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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
  2. <latexit 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ResNet and <latexit 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Neural-ODEs <latexit 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Global

    and local <latexit 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Polyak- Lojasiewicz <latexit 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conditions <latexit sha1_base64="wjGCx/DEUHcsPs/i1kpilipcCXc=">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</latexit> P- L condition <latexit sha1_base64="1yda5C1Gj6i2CXyMNZZ8WEkIZgs=">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</latexit> for Neural-ODEs <latexit 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RKHS Neural-ODEs
  3. ResNet-type Architectures [He et al’ 16] ResNet-34 <latexit sha1_base64="hGNaHRogJoszxpvRv/VDNWjykms=">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</latexit> image

  4. ResNet-type Architectures [He et al’ 16] ResNet-34 <latexit sha1_base64="hGNaHRogJoszxpvRv/VDNWjykms=">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</latexit> image

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skip-connexion <latexit 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xs = xs 1 + v✓s (xs 1)
  5. ResNet-type Architectures [He et al’ 16] ResNet-34 <latexit sha1_base64="hGNaHRogJoszxpvRv/VDNWjykms=">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</latexit> image

    <latexit sha1_base64="T6b9HaNHHjCNOHzV6onUoURA+iA=">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</latexit> ! Makes the “infinite depth” limit non-degenerate. <latexit 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x0 <latexit 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xT <latexit 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! Enable v✓ = 0 initialization, i.e. identity map. <latexit 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x0 <latexit 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x1 <latexit 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x0 <latexit 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x1 <latexit 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skip-connexion <latexit 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xs = xs 1 + v✓s (xs 1)
  6. Infinite Depth and Neural-ODEs <latexit sha1_base64="c+kKnAxKjdK3kNTUmMbn0Klm8uI=">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</latexit> where <latexit sha1_base64="qhSLJgQq/yuorQiDFfjqGL3B6xk=">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</latexit> ResNet

    [He et al, 2016] <latexit 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✓(x0) , xT <latexit sha1_base64="qbpiB4MRNcTm1Jd0Cno/ONu/uAc=">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</latexit> xt+1 = xt + 1 T v✓t (xt) <latexit 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x0 <latexit 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x1 <latexit 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xT
  7. Infinite Depth and Neural-ODEs <latexit sha1_base64="c+kKnAxKjdK3kNTUmMbn0Klm8uI=">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</latexit> where <latexit sha1_base64="qhSLJgQq/yuorQiDFfjqGL3B6xk=">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</latexit> ResNet

    [He et al, 2016] <latexit 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✓(x0) , xT <latexit sha1_base64="qbpiB4MRNcTm1Jd0Cno/ONu/uAc=">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</latexit> xt+1 = xt + 1 T v✓t (xt) <latexit 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x0 <latexit 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Neural ODE [Chen et al, 2018] <latexit 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where <latexit 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T ! +1 <latexit 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dx(t) dt = v✓(t) (x(t)) <latexit 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✓(x(0)) , x(1)
  8. Infinite Depth and Neural-ODEs <latexit sha1_base64="c+kKnAxKjdK3kNTUmMbn0Klm8uI=">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</latexit> where <latexit sha1_base64="qhSLJgQq/yuorQiDFfjqGL3B6xk=">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=</latexit> ResNet

    [He et al, 2016] <latexit 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✓(x0) , xT <latexit sha1_base64="qbpiB4MRNcTm1Jd0Cno/ONu/uAc=">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</latexit> xt+1 = xt + 1 T v✓t (xt) <latexit 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x0 <latexit 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Neural ODE [Chen et al, 2018] <latexit 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where <latexit 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T ! +1 <latexit 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dx(t) dt = v✓(t) (x(t)) <latexit 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✓(x(0)) , x(1) <latexit 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T ! +1 is a singular limit (✓ can “explodes” during training) <latexit 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Trajectories cannot cross: ✓ defines a di↵eomorphism.
  9. Training Dynamic <latexit 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Training: <latexit sha1_base64="RLu3eYgMCGrTjEMHHveYhgoDE0s=">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</latexit> Gradient descent: <latexit

    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✓(k+1) = ✓(k) ⌧rf(✓(k)) <latexit 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min ✓ f(✓) , 1 N PN i=1 ||B ✓(Axi) yi||2 … <latexit 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A + <latexit 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v✓2 <latexit 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A <latexit 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xi <latexit 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B <latexit 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˙ x(t) = v✓(t) (x(t)) <latexit 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✓ <latexit 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✓ <latexit sha1_base64="kGrndrTHBUtoctaPTrDWsqh/Ifw=">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==</latexit> ! No explicit regularization!
  10. Training Dynamic <latexit 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Training: <latexit sha1_base64="RLu3eYgMCGrTjEMHHveYhgoDE0s=">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</latexit> Gradient descent: <latexit

    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✓(k+1) = ✓(k) ⌧rf(✓(k)) <latexit 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Question: convergence of ✓k toward global minimum? <latexit 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min ✓ f(✓) , 1 N PN i=1 ||B ✓(Axi) yi||2 … <latexit 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A + <latexit 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v✓2 <latexit 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A <latexit 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xi <latexit 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B <latexit 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˙ x(t) = v✓(t) (x(t)) <latexit 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✓ <latexit 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✓ <latexit sha1_base64="r96IAeMjpoFWFhQFhuZC9BvddQ4=">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</latexit> Polyak- Lojasiewicz inequality [Liu, Zhu, Belkin 2021]: <latexit sha1_base64="WJTlyP3k/XovgZCzXNquTxdVmv4=">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</latexit> ! conditionning might explodes as T ! +1. <latexit 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! find a suitable limit model and show “implicit” regularization e↵ect. <latexit sha1_base64="A79Qx8UcXQ9zh2DlWDd1UdB3thQ=">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</latexit> Neural tangent kernel [Jacot et al’18]: <latexit sha1_base64="x756YupZY4456NODu+ESBRz6FBU=">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</latexit> local linear expansion. <latexit sha1_base64="kGrndrTHBUtoctaPTrDWsqh/Ifw=">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</latexit> ! No explicit regularization!
  11. Training Dynamic <latexit 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Training: <latexit sha1_base64="RLu3eYgMCGrTjEMHHveYhgoDE0s=">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</latexit> Gradient descent: <latexit

    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✓(k+1) = ✓(k) ⌧rf(✓(k)) <latexit 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Question: convergence of ✓k toward global minimum? <latexit 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min ✓ f(✓) , 1 N PN i=1 ||B ✓(Axi) yi||2 … <latexit 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A + <latexit 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v✓2 <latexit 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A <latexit 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xi <latexit 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B <latexit 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˙ x(t) = v✓(t) (x(t)) <latexit 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✓ <latexit 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✓ <latexit sha1_base64="r96IAeMjpoFWFhQFhuZC9BvddQ4=">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</latexit> Polyak- Lojasiewicz inequality [Liu, Zhu, Belkin 2021]: <latexit sha1_base64="WJTlyP3k/XovgZCzXNquTxdVmv4=">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</latexit> ! conditionning might explodes as T ! +1. <latexit 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! find a suitable limit model and show “implicit” regularization e↵ect. <latexit sha1_base64="A79Qx8UcXQ9zh2DlWDd1UdB3thQ=">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</latexit> Neural tangent kernel [Jacot et al’18]: <latexit sha1_base64="x756YupZY4456NODu+ESBRz6FBU=">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</latexit> local linear expansion. <latexit sha1_base64="6AKBIOH1Xg1CAgj9dUnubCLPkvU=">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</latexit> Mean field for 2 layers perceptron [Chizat-Bach 2018]: <latexit sha1_base64="rX1qUgPrJTvscKFRUzOckZzx4V8=">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</latexit> global convergence. <latexit sha1_base64="kGrndrTHBUtoctaPTrDWsqh/Ifw=">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</latexit> ! No explicit regularization!
  12. <latexit sha1_base64="bO9V1cmBgsouChruZjZtSScFUUg=">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</latexit> ResNet and <latexit sha1_base64="PVNMn9LAp654Mt5laWuDBy8zkkg=">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</latexit> Neural-ODEs <latexit 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Global

    and local <latexit 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Polyak- Lojasiewicz <latexit 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conditions <latexit sha1_base64="wjGCx/DEUHcsPs/i1kpilipcCXc=">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</latexit> P- L condition <latexit sha1_base64="1yda5C1Gj6i2CXyMNZZ8WEkIZgs=">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</latexit> for Neural-ODEs <latexit 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v <latexit 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RKHS Neural-ODEs
  13. Polyak-Łojasiewicz Condition <latexit sha1_base64="c84IgZCfgfqve0vx8DSH4w339nY=">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</latexit> Polyak- Lojasiewicz inequality: <latexit sha1_base64="ioDcHDdBoVrU4jCDBkVy8UfflrQ=">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</latexit> !

    no spurious stationary points. <latexit sha1_base64="zL2WHXB+Xc0bFMGvt6WqjaggjpY=">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</latexit> Example: f strongly convex. <latexit sha1_base64="z9vWMjNYR/bnHmpu5GUHYyEuxWU=">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</latexit> mf(✓) 6 ||rf(✓)||2
  14. Polyak-Łojasiewicz Condition <latexit sha1_base64="c84IgZCfgfqve0vx8DSH4w339nY=">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</latexit> Polyak- Lojasiewicz inequality: <latexit sha1_base64="ioDcHDdBoVrU4jCDBkVy8UfflrQ=">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</latexit> !

    no spurious stationary points. <latexit sha1_base64="zL2WHXB+Xc0bFMGvt6WqjaggjpY=">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</latexit> Example: f strongly convex. <latexit sha1_base64="z9vWMjNYR/bnHmpu5GUHYyEuxWU=">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</latexit> mf(✓) 6 ||rf(✓)||2
  15. Polyak-Łojasiewicz Condition <latexit sha1_base64="c84IgZCfgfqve0vx8DSH4w339nY=">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</latexit> Polyak- Lojasiewicz inequality: <latexit sha1_base64="ioDcHDdBoVrU4jCDBkVy8UfflrQ=">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</latexit> !

