpIRjIJZEUXotlwWeZVvPa8ydT/a+f+FutF1WWuSYiBMBpc0xOX3I4zWbCkTGNU0fl/ibHJrPVtpVc9ngmNxbM3lr6D2Q/it5db3fnR6JatwA8cAUTB3RiNUE6y18ON1o8RLj0xNy9wbfmZM6lZ2zVnia7JuJsZeNKZygKPmtcpa6PJZaLywaLzw1GEH9xqNFnW9tkTP2diio3Yrffk14dZpQHnOUuY9Mo2KPaS0Yyk/qgOWKh/ja9RbltYWSyuE2WrvBthz3gfpnuurs/urYnUPxC30bfrogVH8MsBZGqPPpWvrIzWiIDlfU/bVnv1drJHce2hBJWU6xylnDO069fE6LST9qVrZUrTzxiLoc0snqo22sV0s/2INOcY5keO81Ihr2CJS8ttyBCsW6YrlcwSY+Q/RpyK/oz5mtlubdxKU/AkTb9KsMrwoUpig/rnM295a9Lpnxa8BxoRz5V33gFbzNywpEEZnEtyeZY5vSK5ytJNAHm0P7ee6naJdvIkl0RWUeil+62FjKOo1Y90eW7rHum8/g5ZS6+atu1rw/BJvjhy/s+zohbiqjZWPuly5PxutUK1y5fs6PcxX+Bp9zLGNHVmYKK+M6YpPvbmQRM24EMaHS7NeNJG/meRNZKbdKV/KurWmXM40kI05xniJOwcqES7v7pLTm/uI6UdvjV4PsTY1quEoyWxcqvIDtqWVWalgJUKy67k1KbHWo6r1wvCwVw1jx8lSRmgFE8Hlbqi13YduKVrhszFEoS/oZG9VnGjT/BQu+TsQrihRc/TJIbbBz70udsTNd3Aq4pUqU2YzwBppEwYrMXio+lluUa+jVxZ1m74PB38eMeiakz7GFbWp7ESZl9ym7k//BK1BJiJWetOyeR9sLnxP1jk16U+MFo7vTSz0NzlN+6I5+PSkzMWfD+1vcL0YCv1tU7M+aOp8D8ocmvDQ5xn83rlp3ZyXzaleX+tcfHnQOqB3XjRO7gBWxyymnY+Fyqw38u45SOswrKGuV4v/tR+aj+HUnJcvtxy/OXvh8dapXaQys9Ivbj5nDDef0VzN0Z9nWvTOeE1ufuT/BY3eVGr15t3Tl36pGQOa11JQPpSXjvD2KDLy+lKR+wMuGVLxH/Hnc/xXCa8KGlVyNKGk9yuqqekWPDX95aWrd/qZj0yGTpVMZWomnmjjydgdsSduwc9O4QE2PSVK31TSX4l1f0c7gNohWg+dTacMQhfrIsyCmN20Ad6bc7RVEsszvXTGtwM1ck98H2vled972F6e+e2U+lb9JQnN9bsiFYNSZLK6y2fmVQ96UN6Bo1yQ/t43wDP1lM2iE2hjjz1GOkdFkZL++nmJiAHGhauSLhGhR0sd5Z6Tcg/PJEUVtHulvvVxhE/VTr/cd5Dn88MiuxSIn2NdqFYHuVJzUh04pHqCmYEe6n8LIrRfisvw97IquyU9WJM0x3dQlui19az+JNipc1yYrxkvYh5MZ+oWql2KUb3ZPazPxLYqudCJ93r8qAY/sqRs49t6iXF3Jupzh/MamnMlk72fOxE670l6kNFsWIyP+vh5UcNr4dH/O5XoO5akuyBLD7PtAe7nZUgvUbq5idLTucr6vO3tGmn1V5tE05ysNONAn5Gs3xNI1Lirnv10DpLL1UQVdOy5TicyudMisZMSPz+nHqchQo/e8n316SlHZc5KMvf4EnnhIcvCg86QkWbIUhixkij78PzCxtXV/+tjvXC0feXqr65ce7C98dkN9f+AvC9+LH4iLsHa92vxGYz/A3EInH4v/ij+Kv7W+l3rD60/tf5CTd87pzA/EqV/rb//FyQNUPI=
    m degenerates as ✓ ! +1
    Local P-Ł Condition
    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
