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concrete/docs/user/tutorial/tensor_operations.ipynb
2021-12-15 18:00:19 +03:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "34d13212",
"metadata": {},
"source": [
"# Tensor Operations"
]
},
{
"cell_type": "markdown",
"id": "6999361c",
"metadata": {},
"source": [
"In this tutorial, we'll go over what you can do with tensors. Each supported operation will be written out as a function. Then, all of them will be compiled in a loop and executed with a random input to demonstrate their semantics."
]
},
{
"cell_type": "markdown",
"id": "34fc7213",
"metadata": {},
"source": [
"### Imports"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a62e11a9",
"metadata": {},
"outputs": [],
"source": [
"import concrete.numpy as hnp\n",
"import inspect\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"id": "6180966a",
"metadata": {},
"source": [
"### Inputset Definition"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f8de515c",
"metadata": {},
"outputs": [],
"source": [
"inputset = [np.random.randint(3, 11, size=(3, 2), dtype=np.uint8) for _ in range(10)]"
]
},
{
"cell_type": "markdown",
"id": "ae02c598",
"metadata": {},
"source": [
"### Supported Operation Definitions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "d7eeb83c",
"metadata": {},
"outputs": [],
"source": [
"def reshape(x):\n",
" return x.reshape((2, 3))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "68510258",
"metadata": {},
"outputs": [],
"source": [
"def flatten(x):\n",
" return x.flatten()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "db8f502b",
"metadata": {},
"outputs": [],
"source": [
"def index(x):\n",
" return x[2, 0]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "5e08a6c4",
"metadata": {},
"outputs": [],
"source": [
"def slice_(x):\n",
" return x.flatten()[1:5]"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "b807cc5d",
"metadata": {},
"outputs": [],
"source": [
"def add_scalar(x):\n",
" return x + 10"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "59471d3a",
"metadata": {},
"outputs": [],
"source": [
"def add_tensor(x):\n",
" return x + np.array([[1, 2], [3, 3], [2, 1]], dtype=np.uint8)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "83bf7d53",
"metadata": {},
"outputs": [],
"source": [
"def add_tensor_broadcasted(x):\n",
" return x + np.array([1, 10], dtype=np.uint8)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "ff42df0b",
"metadata": {},
"outputs": [],
"source": [
"def sub_scalar(x):\n",
" return x + (-1)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "0cc14f94",
"metadata": {},
"outputs": [],
"source": [
"def sub_tensor(x):\n",
" return x + (-np.array([[1, 2], [3, 3], [2, 1]], dtype=np.uint8))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "5e83dd23",
"metadata": {},
"outputs": [],
"source": [
"def sub_tensor_broadcasted(x):\n",
" return x + (-np.array([3, 0], dtype=np.uint8))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "9c68c725",
"metadata": {},
"outputs": [],
"source": [
"def mul_scalar(x):\n",
" return x * 2"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "66d065e0",
"metadata": {},
"outputs": [],
"source": [
"def mul_tensor(x):\n",
" return x * np.array([[1, 2], [3, 3], [2, 1]], dtype=np.uint8)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "a04ae50b",
"metadata": {},
"outputs": [],
"source": [
"def mul_tensor_broadcasted(x):\n",
" return x * np.array([2, 3], dtype=np.uint8)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "39fb823b",
"metadata": {},
"outputs": [],
"source": [
"def power(x):\n",
" return x ** 2"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "4257c1c9",
"metadata": {},
"outputs": [],
"source": [
"def truediv(x):\n",
" return x // 2"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "712b965a",
"metadata": {},
"outputs": [],
"source": [
"def dot(x):\n",
" return x.flatten() @ np.array([1, 1, 1, 2, 1, 1], dtype=np.uint8)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "480b6cc7",
"metadata": {},
"outputs": [],
"source": [
"def matmul(x):\n",
" return x @ np.array([[1, 2, 3], [3, 2, 1]], dtype=np.uint8)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "b876272b",
"metadata": {},
"outputs": [],
"source": [
"def clip(x):\n",
" return x.clip(6, 11)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "cec1d224",
"metadata": {},
"outputs": [],
"source": [
"def comparison(x):\n",
" return x > np.array([[10, 5], [8, 11], [3, 7]], dtype=np.uint8)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "668ab894",
"metadata": {},
"outputs": [],
"source": [
"def minimum(x):\n",
" return np.minimum(x, np.array([[10, 5], [8, 11], [3, 7]], dtype=np.uint8))"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "14031662",
"metadata": {},
"outputs": [],
"source": [
"def maximum(x):\n",
" return np.maximum(x, np.array([[10, 5], [8, 11], [3, 7]], dtype=np.uint8))"
]
},
{
"cell_type": "markdown",
"id": "12332a5b",
"metadata": {},
"source": [
"Other than these, we support a lot of numpy functions which you can find more about at [Numpy Support](../howto/numpy_support.md)."