    no spurious stationary points. <latexit sha1_base64="kI5fXwi7ymCUn+8sWlWuAyRczCA=">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</latexit> [Polyak 1963] <latexit sha1_base64="Cj3XCg2H2300+w6wHRs6XU05Xeo=">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</latexit> Theorem: <latexit sha1_base64="B2PG4XQ47kCXQ8UVCrS9/Ha/+a4=">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</latexit> f(✓(k)) 6 1 m 2 k f(✓(0)) <latexit 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✓(k+1) = ✓(k) 1 rf(✓(k)) <latexit sha1_base64="YmIfEsd2whBRfCEvlaj71ICC6Wo=">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</latexit> If rf is -Lipschitz: <latexit sha1_base64="RLu3eYgMCGrTjEMHHveYhgoDE0s=">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</latexit> Gradient descent: <latexit sha1_base64="zL2WHXB+Xc0bFMGvt6WqjaggjpY=">AABFCHictVzrbhTJFS42tw25scnP/OmNYcVGrGMcclFWkRY8xngxYJixYZcBNJeeYaBnepgbhlm/QJSHifInihIpUt4iDxAp+ZVXyLlUdVXPVPepdggt29XV9Z1z6nTVqXNOVdMeJ4PpbGvrH+fe+9rXv/HNb73/7fPf+e73vv+DCx/88Hiazied+KiTJunkUbs1jZPBKD6aDWZJ/Gg8iVvDdhI/bL/cwecPF/FkOkhHjdmbcfxk2OqPBr1BpzWDqmcXPmrO4hPALXdPWsNxEv/mNLrYuxhNZ5N01E/eRJ10tIhPNp9d2Nja3KJ/0Xrhqi5sKP3vMP3gw3+qpuqqVHXUXA1VrEZqBuVEtdQUrsfqqtpSY6h7opZQN4HSgJ7H6lSdB+wcWsXQogW1L+F3H+4e69oR3CPNKaE7wCWBnwkgI3UJMCm0m0AZuUX0fE6UsbaI9pJoomxv4G9b0xpC7Uw9h1oJZ1qG4rAvM9VTv6Y+DKBPY6rB3nU0lTlpBSWPnF7NgMIY6rDchecTKHcIafQcEWZKfUfdtuj5v6gl1uJ9R7edq3+TlJfgilRd9z7NKLTUguhH9Dbn8IzlSYBzHyjEuo9Yek26HlLvR9B+CfV34TqlktFJG64l1Z6WInfg8iF3ROQeXD7knog8gMuHPBCRh3D5kIcaidgJ6dyPr8Plw9dFzvfh8iHvi8gHcPmQD0TkMVw+5LGI/BIuH/JLEXkTLh/ypoi8DZcPeVtENuDyIRsi8gguH/JIRO7C5UPuamTxTJ3AlRKdgTArr0M5zwMtRQI110X5bpB19GFvBMzpTgFWntU1+OvH1gJ0GhdgdwPGXa8AK4+8PbCRfqxsi27RauLD3hKx+zAC/Nh9Efu5elGA/Txgpr0swMpz7QDa+bGy9b0Dd37sHRF7F0p+rLxG3YMaP/ZewIoxLsAeitj76lUBNsTqTwqwst2vg13xY+V1qgHt/dgQazovwMr29Bg8GD9WXq0eQq0f+1DEPlInBdhHIvYLsO5+7BcBK+zbAqxZY8/TCtInfySGGVtGrZXNSiyNgVpL4J9ka0tCvnEb6iVMP8P0CTMUEXsZYi8QcZAhDoLlmmZ2dEr+rsylniHqgYh2tjZhaSa272btsZQEIGoZoraCKPNI8V2bvizIuzA1EnKWrVxYCulTmtlvLMV6PJRbXoO4l0Pw2H5OI/8KRUsYQaGmyqg9z9Z4RkZ0X4Z4TdGb6aXhIeNmmVVwUSciqu1BtUXUGw/qjYiae1BzEbXwoBYiys58F9cMGAFW//gulnTHI4B95OIrAq/gOqw6t2CORjB+DsELfEA19+BvnWJv6SqTDKN5XCcxy/EkZ4knUFqqDai3UWGN4uuEZlgMknHLezrGxzvMbSz1nGMrfJqt5FGWMQmnMyB5+hkd9BYjmk/V6NymmlPy7rhUDX8rm/emVA2/Sxo/JS+eS9XwMy397AyyNzS2cQZsHWbTWGvflqvS4PwL0zDl87TqosXFtzrUYwbpnVSkv6/fzP4Z3ssOlVg/tlyNxtTp3zTXvyo0rJ6njp6rUUHvib1eU4oq92Sk415bripDSqvoSMth76q+GWzT1W/GlKvROASPa4di7qVTrjp6x1lvbLkajWPFec9T8uRNuRqNPt2zPmy5Gg3MtrR0nG/LVS07aoBjZ1uuatVHlAXGHBCPea6xXtGE/KS5pjYg/6A8W+P6/OvrGOZsnmYxQjkl69sW02lna1m5RMZfiMGqzSrKgf7F3PHB8jSWaluMr1iGWW59X6dj13jU/AFoMYLZz3sAUs48AQlNTgKtdwIUr4pRV75nBrct4nCU9FZQTV07E71Fy5ezRvm6Z1QrxWW2t1aPTbLXUxp7Y/IJD0izkh4OCt9wEUVJQwc5Dcn0qujurZ6vee1vibjxCmKcjbQO7QjxTlp5nOrTet3R8SW9yzODi/d87PjFbHNPWxuMeVKyRShLGU+3nckjuXW4rl5RNsfNzyJ6o2ivFmQ1BrQjNRWjUJMtZm98SfeW9hHtySEPptGB9xhpKmPFu2aYRcd8ekQW1bW3Em/Ul8nQcXlKVtfY43J030H3PejqMc4OrBh3odSAmOEI7hoBUc75TFcpaXyiPsl2R1N6g+URfZKzkIYG25s4ZyHLouznOSqvAY2jgaP0cBqrdAy+uUZJjvp98tjYNW/5L9HOrdnfbtEYLx7NxZmYLnHdJq4RzRre1eW7VQ4swdL7ZJv81/JeIr8qHNGGSlyfOpxZLyPa8Y8pgh2TZ5zQbJNmR761m59afWI4HSqzd4672SlZyIjsXwTrU0pjMqIf9+yA2UFni5CQjQyxO4PMu/H5OgNxjFk/bqD4VIMdbzHZsjnxN3Td2TWlscgRA68Dpytj2+jkgHzBmLhOtHW3c7t89UGkPSfhjhKmaMfKZeL/Mf02P2acbKyNCNQwvoGptnW+95FSzII6atEqX26DTFtXyouZDE+11Hb9szJdzElWo4gL5cHVugucO3TPvHCUTEju6VobXkfLsrlIebyiR+xtj6J4tvt9vQKj3FdoldygOdekUdKHUTDLogjTVsoir/It55WnHkZ7+n+hbnWd1xpSjJTN4LKGpPx+TNGaK2UCo5rH70uaTX6tT1ZalfMZ0VgcOnP5K6j9EH4buc19GJ12zircoDHAFOyd1QjXRGstwnjdyPEyI9PQsveWnx2TppVbc5b4mq2bjbEXlakc0qg50VkLUz4LjRcOjReBOmzQXqPVoqk3luiZGFs09G5lKL8q3BoVKM9FyrJHZlCDACndWCqMalekKsf4BvVWpLUl0mrBbHV3A9w5H4L0z/XV2f1VtrpH6ib5Nh3ywDh+6dIsHZDPZWrLIzWmgJyvafvqzv4m1SD3NllQpMznOHHG8K5Th67TTNKP9MqWkp23FsGcW3qt2xgb26Tyz9eQQ5oTU5qXBnGNWsRafleOaMUibTo+R0SZ/xb5VOx3lMfMbmv7TqKcP2HjTZ5VlhdHCiPSv5R521+LXved+DWimHCuves20Kr+hpECY0wmwe9ZTukN4SrHOwns0bbJfq7bKd7FGzkSbZLUS/XbABvDUa8d6+7YMj02ffsptESt27fuayHzS4I5SvzOsqPXolVtqH3U5cr92Wi19CqXvy/Tw3yFr9XHnNq4kYWN8vKYpvo0mAtLVI0LY0K4VOtFFfmrSV5FZt6dCqVsWhvK+UwD25jnFC9J50AR4fPuLnu9uY+FfrTX6LUJ61LjGokSZuNSnR9wLS1mpaKVCMmtl9akxFmPitYLy8NdNawdZ0sZkxVMlJS74dZuH5q5aEXOxjCFjuKTvUVxokvzU7jwd6R8UaLhGJJDrIOfe13tqN13cCrilS5zZjOiGrQJ3ZUYvKX7mW9RrqNXDnWXfgiHcB4D0LUk/YBW1KqyM2VZcpd6OP3XZA0mKhalty2r98HlIvdknVOV/gzIwsm9GSjzTU7VvhgOIT3Jcwnnw/sbUi96ynzbVK0PhrrcgzyHKjzMeYawd25bV+flcirX1zqXUB68DpidF4PDHcDimMW2C7FQE+eNvHsOaB16JdTNavG/9sPwsZyq8wrlNqVvzl4EvHVuF+vMLPrF1eeM5RYymos5hvNMs95Zr8nPj/2/qNKbSp3evHv66JfaMWB4LRXnQ2XpGO+OIitvKBXcH/DJkKr/qL+dk79KeJXRKJKjCiWzX1FMzbSQqZkvL329M89CZLJ0imTKU7PxRJ1Oxu6ofXUTfnYyD7DqKVH+ppL/Itb/HW0XantkPUw2nTMITaqLKQtid9O6dG/P0RZJjGd6+YxvA2pwT/yAavG8711qj2d+G7m+FX9JwnP9jkpVNxeZrO7y2XnVhh7kd+A4F2S+943oTD1ns/gE2jBgj5HPUXGkZL5+XhKiS3HhqqRLQpjRUka57aXcpjNJcQHtdq5vHRrhY73Tj/sOeD6/lWWXIvUzqmvp1QFXakmqQ49Ujykz0Cb9b0GE9gt1Bf5e0WW/pIdrkk7pHeQlOnGelZ8EO/WOC/s14yXKg5lM3UK3Symqt7uH5ZnYWiEXPvFeju+X4PuOlHV6Wy8p7p6o8tzhvITmXMvk7ueOlMl7sh4wmm1l46M8fl6U8FoE9P92Ifq2I+keyNKmbHtE+3kTopdo3eyS9Hyusjxve6tEWvPVJtO0JyvtODBnJMv3BBI97opnP5+DlHI1cQEdd67ziUzptMjAS0men+OA0xCtgN7KfQ3pqURlLkoyD/gSeREgyyKATk+QpidS6IuSaPvw7MLG1dX/62O9cLy9efWXm9fub298dkP/PyDvqx+rn6jLsPb9Sn0G4/9QHQGn36s/qr+ov9Z+V/tD7U+1P3PT985pzI9U7l/t7/8FslBPUw==</latexit> Example: f strongly convex. <latexit 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mf(✓) 6 ||rf(✓)||2
