cat-state/Polarization_Routing_XOR.ipynb

## Polarization_Routing_XOR.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "from math import pi\n",
    "from typing import Tuple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Routing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[1.6784, 2.4763, 1.1539]], grad_fn=<RepeatBackward>),\n",
       " tensor([[0.3223, 2.3602, 1.2148]], grad_fn=<NormBackward3>))"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Input = Tuple[torch.Tensor, torch.Tensor]\n",
    "\n",
    "class SLMRouter(nn.Module):\n",
    "    def __init__(self, n_filters: int):\n",
    "        super().__init__()\n",
    "        self._angles = nn.Parameter(torch.zeros(n_filters).uniform_(0, 3.14159))\n",
    "        #self._angles = nn.Parameter(torch.tensor([0.0, pi / 2, pi / 2]))\n",
    "        \n",
    "    def forward(self, x: Input):\n",
    "        angle, intensity = x\n",
    "\n",
    "        self_vecs = torch.stack([self._angles.cos(), self._angles.sin()]).unsqueeze(0)\n",
    "        in_vecs = torch.stack([angle.cos(), angle.sin()], dim=1)\n",
    "        \n",
    "        infall = self_vecs[:, :, :, None] @ in_vecs[:, :, None, :]\n",
    "        transmitted = (infall * intensity[:, None, None, :]).sum(dim=3).norm(dim=1)\n",
    "\n",
    "        return (self._angles.repeat(intensity.shape[0], 1), transmitted)\n",
    "        \n",
    "s = SLMRouter(3)\n",
    "\n",
    "x = (torch.tensor([[0.0, 0.0, 0.0]]), torch.ones(3)[None, :])\n",
    "s(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-linearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e5622f1400>]"
      ]
     },
     "execution_count": 213,
     "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": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def optical_limiting(x):\n",
    "    return ((x * 5).sigmoid() - 0.5) * 1.8\n",
    "\n",
    "plt.plot(torch.linspace(0, 1).numpy(), optical_limiting(torch.linspace(0, 1)).numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Act(nn.Module):\n",
    "    def __init__(self, activation):\n",
    "        super().__init__()\n",
    "        self._activation = activation\n",
    "        \n",
    "    def forward(self, x):\n",
    "        angle, intensity = x\n",
    "        return (angle, self._activation(intensity))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.6629, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000],\n",
      "        [1.1859],\n",
      "        [1.2430],\n",
      "        [1.1676]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4733, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000],\n",
      "        [1.2728],\n",
      "        [1.2726],\n",
      "        [0.0262]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4276, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000e+00],\n",
      "        [1.7377e+00],\n",
      "        [1.7377e+00],\n",
      "        [3.2093e-05]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000e+00],\n",
      "        [1.7579e+00],\n",
      "        [1.7579e+00],\n",
      "        [6.3294e-06]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000e+00],\n",
      "        [1.7580e+00],\n",
      "        [1.7580e+00],\n",
      "        [1.0729e-07]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000],\n",
      "        [1.7580],\n",
      "        [1.7580],\n",
      "        [0.0000]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000],\n",
      "        [1.7580],\n",
      "        [1.7580],\n",
      "        [0.0000]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000],\n",
      "        [1.7580],\n",
      "        [1.7580],\n",
      "        [0.0000]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000],\n",
      "        [1.7580],\n",
      "        [1.7580],\n",
      "        [0.0000]], grad_fn=<NormBackward3>)\n",
      "tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
      "tensor([0, 1, 1, 0])\n",
      "tensor([[0.0000],\n",
      "        [1.7580],\n",
      "        [1.7580],\n",
      "        [0.0000]], grad_fn=<NormBackward3>)\n"
     ]
    }
   ],
   "source": [
    "xor = {\n",
    "    (0, 0): 0,\n",
    "    (0, 1): 1,\n",
    "    (1, 0): 1,\n",
    "    (1, 1): 0\n",
    "}\n",
    "\n",
    "batch_x = torch.tensor([[0, 0],\n",
    "                        [0, 1],\n",
    "                        [1, 0],\n",
    "                        [1, 1]]).float()\n",
    "\n",
    "batch_y = torch.tensor([0, 1, 1, 0])\n",
    "\n",
    "net = nn.Sequential(\n",
    "    SLMRouter(2),\n",
    "    Act(optical_limiting),\n",
    "    SLMRouter(2),\n",
    "    Act(optical_limiting),\n",
    "    SLMRouter(1)\n",
    ")\n",
    "\n",
    "start_angles = nn.Parameter(torch.zeros(1, 2).uniform_(0, 3.14159).expand(4, 2))\n",
    "\n",
    "optim = torch.optim.Adam([start_angles, *net.parameters()], lr=0.01)\n",
    "\n",
    "for i in range(1000):\n",
    "    optim.zero_grad()\n",
    "    \n",
    "    x = (start_angles, batch_x)\n",
    "    out_angle, out_intensity = net(x)\n",
    "    loss = F.binary_cross_entropy_with_logits(out_intensity.squeeze(), batch_y.float())\n",