]
},
{
"cell_type": "markdown",
"id": "09311480",
"metadata": {},
"source": [
"### Compilation and Homomorphic Evaluation of Supported Operations"
]
},
{
"cell_type": "markdown",
"id": "cf0152a2",
"metadata": {},
"source": [
"Note that some operations require programmable bootstrapping to work and programmable bootstrapping has a certain probability of failure. Usually, it has more than a 99% probability of success but with big bit-widths, this probability can drop to 95%."
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "0cdbc545",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"#######################################################################################\n",
"\n",
"def reshape(x):\n",
" return x.reshape((2, 3))\n",
"\n",
"reshape([[7, 10], [9, 10], [7, 9]]) homomorphically evaluates to [[7, 10, 9], [10, 7, 9]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def flatten(x):\n",
" return x.flatten()\n",
"\n",
"flatten([[4, 7], [6, 3], [9, 8]]) homomorphically evaluates to [4, 7, 6, 3, 9, 8]\n",
"\n",
"#######################################################################################\n",
"\n",
"def index(x):\n",
" return x[2, 0]\n",
"\n",
"index([[8, 4], [9, 6], [9, 10]]) homomorphically evaluates to 9\n",
"\n",
"#######################################################################################\n",
"\n",
"def slice_(x):\n",
" return x.flatten()[1:5]\n",
"\n",
"slice_([[5, 9], [7, 4], [7, 3]]) homomorphically evaluates to [9, 7, 4, 7]\n",
"\n",
"#######################################################################################\n",
"\n",
"def add_scalar(x):\n",
" return x + 10\n",
"\n",
"add_scalar([[10, 9], [9, 9], [8, 9]]) homomorphically evaluates to [[20, 19], [19, 19], [18, 19]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def add_tensor(x):\n",
" return x + np.array([[1, 2], [3, 3], [2, 1]], dtype=np.uint8)\n",
"\n",
"add_tensor([[6, 9], [9, 7], [7, 5]]) homomorphically evaluates to [[7, 11], [12, 10], [9, 6]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def add_tensor_broadcasted(x):\n",
" return x + np.array([1, 10], dtype=np.uint8)\n",
"\n",
"add_tensor_broadcasted([[3, 3], [4, 7], [9, 10]]) homomorphically evaluates to [[4, 13], [5, 17], [10, 20]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def sub_scalar(x):\n",
" return x + (-1)\n",
"\n",
"sub_scalar([[3, 8], [10, 4], [5, 8]]) homomorphically evaluates to [[2, 7], [9, 3], [4, 7]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def sub_tensor(x):\n",
" return x + (-np.array([[1, 2], [3, 3], [2, 1]], dtype=np.uint8))\n",
"\n",
"sub_tensor([[4, 6], [6, 8], [4, 3]]) homomorphically evaluates to [[3, 4], [3, 5], [2, 2]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def sub_tensor_broadcasted(x):\n",
" return x + (-np.array([3, 0], dtype=np.uint8))\n",
"\n",
"sub_tensor_broadcasted([[6, 7], [9, 10], [6, 3]]) homomorphically evaluates to [[3, 7], [6, 10], [3, 3]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def mul_scalar(x):\n",
" return x * 2\n",
"\n",
"mul_scalar([[8, 5], [10, 4], [10, 4]]) homomorphically evaluates to [[16, 10], [20, 8], [20, 8]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def mul_tensor(x):\n",
" return x * np.array([[1, 2], [3, 3], [2, 1]], dtype=np.uint8)\n",
"\n",
"mul_tensor([[7, 3], [10, 3], [6, 10]]) homomorphically evaluates to [[7, 6], [30, 9], [12, 10]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def mul_tensor_broadcasted(x):\n",
