relu_experiments.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d11d41da-e777-4652-8606-8021ef2e7313",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tqdm import tqdm\n",
    "\n",
    "rng = np.random.default_rng()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "41bd8949-bb1f-4e57-9ab0-dfe293eb9e31",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "n = 1000 # number of pure points\n",
    "m = 40 # number of corrupted points\n",
    "\n",
    "d = 10 # dimension of noise\n",
    "\n",
    "l = 100 # number of hidden neurons\n",
    "\n",
    "C = 1 # SNR\n",
    "D = C # loss margin\n",
    "\n",
    "test_n = 10 # number of test points\n",
    "\n",
    "use_bias=True\n",
    "\n",
    "EPOCHS = 100 # number of training steps\n",
    "BATCH_SIZE = 1 # batch size\n",
    "LR = 0.01 # learning rate\n",
    "DROPOUT_RATE = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1efd92e3-66ed-4d37-bd78-301e93dbe562",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize parameters\n",
    "\n",
    "X = rng.standard_normal(size=(n+m,d+1))/ np.sqrt(d)\n",
    "\n",
    "\n",
    "y = np.zeros((n+m,1))\n",
    "y[:n//2] = 1\n",
    "y[n//2:n] = -1\n",
    "y[n:n+m//2] = 1\n",
    "y[-m//2:] = -1\n",
    "\n",
    "X[:,0] = C*y.squeeze() # set signal dimension\n",
    "\n",
    "y_train = y.copy()\n",
    "y_train[-m:] = -y_train[-m:]\n",
    "y_train[y_train < 0] = 0\n",
    "\n",
    "X = torch.tensor(X, requires_grad=False)\n",
    "y = torch.tensor(y, requires_grad=False)\n",
    "y_train = torch.tensor(y_train, requires_grad=False)\n",
    "\n",
    "W = torch.tensor(rng.standard_normal(size=(l,d+1)), requires_grad=True)\n",
    "a = torch.tensor(rng.standard_normal(size=(1,l)), requires_grad=True)\n",
    "\n",
    "if use_bias:\n",
    "    b = torch.tensor(rng.standard_normal(size=(l,1)), requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "65cb3cd8-16ea-4a5a-a4f3-9caf0f9b3b04",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████████████| 100/100 [00:41<00:00,  2.43it/s]\n"
     ]
    }
   ],
   "source": [
    "# train\n",
    "\n",
    "relu = torch.nn.ReLU()\n",
    "drop = torch.nn.Dropout(p=DROPOUT_RATE)\n",
    "\n",
    "if use_bias:\n",
    "    optimizer = torch.optim.SGD([W,a,b], lr=LR)\n",
    "else:\n",
    "    optimizer = torch.optim.SGD([W,a], lr=LR)\n",
    "\n",
    "# cross entropy loss\n",
    "#loss_fn = torch.nn.BCEWithLogitsLoss()\n",
    "# hinge loss\n",
    "loss_fn = lambda output, y_train : torch.sum(relu(D - (2*y_train-1)*output))\n",
    "\n",
    "losses = np.zeros((EPOCHS,))\n",
    "\n",
    "def model_forward(X, test=False):\n",
    "    preactivations = W @ torch.t(X)\n",
    "    if use_bias:\n",
    "        preactivations = preactivations + b\n",
    "    if not test:\n",
    "        preactivations = drop(preactivations)\n",
    "    return torch.t(a @ relu(preactivations))\n",
    "\n",
    "for i in tqdm(range(EPOCHS)):\n",
    "    indices = np.arange(n+m)\n",
    "    rng.shuffle(indices)\n",
    "    indices = indices.reshape((BATCH_SIZE,-1))\n",
    "    \n",
    "    e_loss = 0\n",
    "    for j in range(indices.shape[1]):\n",
    "        batch_inds = indices[:,j].squeeze()\n",
    "        optimizer.zero_grad()\n",
    "        X_batch = X[batch_inds,:].reshape((-1,d+1))\n",
    "        \n",
    "        # infinite uncorrupted training set, seems to work better\n",
    "        # comment out if undesired\n",
    "        if batch_inds < n:\n",
    "            X_batch[1:] = torch.tensor(rng.standard_normal(size=(1,d+1))/ np.sqrt(d), requires_grad=False)\n",
    "            \n",
    "            \n",
    "        output = model_forward(X_batch)\n",
    "        loss = loss_fn(output, y_train[batch_inds].reshape((-1,1)))\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        e_loss += loss.detach().numpy()\n",
    "        \n",
    "    losses[i] = loss_fn(model_forward(X), y_train)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "df2531c7-2814-4db3-982d-6f1ff57eee79",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.311455928327906\n"
     ]
    },
    {
     "data": {