  16. Obstruction for P-Ł for Neural ODE <latexit sha1_base64="IxeOLUkTvceeSFRCo84cOj0XSVA=">AABFCnictVxfc9u4EUeu/67pn8u1j33h1ZdOruNLHTf9M73pzCWW4/iiS5RIdnIXJxlKomUmlKiIlJxE52/Q6Yfp9KXTafvSL9EP0Jn2qV+hi12AACWQC7ppOLZBEL/dxRJY7C7A9KdJnOVbW/+48M7Xvv6Nb37r3W9f/M53v/f99y69/4PDLJ3PBtHBIE3S2aN+mEVJPIkO8jhPokfTWRSO+0n0sP9iRz5/uIhmWZxOevnrafRkHI4m8XE8CHOoenbpShuA4Sx4EGV3o3wzyONx9HE8GUbTaDIMJ3lwGsWjkzz7zbNLG1tXt/BfsF64pgobQv3rpO9/8E9xJIYiFQMxF2MRiYnIoZyIUGRwPRbXxJaYQt0TsYS6GZRifB6JM3ERsHNoFUGLEGpfwO8R3D1WtRO4lzQzRA+ASwI/M0AG4jJgUmg3g7LkFuDzOVKWtVW0l0hTyvYa/vYVrTHU5uIEajmcbumLk33JxbH4NfYhhj5NsUb2bqCozFErUvLA6lUOFKZQJ8tDeD6D8gCRWs8BYjLsu9RtiM//hS1lrbwfqLZz8W+U8jJcgeiq3qcFhVAskH6Ab3MOz0ieBDiPgEKk+ihLp6jrMfZ+Au2XUH8XrjMsaZ304Vpi7VktcgcuF3KHRe7B5ULuscg2XC5km0V24HIhOwopsTPUuRvfhcuF77Kc78PlQt5nkQ/gciEfsMhDuFzIQxb5JVwu5Jcs8hZcLuQtFnkHLhfyDovsweVC9ljkAVwu5AGL3IXLhdxVyOqZOoMrRToxMytvQLnMQ1qKBGpusPLdROvowt70mNODCiw/q1vw141teeg0qsDueoy74wosP/L2wEa6sbwtuo2riQt7m8XuwwhwY/dZ7GfieQX2M4+Z9qICy8+1NrRzY3nr+zncubGfs9i7UHJj+TXqHtS4sfc8VoxpBbbDYu+LlxVYH6s/q8Dydr8LdsWN5depHrR3Y32s6bwCy9vTQ/Bg3Fh+tXoItW7sQxb7SLyqwD5isV+AdXdjv/BYYd9UYPUaexFXkBH6IxHM2DpqYTErZWkK1EKGf1KsLQn6xn2o5zCjAjNCzJhF7BWIPU9Eu0C0veXKCjuaob/Lc+kWiK4nol+sTbKUs+2HRXtZSjwQrQLRWkHUeaTyXeu+LNC70DUcMi9WLlny6VNa2G9ZitR4qLe8GnGvhKCxfYIjfxOjJRlBSU3VUTsp1nhCBnhfhzjF6E33UvPgcXlhFWzUKxbVd6D6LOq1A/WaRc0dqDmLWjhQCxZlZr6NO/IYAUb/8l0s8Y5GAPnI1VcAXsENWHVuwxwNYPx0wAt8gDX34G8XY2/uqpNMRvNynZRZjiclSzyD0lJsQL2JClsYXyc4wyKQjFreUzG+vJO5jaWac2SFz4qVPCgyJv50YpRnVNCR3mKA86kZnTtYc4beHZWa4W8X816XmuF3UeNn6MVTqRk+V9Ln55C9p7C9c2C7MJumSvum3JQG5V+Ihi5fxFVXWlz5VsdqzEh6rxrS31dvZv8c72UHS6QfU25GI7P6l5X614SG0XNm6bkZFek9kderS0HjnkxU3GvKTWVIcRWdKDnMXdM3I9sM1ZvR5WY0OuBx7WDMvbTKTUfvtOiNKTejcSgo73mGnrwuN6MxwnvShyk3oyGzLaGK8025qWWXGqDY2ZSbWvUJZoFlDojGPNUYr2iGftJcUYvRP6jP1tg+//o6JnM2T4sYoZ6S8W2r6fSLtaxeIu0vRGDV8oZySP9ibvlgZRpLsc3GVyRDXlrf1+mYNV5qvg1aDGD20x4AlzNPQEKdk5DWOwGK19ioq9wzjdtmcXKUHK+gjlRtznqLhi9ljcp1z7CWi8tMb40ej9BeZzj2pugTtlGznB7alW+4iiKnoXZJQzy9Jrp7o+ZrWftbLG66gpgWI22AO0K0k1Yfp7q03rV0fFnt8uRw0Z6PGb8y23ysrI2MeVK0RVKWOp52O51HsuvkuropTI6bngX4RqW9WqDViHFHKmOjUJ0tJm98ifeG9gHuyUkeRGMA7zFQVKaCds1kFl3m0wO0qLa95XhLfekMHZUztLraHtejRxZ65EA3j3F2YMW4C6UexAwHcNfziHIuFrpKUeMz8XGxO5riG6yP6JOShdQ0yN5EJQtZF2WflKicAlqOBorS/Wms0tH4ozVKfNTvksfErmXLfxl3bvX+dohjvHo0V2dihsh1G7kGOGtoV5fuVjmQBEvnk230X+t7Kfk14ShtKMf1qcWZ9DLBHf8II9gpesYJzjZudpRb2/mp1SeaU0fovXO5m52ihQzQ/gWwPqU4JgP8sc8O6B10sggJ2kgfuxMX3o3L14nZMWb8uFjQqQYz3iK0ZXPkr+nasyvDsUgRA60DZytjW+ukjb5ghFxnyrqbuV2/+kikOSdhjxKiaMbKFeT/Ef7WP3qcbKyNCKlh+QYyZetc7yPFmEXqKMRVvt4G6ba2lB8WMjxVUpv1z8j0YUmyFkZcUh65Wg+B8wDviZccJTOUO1trQ+toXTZXUp6u6FH29hijeLL7I7UCS7k3cZXcwDl3hKNkBKMgL6II3ZbLIq/yredVpu5HO/u/UDe6LmtNUgyEyeCShrj8foTRmi1lAqOaxu8LnE1urc9WWtXzmeBYHFtz+Suo/QB+a7n1vR+dfskq3MQxQBTMndEI1QRrLfx43Szx0iNT0zL3hp8Zk7qVXXOe+Jqsm4mxF42pdHDUvFJZC10+D43nFo3nnjrs4V6j0aKu15boGRtb9NRupS+/Jtx6DSjPWcq8R6ZRsYeUdizlR3XIUuVjfI16w9LaYmmFMFvt3QB7zvsg3XN9dXZ/VazugbiFvs0APTCKX4Y4S2P0uXRtfaRGFCTn68q+2rP/CGsk9z5aUEmZznHKGUO7TgO8zgpJf6JWthTtvLEI+tzSqWqjbewRln++hhzjnMhwXmrEdWwRKfltOYIVi3TV8jkCzPyH6FOR31EfM9utzTsJSv6EiTdpVhleFClMUP9c5m1/LXrdt+LXAGPCufKu+0Cr+RuWFAijMwluzzLDNyRXOdpJII+2j/Zz3U7RLt7EkugqSr0Uv/WwMRT1mrFujy3dY923n0JLqXXz1l0teH6JN0eO33l29EJc1cbKR12u3J+PVqhWufJ9nR7mK3yNPubYxo4sTJRXxhyJT7y5kETNuBDGh0uzXjSRv5nkTWSm3Slfyrq1plzONJCNOcF4iTsHKhEu7+6K05v7iOlHf41eH7E2NarhKMlsXKryA7allVmpYCVCsuu5NSmx1qOq9cLwsFcNY8fJUkZoBRPB5W6otd2Ho1K0wmdjiMJA0MneqjjRpvkJXPJ3IFxRoubok0Psgp97Q+yI3bdwKuKlKlNmM8AaaROGKzF4qPpZblGvo5cWdZu+Dwd/HjHompM+xhW1qexEmZfcpu5P/xStwUxErPSmZfM+2Fz4nqxzatKfGC0c35tY6G9ymvZFc/DpSZmLPx/a3+B6cSz0t03N+qCp8z0oc2jCQ59n8HvnpnVzXjanen2tc/HlQeuA3nnROLkDWB2zmHY+FmpmvZG3z0Fah+Ma6nq1+F/7ofkYTs15+XLL8Juz5x5vndpFKjMr/eLmc8Zw8xnN1Rz9eaZF74zX5OZH/l/Q6E2lVm/ePn3pl5oxoHktBeVDeekIb48iI68vFbk/4JIhFf8Rf7vAf5XwsqBRJUcTSnq/opqabsFT019eunqnn/nIZOhUyVSmZuKJLp6M3RH74hb87BQeYNNTovRNJf2VWPd3tEOoPUbrobPplEE4wroIsyBmN22I9+YcbZXE8kwvnfHtQY3cE29jrTzvexfbyzO/vVLfqr8kobn+uUjFsBSZrO7ymXnVhx6Ud+AoF6S/9w3wTD1ls+gE2thjj5HOUVGkpL9+XiJiiHHhqqRLROjRUke576TcxzNJUQXtfqlvAxzhU7XTL/cd5Pn8sMguBeJnWBeq1UGu1JxUHYdUjzEz0Ef9b0GE9guxCX83VdktaWdN0gzfQVmiV9az+pNgZ85xYb5mvIx5MJ2pW6h2KUb1ZvewPhPbquRCJ97r8aMa/MiSsotv6wXG3TNRnzuc19CcK5ns/dyJ0HlP0oOMZsNifNTHz4saXguP/t+pRN+xJN0DWfqYbQ9wP2+G9BKlm12Uns5V1udtb9dIq7/aJJrmZKUZB/qMZP2eQKLGXfXsp3OQXK4mqqBjz3U6kcmdFomdlPj5OfU4DRF69Jbvq09POSpzVpK5x5fICw9ZFh50jhlpjlkKI1YSZR+eXdq4tvp/fawXDrevXvvl1ev3tzc+van+H5B3xY/Ej8UVWPt+JT6F8d8RB8Dp9+KP4i/ir63ftf7Q+lPrz9T0nQsK80NR+tf6+38Ba0VP7Q==</latexit> Linear ResNet,