" return x * np.array([2, 3], dtype=np.uint8)\n",
"\n",
"mul_tensor_broadcasted([[6, 7], [3, 4], [7, 6]]) homomorphically evaluates to [[12, 21], [6, 12], [14, 18]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def power(x):\n",
" return x ** 2\n",
"\n",
"power([[6, 4], [6, 8], [3, 10]]) homomorphically evaluates to [[36, 16], [36, 64], [9, 100]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def truediv(x):\n",
" return x // 2\n",
"\n",
"truediv([[9, 5], [4, 7], [3, 7]]) homomorphically evaluates to [[4, 2], [2, 3], [1, 3]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def dot(x):\n",
" return x.flatten() @ np.array([1, 1, 1, 2, 1, 1], dtype=np.uint8)\n",
"\n",
"dot([[4, 10], [4, 3], [5, 8]]) homomorphically evaluates to 37\n",
"\n",
"#######################################################################################\n",
"\n",
"def matmul(x):\n",
" return x @ np.array([[1, 2, 3], [3, 2, 1]], dtype=np.uint8)\n",
"\n",
"matmul([[7, 10], [3, 8], [3, 3]]) homomorphically evaluates to [[37, 34, 31], [27, 22, 17], [12, 12, 12]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def clip(x):\n",
" return x.clip(6, 11)\n",
"\n",
"clip([[9, 5], [10, 10], [4, 6]]) homomorphically evaluates to [[9, 6], [10, 10], [6, 6]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def comparison(x):\n",
" return x > np.array([[10, 5], [8, 11], [3, 7]], dtype=np.uint8)\n",
"\n",
"comparison([[4, 4], [5, 10], [7, 6]]) homomorphically evaluates to [[0, 0], [0, 0], [1, 0]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def maximum(x):\n",
" return np.maximum(x, np.array([[10, 5], [8, 11], [3, 7]], dtype=np.uint8))\n",
"\n",
"maximum([[9, 7], [4, 10], [6, 8]]) homomorphically evaluates to [[10, 7], [8, 11], [6, 8]]\n",
"\n",
"#######################################################################################\n",
"\n",
"def minimum(x):\n",
" return np.minimum(x, np.array([[10, 5], [8, 11], [3, 7]], dtype=np.uint8))\n",
"\n",
"minimum([[4, 9], [10, 8], [10, 7]]) homomorphically evaluates to [[4, 5], [8, 8], [3, 7]]\n",
"\n"
]
}
],
"source": [
"functions = [\n",
" reshape,\n",
" flatten,\n",
" index,\n",
" slice_,\n",
" add_scalar,\n",
" add_tensor,\n",
" add_tensor_broadcasted,\n",
" sub_scalar,\n",
" sub_tensor,\n",
" sub_tensor_broadcasted,\n",
" mul_scalar,\n",
" mul_tensor,\n",
" mul_tensor_broadcasted,\n",
" power,\n",
" truediv,\n",
" dot,\n",
" matmul,\n",
" clip,\n",
" comparison,\n",
" maximum,\n",
" minimum,\n",
"]\n",
"\n",
"for function in functions:\n",
" compiler = hnp.NPFHECompiler(function, {\"x\": \"encrypted\"})\n",
" circuit = compiler.compile_on_inputset(inputset)\n",
" \n",
" sample = np.random.randint(3, 11, size=(3, 2), dtype=np.uint8)\n",
" result = circuit.run(sample)\n",
" \n",
" print(\"#######################################################################################\")\n",
" \n",
" print()\n",
" print(f\"{inspect.getsource(function)}\")\n",
" print(f\"{function.__name__}({sample.tolist()}) homomorphically evaluates to {result if isinstance(result, int) else result.tolist()}\")\n",
" print()\n",
"\n",
" expected = function(sample)\n",
" if not np.array_equal(result, expected):\n",
" print(f\"(It should have been evaluated to {expected if isinstance(expected, int) else expected.tolist()} but it didn't due to an error during PBS)\")\n",
" print()"
]
}
],
"metadata": {
"execution": {
"timeout": 10800
}
},
"nbformat": 4,
"nbformat_minor": 5
}