    "    loss.backward()\n",
    "    \n",
    "    optim.step()\n",
    "    if i % 100 == 0:\n",
    "        print(loss)\n",
    "        print(batch_y)\n",
    "        print(out_intensity)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 23,
	"metadata": {},
	"outputs": [],
	"source": [
	"import torch\n",
	"import torch.nn as nn\n",
	"import torch.nn.functional as F\n",
	"from math import pi\n",
	"from typing import Tuple"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Routing"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 212,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"(tensor([[1.6784, 2.4763, 1.1539]], grad_fn=<RepeatBackward>),\n",
	" tensor([[0.3223, 2.3602, 1.2148]], grad_fn=<NormBackward3>))"
	]
	},
	"execution_count": 212,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"Input = Tuple[torch.Tensor, torch.Tensor]\n",
	"\n",
	"class SLMRouter(nn.Module):\n",
	" def __init__(self, n_filters: int):\n",
	" super().__init__()\n",
	" self._angles = nn.Parameter(torch.zeros(n_filters).uniform_(0, 3.14159))\n",
	" #self._angles = nn.Parameter(torch.tensor([0.0, pi / 2, pi / 2]))\n",
	" \n",
	" def forward(self, x: Input):\n",
	" angle, intensity = x\n",
	"\n",
	" self_vecs = torch.stack([self._angles.cos(), self._angles.sin()]).unsqueeze(0)\n",
	" in_vecs = torch.stack([angle.cos(), angle.sin()], dim=1)\n",
	" \n",
	" infall = self_vecs[:, :, :, None] @ in_vecs[:, :, None, :]\n",
	" transmitted = (infall * intensity[:, None, None, :]).sum(dim=3).norm(dim=1)\n",
	"\n",
	" return (self._angles.repeat(intensity.shape[0], 1), transmitted)\n",
	" \n",
	"s = SLMRouter(3)\n",
	"\n",
	"x = (torch.tensor([[0.0, 0.0, 0.0]]), torch.ones(3)[None, :])\n",
	"s(x)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Non-linearity"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 213,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"[<matplotlib.lines.Line2D at 0x1e5622f1400>]"
	]
	},
	"execution_count": 213,
	"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": [
	"import matplotlib.pyplot as plt\n",
	"\n",
	"def optical_limiting(x):\n",
	" return ((x * 5).sigmoid() - 0.5) * 1.8\n",
	"\n",
	"plt.plot(torch.linspace(0, 1).numpy(), optical_limiting(torch.linspace(0, 1)).numpy())"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 214,
	"metadata": {},
	"outputs": [],
	"source": [
	"class Act(nn.Module):\n",
	" def __init__(self, activation):\n",
	" super().__init__()\n",
	" self._activation = activation\n",
	" \n",
	" def forward(self, x):\n",
	" angle, intensity = x\n",
	" return (angle, self._activation(intensity))"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 225,
	"metadata": {},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"tensor(0.6629, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000],\n",
	" [1.1859],\n",
	" [1.2430],\n",
	" [1.1676]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4733, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000],\n",
	" [1.2728],\n",
	" [1.2726],\n",
	" [0.0262]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4276, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000e+00],\n",
	" [1.7377e+00],\n",
	" [1.7377e+00],\n",
	" [3.2093e-05]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000e+00],\n",
	" [1.7579e+00],\n",
	" [1.7579e+00],\n",
	" [6.3294e-06]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000e+00],\n",
	" [1.7580e+00],\n",
	" [1.7580e+00],\n",
	" [1.0729e-07]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000],\n",
	" [1.7580],\n",
	" [1.7580],\n",
	" [0.0000]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000],\n",
	" [1.7580],\n",
	" [1.7580],\n",
	" [0.0000]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000],\n",
	" [1.7580],\n",
	" [1.7580],\n",
	" [0.0000]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000],\n",
	" [1.7580],\n",
	" [1.7580],\n",
	" [0.0000]], grad_fn=<NormBackward3>)\n",
	"tensor(0.4261, grad_fn=<BinaryCrossEntropyWithLogitsBackward>)\n",
	"tensor([0, 1, 1, 0])\n",
	"tensor([[0.0000],\n",
	" [1.7580],\n",
	" [1.7580],\n",
	" [0.0000]], grad_fn=<NormBackward3>)\n"
	]
	}
	],
	"source": [
	"xor = {\n",
	" (0, 0): 0,\n",
	" (0, 1): 1,\n",
	" (1, 0): 1,\n",
	" (1, 1): 0\n",
	"}\n",
	"\n",
	"batch_x = torch.tensor([[0, 0],\n",
	" [0, 1],\n",
	" [1, 0],\n",
	" [1, 1]]).float()\n",
	"\n",
	"batch_y = torch.tensor([0, 1, 1, 0])\n",
	"\n",
	"net = nn.Sequential(\n",
	" SLMRouter(2),\n",
	" Act(optical_limiting),\n",
	" SLMRouter(2),\n",
	" Act(optical_limiting),\n",
	" SLMRouter(1)\n",
	")\n",
	"\n",
	"start_angles = nn.Parameter(torch.zeros(1, 2).uniform_(0, 3.14159).expand(4, 2))\n",
	"\n",
	"optim = torch.optim.Adam([start_angles, *net.parameters()], lr=0.01)\n",
	"\n",
	"for i in range(1000):\n",
	" optim.zero_grad()\n",
	" \n",
	" x = (start_angles, batch_x)\n",
	" out_angle, out_intensity = net(x)\n",
	" loss = F.binary_cross_entropy_with_logits(out_intensity.squeeze(), batch_y.float())\n",
	" loss.backward()\n",
	" \n",
	" optim.step()\n",
	" if i % 100 == 0:\n",
	" print(loss)\n",
	" print(batch_y)\n",
	" print(out_intensity)"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.6.10"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}