    time-independant weights: <latexit sha1_base64="t7eG4Pjr6u0TNKVBuMuFuZ5awqE=">AABE7nictVzdchPJFW42fxvyxyaXuZmNlxSbIsQQ8lO1tVULlgEvXjBINuwioDTSWBaMNUIjCYPWr5HKTSqVXOUt8hx5gFQlV3mFnJ/u6R6pZ06PQ5iy3dPT3zmnz3SfPud0D/EkHeWzzc1/nHvvG9/81re/8/53z3/v+z/44Y8ufPDjgzybT/vJfj9Ls+njuJcn6Wic7M9GszR5PJkmveM4TR7FL7fw+aNFMs1H2bgzezNJnh73huPR4ajfm0HVs+4gm0Un0adRd3YUnTy/sLF5ZZP+ReuFq7qwofS/veyDD/+pumqgMtVXc3WsEjVWMyinqqdyuJ6oq2pTTaDuqVpC3RRKI3qeqFN1HrBzaJVAix7UvoTfQ7h7omvHcI80c0L3gUsKP1NARuoiYDJoN4Uycovo+ZwoY20V7SXRRNnewN9Y0zqG2pk6gloJZ1qG4rAvM3Wofk99GEGfJlSDvetrKnPSCkoeOb2aAYUJ1GF5AM+nUO4T0ug5IkxOfUfd9uj5v6gl1uJ9X7edq3+TlBfhilRb9z4rKPTUguhH9Dbn8IzlSYHzECgkuo9Yek26Pqbej6H9EurvwXVKJaOTGK4l1Z7WIrfg8iG3RORtuHzI2yJyFy4fcldE7sHlQ+5pJGKnpHM/vg2XD98WOT+Ay4d8ICIfwuVDPhSRB3D5kAci8iu4fMivROQtuHzIWyLyLlw+5F0R2YHLh+yIyH24fMh9EbkNlw+5rZHVM3UKV0Z0RsKsvAHlMg+0FCnU3BDlu0nW0Ye9GTCn+xVYeVa34K8f2wrQaVKB3Q4Yd4cVWHnk3QYb6cfKtugOrSY+7B0RuwMjwI/dEbGfqxcV2M8DZtrLCqw813ahnR8rW98v4M6P/ULE3oOSHyuvUfehxo+9H7BiTCqweyL2gXpVgQ2x+tMKrGz322BX/Fh5nepAez82xJrOK7CyPT0AD8aPlVerR1Drxz4SsY/VSQX2sYj9Eqy7H/tlwAr7tgJr1tjztIIMyR9JYMbWUesVsxJLE6DWE/inxdqSkm8cQ72EGRaYIWGORcTtAnE7ELFbIHaD5coLO5qTvytzaReIdiAiLtYmLM3E9oOiPZbSAESrQLRWEHUeKb5r05cFeRemRkLOipULSyF9ygr7jaVEj4d6y2sQ90sIHttHNPIvU7SEERRqqo7aUbHGMzKi+zrEa4reTC8NDxk3K6yCizoRUbEHFYuoNx7UGxE196DmImrhQS1ElJ35Lq4bMAKs/vFdLOmORwD7yNVXBF7BDVh17sAcjWD87IEX+JBq7sPfNsXe0lUnGUbzuE5iluNpyRJPobRUG1Bvo8IWxdcpzbAEJOOW93WMj3eY21jqOcdW+LRYyaMiYxJOZ0TyDAs66C1GNJ+a0blLNafk3XGpGf5OMe9NqRl+mzR+Sl48l5rhZ1r62Rlk72hs5wzYNsymida+LTelwfkXpmHK52nVRYuLb/VYjxmkd9KQ/o5+MztneC9bVGL92HIzGrnTv7zUvyY0rJ5zR8/NqKD3xF6vKUWNezLWca8tN5Uho1V0rOWwd03fDLYZ6Ddjys1o7IHHtUUx99IpNx29k6I3ttyMxoHivOcpefKm3IzGkO5ZH7bcjAZmW3o6zrflppYdNcCxsy03tepjygJjDojHPNdYr2hKftJcUxuRf1CfrXF9/vV1DHM2z4oYoZ6S9W2r6cTFWlYvkfEXErBqs4ZyoH8xd3ywMo2luibGVyzDrLS+r9Oxazxqfhe0GMHs5z0AKWeegoQmJ4HWOwWKV8Woq9wzg7sm4nCUHK6gurp2JnqLli9njcp1z6lWistsb60eu2Svcxp7E/IJd0mzkh52K99wFUVJQ7slDcn0mujurZ6vZe1virjJCmJSjLQ+7QjxTlp9nOrTetvR8UW9yzODi/d87PjFbPOhtjYY82Rki1CWOp5uO5NHcutwXb2sbI6bn0X0RtFeLchqjGhHKhejUJMtZm98SfeW9j7tySEPptGH9xhpKhPFu2aYRcd8ekQW1bW3Em/Ul8nQcTknq2vscT166KCHHnTzGGcLVox7UOpAzLAPd52AKOd8oauMND5Vvyx2RzN6g/URfVqykIYG25ukZCHrouyjEpXXgMbRwFF6OI1VOgbfXaMkR/0+eWzsWrb8F2nn1uxv92iMV4/m6kzMgLheI64RzRre1eW7VQ4swdL75Br5r/W9RH5NOKINlbg+czizXsa0459QBDshzzil2SbNjnJrNz+1+sRw2lNm7xx3szOykBHZvwjWp4zGZEQ/7tkBs4POFiElGxlid0aFd+PzdUbiGLN+3EjxqQY73hKyZXPib+i6syunscgRA68Dpytj2+hkl3zBhLhOtXW3c7t+9UGkPSfhjhKmaMfKJeL/Mf02P2acbKyNCNQwvoFc2zrf+8goZkEd9WiVr7dBpq0r5UeFDM+01Hb9szJ9VJKsRREXyoOr9QA49+meeeEomZLc+VobXkfrsrlIebKiR+ztIUXxbPeHegVGuS/TKrlBc65Lo2QIo2BWRBGmrZRFXuVbz6tMPYx2/n+hbnVd1hpSjJTN4LKGpPx+QtGaK2UKo5rH70uaTX6tT1da1fMZ01g8duby11D7Ifw2cpv7MDpxySrcpDHAFOyd1QjXRGstwnjdLPEyI9PQsveWnx2TppVbc5b4mq2bjbEXjans0ag50VkLUz4LjRcOjReBOuzQXqPVoqk3lui5GFt09G5lKL8m3DoNKM9FyrJHZlCjACndWCqM6kCkKsf4BvVWpLUp0urBbHV3A9w5H4L0z/XV2f11sbpH6hb5Nn3ywDh+GdAsHZHPZWrrIzWmgJyva/vqzv4u1SD3mCwoUuZznDhjeNepT9dpIenP9cqWkZ23FsGcW3qt2xgb26Xyr9eQxzQncpqXBnGdWiRafleOaMUiXXF8jogy/z3yqdjvqI+Z3db2nUQlf8LGmzyrLC+OFMakfynztrMWve448WtEMeFce9cx0Gr+hpECY0wmwe9Z5vSGcJXjnQT2aGOyn+t2infxxo5EV0jqpfo0wMZw1GvHuju2TI9N334BLVHr9q37Wsj80mCOEr+z7Oj1aFU71j7qcuX+bLR6epUr39fpYb7C1+pjTm3cyMJGeWVMV30SzIUlasaFMSFcmvWiifzNJG8iM+9OhVI2rQ3lcqaBbcwRxUvSOVBE+Ly7S15v7mOhH/EavZiwLjWukShhNi7T+QHX0mJWKlqJkNx6aU1KnfWoar2wPNxVw9pxtpQJWcFUSbkbbu32oVuKVuRsDFPoKz7ZWxUnujQ/gQt/R8oXJRqOITnENvi5N9SW2n4HpyJe6TJnNiOqQZswWInBe7qf5Rb1OnrlUHfph3AI5zECXUvSj2hFbSo7U5Yld6mH039N1mCqElF627J5H1wuck/WOTXpz4gsnNybkTLf5DTti+EQ0pMyl3A+vL8h9eJQmW+bmvXBUJd7UObQhIc5zxD2zm3r5rxcTvX6WucSyoPXAbPzYnC4A1gds9h2IRZq6ryRd88BrcNhDXWzWvyv/TB8LKfmvEK55fTN2YuAt87tEp2ZRb+4+Zyx3EJGczXHcJ5Z0TvrNfn5sf8XNXpTmdObd08f/VI7BgyvpeJ8qCwd491RZOUNpYL7Az4ZMvUf9fdz8lcJrwoaVXI0oWT2K6qpmRYyNfPlpa935lmITJZOlUxlajaeaNPJ2C21o27Bz1bhATY9JcrfVPJfxPq/ox1A7SFZD5NN5wxCl+oSyoLY3bQB3dtztFUS45lePuPbgRrcE9+lWjzve4/a45nfTqlv1V+S8Fz/QmVqUIpMVnf57LyKoQflHTjOBZnvfSM6U8/ZLD6Bdhywx8jnqDhSMl8/LwkxoLhwVdIlIcxoqaMceynHdCYpqaAdl/rWpxE+0Tv9uO+A5/N7RXYpUr+iup5eHXCllqTa80j1hDIDMel/EyK036jL8PeyLvsl3VuTNKd3UJboxHlWfxLs1Dsu7NeMFykPZjJ1C90uo6je7h7WZ2JblVz4xHs9fliDHzpStultvaS4e6rqc4fzGppzLZO7nztWJu/JesBotleMj/r4eVHDaxHQ/7uV6LuOpLdBlpiy7RHt502JXqp1s03S87nK+rztnRppzVebTNOerLTjwJyRrN8TSPW4q579fA5SytUkFXTcuc4nMqXTIiMvJXl+TgJOQ/QCeiv3NaSnEpW5KMk84EvkRYAsiwA6h4I0hyKFoSiJtg/PL2xcXf2/PtYLB9euXP3tlesPrm98dlP/PyDvq5+qn6lLsPb9Tn0G439P7Svcvf+j+ov6a2vS+kPrT60/c9P3zmnMT1TpX+tv/wUpTkRv</latexit> ˙ x = ✓x <latexit 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✓(x) = e✓x <latexit sha1_base64="waTHm3fQpdQQpFlwopY3HfEpmdU=">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</latexit> For yj = xi, i.e. learning Id: <latexit