Custom differentiable in Swift for TensorFlow

custom-differentiable.ipynb

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      "text/plain": [
       "('inline', 'module://ipykernel.pylab.backend_inline')\n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import TensorFlow\n",
    "import Python\n",
    "\n",
    "%include \"EnableIPythonDisplay.swift\"\n",
    "IPythonDisplay.shell.enable_matplotlib(\"inline\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.125\r\n"
     ]
    }
   ],
   "source": [
    "import Glibc\n",
    "print(pow(0.5, 3))"
   ]
  },
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   "cell_type": "code",
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     "traceback": [
      "error: <Cell 3>:2:33: error: expression is not differentiable\nvalueWithGradient(at: a) { a in pow(a, 3) }\n                                ^\n\n<Cell 3>:2:33: note: cannot differentiate functions that have not been marked '@differentiable' and that are defined in other files\nvalueWithGradient(at: a) { a in pow(a, 3) }\n                                ^\n\n"
     ]
    }
   ],
   "source": [
    "let a: Float = 0.5\n",
    "valueWithGradient(at: a) { a in pow(a, 3) }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "@differentiableに対応していない場合、以下のようにエラーが表示されます。\n",
    "\n",
    "```\n",
    "error: expression is not differentiable\n",
    "```\n",
    "\n",
    "独自に pow の偏微分を記述してみます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "▿ 2 elements\n",
       "  - value : 0.125\n",
       "  ▿ gradient : 2 elements\n",
       "    - .0 : 0.75\n",
       "    - .1 : -0.08664339756999316\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func myPow(_ x: Double, _ num: Double) -> Double {\n",
    "  return pow(x, num)\n",
    "}\n",
    "\n",
    "@derivative(of: myPow)\n",
    "func myPowDerivative(_ x: Double, _ num: Double) -> (value: Double, pullback: (Double) -> (Double, Double)) {\n",
    "  return (\n",
    "    value: myPow(x, num),\n",
    "    pullback: {\n",
    "      chain in (\n",
    "        chain * num * myPow(x, num - 1),\n",
    "        chain * myPow(x, num) * log(x)\n",
    "      )\n",
    "    }\n",
    "  )\n",
    "}\n",
    "\n",
    "@differentiable\n",
    "func power(_ x: Double, _ num: Double) -> Double {\n",
    "  return myPow(x, num)\n",
    "}\n",
    "let a: Double = 0.5\n",
    "let b: Double = 3\n",
    "\n",
    "valueWithGradient(at: a, b) { a, b in power(a, b) }"
   ]
  }
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