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IFI/1xE+GBQVpkYyZquYuiuyIvdAWeS1BoIyEszvV6xaN3JVh6ZqkBdVRee4iMhdYDWwGiowxzlbPKqDIvjwLOBZ1t3J7rP9j3SQiW0RkS21t7WjnfVIsKEjnSH07vaEwNS3dEXHPTfXhdolG7sqIOIKeleJVz10ZFicQSLjI3UFE0oE/A58xxsQ0JzVWu6NRdbkwxtxhjFlnjFlXUFAwmrueNAsK0ukNGfZWtdLaHYyIu8sl5Kf71HNXRsSxZTJTvBq5K8PSNUkF5uISdxHxYgn7vcaYB+zhasdusX/X2OMVQGnU3UvssYRhQaGVDumUIXA8d4CCDM11V0bGicYyAxq5K8MT8dwTzZYREQHuAvYYY34QddPDwA325RuAh6LGr7ezZjYAzVH2TUIw306HfPlAPWDluDsUpPvVc1dGJNqW0chdGQ4nBbJrgv9P4tnEdDZwHbBDRLbZY18Gvg3cLyI3AkeA99u3/R24DCgDOoAPj+WEx4LMgJfCDD+vHrJa8BVGiXthRoBdx1uGuquiAGrLKPEzWZH7iOJujHkRkCFuvmiQ4w1wy0nOa9yZX5DGpoOWuPe3ZeraugmFTWTjk6L0xxH0zICHUNjQGwrjdU+LPYHKKOlK9AXVZMMpQ5Dmc5MR8EbGCzP9hA00DFLB7buPvcXNv9k6YXNUEhcnCstMsf53NHpXhqIrqLVlJhRH3IuiLBno28hU09pFQUZfRB8Mhfnd5qM0dfbS0N5Dbppv4iarJBx9kbsl7l29IdL90/btpAyDI+o9GrlPDE7GTGGUJRN9vX/GzNYjjTR29GIMvLB/YvPylcQjekE1+rqi9Cdhd6gmK04BsRkDInenvkysuD++uxqf20VWipfn99WhTG+6gyHcLiHNb1UP1XRIZSgi2TJqy0wMM7NSyE/3RewZB8eKiY7cjTE8vruKsxfmkeb38ML+WowxWFmiynSkuzeM3+PC73FHrivKYExW5D5txd3lEh77zHmkB2L/BCk+Nxl+T4y4v1XVyrGGTj6xcSFul/C37ZW8VdXKsuLMiZ62kiB0B21x91pffru0YYcyBH3irpH7hJGX7h90vDDTz+7jLZHo/Ind1YjARcsKCdsfvs/vq1Vxn8Z0B0P4PW4CGrkrI+DYMr0hM6Ep1tPWcx+Oa8+Yw6uHG/jZswcAeHx3FWtm51CYEWBGVoAlRRk8r4uq05ruYBi/VyN3ZWS6Jqklo4r7IHz47LlcuWom33t8L7/ddISdFS28bXlR5PbzFufz2qFGOnqCkzhLZTLp89xdkeuKMhjR/xsT+X+i4j4IIsK33nMqy2Zk8tW/7ATg7THiXkBPKMxme4erMv2I2DJed+S6ogxGV28oYsVM5KKqivsQpPjc3HH9WnLTfCwuSmd+VFbN6XNz8XtcPLdPrZnpSmRBVSN3ZQS6ekOR/RATmQ45rRdUR6IkJ5W/feocwia2VH3A6+aM+Xk8r+I+bemxPXeN3JWR6AqGKcwM0NDeo5F7IjEzO4WSnNQB4xcuKeBgXTsH7V6syvTCitzdkch9ojvbK1OD3lCYUNhE7WTWBdWE52Lbg39qT80IRyrJiOW5a+SuDI9jw2SnOraMRu4JT0lOKsuKM3lid/WQxxhjtKtTkuJ47h6X4BKN3JXB6bTFXSP3KcbblhWy5UjDoOWBAR5+8zhnfuspalq0J2uyYaVCuhER/B63Ru7KoDgL7dmOuCdS5C4ivxKRGhHZGTX2XyJSISLb7J/Lom67VUTKRGSviFwyXhNPBN62fAZhA0+/Nbg189C24wTDhsP1HRM8M2W86Q6GIhuYAl6XRu7KoHT1i9wncrNbPJH73cClg4zfZoxZZf/8HUBElgNXAyvs+/xMRNxjNdlEY+WsTGZkBnhyEGumrTvIi/ut6pGVzZ0TPTVlnHFsGUAjd2VInA/9zESM3I0xzwPx7ta5Avi9MabbGHMIq4/q+pOYX0IjIly8vJDn99cOyF99dm8NPSHrhaxsVlsm2XCyZcCK3BO9nrsxZsKbRSh9kfpk1P0/Gc/9kyKy3bZtcuyxWcCxqGPK7bEBiMhNIrJFRLbU1k7dfPGLlxXR0RPilQP1MeOP7qwiL81Hht9DlYp7UhG009uiI/dEr+f+6M4q1n3jCS2ZMcH0ZctYndumwoLq7cACYBVQCXx/tA9gjLnDGLPOGLOuoKDgBKcx+Zy5II80n5sn9vRZM93BEM/ureVty4sozg6oLZNkONFXtOee6JH7vuo2WrqC1LcNvvivjA+OLdO3QzXBI3djTLUxJmSMCQO/pM96qQBKow4tsceSFr/HzflLCnh8VxVNHdYb5+Wyetq6g1yyYgYzslI0ck8yIuJu2zJTIXJvtP83W7s0cp9I+i+oJnzkLiLFUVffDTiZNA8DV4uIX0TmAYuAV09uionPR8+dT0tXkI/c/RqdPSEe21VFut/DWQvzKM4MqOeeZDhvUJ9jy0yByN0JPNq6VdwnEkfcU31uvG6Z0P+TEWvLiMh9wEYgX0TKgf8ENorIKsAAh4GPAxhjdonI/cBuIAjcYoxJ7JBmDFgzO4cfXb2aT9y7lU/cu5Xt5c1sXFKA3+NmRlaA2rZuekNhvG7dVpAMOBkP0Z57XYLbHU2dvQC0dvVO8kymF11RFl5ggr/hjSjuxphrBhm+a5jjvwl882QmNRW5dOUMvvnuU7j1gR0AXLJiBgDFWQGMsRpuz8pOmcwpKmPEAFvG60r4VMjGDkfcNXKfSLptMQ943RP+DU+rQo4h16yfTXNnLw+8Xs4FSwsBKLYFvbKpU8U9SXCE3IncAx53wpf8dWyZVrVlJhQnUk/xuq39EBP4f6LiPsbcfP4Cbj5/QeR6cVYA0Fz3ZKJ/tsyUiNzbnQVVtWUmkq7eMG6X4HVbLRkTbYeqchLMsMVdM2aShz7P3d7ElOCReyhsaLHtGLVlJpbO3hCB6J3MiZ4KqcRPht9Dms99UpF7OGy45Lbn+d5je8dwZsqJ0t+WmeiIbLQ0d/ZF620q7hNKV28oUhba75nYb3gq7uOMiDAjK0BVy4lvZNp8qIG91a386qVDNHfo1+rJZsAmJo+b3pAhFDbD3W3ScHLcQW2ZiaarNxwR94DXpZF7slGclXJSkfvDb1bg87jo6Anx281HxnBmyonQF7n3ZctEjycaTVHirnnuE0tXVPXQiS4wp+I+AczICsTluXf1hrj1gR1sL2+KjHUHQzyyvZJ3nlLMuYvyufvlwwkrItOF/nnugQRvkt1kf9tL8boj3rsyMXT3hgh4om0ZjdyTiuKsADWt3QRDw7+wv3juIPe9epQv/HF75Njn9tbS0hXkilUzuem8+dS2dvPQG8cnYtrKEPTluTueu/XmTVTf3clxL81N0QXVCcayZfr+T1Tck4wZWQFCYUNt29At9441dPCzZ8uYn5/G3upW/rDFKq750Lbj5KX5OGdhPucszGdZcSZ3vHCQcIL6u9OBiC0TtVAGiRy5W7bM7NxU2rrVc59IohdUAx7XhO5QVXGfAGZm2RuZhrFmvvHIblwi/PajZ7B+Xi7ff3wfx5s6eXJPNZefWozH7UJEuOm8eZTVtPHsPm3MPVn09IvcAwkeuTd19OJ2CcVZGrlPNF3BqGyZCd6hquI+AYyU6/7cvloe21XNJy9cyMzsFP7j8uU0dvRw3V2b6Q6GuWJ1X0n8y0+dSWGGnz9vTepimwBUt3Rxz8uHMSaxvqV0B8O4BDwuARI/cm/s6CErxUtmiofWrmDC/T2TmRhbxuOOlCOYCFTcJ4Dhdql29Yb42sO7mJuXykfPnQfAyllZvG9tCQdq25mdm8rq0uzI8V63i1Wl2bxV1TIhc59M/vx6Of/58C6ONSRWPXynC5OIJe5OZJaolSGbOnrJTvWS7vcSChvt9zqBdEUtqAa8rkghsYlAxX0CyErxEvC6qOrXtCMcNnz+/jc5VN/O169YGUmtA/i3S5aQleLl/etKIiLisLgog8P1HUnfNq2mxVqjKKttneSZxNLd25feBn2Re6LWdG/s6CEn1UdGwKo2ornuE0dXb5iAr6/ufyhsRkysGCtU3CcAERk01/27j+/lkR2V3PqOpZy3OLYbVWFGgJe/dCGf2LhwwOMtKkonFDYcqmsf13lPNtUt1t9rf3XbJM8klujm2DA1IvecVG+fuI9hrvs/dlROi2+RJ0r/VEiYuP8TFfcJYkZmbK77fa8e5fZnD3DtGbP52LnzB71Pmt+DyyUDxhcVZgCwrzqxItqxJiLuNYko7n3fshI9cm/q6CErJTpyHztxv/XBHdz+7IExe7xko7M3FPHcIwvvE/R/ouI+QRRn9XVkevjN43z1Lzs5f3EBX3vXigG2y0jML0jDJbA/6cXdsmUST9xDkxK5v3msib1Vo3/NGyORu9XqbaxsmWAoTFNHL0cbOsbk8ZKNYChMMGxiasuARu5Jx4ysANUtXfzfS4f49O/fYO2cHH567Ro8J9CdKeB1MzcvjX397IqKpk4O1iaWEJ4oxhhqWq0PwwM1bQmV4dHdG54Uz/1LD+zgG4/sHtV9unpDdPaGyEnzke63IvexKh7mdHc6puI+KM7iaSCqNDQkkLiLyK9EpEZEdkaN5YrIEyKy3/6dY4+LiPxIRMpEZLuIrBnPyU8lirNTCIYNX/vrbi5eVsSvP7I+8mY7ERYVpbO/JjaK+7f73+Sj92w52akmBI0dvfSGDAsK0mjrDlLVkjglkwfaMhMTude0dI1aSJ2KkNnRnvtYibu9OaqurYf2capZs728ieX/8SiVzYmVMRUPXVFdmICI955ItszdwKX9xr4EPGWMWQQ8ZV8HeAdWU+xFwE3A7WMzzanPnNxUAN6/roTbr10TecFPFCdjxtkt2d4dZMuRBg7WtUe8aoeymjbufOHglHqDOOdwzsJ8ILEWVfvbMk5ENp5v2mAoTENHD8ebu0a1O9mpCJmd4ovYMi1jZMs0tPc9zrHG8Yne3zzWREdPiIO1Uy95ICLuAwrMJUjkbox5HmjoN3wFcI99+R7gyqjxXxuLTUC2iBSP0VynNOcszOfhT57Nd9576glZMf1ZWBibMbP5UD29IetN/+qh2Jfrtif28Y1H9nD2t5/mI3e/xssH6gY8XlVzF195cEfClBR2xP1sR9wTyHfvny0zEV5qQ0cPxli7Y+vahy5j0Z9GW4BzUr19tswYRdkN7X3VJo/Wj4+4lzdZAUl9e2I3IB8MZz9BdFVIYMI2Mp2oyhQZYyrty1VAkX15FnAs6rhye2wAInKTiGwRkS21tbUnOI2pg8slnFqSPerF06FYXORkzFii98L+OvweF6k+d4y4B0NhXthfy8XLiviXjQvYUdHM9Xe9GvPGBHhoWwX3bj7Klx/ckRD+tpPjvqw4k5xUL2U1ibN43N0bxhcl7iJiVfwbxzdtXWvf63W8KX6LqrnTjtxTfbhdQprPPWa2THSd+PFaVK1otMS9YZi6TIlKf1tmyi2oGksJRq0Gxpg7jDHrjDHrCgoKRr6DEsP8gjTcLqHMzph5qayO9fNyWTsnh9cO94n7tmNNtHQFeffqWXzhkqX8/ENrCIYNmw/Wxzze5kMNuAQe2VHJH7eWT+i5DIYTuRdm+llUmEFZQkXuoRjPHca/nGtdlLgdb4rfXnMqQuakWZZMesAzZguqjrgHvK5xW1StsM+1fzAyFXAs075mHYnnuQ9GtWO32L+dKlYVQGnUcSX2mDLG+D1u5uSlsq+6jeqWLvZVt3HOwnzOmJfLW1WtkcWu5/bV4pI+7/rUkmxSfW5eiRL3UNjw2qEG3r+ulDPn5/FfD++a9A1S1a1d5KR68XvcLCxKZ1914mTM9LdlwHrjjmed/Whxd6LZeIj23AEyAl5ax6gyZGN7DyleNwsK0sc9cp/KtkxfD9WpEbk/DNxgX74BeChq/Ho7a2YD0Bxl3yhjzOLCDPbVtPLifstDP2dRPqfPzQXgtcONgCXua2bnkJVqRW5et4t1c3PZFCXueypbaO0OcuaCPH7wgdPwul186r7X+fPWch7ZXskL+2snvIVcdUs3RZlWTZ5Fhek0d/ZS1za6N/h4fRh0B2NTIcHuozqONVsccfe6JRLNxkNTRy9+j4sUewt8RsAzZrZMQ3svuWk+Zuemjou4d/WGqGnttp9rKop7f1tmYncyx5MKeR/wCrBERMpF5Ebg28DbRGQ/cLF9HeDvwEGgDPgl8IlxmbUCWOmQR+o7eHpvDXlpPpbNyOS00mx8bhevHqqnrq2b7eXNnN+vtMGG+bnsq26LCIYj9Ovn5VKclcJ33nsqb1W28vk/vsktv3ud6+56lQden1irpqali0Jb3BcWpgMMSP0cjo6eIKd/80ke2jb2Xxy7ewfaMoFxbqFW19aDz+NiXn7aKMXdqivjkO4fKO4n+iHY2NFDdqqX2bmpHGvsHPMeA9HlOqZ05B7VQ9UaTxBbxhhzjTGm2BjjNcaUGGPuMsbUG2MuMsYsMsZcbIxpsI81xphbjDELjDGnGGOSI+k6QVlUlEEobHhsZxVnLczH5RICXjerSrN59VADL+y3FqrPXxIr7mfOzwP6RH3zoQZm56ZSbNedv3TlDLZ89WKe+8JGHvvMeczNS+Uv4yCSw1Hd0k1Rhh/oK7dwYBS++57KFuraenjwjXEQ90FsmbGM3I/Utw/IaKlr7aYg3c+s7JRRe+7Z9rc2gMyAN2aH6p7KFpb8+6McPgEbrrGjh9w0H6W5qfQEw5Eoe6xwLJmcVO+UjtxTEjVyVxKXxUVWRBsMG85ZmBcZXz8vl53HW3hkexV5aT5WzsyKud8ps7JI93vYdLCecNjw2uEGzpiXG3NMdqqPOXlpLJmRwbtWzeLlA/XUnORGongjRKdrlWPLFGX6yfB7RpUOubvSivJfPlBPR8/YbbBxtpQPXFAdm8g9HDZc8dOX+PHT+2PGa9u6yU/3MStndOLeZEfXDv1tmW3HmugJhk+o+Fdju/WtYLa9h2OsrZmKJuvxTinJpnEKintnxJbpv0M1QSJ3JXGZl29lzACcs6gvOl8/L5dQ2PDknmrOW1wwoPiYx+3i9Lk5vHKgnr3VrTR19HLG/DyG4opVMzHGqokzHI3tPfz0mTLO/vbT/Pff9wy4/VP3vcGVP31pxA+J+vZuQmFDUaYVuYsIC4vSR7WR6a1KS6x6gmFeLutbXzDG8Ln7t3H/a8eGuuuw9IRic5cdAmMUuVc0ddLU0TvgW0pdWw/56X5mZqfQ2NEb9weWVVcm1paJ/lZwxM5PH65L2FA0tPdEPHcYB3Fv7MQlsLw4k8aOninXWtKJ3Pu3Y5yoevoq7lMYv8fN3LxU5uenMSs7JTK+Zk5ORPT7++0OG+bncaC2nb9ttwS7f+QezYKCdE6ZlTWkuNe0dvEfD+3kzG8/xXcf20sobPjVi4di0uO2Hmnkb9sr2Xasiff+/OVhbQAnx93x3AEWFqSPKnLfU9nCmtnZpPncPPVWX0vCLUcaeeD1Cr759z0ntFPT6bY0wJYZo8jdWVfo36Ckrq2bfNuWgfjTIa1GHX3inhHw0tETitQUd16jobqEDUUwFKalK0h2qpeZ2Sm4ZOzFvbypk6LMAEWZfsKmr5bNVKG7X20ZEcHncWnkrsTHV965jP9614qYsXS/h5UzMxGBcxflD3q/MxdYkfo9Lx9hVnYKpXb0NRRXrJrJ9vLmmMJkHT1BfvTUfjZ+91l+t/ko7zptJo995jwevOUsXC7hJ0+XRY793yf3kZfm43cfO4P27hDvvf1ldpQ3D/pcTo57UZS4LypKp66tOy5RC4cNb1W1cmpJNucuKuCZt2oiltDdLx8mxeumubOXX714aMTH6o/zhh2woDpGkbvz7eRYY0dkzuGwoaG9h/wMX0Tcy+NIhzTGDLBl0u36Mu3dlsAcabA+ZEdbu8cR2tw0Hz6Pi+KslDHPda9o7GRWdgq5adaHU8ModuYmAl29IUTAF7Uj3drsppG7EgcXLi0a0OgD4Poz53LDmXPJS/cPer8VM7PICFhf0dcPE7U7XH7qTET6rJmtRxq4+PvP8YMn9nHeogKe+Nz5/M9Vp7FkRgbFWSl8cP1s/vR6OYfr2u3F3TpuPn8BZy3I5083n0nA6+ZDd20eNIJ3Sv06tox1noUEvC5u+s2WEbfPH23ooKMnxLLiDC5cVkhVSxe7K1uoau7i0Z1VXHvGbC5ZUcRdLxyK7AcAKxodKapybh+vyN3ZrNXRE4osIjZ29BAKm4gtA/HtUm3rDhIMG3L6ee5g1ZcxxpywLeN44I7lMx7pkBVNnczKSSEvzfo/qB9lKuxk47TYi96Vbv2fqLgrJ8F715YMiOijcbskYsUMZ8k4zMgKsGFeHg9tO87/vXSID/xiEx63iz/efCY/v24t8/LTYo7/xAUL8LqFHz29n9ue2Ed+up8PbZgDwPyCdO772AZE4GO/3jKgvnh1SxcikB/1wbSwMIOfXbuGPZWt3PybrcO2GNxj++3LijPZaGcKPfNWDfduPkLYGK4/cy6ffdtiWruD3PmCFb1vOdzAuf/zDB//zdZh/w7O8w7muY9FRLa/pi1iqTnRuZPfn5/upygzgNslkcXG4WjqcCpC9tkymVGVIZs7eyOLq6O1ZZwPHieqHmtxD4UNVc1dzMpOieyunWoZM9HNsR2s/xO1ZZRx5pyF+Yj0WTQjceXqmRyqa+drf93NxiWF/PVT50Q2TfWnMCPAdRvm8MDrFbxysJ5PbFwQ2UgDMDsvlZ99cA0H69r57B+2xSyW1bR2kZfmx9uvwNqFS4v49ntO4cWyOj53/7Yhq1zuqWzBJVb9ncKMAKeVZPHorirue/UoFy0tZHZeKktnZPLOU4v5v5cOcdsT+/jAHZuob+/h2b21w5Y6GMqW8XvcJ52/bIyhrKaNtXNygL5Ki85+hPx0P26XMCMzEFfk7oh77IKqJZRt3cFI1D4/P42qlq5R5btHdr7a3wpm56VS29pNZ8/YCFd1SxfBsImN3KecuIcGVH8d7zIV0ai4T2Ou3TCHv37yHObkpY18MHDpymJWlWbzxUuXcMd1a8lK8Q57/MfPX0CK101Rpp8PnjF7wO1nLcznP/9pOU/uqeG2J/dFxq3dqYPbSe9bV8r/u3Qpf9teyZnfeprzv/sMX3lwR8zi6O7KVuYXpEfeWBcsLWRnhZX3fsNZcyPHffbiRXT0hvjhU/t5+/IiHvvMeXjdwu82Hx3ynIa0Zbwn/6ataumirTvIhUsLgb5FVUfcCzIskZ6VnRLXRqb+AgzENMl2Iu3183LpCYYjdWjiwTnWidydNZuxKv3rnN+UjtyD4UHEfXw3u0Vz4t0ilCmP1+1i5ayskQ+0yUrx8pdbzo77+Px0Pz+/bi3pfveQ9euv2zCHN48187NnD3DtGXMiHauiF1P78y8bF3DB0gJeKqtn08F67t18lIIMP5+5eDFgZ8rY0S/ARUuL+N8n97OgIC1SYwcsq+frV6zE6xI+cHopIsLbV8zgz6+X88VLlww65+GzZcIYY0648qezmLqqNJucVG9EKGtb+yJ3gFk5KQPKOg+GI+6Dee6tXcGIgK6fl8vvXztGZXNnRKxHomEQzx2s0r+LizKiPgRPrG+Bs4GpJCcFv8dNht8z9cS9NzRIDaLxLVMRjUbuyrhy/uIC1s4Z2tMXET5z8SLCxnDv5iOAFbkXZgweuTssnZHJjefM45fXr+P8xQXcu/koPcEwzZ29VDR1sqw4I3LsipmZXLKiiC9csmSA8F63YQ5Xr58dGb92/WyaO3v5+47BSyJFbJlBvm5H334iOKmeiwrTKclJjfHcvW6JfFOamR2gqqVrxHo/fV2YomwZR9y7gxyt76Agwx9ZLxmN797Y3kOqr+9D2xH3g3Vt3PPyYTb891Pccu8bcT9ef5wPHmcBOTfdNyXFfTIjdxV3ZdIpzU3loqVF/G7zUdq7g9S3d8fkuI/EP581l9rWbh7bVRXZvLSsODNyu8sl/OK6dVy6cuS+MWcuyGNeftqQ1sxQtkykSfZJRGVlNa3kpvnIS/dTmptCeUOf556X5o98AM3KTiUUNgM6bvWnstlamI62zzKjmmQfaWiPKTsxmoyZ/pujnGYg33l0L//58C5CYcPz+2tPeB2ivNH6FpHqsz6MctNixT0cNvz6lcNj1nhkPOgeZEF1LOy7eFFxVxKCfz5rLvXtPdz98mGMYUjPfTDOX1zA7NxU7nn5cCRTZnmUuI8GEeGa9aVsOdLI3qqBhcr6FlQHft0GIk29T4T91W2RImmlduQeDhtrA1NGn5DOzLY++EbK+X96Tw2nz8mNWZj2e1x4XEJblxW5z8lNpSDDWqgd6cMimsaOnogXDtbfbe2cHObmpXLn9ev4/vtX0RMM88bRprgfM5qKps6YjXl5ab6YBdVt5U38x0O7eHjb8LumJ5JDde38049fjHzr6AqGInVlHAJjsPAeLyruSkJw9sI8Fham8/PnDgBQlBF/5O5yCdefOYctRxp58I0KctN8I9o6w3HV2lJ8bhfffWwvL5XVUR9VSz3iufd7056/uIB0v4cvP7gjsvtzOJo7e3n3z16KlGs2xrC/po1FtriX5KbSE7KKcTm7Ux1KcizRG25R9UBtG3urW3nHKTNixkWEjICH+rYeKlu6KM1Nxe0SCjP8o4rcG9pjq00C3POR9Tz1+Y1cvLyI9fNycQkxfQNGQ0VjR4y4W5F73+uwz/7g3VedOB267t10hB0VzfzDtvQ6ewaxZTRyV6YbIsINZ86J5F0Pt6A6GO9bW0qK182b5c0sK844qXaGuWk+rj9zDk/uqebaOzez9htPctXtL9PRExzSlinJSeUbV67ktcON/DhqZ+6B2ja+99jeiP/tcP9rx3jjaBPffnQPxliF0po7eyPiXprj7ETtoK61J0bcHRtlOHF/dGcVYFX47E9GwMtbVS0YA3PyLK+8KDMwOs/drgg5FFkpXlbMzIrpGwBw5wsHuXmEvQTGmMgGJofcND8N7T2RdM29tqgnSoeuYCjMX+xvEc/ts6qxdgWHSIWcoAVVzZZREob3rCnhfx7dS2t3cFS2DEBWqpcrV8/ivlePsnTGiVky0Xz18uXcvHEBe6taef1II7c9uY8v/HE7q0qzgYHiDnDl6lk8v7+WHz+9n9Pn5rL1SCM/faaMnlCYzt4Q/375csASgrtfPkyG38POihae3VeL37ZOFtrljUty+opx1bfHRu5pfg/Zqd5hbZl/7Kxk9ezsyAdBNOl+D3vsyNdZCC3OCowqCm4cJHLvz5kL8rj7pcORhcXeUJifP3eAurYe2rqDkYbd/Wlo76GrN9wvcvfSGzK0dgfJDHgjmUWjqfE/nrxYVkddWzcLCtLYfLCBjp7gEJuY3HTpgqoy3Ujze7jmjNlkBDxDlk0Yjn8+ay4el7AuKg3yZMhP93P2wnw+ddEivvSOpTyyo5JfbzoMDJ3i9/UrVjI7N5UP3bWZ257cxyUrZ/DOU4v5zStHIrVXHttVTUVTJ9+56lRmZafwk6fLIsK6yC7j7Fgvu4630Bsy5KfHCums7JQh2+0dre9gZ0ULlw2xgJwR8ER22s62I3crBTW+2i29dtGwEcV9fh49oTBbj1hdwZ7aUxPZbeusjQxGJMe9X+QO0GDff191KyJWZlX/b0WTwYNvVJCV4uXLly2jJxRm08F6OxVy8iJ3FXclofjiJUt48nPnR7bgj4YlMzJ45daLBrUiTpaPnTufd502M7KxyOsefH7pfg8/+eAazl2Uz90fPp0fX7Oaf3/nckTgB09YG7XuevEgc/JSuWTFDD5+/ny2Hmnk968dIyPgiawVBLxuCjP8vHHUEsaCfmsIK2dmselgQ0xvVYdHd1me71B/hww7YybF66bA/hAtzgrQ1h0cUApiMJoiG5iG38S2bq5VnfSVA5Y1c/+WY5HyBzsrBi8aB7DPjsr7L6gCNHT00NTRQ01rd2R3dFm/6L22tTuudY+xoq07yGO7qrj81GLOXphPitfNc3tr7WyZwVMhJ6If8EmJu4gcFpEdIrJNRLbYY7ki8oSI7Ld/j00YpUwLPG7XqP32aAoy/Cfltw+FiPCd957KipmZZAQ8wz7HyllZ/ObGM9i4xNppOiMrwEfOmcdftlVw7+YjvH60iQ+fNRe3S3j/ulIKMvy8VdXKosL0mMctzU1l53Erws3v903mpvPn0x0M8cvnDw54/r/vqOKUWVlDVvp0NjLNzk2NPN8M276Jx3ePbI4aYcNTRsDLyllZvHKwnqrmLp7dW8N1Z84hP93HruODR+4v7q/jPx7aybz8tEjmEPTthG1o64mI/+WnWt9Mouv8t3UHufB7z3L1HZsmLKL/x45KunrDvGdNCQGvmzMX5PHM3lp6QoOkQnpchI3VYGe8GYvI/QJjzCpjzDr7+peAp4wxi4Cn7OuKMuVJ8bm596Nn8LuPbhj1fW8+fwGZAS9feXAnGX4PV60rBawI/WPnzgP62gk6lOSkROyT/uK+oCCdd502k1+/ciQmm+d4UyfbjjUN++3FEfdo8Z9hf6DGkzHjVITMHcGWAcuaefNYE7/ZdJiwgfevK2X5zKxBI/dHd1bxkbtfY3ZuKn/4+IaYqLev7G9PxMK6YIlVKTS6zv+Www20dgfZcqSRD/zilZPuHhYPD75Rwdy8VNbMzgaszCmntEP/yN25PhHpkONhy1wB3GNfvge4chyeQ1EmhexUH6eUxF+ywSErxcsnL1gIwNXrS2MWE689Yw7LijMH9LotzekT3/6eO8AnL1xEVzDEHS9Y0buJ2uX7jmHE3XluJ1MGLFsGBo/cO3tC3PybrZGSB301a+IQ9wV5BMOGO54/yIb5uczJS2PlzEzKatpidmq+sL+WW373OitmZfL7mzZQ2C8VNs8+/3pb3NP9HkpyUlhYGNvEZdPBBrxu4RfXreVIfQdX/fwVdh0f2gI6WSqbO3nlYD1Xrp4V+RYU3SAnMEgNIpiYPqonK+4GeFxEtorITfZYkTHG2btdBRQNdkcRuUlEtojIltra2pOchqIkPtefNYcvXLKEf9m4MGY8ze/hH58+l8tOiV0ALc21rBK3SwZdvFxYaEXvzmLtZ/+wjZ8+c4C3Ly9ifkH6gOMdHM99dlTkXmhnJw3WtOOHT+3n0V1V/OxZK8WzoT22aNhwrJuTg8cl9IYMHzjd+rayYmYWwbBhX1WfKP9u81Hy0nz89sYzBv3QSPV5CHhdNLR3s6+6lUVFloW1qDCD/VFZPpsO1nNaSTaXrJjBvR87g5auXt75oxd5389f5qFtFWO+9f++V612je9ZXRIZm5ufFvngHCwVEqaGuJ9jjFkDvAO4RUTOi77RWKsGg5pLxpg7jDHrjDHrCgoGbwWnKMmE3+PmlgsWxl2cy4ncc9N8A/rgOnzqwoV09oa46AfP8fCbx/nc2xZz+4fWDvu4Ec89KnL3e9zkp/sG2DJ7q1q584WDZKV4eX5fLVXNXYNWmxyKNL+H00qzyQh4eIedvbNylpWqutOOqLt6Qzy3r5a3rygibYj0SIC8NL8dubex2LawFhamU9ncRWtXL+3dQXZUNLPB7ge8ZnYOz3x+I1+5bBm1rd18+vfbOO9/nuHOFw7SPgZlC7p6Q/x20xEuWloU87eEvuh9ytoyxpgK+3cN8CCwHqgWkWIA+3fN0I+gKMpQOJ54f789moWFGbx/bSl5aT7u+9gG/vWiRSNmGpXkpOBxCYuLYj1+ayNTX3plOGz48oM7yAh4uPvDpxM28OfXy2ls7yHNN3Slz/58/YoV/OK6tZHjS3NSyfB7InbJS2V1dPSEePvy4bOcctN8lNW00dDew+IZ1tydcyiraWPLkUZCYRMRd7AWfT923nye/vxG7v7w6czPT+cbj+zh7O88zYNvlMc1/6H4yxsVNLT3cOM58wbc5oh7qm+IyH0C0iFPeBOTiKQBLmNMq3357cDXgYeBG4Bv278fGouJKsp0Y0ZWAJcM7rdH8633nAIwZHTfn/MXF/DKrRcNSK8szgrE9Gb9w5ZjbD3SyHevOpXVs3NYPy+XP20tZ3Vpdlx+u8OKmbFrFC6XsGxmZiRj5vFd1WT4PTGiPBg5aT5e3G9ZuIvt/QDOjt79NW0cqmvH6xbWzMkecF+XS9i4pJCNSwp5/WgjX//rbr764E7OXVQw5IdnWU0bB2vbePuKgR86xhjuevEQK2ZmsmH+wKqnG5cU8q33nDKgBaaT9z4RlSFPJnIvAl4UkTeBV4FHjDGPYon620RkP3CxfV1RlFHidbtYXJTB/Pzhm6m4XBK3sIOV1tlf2IFILX2wimB9+x9vcca8XK5aa/nJ71tbwqG6dp7fXxu3tTQUK2dmsaeyhZ5gmCf3VHPB0kJ8g+z6jSYvzYeTQehE7KW5qfg8LvZXt7LpYD2nlmRHKkkOxZrZOXz//afRFQzz02fKBj2mqrmLa365iZt/u3XQgmrP769jf00bN54zb9C0WLdLuGb97EFrywATUtP9hMXdGHPQGHOa/bPCGPNNe7zeGHORMWaRMeZiY8zIXQUURRmU39+0gVsvWzYhz1WclUJjRy97Klu4+o5XcLuEb73nlIh4XXZKMak+N3VtPSPmuI/EipmZdPWG+dPWcurbe3j7ikHzLmJwPlCyUryRzV5ul7CgIJ03jzWzvbx50Ch6MBYUpHPVmhLu3XSU8n7do7qDIW7+7VbauoKEDTy0rWLA/e984SCFGX4uP3VmXM/nMFUid0VRxpnsVF/c3vbJ4uS6f+AXr9AbMvzuY2fEZN2k+T2RjUO5cSymDofTAewnT+/H53ZFNnwNhyPui4tiN3stLkrn1cMNA/z2kfj0xYtA4IdP7o+MGWP497/sZNuxJm77wGmsmZ3Nn7dWxOwo3VvVygv767jhrLkjftvoz1TKllEUJUmYYee6u13CvR89Y9ACbO+zN1+dbOS+oCANv8fF8eYuzl6YN2QRsWicEgSL+i0EO767xyWR5uLxMDM7hes3zOHPr5ezvbyJp9+q5ot/2s79W8r51IULuXRlMe9ZU8Le6lZ2R9XC+d7je0nzufng+oF9gUdiymTLKIqSPJxaksUVq2byu49tiOlkFc26OTl88IzZvG35yDbKcHjcLpbaGS+DLVgOhhO5L+kn7k4lzdNKR/bb+/OJCxaS6vPwrp+8xEfu3sJftx/nmvWlfNbux3v5qcX43C4eeN2yZl4qq+OJ3dXccuHCE/qAm8jIXUv+KooCWJubfnj16mGPERH++92njMnzrZyVxfaKZi5aNrIlA1ZOu9ctrJsbG507lTTj9dujyU3z8b33ncq2Y82cszCfdXNzYmyw7FQfFy0r5KFtFXzhkiV8/a+7Kc1N4SNnD0x/jIeJ3KGq4q4oyqTwLxsXcP7iggGlBoZifkE6u79+aUzbQID5+Wn85z8t552njNwjdzAuXVk8bH/d96wp4R87q/jX+95gb3UrP//QmhNeB3EWVHeWNxMKmxOqfhovKu6KokwKJTmpkaYk8dJf2MH6NvHhE4yk4+H8xQXkpvl4fHc1G+bnckmcNtJgZAY8/NNpM/nDlmO8VdXCt9976pAW2MminruiKMow+Dwu3nXaTETg3y9fflIlpUWEH129ih9ds5ryxk7+6ccvcteLh8Zwtn1o5K4oijIC/3bJEq5aWzJgt+2JICK867SZnLswn288soc5Q9TdP1lU3BVFUUYg3e+J5OaPFTlpPr7//tPG9DGjUVtGURQlCVFxVxRFSUJU3BVFUZIQFXdFUZQkRMVdURQlCVFxVxRFSUJU3BVFUZIQFXdFUZQkRKKL0E/aJERqgSMnePd8oG4MpzNVmI7nPR3PGabneU/Hc4bRn/ccY0zBYDckhLifDCKyxRizbrLnMdFMx/OejucM0/O8p+M5w9iet9oyiqIoSYiKu6IoShKSDOJ+x2RPYJKYjuc9Hc8Zpud5T8dzhjE87ynvuSuKoigDSYbIXVEURemHiruiKEoSMqXFXUQuFZG9IlImIl+a7PmMByJSKiLPiMhuEdklIp+2x3NF5AkR2W//zhnpsaYiIuIWkTdE5G/29Xkistl+zf8gIr7JnuNYIiLZIvInEXlLRPaIyJnT4bUWkc/a/987ReQ+EQkk42stIr8SkRoR2Rk1NujrKxY/ss9/u4isGc1zTVlxFxE38FPgHcBy4BoRWT65sxoXgsDnjTHLgQ3ALfZ5fgl4yhizCHjKvp6MfBrYE3X9O8BtxpiFQCNw46TMavz4IfCoMWYpcBrWuSf1ay0is4B/BdYZY1YCbuBqkvO1vhu4tN/YUK/vO4BF9s9NwO2jeaIpK+7AeqDMGHPQGNMD/B64YpLnNOYYYyqNMa/bl1ux3uyzsM71Hvuwe4ArJ2WC44iIlADvBO60rwtwIfAn+5CkOm8RyQLOA+4CMMb0GGOamAavNVbLzxQR8QCpQCVJ+FobY54HGvoND/X6XgH82lhsArJFpDje55rK4j4LOBZ1vdweS1pEZC6wGtgMFBljKu2bqoCiyZrXOPK/wBeBsH09D2gyxgTt68n2ms8DaoH/s62oO0UkjSR/rY0xFcD3gKNYot4MbCW5X+tohnp9T0rjprK4TytEJB34M/AZY0xL9G3GymdNqpxWEbkcqDHGbJ3suUwgHmANcLsxZjXQTj8LJklf6xysKHUeMBNIY6B1MS0Yy9d3Kot7BVAadb3EHks6RMSLJez3GmMesIerna9o9u+ayZrfOHE28C4ROYxluV2I5Udn21/dIfle83Kg3Biz2b7+JyyxT/bX+mLgkDGm1hjTCzyA9fon82sdzVCv70lp3FQW99eARfaKug9rAebhSZ7TmGP7zHcBe4wxP4i66WHgBvvyDcBDEz238cQYc6sxpsQYMxfrtX3aGHMt8AxwlX1YUp23MaYKOCYiS+yhi4DdJPlrjWXHbBCRVPv/3TnvpH2t+zHU6/swcL2dNbMBaI6yb0bGGDNlf4DLgH3AAeArkz2fcTrHc7C+pm0Httk/l2H5z08B+4EngdzJnus4/g02An+zL88HXgXKgD8C/sme3xif6ypgi/16/wXImQ6vNfA14C1gJ/AbwJ+MrzVwH9a6Qi/WN7Ubh3p9AcHKCDwA7MDKJor7ubT8gKIoShIylW0ZRVEUZQhU3BVFUZIQFXdFUZQkRMVdURQlCVFxVxRFSUJU3BVFUZIQFXdFUZQk5P8DdVWAukUhsCQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(losses)\n",
    "print(losses[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "85ceb6b1-27f0-4696-ba28-42148ed3ac72",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "999 1000 0.999\n",
      "36 40 0.9\n",
      "1035 1040 0.9951923076923077\n"
     ]
    }
   ],
   "source": [
    "output = model_forward(X, test=True)\n",
    "print(torch.sum((output[:n]>0) == y_train[:n]).item(), n, torch.sum((output[:n]>0) == y_train[:n]).item()/n)\n",
    "print(torch.sum((output[-m:]>0) == y_train[-m:]).item(), m, torch.sum((output[-m:]>0) == y_train[-m:]).item()/m)\n",
    "print(torch.sum((output>0) == y_train).item(), n+m, torch.sum((output>0) == y_train).item()/(n+m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b1d00cd2-0e81-4647-9925-d4f04107fd9b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 5.4362],\n",
      "        [ 3.5057],\n",
      "        [ 4.1574],\n",
      "        [ 5.6392],\n",
      "        [ 7.3480],\n",
      "        [-4.4773],\n",
      "        [-2.2879],\n",
      "        [-2.5043],\n",
      "        [-8.1601],\n",
      "        [-4.2102]], dtype=torch.float64, grad_fn=<TBackward>)\n"
     ]
    }
   ],
   "source": [
    "test_X = torch.tensor(rng.standard_normal(size=(test_n,d+1)), requires_grad = False) / np.sqrt(d)\n",
    "test_X[:test_n//2,0] = C\n",
    "test_X[test_n//2:,0] = -C\n",
    "print(model_forward(test_X, test=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7f8906a4-eeca-484b-ac0d-e2db889bb759",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.29427893 2.1779641  3.39236843 3.32140583 2.99703953 3.37087504\n",
      " 3.4543389  2.93062497 3.31307921 2.94367255 3.73581741 2.63847502\n",
      " 2.68610037 1.70844894 3.49611908 4.33551796 3.06930529 2.48851197\n",
      " 3.11785934 4.10803434 1.37777626 3.79905916 3.13240221 4.10256815\n",
      " 2.38711809 4.26649952 3.38613266 3.65373334 2.25327999 2.82574601\n",
      " 3.78286291 2.75231639 4.14922002 3.32336528 3.73610101 3.10397085\n",
      " 3.71820223 3.61654631 2.83051504 3.77334909 4.28442243 3.18160197\n",
      " 2.90758703 3.70487194 3.84170143 4.6217823  2.88177875 2.08320355\n",
      " 2.21721874 2.54548809 3.55272481 1.9187607  2.67763619 3.19181329\n",
      " 3.25378628 3.18152986 2.41809313 3.89209637 3.63871832 2.5630058\n",
      " 3.26412757 2.63502213 2.13756589 3.47457253 3.02487322 4.06962365\n",
      " 3.3153464  3.22120307 2.72788296 2.26551118 4.26523296 3.98083096\n",
      " 3.92703381 3.79530034 3.17415758 3.09707054 3.56386357 2.18027432\n",
      " 2.40562126 3.1196871  2.33488541 2.76443492 3.10493896 2.64504976\n",
      " 3.75671511 3.05530605 3.94724111 2.53675574 2.80969893 3.44749126\n",
      " 2.71742192 3.35112408 3.6249538  2.6063721  2.12421352 3.99740274\n",
      " 2.4458728  3.48152875 2.68658814 3.20992472]\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.norm(W.detach().numpy()[:,1:], axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ed5f9b81-423a-45f8-8633-b104d2292db0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.10610926 -0.80414569  0.28668809 -0.25049222 -0.98108926 -1.17024911\n",
      "  0.74240746  0.60944578 -0.04290286 -0.06408065  0.49756071  0.90033487\n",
      "  0.20602317  1.44145342 -0.69863837 -0.21713445  0.29824765 -0.3041391\n",
      "  0.52967948 -1.6558592  -1.73239135  0.31089245 -0.43677266  0.33443072\n",
      " -0.6151374  -0.38995706  0.827352    0.92475406  2.47440967 -2.28121583\n",
      " -0.44809873  2.4199334   0.91308314  0.6233928  -0.66930626 -1.4739356\n",
      " -0.02528747  0.21342447 -0.33760923  0.33260475 -1.58588856 -0.30113667\n",
      "  1.16052901  0.05530491 -0.04088201  0.99376131  1.18010518 -2.44988639\n",
      " -1.03310954  0.23530502  0.68801095 -0.18377965  0.30464257 -0.91654503\n",
      " -0.33078278  0.23840754 -1.06127515  0.75277552  1.26606643  0.02223338\n",
      " -1.18806827  0.28008882  1.55505071  0.8954318   2.72718448 -0.30884742\n",
      "  0.49631016 -1.24315112  0.25065221 -1.52473357  0.01333199 -1.50340556\n",
      " -0.97226911 -0.74781237 -0.12516005 -1.19964256  0.87503372  0.47640999\n",
      "  0.57286732  0.22534123  0.59182816  0.49749038  0.03479441  1.26303913\n",
      "  1.93924604 -0.51717436  1.61136179 -0.93568515  0.92809524 -0.74583291\n",
      "  0.58642901 -0.83173459 -0.73302654 -0.3717427   0.64523068  1.07064592\n",
      " -1.26134377  0.8899675  -0.1621229   0.43489885]\n"
     ]
    }
   ],
   "source": [
    "print(W.detach().numpy()[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6ad8b6f3-d41a-416b-b5bd-0ecb8664bc48",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  31.0461011    -2.70841977   11.83295916  -13.25951677   -3.05480823\n",
      "   -2.88047648    4.65288817    4.80867215  -77.22281091  -45.93699293\n",
      "    7.50826443    2.93054852   13.03785593    1.1852266    -5.00418991\n",
      "  -19.96697464   10.29112999   -8.18215082    5.88631326   -2.48090801\n",