sha1_base64="XY6WqX8kPJU7sq5nmngGZEW6eVI=">AABFCnictVxZcxTJES7W1xpfrP3ol14LHGDLWMj4iNhwxIJGCC0CBDMS7DJAzNEzGuiZHubimNU/cPjHOPzicNh+8Z/wD3CE/eS/4DyquqpnqjurZUyHpOrq+jKzsquyMrOqaY+TwXS2tfWPcx985atf+/o3Pvzm+W99+zvf/d6Fj75/PE3nk0581EmTdPK43ZrGyWAUH80GsyR+PJ7ErWE7iR+1X+7g80eLeDIdpKPG7O04fjps9UeD3qDTmkHV8wuXL/YuN2cnV6LmbDJojfpJ/CpqjtLJcBk/g/rop1Fzv3v6bPvi8wsbW1e36F+0XrimCxtK/ztMP/r4n6qpuipVHTVXQxWrkZpBOVEtNYXribqmttQY6p6qJdRNoDSg57E6VecBO4dWMbRoQe1L+N2Huye6dgT3SHNK6A5wSeBnAshIXQJMCu0mUEZuET2fE2WsLaK9JJoo21v429a0hlA7UydQK+FMy1Ac9mWmeuo31IcB9GlMNdi7jqYyJ62g5JHTqxlQGEMdlrvwfALlDiGNniPCTKnvqNsWPf8XtcRavO/otnP1b5LyElyRquvepxmFlloQ/Yje5hyesTwJcO4DhVj3EUuvSddD6v0I2i+h/h5cp1QyOmnDtaTa01LkDlw+5I6I3IPLh9wTkQdw+ZAHIvIQLh/yUCMROyGd+/F1uHz4usj5AVw+5AMR+RAuH/KhiDyGy4c8FpFfwOVDfiEib8HlQ94SkXfg8iHviMgGXD5kQ0QeweVDHonIXbh8yF2NLJ6pE7hSojMQZuUNKOd5oKVIoOaGKN9Nso4+7M2AOd0pwMqzugZ//dhagE7jAuxuwLjrFWDlkbcHNtKPlW3RbVpNfNjbInYfRoAfuy9iP1MvCrCfBcy0lwVYea4dQDs/Vra+d+HOj70rYu9ByY+V16j7UOPH3g9YMcYF2EMR+0C9KsCGWP1JAVa2+3WwK36svE41oL0fG2JN5wVY2Z4egwfjx8qr1SOo9WMfidjH6k0B9rGI/Rysux/7ecAK+64Aa9bY87SC9MkfiWHGllFrZbMSS2Og1hL4J9nakpBv3IZ6CdPPMH3CDEXEXobYC0QcZIiDYLmmmR2dkr8rc6lniHogop2tTViaie27WXssJQGIWoaorSDKPFJ816YvC/IuTI2EnGUrF5ZC+pRm9htLsR4P5ZbXIO7nEDy2T2jkb1K0hBEUaqqM2km2xjMyovsyxGuK3kwvDQ8ZN8usgot6I6LaHlRbRL31oN6KqLkHNRdRCw9qIaLszHdxzYARYPWP72JJdzwC2EcuviLwCm7AqnMb5mgE4+cQvMCHVHMf/tYp9pauMskwmsd1ErMcT3OWeAKlpdqAehsV1ii+TmiGxSAZt7yvY3y8w9zGUs85tsKn2UoeZRmTcDoDkqef0UFvMaL5VI3OHao5Je+OS9Xwt7N5b0rV8Luk8VPy4rlUDT/T0s/OIHtDYxtnwNZhNo219m25Kg3OvzANUz5Pqy5aXHyrQz1mkN6bivT39ZvZP8N72aES68eWq9GYOv2b5vpXhYbV89TRczUq6D2x12tKUeWejHTca8tVZUhpFR1pOexd1TeDbbr6zZhyNRqH4HHtUMy9dMpVR+84640tV6NxrDjveUqevClXo9Gne9aHLVejgdmWlo7zbbmqZUcNcOxsy1Wt+oiywJgD4jHPNdYrmpCfNNfUBuQflGdrXJ9/fR3DnM2zLEYop2R922I67WwtK5fI+AsxWLVZRTnQv5g7PliexlJti/EVyzDLre/rdOwaj5o/AC1GMPt5D0DKmScgoclJoPVOgOI1MerK98zgtkUcjpLeCqqpa2eit2j5ctYoX/ecaqW4zPbW6rFJ9npKY29MPuEBaVbSw0HhGy6iKGnoIKchmV4V3b3T8zWv/S0RN15BjLOR1qEdId5JK49TfVqvOzq+pHd5ZnDxno8dv5ht7mlrgzFPSrYIZSnj6bYzeSS3DtfVTWVz3PwsojeK9mpBVmNAO1JTMQo12WL2xpd0b2kf0Z4c8mAaHXiPkaYyVrxrhll0zKdHZFFdeyvxRn2ZDB2Xp2R1jT0uR/cddN+Drh7j7MCKcQ9KDYgZjuCuERDlnM90lZLGJ+pn2e5oSm+wPKJPchbS0GB7E+csZFmUfZKj8hrQOBo4Sg+nsUrH4JtrlOSo3yePjV3zlv8S7dya/e0WjfHi0VyciekS123iGtGs4V1dvlvlwBIsvU+2yX8t7yXyq8IRbajE9ZnDmfUyoh3/mCLYMXnGCc02aXbkW7v5qdUnhtOhMnvnuJudkoWMyP5FsD6lNCYj+nHPDpgddLYICdnIELszyLwbn68zEMeY9eMGik812PEWky2bE39D151dUxqLHDHwOnC6MraNTg7IF4yJ60Rbdzu3y1cfRNpzEu4oYYp2rFwm/lfot/kx42RjbUSghvENTLWt872PlGIW1FGLVvlyG2TaulJezGR4pqW265+V6WJOshpFXCgPrtZd4Nyhe+aFo2RCck/X2vA6WpbNRcrjFT1ib3sUxbPd7+sVGOXepFVyg+Zck0ZJH0bBLIsiTFspi7zKt5xXnnoY7en/hbrVdV5rSDFSNoPLGpLy+zFFa66UCYxqHr8vaTb5tT5ZaVXOZ0RjcejM5S+h9mP4beQ292F02jmrcJPGAFOwd1YjXBOttQjjdTPHy4xMQ8veW352TJpWbs1Z4mu2bjbGXlSmckij5o3OWpjyWWi8cGi8CNRhg/YarRZNvbFEz8XYoqF3K0P5VeHWqEB5LlKWPTKDGgRI6cZSYVS7IlU5xjeodyKtLZFWC2aruxvgzvkQpH+ur87uL7PVPVK3yLfpkAfG8UuXZumAfC5TWx6pMQXkfF3bV3f2N6kGubfJgiJlPseJM4Z3nTp0nWaS/livbCnZeWsRzLml17qNsbFNKv9iDTmkOTGleWkQ16lFrOV35YhWLNJVx+eIKPPfIp+K/Y7ymNltbd9JlPMnbLzJs8ry4khhRPqXMm/7a9HrvhO/RhQTzrV33QZa1d8wUmCMyST4PcspvSFc5XgngT3aNtnPdTvFu3gjR6KrJPVS/TbAxnDUa8e6O7ZMj03ffgItUev2rftayPySYI4Sv7Ps6LVoVRtqH3W5cn82Wi29yuXvy/QwX+Fr9TGnNm5kYaO8PKapPgnmwhJV48KYEC7VelFF/mqSV5GZd6dCKZvWhnI+08A25oTiJekcKCJ83t1lrzd3RehHe41em7AuNa6RKGE2LtX5AdfSYlYqWomQ3HppTUqc9ahovbA83FXD2nG2lDFZwURJuRtu7fahmYtW5GwMU+goPtlbFCe6ND+BC39HyhclGo4hOcQ6+Lk31I7afQ+nIl7pMmc2I6pBm9BdicFbup/5FuU6euVQd+mHcAjnMQBdS9IPaEWtKjtTliV3qYfTf03WYKJiUXrbsnofXC5yT9Y5VenPgCyc3JuBMt/kVO2L4RDSkzyXcD68vyH1oqfMt03V+mCoyz3Ic6jCw5xnCHvntnV1Xi6ncn2tcwnlweuA2XkxONwBLI5ZbLsQCzVx3sj754DWoVdC3awW/2s/DB/LqTqvUG5T+ubsRcBb53axzsyiX1x9zlhuIaO5mGM4zzTrnfWa/PzY/4sqvanU6c37p49+qR0DhtdScT5Ulo7x7iiy8oZSwf0Bnwyp+o/62zn5q4RXGY0iOapQMvsVxdRMC5ma+fLS1zvzLEQmS6dIpjw1G0/U6WTsjtpXt+BnJ/MAq54S5W8q+S9i/d/RdqG2R9bDZNM5g9CkupiyIHY3rUv39hxtkcR4ppfP+DagBvfED6gWz/veo/Z45reR61vxlyQ81++qVHVzkcnqLp+dV23oQX4HjnNB5nvfiM7UczaLT6ANA/YY+RwVR0rm6+clIboUF65KuiSEGS1llNteym06kxQX0G7n+tahET7WO/2474Dn81tZdilSP6e6ll4dcKWWpDr0SPWEMgNt0v8WRGi/VJvwd1OX/ZIerkk6pXeQl+iN86z8JNipd1zYrxkvUR7MZOoWul1KUb3dPSzPxNYKufCJ93J8vwTfd6Ss09t6SXH3RJXnDuclNOdaJnc/d6RM3pP1gNFsKxsf5fHzooTXIqD/dwrRdxxJ90CWNmXbI9rPmxC9ROtml6Tnc5XledvbJdKarzaZpj1ZaceBOSNZvieQ6HFXPPv5HKSUq4kL6LhznU9kSqdFBl5K8vwcB5yGaAX0Vu5rSE8lKnNRknnAl8iLAFkWAXR6gjQ9kUJflETbh+cXNq6t/l8f64Xj7avXfnX1+oPtjU9v6v8H5EP1Q/UjdRnWvl+rT2H8H6oj4PR79Uf1F/XX2u9qf6j9qfZnbvrBOY35gcr9q/39v5+dTsM=</latexit> f(✓) , ||e✓ + Id||2 <latexit sha1_base64="67xKL37ihrpcZBK1n5G+cmE+Ahs=">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</latexit> ✓(k+1) = ✓(k) 1 rf(✓(k))
  17. Obstruction for P-Ł for Neural ODE <latexit sha1_base64="IxeOLUkTvceeSFRCo84cOj0XSVA=">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</latexit> Linear ResNet,

