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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Nearest Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Server's Data Setup\n",
"The server owns coordinates to points of interest like restaurants and commerces. The coordinates are kept in a LookupTable"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from concrete import fhe\n",
"import numpy\n",
"\n",
"\n",
"# Database of Points of Interests\n",
"points_array = numpy.array([\n",
" [2, 3], [1, 5], [3, 2], [5, 2], [1, 1],\n",
" [9, 4], [13, 2], [14, 13], [9, 8], [8, 0],\n",
" [2, 10], [3, 8], [8, 12], [4, 10], [7, 7],\n",
"])\n",
"N_PTS = points_array.shape[0]\n",
"points = fhe.LookupTable(points_array.flatten())\n",
"\n",
"\n",
"def get_point(index):\n",
" return (points[2*index], points[2*index + 1])\n",
"\n",
"\n",
"def all_distances(x, y):\n",
" xs = numpy.arange(0, 2 * N_PTS, 2)\n",
" ys = numpy.arange(1, 2 * N_PTS, 2)\n",
" a = abs(points[xs] - x)\n",
" b = abs(points[ys] - y)\n",
" return a + b"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use swap sort to find the $K$ nearest points to a given point. However, we are interested in the indices of the elements, not just their distances. We must therefore work on tuples of index and distance, effectively implementing numpy argpartition."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# TLUs\n",
"relu = fhe.univariate(lambda x: x if x > 0 else 0)\n",
"is_positive = fhe.univariate(lambda x: 1 if x > 0 else 0)\n",
"arg_selection = fhe.univariate(lambda x: (x-1)//2 if x % 2 else 0) # relu packed with a flag (alternating between 0 and relu)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def swap(this_idx, this_dist, that_idx, that_dist):\n",
" \"\"\"\n",
" Swaps this and that if this > that. \n",
" We must pass both the index and the distance for both this and that.\n",
"\n",
" Returns:\n",
" idxmin, min, idxmax, max of this and that based on distance\n",
" \"\"\"\n",
" diff = this_dist - that_dist\n",
" idx = arg_selection(2 * (this_idx - that_idx) + is_positive(diff))\n",
" dist = relu(diff)\n",
"\n",
" idx_min = this_idx - idx\n",
" idx_max = that_idx + idx \n",
" dist_min = this_dist - dist\n",
" dist_max = that_dist + dist\n",
" return fhe.array([idx_min, dist_min, idx_max, dist_max])\n",
"\n",
"\n",
"@fhe.compiler({\"x\": \"encrypted\", \"y\": \"encrypted\"})\n",
"def knn(x, y):\n",
" dist = all_distances(x, y)\n",
" idx = list(range(N_PTS))\n",
" for k in range(2):\n",
" for i in range(k+1, N_PTS):\n",
" idx[k], dist[k], idx[i], dist[i] = swap(idx[k], dist[k], idx[i], dist[i])\n",
" return fhe.array([get_point(idx[j]) for j in range(2)])\n",
"\n",
"\n",
"inputset = [(4, 3), (0, 0), (15, 3), (4, 15)]\n",
"\n",
"circuit = knn.compile(inputset)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Client\n",
"The client simply invokes the server's nearest neighbours circuit."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"57.9 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
]
}
],
"source": [
"%%timeit -r 1 -n 1\n",
"circuit.client.keys.generate()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def nearest(x, y):\n",
" ex, ey = circuit.encrypt(x, y)\n",
" res = circuit.run(ex, ey) # Simulate request to the server\n",
" return circuit.decrypt(res)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Benchmarks"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"21.7 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
]
}
],
"source": [
"%%timeit -r 1 -n 1\n",
"nearest(4, 3)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "zama",
"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": "3.9.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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