    Example: 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
    f(✓) = |e✓1+i✓2 + 1|2
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    m(R) = e 2||✓||
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    f(✓)

    View Slide

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    ! repulses spurious minima at +1
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    m(||✓||)f(✓) 6 ||rf(✓)||2
    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
    m degenerates as ✓ ! +1
    Local P-Ł Condition
    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
    Example: AABFB3ictVxZbxy5EaY318a5vMljXnqjVWBnHUdSnANYLLC2JMtaa23ZM5K967GFOXpGY/dMj+fyMdYPCPJjgrwEQfIQ5GfkBwRInvIXUgfZZM+wu9iK44YkNptfVbGaLFYV2W6Nkv5kurHxjwvvfe3r3/jmt97/9sXvfPd73//BpQ9+eDxJZ+N2fNROk3T8qNWcxEl/GB9N+9MkfjQax81BK4kftp5v4/OH83g86afD+vT1KH4yaPaG/W6/3ZxC1cml9e7lxvT0SvRp9DZ+uoDiyebHjf6gOT2N8Gbr7OPNt0+3Ti6tbVzboH/RamFTF9aU/neYfvDhP1VDdVSq2mqmBipWQzWFcqKaagLXY7WpNtQI6p6oBdSNodSn57E6UxcBO4NWMbRoQu1z+N2Du8e6dgj3SHNC6DZwSeBnDMhIrQMmhXZjKCO3iJ7PiDLWFtFeEE2U7TX8bWlaA6idqlOolXCmZSgO+zJVXfVb6kMf+jSiGuxdW1OZkVZQ8sjp1RQojKAOyx14PoZym5BGzxFhJtR31G2Tnv+LWmIt3rd125n6N0m5Dlekarr3aUahqeZEP6K3OYNnLE8CnHtAIdZ9xNJL0vWAej+E9guovwvXGZWMTlpwLaj2rBS5DZcPuS0i9+DyIfdE5AFcPuSBiDyEy4c81EjEjknnfnwNLh++JnK+D5cPeV9EPoDLh3wgIo/h8iGPReRXcPmQX4nIW3D5kLdE5B24fMg7IrIOlw9ZF5FHcPmQRyJyFy4fclcji2fqGK6U6PSFWXkDynkeaCkSqLkhyneTrKMPezNgTrcLsPKs3oG/fuxOgE7jAuxuwLjrFmDlkbcHNtKPlW3RbVpNfNjbInYfRoAfuy9iP1fPCrCfB8y05wVYea4dQDs/Vra+X8CdH/uFiL0LJT9WXqPuQY0fey9gxRgVYA9F7H31ogAbYvXHBVjZ7tfArvix8jpVh/Z+bIg1nRVgZXt6DB6MHyuvVg+h1o99KGIfqVcF2Eci9kuw7n7slwEr7JsCrFljL9IK0iN/JIYZW0atmc1KLI2AWlPgn2RrS0K+cQvqJUwvw/QIMxARexliLxBxkCEOguWaZHZ0Qv6uzKWWIWqBiFa2NmFpKrbvZO2xlAQgdjLEzhKizCPFd236MifvwtRIyGm2cmEppE9pZr+xFOvxUG55DeJeDsFj+5RG/lWKljCCQk2VUTvN1nhGRnRfhnhJ0ZvppeEh46aZVXBRr0RUy4NqiajXHtRrETXzoGYiau5BzUWUnfkurhEwAqz+8V0s6I5HAPvIxVcEXsENWHVuwxyNYPwcghf4gGruwd8axd7SVSYZRvO4TmKW40nOEo+htFBrUG+jwh2KrxOaYTFIxi3v6Rgf7zC3sdBzjq3wWbaSR1nGJJxOn+TpZXTQW4xoPlWjc4dqzsi741I1/O1s3ptSNfwuafyMvHguVcNPtfTTc8he19j6ObA1mE0jrX1brkqD8y9Mw5Qv0qqLFhff6kCPGaT3qiL9ff1m9s/xXrapxPqx5Wo0Jk7/Jrn+VaFh9Txx9FyNCnpP7PWaUlS5J0Md99pyVRlSWkWHWg57V/XNYJuOfjOmXI3GIXhc2xRzL5xy1dE7ynpjy9VoHCvOe56RJ2/K1Wj06J71YcvVaGC2panjfFuuatlRAxw723JVqz6kLDDmgHjMc431isbkJ800tT75B+XZGtfnX13HMGfzNIsRyilZ37aYTitby8olMv5CDFZtWlEO9C9mjg+Wp7FQW2J8xTJMc+v7Kh27xqPmD0CLEcx+3gOQcuYJSGhyEmi9E6C4KUZd+Z4Z3JaIw1HSXUI1dO1U9BYtX84a5etOqFaKy2xvrR4bZK8nNPZG5BMekGYlPRwUvuEiipKGDnIakulV0d0bPV/z2t8QcaMlxCgbaW3aEeKdtPI41af1mqPjdb3LM4WL93zs+MVsc1dbG4x5UrJFKEsZT7edySO5dbiuXlU2x83PInqjaK/mZDX6tCM1EaNQky1mb3xB95b2Ee3JIQ+m0Yb3GGkqI8W7ZphFx3x6RBbVtbcSb9SXydBxeUJW19jjcnTPQfc86OoxzjasGHehVIeY4Qju6gFRzsVMVylpfKx+nu2OpvQGyyP6JGchDQ22N3HOQpZF2ac5Ki8BjaOBo/RwGst0DL6xQkmO+n3y2Ng1b/nXaefW7G83aYwXj+biTEyHuG4R14hmDe/q8t0yB5Zg4X2yRf5reS+RXxWOaEMlrk8dzqyXIe34xxTBjsgzTmi2SbMj39rNTy0/MZwOldk7x93slCxkRPYvgvUppTEZ0Y97dsDsoLNFSMhGhtidfubd+HydvjjGrB/XV3yqwY63mGzZjPgbuu7smtBY5IiB14GzpbFtdHJAvmBMXMfautu5Xb76INKek3BHCVO0Y+Uy8b9Cv82PGSdrKyMCNYxvYKJtne99pBSzoI6atMqX2yDT1pXyo0yGp1pqu/5ZmT7KSbZDERfKg6t1Bzi36Z554SgZk9yTlTa8jpZlc5HyaEmP2NsuRfFs93t6BUa5r9IquUZzrkGjpAejYJpFEaatlEVe5lvOK089jPbk/0Ld6jqvNaQYKZvBZQ1J+f2YojVXygRGNY/f5zSb/FofL7Uq5zOksThw5vJbqP0Qfhu5zX0YnVbOKtykMcAU7J3VCNdEKy3CeN3M8TIj09Cy95afHZOmlVtznviarZuNseeVqRzSqHmlsxamfB4azxwazwJ1WKe9RqtFU28s0YkYW9T1bmUovyrc6hUoz0TKskdmUP0AKd1YKoxqR6Qqx/gG9UaktSHSasJsdXcD3DkfgvTP9eXZ/TZb3SN1i3ybNnlgHL90aJb2yecyteWRGlNAzte1fXVnf4NqkHuLLChS5nOcOGN416lN11km6U/1ypaSnbcWwZxbeqnbGBvboPIvV5ADmhMTmpcGcZ1axFp+V45oySJdc3yOiDL/TfKp2O8oj5nd1vadRDl/wsabPKssL44UhqR/KfO2vxK97jvxa0Qx4Ux71y2gVf0NIwXGmEyC37Oc0BvCVY53EtijbZH9XLVTvIs3dCS6RlIv1KcBNoajXjvW3bFlemz69jNoiVq3b93XQuaXBHOU+J1nR69Jq9pA+6iLpfvz0WrqVS5/X6aH2RJfq48ZtXEjCxvl5TEN9UkwF5aoGhfGhHCp1osq8leTvIrMvDsVStm0NpTzmQa2MacUL0nnQBHh8+4ue725K0I/Wiv0WoR1qXGNRAmzcanOD7iWFrNS0VKE5NZLa1LirEdF64Xl4a4a1o6zpYzJCiZKyt1wa7cPjVy0ImdjmEJb8cneojjRpfkJXPg7Ur4o0XAMySHWwM+9obbV7js4FfFClzmzGVEN2oTOUgze1P3MtyjX0QuHuks/hEM4jz7oWpK+TytqVdmZsiy5Sz2c/kuyBmMVi9LbltX74HKRe7LKqUp/+mTh5N70lfkmp2pfDIeQnuS5hPPh/Q2pF11lvm2q1gdDXe5BnkMVHuY8Q9g7t62r83I5letrlUsoD14HzM6LweEOYHHMYtuFWKix80bePQe0Dt0S6ma1+F/7YfhYTtV5hXKb0DdnzwLeOreLdWYW/eLqc8ZyCxnNxRzDeaZZ76zX5OfH/l9U6U2lTm/ePX30S+0YMLwWivOhsnSMd0eRlTeUCu4P+GRI1X/U3y7IXyW8yGgUyVGFktmvKKZmWsjUzJeXvt6ZZyEyWTpFMuWp2XiiRidjt9W+ugU/25kHWPWUKH9TyX8R6/+OtgO1XbIeJpvOGYQG1cWUBbG7aR26t+doiyTGM718xrcONbgnfkC1eN73LrXHM7/1XN+KvyThuf6FSlUnF5ks7/LZedWCHuR34DgXZL73jehMPWez+ATaIGCPkc9RcaRkvn5eEKJDceGypAtCmNFSRrnlpdyiM0lxAe1Wrm9tGuEjvdOP+w54Pr+ZZZci9Quqa+rVAVdqSapDj1SPKTPQIv1vQIT2K3UV/l7VZb+khyuSTugd5CV65TwrPwl25h0X9mvGdcqDmUzdXLdLKaq3u4flmdidQi584r0c3yvB9xwpa/S2nlPcPVblucNZCc2Zlsndzx0qk/dkPWA028zGR3n8PC/hNQ/o/51C9B1H0j2QpUXZ9oj288ZEL9G62SXp+Vxled72dom05qtNpmlPVtpxYM5Ilu8JJHrcFc9+Pgcp5WriAjruXOcTmdJpkb6Xkjw/RwGnIZoBvZX7GtJTicpMlGQW8CXyPECWeQCdriBNV6TQEyXR9uHk0trm8v/1sVo43rq2+etr1+9fX/vspv5/QN5XP1Y/UZdh7fuN+gzG/6E6Ak6/V39Uf1F/3fndzh92/rTzZ2763gWN+ZHK/dv5+38BfwJNVA==
    f(✓) = |e✓1+i✓2 + 1|2
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    m(R) = e 2||✓||
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    f(✓)

    View Slide

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    ! repulses spurious minima at +1
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    m(||✓||)f(✓) 6 ||rf(✓)||2
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    m degenerates as ✓ ! +1
    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
    Theorem : 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
    [Liu, Zhu, Belkin 2021]
    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
    then
    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
    If ✓(0) and R > 0 satisfies
    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