    time-independant weights: <latexit sha1_base64="t7eG4Pjr6u0TNKVBuMuFuZ5awqE=">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</latexit> ˙ x = ✓x <latexit 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✓(x) = e✓x <latexit sha1_base64="waTHm3fQpdQQpFlwopY3HfEpmdU=">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</latexit> For yj = xi, i.e. learning Id: <latexit sha1_base64="XY6WqX8kPJU7sq5nmngGZEW6eVI=">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</latexit> f(✓) , ||e✓ + Id||2 <latexit sha1_base64="74mWKZWxPGMDwJqADej242G+u3o=">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</latexit> Proposition: <latexit sha1_base64="GgPa/HzCW8aFxiVp5eoVrSAhgZk=">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</latexit> ˜ f(z) , |ez + 1|2 <latexit sha1_base64="n8bKIi74SGsQ0JlHJ3yE0SBEpy4=">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</latexit> If ✓(0) = U diag(z(0) 1 , . . . , z(0) d )U⇤, <latexit sha1_base64="jhIdMpLhbSP5sTtM+QmgUNHYeEA=">AABFG3ictVxLcxu5EYY3r43z8ibHXGYjO2VvKY6kOK/a2qq1JVvWWmvLJiV717RVfIwoWiMOzSHpB1c/JZWfkkMql1QqOeWQH5Cq5JS/kH4AAwyJmcYojqckYTD4uhs9QKO7gXFnlAyyydraPy6897Wvf+Ob33r/2xe/893vff8Hlz744UGWTsfdeL+bJun4SaedxclgGO9PBpMkfjIax+3TThI/7pxs4vPHs3icDdJhc/JmFD87bfeHg6NBtz2BqsNLv50cx8Pocmty/Hx+9eTa2Sf7Uas3aPevvj1c55rVVtJLJ9nq28MeV1yL9p9/dDk6vLSydn2N/kXLhXVdWFH63176wYf/VC3VU6nqqqk6VbEaqgmUE9VWGVxP1bpaUyOoe6bmUDeG0oCex+pMXQTsFFrF0KINtSfwuw93T3XtEO6RZkboLnBJ4GcMyEhdAUwK7cZQRm4RPZ8SZawtoz0nmijbG/jb0bROoXaijqFWwpmWoTjsy0Qdqd9QHwbQpxHVYO+6msqUtIKSR06vJkBhBHVY7sHzMZS7hDR6jgiTUd9Rt216/i9qibV439Vtp+rfJOUVuCLV0L1PcwptNSP6Eb3NKTxjeRLg3AcKse4jll6Rrk+p90NoP4f6+3CdUcnopAPXnGrPKpGbcPmQmyJyGy4fcltE7sLlQ+6KyD24fMg9jUTsmHTuxzfg8uEbIueHcPmQD0XkI7h8yEci8gAuH/JARH4Jlw/5pYi8A5cPeUdE3oPLh7wnIptw+ZBNEbkPlw+5LyJvw+VD3tbI8pk6hislOgNhVt6EcpEHWooEam6K8t0i6+jD3gqY090SrDyrt+CvH7sVoNO4BHs7YNwdlWDlkbcNNtKPlW3RXVpNfNi7InYHRoAfuyNiP1MvSrCfBcy0kxKsPNd2oZ0fK1vfz+HOj/1cxN6Hkh8rr1EPoMaPfRCwYoxKsHsi9qF6WYINsfrjEqxs9xtgV/xYeZ1qQns/NsSaTkuwsj09AA/Gj5VXq8dQ68c+FrFP1OsS7BMR+wVYdz/2i4AV9m0J1qyxF2kF6ZM/EsOMraLWzmcllkZArS3wT/K1JSHfuAP1EqafY/qEORUR2zliOxCxmyN2g+XKcjuakb8rc2nkiEYgopOvTViaiO17eXssJQGIrRyxtYCo8kjxXZu+zMi7MDUScpKvXFgK6VOa228sxXo8VFteg3hQQPDYPqaRv0rREkZQqKkqasf5Gs/IiO6rEK8oejO9NDxk3CS3Ci7qtYjqeFAdEfXGg3ojoqYe1FREzTyomYiyM9/FtQJGgNU/vos53fEIYB+5/IrAK7gJq85dmKMRjJ898AIfUc0D+Nug2Fu6qiTDaB7XScxyPCtY4jGU5moF6m1UuEXxdUIzLAbJuOUDHePjHeY25nrOsRU+y1fyKM+YhNMZkDz9nA56ixHNp3p07lHNGXl3XKqHv5vPe1Oqh79NGj8jL55L9fATLf3kHLI3NbZ5DmwDZtNIa9+W69Lg/AvTMOWLtOqixcW3eqrHDNJ7XZP+jn4zO+d4L5tUYv3Ycj0amdO/rNC/OjSsnjNHz/WooPfEXq8pRbV7MtRxry3XlSGlVXSo5bB3dd8MtunpN2PK9Wjsgce1STH33CnXHb2jvDe2XI/GgeK85xl58qZcj0af7lkftlyPBmZb2jrOt+W6lh01wLGzLde16kPKAmMOiMc811ivaEx+0lRTG5B/UJ2tcX3+5XUMczbP8xihmpL1bcvpdPK1rFoi4y/EYNUmNeVA/2Lq+GBFGnO1IcZXLMOksL4v07FrPGp+F7QYweznPQApZ56AhCYngdY7AYrrYtRV7JnBbYg4HCVHC6iWrp2I3qLly1mjYt0h1Upxme2t1WOL7HVGY29EPuEuaVbSw27pGy6jKGlot6AhmV4d3b3V87Wo/TURN1pAjPKR1qUdId5Jq45TfVpvODq+ond5JnDxno8dv5htPtLWBmOelGwRylLF021n8khuHa6rq8rmuPlZRG8U7dWMrMaAdqQyMQo12WL2xud0b2nv054c8mAaXXiPkaYyUrxrhll0zKdHZFFdeyvxRn2ZDB2XM7K6xh5Xo/sOuu9B149xNmHFuA+lJsQM+3DXDIhyLua6SknjY/WzfHc0pTdYHdEnBQtpaLC9iQsWsirKPi5QeQVoHA0cpYfTWKRj8K0lSnLU75PHxq5Fy3+Fdm7N/nabxnj5aC7PxPSI6wZxjWjW8K4u3y1yYAnm3icb5L9W9xL51eGINlTi+tzhzHoZ0o5/TBHsiDzjhGabNDuKrd381OITw2lPmb1z3M1OyUJGZP8iWJ9SGpMR/bhnB8wOOluEhGxkiN0Z5N6Nz9cZiGPM+nEDxaca7HiLyZZNib+h686ujMYiRwy8DpwtjG2jk13yBWPiOtbW3c7t6tUHkfachDtKmKIdK1eJ/zX6bX7MOFlZGhGoYXwDmbZ1vveRUsyCOmrTKl9tg0xbV8rLuQzPtdR2/bMyXS5ItkURF8qDq3UPOHfpnnnhKBmT3NlSG15Hq7K5SHm0oEfs7RFF8Wz3+3oFRrlXaZVcoTnXolHSh1EwyaMI01bKIi/yreZVpB5GO/u/ULe6LmoNKUbKZnBZQ1J+P6ZozZUygVHN4/eEZpNf6+OFVtV8hjQWT525/BXUfgi/jdzmPoxOp2AVbtEYYAr2zmqEa6KlFmG8bhV4mZFpaNl7y8+OSdPKrTlPfM3WzcbYs9pU9mjUvNZZC1M+D40XDo0XgTps0l6j1aKpN5boUIwtmnq3MpRfHW7NGpSnImXZIzOoQYCUbiwVRrUnUpVjfIN6K9JaE2m1Yba6uwHunA9B+uf64uz+Kl/dI3WHfJsueWAcv/Rolg7I5zK11ZEaU0DON7R9dWd/i2qQe4csKFLmc5w4Y3jXqUvXWS7pT/XKlpKdtxbBnFt6pdsYG9ui8i+WkKc0JzKalwZxg1rEWn5XjmjBIl13fI6IMv9t8qnY76iOmd3W9p1EBX/Cxps8qywvjhSGpH8p87azFL3uOPFrRDHhVHvXHaBV/w0jBcaYTILfs8zoDeEqxzsJ7NF2yH4u2ynexRs6El0nqefqkwAbw1GvHevu2DI9Nn37CFqi1u1b97WQ+SXBHCV+59nRa9Oqdqp91PnC/flotfUqV7yv0sN0ga/Vx5TauJGFjfKKmJb6OJgLS1SPC2NCuNTrRR3560leR2benQqlbFobysVMA9uYY4qXpHOgiPB5d1e93tw1oR+dJXodwrrUuEaihNm4VOcHXEuLWaloIUJy66U1KXHWo7L1wvJwVw1rx9lSxmQFEyXlbri124dWIVqRszFMoav4ZG9ZnOjS/Bgu/B0pX5RoOIbkEBvg595Um+r2OzgV8VKXObMZUQ3ahN5CDN7W/Sy2qNbRS4e6Sz+EQziPAehakn5AK2pd2ZmyLLlLPZz+K7IGYxWL0tuW9fvgcpF7ssypTn8GZOHk3gyU+Sanbl8Mh5CeFLmE8+H9DakXR8p821SvD4a63IMihzo8zHmGsHduW9fn5XKq1tcyl1AevA6YnReDwx3A8pjFtguxUGPnjbx7Dmgdjiqom9Xif+2H4WM51ecVyi2jb85eBLx1bhfrzCz6xfXnjOUWMprLOYbzTPPeWa/Jz4/9v6jWm0qd3rx7+uiX2jFgeM0V50Nl6RjvjiIrbygV3B/wyZCq/6g/XJC/SniZ0yiTow4ls19RTs20kKmZLy99vTPPQmSydMpkKlKz8USDTsZuqh11B342cw+w7ilR/qaS/yLW/x1tD2qPyHqYbDpnEFpUF1MWxO6m9ejenqMtkxjP9PIZ3ybU4J74LtXied/71B7P/DYLfSv/koTn+ucqVb1CZLK4y2fnVQd6UNyB41yQ+d43ojP1nM3iE2inAXuMfI6KIyXz9fOcED2KCxclnRPCjJYqyh0v5Q6dSYpLaHcKfevSCB/pnX7cd8Dz+e08uxSpn1NdW68OuFJLUu15pHpKmYEO6X8NIrRfqlX4u6rLfkn3liTN6B0UJXrtPKs+CXbmHRf2a8YrlAczmbqZbpdSVG93D6szsVulXPjEezW+X4HvO1I26G2dUNw9VtW5w2kFzamWyd3PHSqT92Q9YDTbzsdHdfw8q+A1C+j/vVL0PUfSbZClQ9n2iPbzxkQv0bq5TdLzucrqvO3dCmnNV5tM056stOPAnJGs3hNI9Lgrn/18DlLK1cQldNy5zicypdMiAy8leX6OAk5DtAN6K/c1pKcSlakoyTTgS+RZgCyzADpHgjRHIoW+KIm2D4eXVtYX/6+P5cLBxvX1X12/8XBj5dNb+v8BeV/9WP1EXYW179fqUxj/e2ofOP1e/Un9Vf1t63dbf9z689ZfuOl7FzTmR6rwb+vv/wXlAlR7</latexit> then ✓(k) = U diag(z(k) 1 , . . . , z(k) d )U⇤ <latexit sha1_base64="z5bQ9WrBzerqR9GX4amXiWeyutg=">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=</latexit> where z(k) i 2 C is a gradient descent of <latexit sha1_base64="67xKL37ihrpcZBK1n5G+cmE+Ahs=">AABFHXictVzdc9u4EUeuX9f0K9c+9oVXXzpJm0vtNP2YydzMJZbj+KJLlEh2chclGVKiZMW0qIiS8qHT39LpX9KnTl86nfap0z+gM+1T/4UudgEClEAu6Kbh2AZB/HYXS2CxuwATTZJRNtve/se597729W9881vvf/v8d777ve//4MIHPzzK0vm0Fx/20iSdPo7CLE5G4/hwNpol8ePJNA5PoyR+FJ3syuePFvE0G6XjzuzNJH56Gg7Ho8GoF86g6vmFG93Z8bPlpZOf71xeBZ8E6g7KHwfdwTTsLXdWy24Ur4LuOIySMBhcyptcfn5ha/vqNv4LNgs7qrAl1L9W+sGH/xRd0Rep6Im5OBWxGIsZlBMRigyuJ2JHbIsJ1D0VS6ibQmmEz2OxEucBO4dWMbQIofYEfg/h7omqHcO9pJkhugdcEviZAjIQFwGTQrsplCW3AJ/PkbKsLaO9RJpStjfwN1K0TqF2Jo6hlsPplr442ZeZGIjfYh9G0KcJ1sje9RSVOWpFSh5YvZoBhQnUyXIfnk+h3EOk1nOAmAz7LnUb4vN/YUtZK+97qu1c/BulvAhXINqq92lOIRQLpB/g25zDM5InAc5DoBCrPsrSK9T1KfZ+DO2XUH8PrhWWtE4iuJZYu6pE7sLlQu6yyH24XMh9FtmEy4VsssgWXC5kSyEldoo6d+PbcLnwbZbzA7hcyAcs8iFcLuRDFnkElwt5xCK/hMuF/JJF3obLhbzNIu/C5ULeZZEduFzIDos8hMuFPGSRe3C5kHsKWT5Tp3ClSGfEzMqbUC7ykJYigZqbrHy30Dq6sLc85nSvBMvP6gb8dWMbHjqNS7B7HuNuUILlR94+2Eg3lrdFd3A1cWHvsNgDGAFu7AGL/Uy8KMF+5jHTTkqw/FxrQjs3lre+n8OdG/s5i70HJTeWX6PuQ40be99jxZiUYFss9oF4WYL1sfrTEixv99tgV9xYfp3qQHs31seazkuwvD09Ag/GjeVXq0dQ68Y+YrGPxesS7GMW+wVYdzf2C48V9m0JVq+x53EFGaI/EsOMraIW5rNSliZALWT4J/nakqBvHEE9hxnmmCFiTlnEfo7Y90Q0c0TTW64st6MZ+rs8l3aOaHsionxtkqUZ276ft5elxAPRyBGNNUSVRyrfte7LAr0LXcMhZ/nKJUs+fUpz+y1LsRoP1ZZXI+4XEDS2j3HkX8FoSUZQUlNV1I7zNZ6QAd5XIV5h9KZ7qXnwuFluFWzUaxYVOVARi3rjQL1hUXMHas6iFg7UgkWZmW/juh4jwOhfvosl3tEIIB+5/ArAK7gJq84dmKMBjJ8WeIEPseY+/G1j7M1dVZLJaF6ukzLL8bRgiadQWootqDdRYQPj6wRnWAySUcv7KsaXdzK3sVRzjqzwKl/Jgzxj4k9nhPIMczrSWwxwPtWjcxdrVujdUake/k4+73WpHn4PNb5CL55K9fAzJf3sDLJ3FLZzBmwbZtNEad+U69Kg/AvR0OXzuOpKiyvf6qkaM5Le65r0D9SbOTjDe9nFEunHlOvRyKz+ZYX+1aFh9JxZeq5HRXpP5PXqUlC7J2MV95pyXRlSXEXHSg5zV/fNyDZ99WZ0uR6NFnhcuxhzL61y3dE7yXtjyvVoHAnKe67Qk9flejSGeE/6MOV6NGS2JVRxvinXtexSAxQ7m3Jdqz7GLLDMAdGYpxrjFU3RT5oraiP0D6qzNbbPv7mOyZzNszxGqKZkfNtyOlG+llVLpP2FGKzarKYc0r+YWz5YkcZSXGPjK5JhVljfN+mYNV5qvglaDGD20x4AlzNPQEKdk5DWOwGKO2zUVeyZxl1jcXKUDNZQXVU7Y71Fw5eyRsW651jLxWWmt0aPXbTXGY69CfqETdQsp4dm6Rsuo8hpqFnQEE+vju7eqvla1P42i5usISb5SOvhjhDtpFXHqS6tty0dX1S7PDO4aM/HjF+ZbR4oayNjnhRtkZSliqfdTueR7Dq5rl4RJsdNzwJ8o9JeLdBqjHBHKmOjUJ0tJm98ifeG9iHuyUkeRKMH7zFQVCaCds1kFl3m0wO0qLa95XhLfekMHZUztLraHlejhxZ66EDXj3F2YcW4B6UOxAyHcNfxiHLO57pKUeNT8XG+O5riG6yO6JOChdQ0yN7EBQtZFWUfF6i8ArQcDRSl+9NYp6Px3Q1KfNTvksfErkXLfxF3bvX+dohjvHw0l2di+sj1GnINcNbQri7drXMgCZbOJ9fQf63upeRXh6O0oRzXZxZn0ssYd/xjjGAn6BknONu42VFsbeen1p9oTi2h987lbnaKFjJA+xfA+pTimAzwxz47oHfQySIkaCN97M4o925cvs6IHWPGjxsJOtVgxluMtmyO/DVde3ZlOBYpYqB1YLU2trVOmugLxsh1qqy7mdvVq49EmnMS9ighimasXEL+l/G3/tHjZGtjREgNyzeQKVvneh8pxixSRyGu8tU2SLe1pfwol+GZktqsf0amjwqSNTDikvLI1boPnHt4T7zkKJmi3NlGG1pHq7K5kvJkTY+ytwOM4snuD9UKLOW+gqvkFs65Lo6SIYyCWR5F6LZcFnmdbzWvInU/2tn/hbrRdVFrkmIgTAaXNMTl92OM1mwpExjVNH5PcDa5tT5da1XNZ4xj8dSay19B7YfwW8ut7/3oRAWrcAvHAFEwd0YjVBNstPDjdavAS49MTcvcG35mTOpWds1Z4muybibGXtSm0sJR81plLXT5LDReWDReeOqwg3uNRou6Xlui52xs0VG7lb786nDr1KA8ZynzHplGjTyktGMpP6p9liof42vUW5bWNksrhNlq7wbYc94H6Z7r67P7q3x1D8Rt9G166IFR/NLHWTpCn0vXVkdqREFyvq7sqz37u1gjuUdoQSVlOscpZwztOvXwWuWS/lStbCnaeWMR9LmlV6qNtrFdLP9yA3mKcyLDeakR17FFrOS35QjWLNJVy+cIMPMfok9Ffkd1zGy3Nu8kKPgTJt6kWWV4UaQwRv1zmbeDjej1wIpfA4wJ58q7joBW/TcsKRBGZxLcnmWGb0iucrSTQB5thPZz007RLt7YkugqSr0Un3jYGIp6zVi3x5buse7bz6Cl1Lp5664WPL/EmyPH7yw7eiGuaqfKR12u3Z+NVqhWueJ9lR7ma3yNPubYxo4sTJRXxHTFDW8uJFE9LoTx4VKvF3Xkryd5HZlpd8qXsm6tKRczDWRjjjFe4s6BSoTLu7vk9OYuM/2INuhFiLWpUQ1HSWbjUpUfsC2tzEoFaxGSXc+tSYm1HpWtF4aHvWoYO06WMkYrmAgud0Ot7T50C9EKn40hCj1BJ3vL4kSb5g245O9AuKJEzdEnh9gGP/em2BV77+BUxEtVpsxmgDXSJvTXYvBQ9bPYolpHLy3qNn0fDv48RqBrTvoRrqh1ZSfKvOQ2dX/6r9AaTEXMSm9a1u+DzYXvySanOv0ZoYXjezMS+pucun3RHHx6UuTiz4f2N7heDIT+tqleHzR1vgdFDnV46PMMfu/ctK7Py+ZUra9NLr48aB3QOy8aJ3cAy2MW087HQk2tN/LuOUjrMKigrleL/7Ufmo/hVJ+XL7cMvzl74fHWqV2sMrPSL64/Zww3n9FcztGfZ5r3znhNbn7k/wW13lRq9ebd05d+qRkDmtdSUD6Ul47w9igy8vpSkfsDLhlS8R/xh3P8VwkvcxplctShpPcryqnpFjw1/eWlq3f6mY9Mhk6ZTEVqJp5o48nYXXEgbsPPbu4B1j0lSt9U0l+JdX9H24faAVoPnU2nDEIX62LMgpjdtD7em3O0ZRLLM710xrcDNXJPvIm18rzvPWwvz/x2Cn0r/5KE5vrnIhX9QmSyvstn5lUEPSjuwFEuSH/vG+CZespm0Qm0U489RjpHRZGS/vp5iYg+xoXrki4RoUdLFeXISTnCM0lxCe2o0LcejvCJ2umX+w7yfH6YZ5cC8QusC9XqIFdqTqqWQ6onmBmIUP/bEKH9SlyBv1dU2S1pa0PSDN9BUaLX1rPqk2Ar57gwXzNexDyYztQtVLsUo3qze1idiW2UcqET79X4YQV+aEnZxrd1gnH3VFTnDucVNOdKJns/dyx03pP0IKPZMB8f1fHzooLXwqP/d0vRdy1J90GWCLPtAe7nTZFeonSzh9LTucrqvO2dCmn1V5tE05ysNONAn5Gs3hNI1Lgrn/10DpLL1cQldOy5TicyudMiIyclfn5OPE5DhB695fvq01OOypyVZO7xJfLCQ5aFB50BI82ApTBkJVH24fmFrZ31/+tjs3B07erOr69ef3B969Nb6v8BeV/8WPxEXIK17zfiUxj/LXEInH4v/iT+Kv7W+F3jj40/N/5CTd87pzA/EoV/jb//F663VYs=</latexit> ✓(k+1) = ✓(k) 1 rf(✓(k)) <latexit 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˜ f(z) <latexit sha1_base64="+mn5/F2T4fq+jafTzcdX4rHQt+8=">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</latexit> Problem: ˜ f does not satisfies P- L <latexit sha1_base64="BtmxpjnwGvHetT4vYBO09IOFb6M=">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</latexit> For Im(z(0)) = 0 mod 2⇡ , |z(k)| ! +1.
  18. <latexit sha1_base64="LatEwajuaiTfHvX05LOR/IrfgD0=">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</latexit> ! repulses spurious minima at +1 <latexit sha1_base64="KrT/DckhDtD02cZai6tlUgwCMZU=">AABFEnictVxtj9u4EWaub9f0Ldd+7Bdd91IkRS7dbNMX4FDgkvVmsxcncWLvJndxEki27HUiW45lOy8+/4uiP6YoUBRF+6l/oD+gQPupf6EzQ1KkbEpDba8Rdpei+MwMR+RwZkglmiajbL67+49z733t69/45rfe//b573z3e9//wYUPfniSpYtZLz7upUk6exyFWZyMJvHxfDRP4sfTWRyOoyR+FL3cx+ePlvEsG6WTzvztNH46DoeT0WDUC+dQ9fzC7vhSd5LOxqvu/HR9ORhcgr+Xg24SvwpU/SSMklA9WD/be35hZ/fqLv0LtgvXVGFHqH+t9IMP/ym6oi9S0RMLMRaxmIg5lBMRigyuJ+Ka2BVTqHsqVlA3g9KInsdiLc4DdgGtYmgRQu1L+D2EuyeqdgL3SDMjdA+4JPAzA2QgLgImhXYzKCO3gJ4viDLWltFeEU2U7S38jRStMdTOxSnUcjjd0heHfZmLgfgN9WEEfZpSDfaup6gsSCsoeWD1ag4UplCH5T48n0G5R0it54AwGfUddRvS839RS6zF+55quxD/JikvwhWItup9mlMIxZLoB/Q2F/BMypMA5yFQiFUfsfSadD2m3k+g/Qrq78G1ppLWSQTXimrXlch9uFzIfRZ5CJcLecgim3C5kE0W2YLLhWwpJGJnpHM3vg2XC99mOT+Ay4V8wCIfwuVCPmSRJ3C5kCcs8gu4XMgvWOQtuFzIWyzyDlwu5B0W2YHLheywyGO4XMhjFnkAlwt5oJDlM3UGV0p0RsysvAHlIg+0FAnU3GDlu0nW0YW96TGneyVYflY34K8b2/DQaVyCPfAYd4MSLD/yDsFGurG8LbpNq4kLe5vFHsEIcGOPWOxn4kUJ9jOPmfayBMvPtSa0c2N563sX7tzYuyz2HpTcWH6Nug81bux9jxVjWoJtsdgH4lUJ1sfqz0qwvN1vg11xY/l1qgPt3Vgfa7oowfL29AQ8GDeWX60eQa0b+4jFPhZvSrCPWeznYN3d2M89Vth3JVi9xp6nFWRI/kgMM7aKWpjPSixNgVrI8E/ytSUh3ziCeg4zzDFDwoxZxGGOOPRENHNE01uuLLejGfm7PJd2jmh7IqJ8bcLSnG3fz9tjKfFANHJEYwNR5ZHiu9Z9WZJ3oWs45DxfubDk06c0t99YitV4qLa8GnG/gJBj+5RG/hWKljCCQk1VUTvN13iJDOi+CvGaojfdS82Dx81zq2Cj3rCoyIGKWNRbB+oti1o4UAsWtXSglizKzHwb1/UYAUb/+C5WdCdHgPSRy68AvIIbsOrchjkawPhpgRf4kGruw982xd7cVSUZRvO4TmKW42nBEs+gtBI7UG+iwgbF1wnNsBgkky3vqxgf7zC3sVJzTlrhdb6SB3nGxJ/OiOQZ5nTQWwxoPtWjc4dq1uTdyVI9/O183utSPfwBaXxNXrws1cPPlfTzM8jeUdjOGbBtmE1TpX1TrktD5l8kDV0+T6suWlx8q2M1ZpDem5r0j9SbOTrDe9mnktSPKdejkVn9ywr9q0PD6Dmz9FyPCnpP0uvVpaB2TyYq7jXlujKktIpOlBzmru6bwTZ99WZ0uR6NFnhc+xRzr6xy3dE7zXtjyvVonAiZ91yTJ6/L9WgM6V7qw5Tr0cBsS6jifFOua9lRAzJ2NuW6Vn1CWWDMAckxL2uMVzQjP2mhqI3IP6jO1tg+//Y6hjmbZ3mMUE3J+LbldKJ8LauWSPsLMVi1eU050L9YWD5YkcZK7LHxlZRhXljft+mYNR413wQtBjD75R4AlzNPQEKdk0DrnQDFa2zUVeyZxu2xOBwlgw1UV9XOWW/R8JVZo2Ldc6rl4jLTW6PHLtnrjMbelHzCJmmW00Oz9A2XUeQ01CxoiKdXR3fv1Hwtan+XxU03ENN8pPVoR0jupFXHqS6tty0dX1S7PHO45J6PGb+YbR4oa4MxT0q2CGWp4mm303kkuw7X1SvC5Ljls4DeKNqrJVmNEe1IZWwUqrPF0htf0b2hfUx7cshD0ujBewwUlamQu2aYRcd8ekAW1ba3HG/Ul87QyXJGVlfb42r00EIPHej6Mc4+rBj3oNSBmOEY7joeUc75XFcpaXwmPs53R1N6g9URfVKwkJqGtDdxwUJWRdmnBSqvAY2jQUbp/jQ26Wh8d4sSH/W75DGxa9HyX6SdW72/HdIYLx/N5ZmYPnHdI64BzRq5qyvvNjlICVbOJ3vkv1b3EvnV4Yg2lOP6zOIs9TKhHf+YItgpecYJzTZudhRb2/mpzSeaU0vovXPczU7JQgZk/wJYn1IakwH92GcH9A66tAgJ2UgfuzPKvRuXrzNix5jx40ZCnmow4y0mW7Yg/pquPbsyGosyYpDrwHpjbGudNMkXjInrTFl3M7erVx9EmnMS9iiRFM1YuUT8L9Nv/aPHyc7WiEAN4xvIlK1zvY+UYhbUUUirfLUN0m1tKT/KZXimpDbrn5Hpo4JkDYq4UB5crfvAuUf3kheOkhnJnW21ketoVTYXKU839Ii9HVAUL+3+UK3AKPcVWiV3aM51aZQMYRTM8yhCt+WyyJt8q3kVqfvRzv4v1I2ui1pDioEwGVypIS6/H1O0ZkuZwKiW4/clzSa31mcbrar5TGgsjq25/CXUfgi/tdz63o9OVLAKN2kMSArmzmhE1gRbLfx43Szw0iNT0zL3hp8Zk7qVXXOW+FpaNxNjL2tTadGoeaOyFrp8FhovLBovPHXYob1Go0Vdry3Rcza26KjdSl9+dbh1alBesJR5j0yjRh5S2rGUH9U+S5WP8TXqHUtrl6UVwmy1dwPsOe+DdM/1zdn9Zb66B+IW+TY98sBk/NKnWToin0vXVkdqkgJyvq7sqz37u1SD3COyoEhZnuPEGSN3nXp0rXNJf6pWtpTsvLEI+tzSa9VG29gulX+xhRzTnMhoXmrEdWoRK/ltOYINi3TV8jkCyvyH5FNJv6M6ZrZbm3cSFPwJE2/KWWV4yUhhQvrnMm9HW9HrkRW/BhQTLpR3HQGt+m8YKUiMziS4PcuM3hCucnInQXq0EdnPbTsld/EmlkRXSeqV+K2HjZFRrxnr9tjSPdZ9+xm0RK2bt+5qwfNLvDly/M6yoxfSqjZWPupq4/5stEK1yhXvq/Sw2OBr9LGgNnZkYaK8IqYrPvHmIiWqx0VifLjU60Ud+etJXkdmuTvlS1m31pSLmQZpY04pXuLOgSLC5d1dcnpzl5l+RFv0IsLa1GQNRwmzcanKD9iWFrNSwUaEZNdza1JirUdl64XhYa8axo5LSxmTFUwEl7uRre0+dAvRCp+NkRR6Qp7sLYsTbZqfwIW/A+GKEjVHnxxiG/zcG2JfHHwFpyJeqbLMbAZUgzahvxGDh6qfxRbVOnplUbfp+3Dw5zECXXPSj2hFrSu7pMxLblP3p/+arMFMxKz0pmX9Pthc+J5sc6rTnxFZOL43I6G/yanbF83BpydFLv585P4G14uB0N821euDps73oMihDg99nsHvnZvW9XnZnKr1tc3Fl4dcB/TOi8bhDmB5zGLa+ViomfVGvnoOaB0GFdT1avG/9kPzMZzq8/LlltE3Zy883rpsF6vMLPrF9eeM4eYzmss5+vNM894Zr8nNT/p/Qa03lVq9+erpo19qxoDmtRIyH8pLJ/H2KDLy+lLB/QGXDKn4j/jTOf6rhFc5jTI56lDS+xXl1HQLnpr+8tLVO/3MRyZDp0ymIjUTT7TpZOy+OBK34Gc/9wDrnhKV31TKv4h1f0fbh9oBWQ+dTZcZhC7VxZQFMbtpfbo352jLJMYzvfKMbwdqcE+8SbV43vcetcczv51C38q/JJFz/a5IRb8QmWzu8pl5FUEPijtwMhekv/cN6Ey9zGbJE2hjjz1GeY5KRkr66+cVIfoUF25KuiKEHi1VlCMn5YjOJMUltKNC33o0wqdqpx/3HfB8fphnlwLxc6oL1eqAKzUnVcsh1RPKDESk/12I0H4prsDfK6rslrS1JWlG76Ao0RvrWfVJsLVzXJivGS9SHkxn6paqXUpRvdk9rM7ENkq5yBPv1fhhBX5oSdmmt/WS4u6ZqM4dLipoLpRM9n7uROi8p9QDRrNhPj6q4+dlBa+lR//vlKLvWJIegiwRZdsD2s+bEb1E6eaApJfnKqvztrcrpNVfbUqa5mSlGQf6jGT1nkCixl357JfnILlcTVxCx57r8kQmd1pk5KTEz8+px2mI0KO3fF99espRWbCSLDy+RF56yLL0oDNgpBmwFIasJMo+PL+wc23z//rYLpzsXb32q6vXH1zf+fSm+n9A3hc/Fj8Rl2Dt+7X4FMZ/SxwDp9+LP4q/ir81ftf4Q+PPjb/Ipu+dU5gficK/xt//CyLqUmg=</latexit>