      "   -0.79530313   12.21985001   -7.17169938   12.26731847   -3.88062585\n",
      "  -10.94094693    4.09273521    3.95103249    0.91063336   -1.23870174\n",
      "   -8.44203       1.13735212    4.54418642    5.33109348   -5.58204998\n",
      "   -2.1059067  -147.03733091   16.94532186   -8.38399791   11.34484417\n",
      "   -2.70159111  -10.56530914    2.50539798   66.98993105  -93.97046095\n",
      "    4.65079718    2.44196771   -0.8503266    -2.14616035   10.81782309\n",
      "    5.16376199  -10.44055037    8.78943543   -3.48244022   -9.83662547\n",
      "   13.3449215    -2.27847899    5.17032804    2.87403427  115.27736185\n",
      "   -2.74742424    9.40780899    1.37459562    3.88033186    1.10915607\n",
      "  -13.17680961    6.67998894   -2.5911597    10.88313944   -1.48584069\n",
      "  319.92474187   -2.64787565   -4.03903999   -5.07520402  -25.3607897\n",
      "   -2.58166111    4.07283       4.5764664     4.19926426   13.84428014\n",
      "    3.9452084     5.55676059   89.2367245     2.09419464    1.93720396\n",
      "   -5.90769046    2.44963057   -2.71112108    3.02738211   -4.62233727\n",
      "    4.63384636   -4.02907866   -4.94518768   -7.01122605    3.29217689\n",
      "    3.73363656   -1.93910087    3.91197291  -16.57130616    7.3808535 ]\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.norm(W.detach().numpy()[:,1:], axis=1) / W.detach().numpy()[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2d3cc6fe-c5d9-4686-b61f-d7a011eb9bac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f43b02d9c70>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(np.abs(np.linalg.norm(W.detach().numpy()[:,1:], axis=1) / W.detach().numpy()[:,0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "594ae533-a725-4d5d-9fd4-8a4e65976885",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.01069515 -0.46643998 -0.17517561  0.17902391  2.34611064  1.21039558\n",
      "  -0.2114499  -1.00668637 -0.049391    0.05459874  0.30972236 -1.14949871\n",
      "   0.30081013 -0.4478084   0.18360429  0.22107707 -0.40114097 -0.08046094\n",
      "  -0.43580881 -0.52620004  1.35351767  0.59598412  0.07035422  0.32942818\n",
      "  -0.69301036 -0.47054994 -0.94748305  0.68329541  3.13431203  0.40041056\n",
      "  -0.39631121 -0.7005392  -0.46106977  0.069057    0.25182293 -2.11223046\n",
      "   0.02276516  0.46702709  0.09885205 -0.31175756  1.80286073  0.13297209\n",
      "  -1.35686083 -0.04953869  0.07054033  0.26537272  0.6520955   0.46533694\n",
      "  -2.32285172  0.11987266  0.40168439 -0.14226498 -0.16138457 -1.25592032\n",
      "   0.01033011  0.03488843 -0.63021878 -0.40398376  1.64266586 -0.00474453\n",
      "   2.5255142   0.21207564  1.61897711 -1.08251178  2.17945517 -0.13402474\n",
      "  -0.14424499 -0.33229859 -0.38133021  0.57440575  0.0299526   2.37372141\n",
      "  -0.7098449  -1.03188139 -0.06925087  0.60399727  2.08535498 -0.43641281\n",
      "  -0.39999474 -0.34901662 -0.71637182 -0.1845605   0.04548905  0.60666964\n",
      "  -1.28812225 -0.1294101   1.24755124  0.99915282  0.49422629 -0.24204981\n",
      "   0.67088145  0.44502291  0.99848912  0.11599186 -0.69732741  0.97981129\n",
      "   2.08166731 -0.04764384 -0.02752696  0.06509704]]\n"
     ]
    }
   ],
   "source": [
    "print(W.detach().numpy()[:,0] * a.detach().numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "42eba3bd-f881-43db-96c5-c4f317b21e53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.39035086 -0.48611768 -0.63740161 ...  0.62155864 -0.1101962\n",
      "   0.130968  ]\n",
      " [ 0.75858992  0.84200088  0.3707224  ... -0.58552633 -1.50970886\n",
      "   0.72176887]\n",
      " [-1.26281854 -0.90906456 -2.7739677  ...  1.36036923  1.7347017\n",
      "  -0.48917957]\n",
      " ...\n",
      " [-0.6124366   0.20119976 -0.3359624  ...  0.27263576 -1.46952069\n",
      "  -1.61960898]\n",
      " [ 0.6484516   1.0883205  -0.21034001 ... -1.47708068 -0.32293204\n",
      "   1.26721656]\n",
      " [-1.13205853 -1.77775919  1.47511345 ...  1.38289518  0.70818809\n",
      "  -0.75675077]]\n"
     ]
    }
   ],
   "source": [
    "print((W[:,1:] @ torch.t(X[-m:,1:])).detach().numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "dcfd84c5-3d23-4114-b958-a0c3de322ce7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.3408],\n",
      "        [-0.0317],\n",