    m(||✓||)f(✓) 6 ||rf(✓)||2 <latexit 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m degenerates as ✓ ! +1 Local P-Ł Condition <latexit 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Example: <latexit sha1_base64="uMb9TY9H272BhFSDEBpOnE8ZCr0=">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</latexit> f(✓) = |e✓1+i✓2 + 1|2 <latexit sha1_base64="jXOqp+mga4D2gd3Q6AT21lU+iLw=">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</latexit> m(R) = e 2||✓|| <latexit 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f(✓)
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repulses spurious minima at +1 <latexit sha1_base64="KrT/DckhDtD02cZai6tlUgwCMZU=">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</latexit>

    m(||✓||)f(✓) 6 ||rf(✓)||2 <latexit 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m degenerates as ✓ ! +1 Local P-Ł Condition <latexit 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Example: <latexit sha1_base64="uMb9TY9H272BhFSDEBpOnE8ZCr0=">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==</latexit> f(✓) = |e✓1+i✓2 + 1|2 <latexit sha1_base64="jXOqp+mga4D2gd3Q6AT21lU+iLw=">AABE+XictVxZcxu5EYY318a5vMlDHvIyG61T3pTXkRXnqNraqrVFWdZatmmTkr1r2i4eI4r2kEPz8sHlj0nlJZVKnvID8jvyA1KVPOUvpA9ggCEx0xjF8ZQkDAZfd6MHaHQ3MO6Mk8F0tr39j3PvfeOb3/r2d97/7vnvff8HP/zRhQ9+fDxN55NufNRNk3TyqNOexslgFB/NBrMkfjSexO1hJ4kfdl7s4vOHi3gyHaSj5uzNOH4ybPdHg5NBtz2DqmcXfjq89ODj6LMofrr8ZKc1SifDZWt2ulo9u7C1fWWb/kWbhau6sKX0v3r6wYf/VC3VU6nqqrkaqliN1AzKiWqrKVyP1VW1rcZQ90QtoW4CpQE9j9VKnQfsHFrF0KINtS/gdx/uHuvaEdwjzSmhu8AlgZ8JICN1ETAptJtAGblF9HxOlLG2iPaSaKJsb+BvR9MaQu1MnUKthDMtQ3HYl5k6Ub+nPgygT2Oqwd51NZU5aQUlj5xezYDCGOqw3IPnEyh3CWn0HBFmSn1H3bbp+b+oJdbifVe3nat/k5QX4YpUQ/c+zSi01YLoR/Q25/CM5UmAcx8oxLqPWHpFuh5S70fQfgn1d+FaUcnopAPXkmpXpchduHzIXRG5D5cPuS8iD+HyIQ9FZB0uH7KukYidkM79+AZcPnxD5HwfLh/yvoh8AJcP+UBEHsPlQx6LyK/g8iG/EpE34fIhb4rI23D5kLdFZBMuH7IpIo/g8iGPROQeXD7knkYWz9QJXCnRGQiz8jqU8zzQUiRQc12U7wZZRx/2RsCc7hZg5Vldg79+bC1Ap3EBdi9g3J0UYOWRtw820o+VbdEtWk182Fsi9gBGgB97IGK/UM8LsF8EzLQXBVh5rh1COz9Wtr534M6PvSNi70LJj5XXqHtQ48feC1gxxgXYuoi9r14WYEOs/qQAK9v9BtgVP1Zep5rQ3o8NsabzAqxsT4/Bg/Fj5dXqIdT6sQ9F7CP1ugD7SMR+Cdbdj/0yYIV9W4A1a+x5WkH65I/EMGPLqLWzWYmlMVBrC/yTbG1JyDfuQL2E6WeYPmGGImI/Q+wHIg4zxGGwXNPMjk7J35W5NDJEIxDRydYmLM3E9r2sPZaSAEQtQ9TWEGUeKb5r05cFeRemRkLOspULSyF9SjP7jaVYj4dyy2sQ93IIHtunNPIvU7SEERRqqozaabbGMzKi+zLEK4reTC8NDxk3y6yCi3otojoeVEdEvfGg3oiouQc1F1ELD2ohouzMd3GtgBFg9Y/vYkl3PALYRy6+IvAKrsOqcwvmaATjpw5e4AOquQd/GxR7S1eZZBjN4zqJWY4nOUs8gdJSbUG9jQprFF8nNMNikIxb3tMxPt5hbmOp5xxb4VW2kkdZxiSczoDk6Wd00FuMaD5Vo3Obalbk3XGpGv5WNu9NqRp+jzS+Ii+eS9XwMy397AyyNzW2eQZsA2bTWGvflqvS4PwL0zDl87TqosXFtzrUYwbpva5I/0C/mYMzvJddKrF+bLkajanTv2muf1VoWD1PHT1Xo4LeE3u9phRV7slIx722XFWGlFbRkZbD3lV9M9imp9+MKVejUQePa5di7qVTrjp6x1lvbLkajWPFec8VefKmXI1Gn+5ZH7ZcjQZmW9o6zrflqpYdNcCxsy1XteojygJjDojHPNdYr2hCftJcUxuQf1CerXF9/s11DHM2T7MYoZyS9W2L6XSytaxcIuMvxGDVZhXlQP9i7vhgeRpLtSPGVyzDLLe+b9Kxazxq/hC0GMHs5z0AKWeegIQmJ4HWOwGKV8WoK98zg9sRcThKTtZQLV07E71Fy5ezRvm6Z1QrxWW2t1aPLbLXUxp7Y/IJD0mzkh4OC99wEUVJQ4c5Dcn0qujurZ6vee1vi7jxGmKcjbQu7QjxTlp5nOrTesPR8UW9yzODi/d87PjFbPOJtjYY86Rki1CWMp5uO5NHcutwXb2sbI6bn0X0RtFeLchqDGhHaipGoSZbzN74ku4t7SPak0MeTKML7zHSVMaKd80wi4759IgsqmtvJd6oL5Oh4/KUrK6xx+XovoPue9DVY5xdWDHuQqkJMcMR3DUDopzzma5S0vhEfZLtjqb0Bssj+iRnIQ0NtjdxzkKWRdmnOSqvAI2jgaP0cBrrdAy+tUFJjvp98tjYNW/5L9LOrdnfbtMYLx7NxZmYHnHdIa4RzRre1eW7dQ4swdL7ZIf81/JeIr8qHNGGSlyfOpxZLyPa8Y8pgh2TZ5zQbJNmR761m59af2I41ZXZO8fd7JQsZET2L4L1KaUxGdGPe3bA7KCzRUjIRobYnUHm3fh8nYE4xqwfN1B8qsGOt5hs2Zz4G7ru7JrSWOSIgdeB1drYNjo5JF8wJq4Tbd3t3C5ffRBpz0m4o4Qp2rFyifh/TL/NjxknWxsjAjWMb2CqbZ3vfaQUs6CO2rTKl9sg09aV8qNMhqdaarv+WZk+yklWo4gL5cHVugecu3TPvHCUTEju6UYbXkfLsrlIebymR+ztCUXxbPf7egVGuS/TKrlFc65Fo6QPo2CWRRGmrZRFXudbzitPPYz29P9C3eo6rzWkGCmbwWUNSfn9mKI1V8oERjWP3xc0m/xan6y1KuczorE4dOby11D7Ifw2cpv7MDqdnFW4QWOAKdg7qxGuiTZahPG6keNlRqahZe8tPzsmTSu35izxNVs3G2MvKlOp06h5rbMWpnwWGs8dGs8DddikvUarRVNvLNEzMbZo6t3KUH5VuDUrUJ6LlGWPzKAGAVK6sVQY1Z5IVY7xDeqtSGtbpNWG2eruBrhzPgTpn+vrs/vrbHWP1E3ybbrkgXH80qNZOiCfy9SWR2pMATlf0/bVnf0tqkHuHbKgSJnPceKM4V2nLl2rTNJf6JUtJTtvLYI5t/RKtzE2tkXlX28ghzQnpjQvDeIatYi1/K4c0ZpFuuL4HBFl/tvkU7HfUR4zu63tO4ly/oSNN3lWWV4cKYxI/1Lm7WAjej1w4teIYsK59q47QKv6G0YKjDGZBL9nOaU3hKsc7ySwR9sh+7lpp3gXb+RIdIWkXqrPAmwMR712rLtjy/TY9O2X0BK1bt+6r4XMLwnmKPE7y45em1a1ofZRl2v3Z6PV1qtc/r5MD/M1vlYfc2rjRhY2ystjWurTYC4sUTUujAnhUq0XVeSvJnkVmXl3KpSyaW0o5zMNbGNOKV6SzoEiwufdXfJ6cx8L/ehs0OsQ1qXGNRIlzMalOj/gWlrMSkVrEZJbL61JibMeFa0Xloe7alg7zpYyJiuYKCl3w63dPrRy0YqcjWEKXcUne4viRJfmp3Dh70j5okTDMSSH2AA/97raVXvv4FTES13mzGZENWgTemsxeFv3M9+iXEcvHeou/RAO4TwGoGtJ+gGtqFVlZ8qy5C71cPqvyBpMVCxKb1tW74PLRe7JJqcq/RmQhZN7M1Dmm5yqfTEcQnqS5xLOh/c3pF6cKPNtU7U+GOpyD/IcqvAw5xnC3rltXZ2Xy6lcX5tcQnnwOmB2XgwOdwCLYxbbLsRCTZw38u45oHU4KaFuVov/tR+Gj+VUnVcotyl9c/Y84K1zu1hnZtEvrj5nLLeQ0VzMMZxnmvXOek1+fuz/RZXeVOr05t3TR7/UjgHDa6k4HypLx3h3FFl5Q6ng/oBPhlT9R/39nPxVwsuMRpEcVSiZ/YpiaqaFTM18eenrnXkWIpOlUyRTnpqNJxp0MnZXHaib8LObeYBVT4nyN5X8F7H+72h7UHtC1sNk0zmD0KK6mLIgdjetR/f2HG2RxHiml8/4NqEG98QPqRbP+96l9njmt5nrW/GXJDzX76hU9XKRyfoun51XHehBfgeOc0Hme9+IztRzNotPoA0D9hj5HBVHSubr5yUhehQXrku6JIQZLWWUO17KHTqTFBfQ7uT61qURPtY7/bjvgOfz21l2KVK/orq2Xh1wpZakqnukekyZgQ7pfxsitN+oy/D3si77Ja1vSDqld5CX6LXzrPwk2Mo7LuzXjBcpD2YydQvdLqWo3u4elmdia4Vc+MR7Ob5fgu87Ujbobb2guHuiynOH8xKacy2Tu587UibvyXrAaLadjY/y+HlRwmsR0P/bhejbjqT7IEuHsu0R7edNiF6idbNH0vO5yvK87a0Sac1Xm0zTnqy048CckSzfE0j0uCue/XwOUsrVxAV03LnOJzKl0yIDLyV5fo4DTkO0A3or9zWkpxKVuSjJPOBL5EWALIsAOieCNCcihb4oibYPzy5sXV3/vz42C8c7V67+9sq1+9e2Pr+h/x+Q99XP1M/VJVj7fqc+h/FfV0fkZfxR/UX9tbas/aH2p9qfuel75zTmJyr3r/a3/wKmnEhh</latexit> m(R) = e 2||✓|| <latexit 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f(✓)
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repulses spurious minima at +1 <latexit sha1_base64="KrT/DckhDtD02cZai6tlUgwCMZU=">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