      "        [ 0.7383],\n",
      "        [ 0.7206],\n",
      "        [-1.0845],\n",
      "        [-0.7643],\n",
      "        [ 0.4551],\n",
      "        [-1.3336],\n",
      "        [ 0.0607],\n",
      "        [-0.6888],\n",
      "        [-1.3644],\n",
      "        [ 0.0298],\n",
      "        [ 1.1423],\n",
      "        [ 0.6650],\n",
      "        [-0.3301],\n",
      "        [ 0.3905],\n",
      "        [-1.3722],\n",
      "        [ 0.1072],\n",
      "        [-0.9127],\n",
      "        [ 1.2521],\n",
      "        [ 0.5653],\n",
      "        [-0.9636],\n",
      "        [ 0.2994],\n",
      "        [ 0.4253],\n",
      "        [ 0.5120],\n",
      "        [-0.0971],\n",
      "        [-1.3439],\n",
      "        [-0.4106],\n",
      "        [ 0.2065],\n",
      "        [ 0.6287],\n",
      "        [-0.8623],\n",
      "        [-0.4176],\n",
      "        [ 0.0773],\n",
      "        [ 1.0225],\n",
      "        [ 0.1338],\n",
      "        [ 0.4266],\n",
      "        [-0.4832],\n",
      "        [-1.1098],\n",
      "        [ 0.8383],\n",
      "        [ 0.0110],\n",
      "        [ 0.5958],\n",
      "        [ 0.3645],\n",
      "        [ 0.6053],\n",
      "        [-1.2527],\n",
      "        [-0.8005],\n",
      "        [-1.4077],\n",
      "        [ 0.9118],\n",
      "        [-1.0304],\n",
      "        [-0.4667],\n",
      "        [ 0.1902],\n",
      "        [ 0.4959],\n",
      "        [ 0.9708],\n",
      "        [ 0.6034],\n",
      "        [-0.0322],\n",
      "        [-1.2950],\n",
      "        [-0.7339],\n",
      "        [-0.2365],\n",
      "        [ 1.2263],\n",
      "        [-0.0123],\n",
      "        [-1.2743],\n",
      "        [-1.4708],\n",
      "        [ 0.1888],\n",
      "        [ 0.0276],\n",
      "        [-0.9730],\n",
      "        [ 0.0851],\n",
      "        [-1.2354],\n",
      "        [ 0.5096],\n",
      "        [-0.3587],\n",
      "        [ 0.6041],\n",
      "        [-0.5176],\n",
      "        [-0.2405],\n",
      "        [-0.2742],\n",
      "        [ 0.5742],\n",
      "        [ 0.6402],\n",
      "        [ 1.2742],\n",
      "        [ 0.6639],\n",
      "        [-1.3018],\n",
      "        [-0.1899],\n",
      "        [ 0.4983],\n",
      "        [ 0.7966],\n",
      "        [-0.1237],\n",
      "        [ 0.1962],\n",
      "        [-1.2051],\n",
      "        [ 0.7391],\n",
      "        [-0.4974],\n",
      "        [ 0.0882],\n",
      "        [-1.3420],\n",
      "        [ 1.1957],\n",
      "        [-0.7046],\n",
      "        [ 0.6179],\n",
      "        [ 0.1543],\n",
      "        [ 0.0239],\n",
      "        [-0.9159],\n",
      "        [ 1.3576],\n",
      "        [ 0.6977],\n",
      "        [-0.5806],\n",
      "        [-0.5572],\n",
      "        [ 0.5464],\n",
      "        [-0.9143],\n",
      "        [-1.4313]], dtype=torch.float64, requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6df62383-47f0-4ff8-b7f5-a719c338b354",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.1008,  0.5800, -0.6110, -0.7147, -2.3913, -1.0343, -0.2848, -1.6518,\n",
      "          1.1512, -0.8520,  0.6225, -1.2767,  1.4601, -0.3107, -0.2628, -1.0182,\n",
      "         -1.3450,  0.2646, -0.8228,  0.3178, -0.7813,  1.9170, -0.1611,  0.9850,\n",
      "          1.1266,  1.2067, -1.1452,  0.7389,  1.2667, -0.1755,  0.8844, -0.2895,\n",
      "         -0.5050,  0.1108, -0.3762,  1.4331, -0.9003,  2.1883, -0.2928, -0.9373,\n",
      "         -1.1368, -0.4416, -1.1692, -0.8957, -1.7255,  0.2670,  0.5526, -0.1899,\n",
      "          2.2484,  0.5094,  0.5838,  0.7741, -0.5298,  1.3703, -0.0312,  0.1463,\n",
      "          0.5938, -0.5367,  1.2975, -0.2134, -2.1257,  0.7572,  1.0411, -1.2089,\n",
      "          0.7992,  0.4340, -0.2906,  0.2673, -1.5214, -0.3767,  2.2467, -1.5789,\n",
      "          0.7301,  1.3799,  0.5533, -0.5035,  2.3832, -0.9160, -0.6982, -1.5488,\n",
      "         -1.2104, -0.3710,  1.3074,  0.4803, -0.6642,  0.2502,  0.7742, -1.0678,\n",
      "          0.5325,  0.3245,  1.1440, -0.5351, -1.3621, -0.3120, -1.0807,  0.9152,\n",
      "         -1.6504, -0.0535,  0.1698,  0.1497]], dtype=torch.float64,\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "print(a)"
   ]
  }
 ],
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