669 lines
24 KiB
Python
669 lines
24 KiB
Python
import bisect
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from cmath import isnan
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from email.mime import base
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import matplotlib.pyplot as plt
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import hashlib
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import math
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import numpy as np
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import random
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import statistics
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from pkg_resources import get_distribution
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from scipy import stats
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def encode(v):
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byte_values = []
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for i in range(0, math.ceil(len(v) / 8)):
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x = 0
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for j in range(0, 8):
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index = i * 8 + j
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if index >= len(v):
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continue
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x <<= 1
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x |= int(v[index])
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byte_values.append(x)
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return bytearray(byte_values)
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def sha(v):
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x = encode(v)
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m = hashlib.sha256()
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m.update(x)
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result = m.digest()
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return result[0] & 0b1
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def xor(v):
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total = np.sum(v)
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value = total % 2
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return np.sum(v) % 2
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def hamming_distance(a, b, scratch):
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np.logical_xor(a, b, scratch)
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return sum(scratch)
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def index_hash(indices):
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return ','.join([str(index) for index in sorted(indices)])
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def bin_div(a, b):
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if a == 0 and b == 0:
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return 2
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if a == 1 and b == 0:
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return -1
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if a == 0 and b == 1:
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return 0
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return 1
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class Candidate():
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def __init__(self, indices):
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self.indices = indices[:]
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self.uplift = 0
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def evaluate(self, x):
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if len(x) in self.indices:
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return 0
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value = 1
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for index in self.indices:
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value *= x[index]
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return value
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def id(self):
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return index_hash(self.indices)
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def eval_str(self):
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parts = []
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for index in self.indices:
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parts.append('x[' + str(index) + ']')
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return '*'.join(parts)
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class Probabilities():
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def __init__(self):
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self.N = 8
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self.actual_N = self.N * 2
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self.num_terms = 1
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self.num_candidates = 100
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# self.sample_size = self.N ** 2
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self.sample_size = 64
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self.p = np.zeros((self.actual_N + 1,))
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self.p_temp = np.empty_like(self.p)
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self.next_p = np.empty_like(self.p)
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self.knowns = []
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self.stops = set()
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self.reset_p()
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self.epoch = 0
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self.inputs = np.zeros((self.sample_size, self.actual_N)).astype(np.int32)
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self.raw_inputs = np.zeros((self.sample_size, self.N)).astype(np.int32)
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self.masked_distances = np.zeros((self.sample_size, self.sample_size))
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self.distances = np.zeros((self.sample_size, self.sample_size))
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self.xor_square = np.zeros((self.sample_size, self.sample_size))
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self.base_outputs = np.zeros((self.sample_size)).astype(np.int32)
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self.outputs = np.zeros((self.sample_size)).astype(np.int32)
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self.expected_outputs = np.zeros((self.sample_size)).astype(np.int32)
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self.output_xor = np.zeros((self.sample_size)).astype(np.int32)
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self.mask = np.zeros((self.sample_size))
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self.numerators = np.zeros((self.sample_size))
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self.denominators = np.zeros((self.sample_size))
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self.coherences = np.zeros((self.sample_size))
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self.max_coherences = np.zeros((self.actual_N + 1))
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self.max_candidates = [None for _ in range(0, self.actual_N)]
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self.uplifts = np.zeros((self.actual_N))
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self.uplift_means = np.zeros((self.actual_N))
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self.uplift_medians = np.zeros((self.actual_N))
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self.uplift_convergences = np.zeros((self.actual_N))
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# self.subspace_uplift_samples = [[] for _ in range(0, self.actual_N)]
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self.superspace_uplift_samples = []
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self.subspace_uplifts = np.zeros((self.actual_N))
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self.uplift_ranges = [[0, 0] for _ in range(0, self.actual_N)]
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self.uplift_stddevs = np.zeros((self.actual_N))
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self.samples = 1000
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# self.samples = 200
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self.base_coherence_samples = np.zeros((self.samples))
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self.coherence_samples = np.zeros((self.actual_N, self.samples))
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self.subspace_uplift_left_samples = np.zeros((self.actual_N, self.samples))
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self.subspace_uplift_right_samples = np.zeros((self.actual_N, self.samples))
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self.layers = []
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self.layer_confidence = {}
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self.base = None
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self.scratch = np.zeros((self.N,))
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self.last_value = -1
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self.rounds = 0
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self.average_delta_over_null = 0
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self.visited = set()
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self.candidate_pool = []
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self.candidate_ids = set()
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self.has_added_layer = False
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def randomize_inputs(self):
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for i in range(0, self.sample_size):
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for j in range(0, self.N):
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val = random.randint(0, 1)
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self.raw_inputs[i][j] = val
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self.inputs[i][j * 2] = val
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self.inputs[i][j * 2 + 1] = val ^ 1
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def populate_distances(self):
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for i in range(0, len(self.raw_inputs)):
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x_a = self.raw_inputs[i]
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for j in range(0, len(self.raw_inputs)):
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if i == j:
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continue
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x_b = self.raw_inputs[j]
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distance = hamming_distance(x_a, x_b, self.scratch)
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self.distances[i][j] = 1.0 / (2 ** (distance - 1)) if distance > 0 else 0
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# self.distances[i][j] = 1.0 / (distance ** 2) if distance > 0 else 0
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def compute_expected_outputs(self):
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for i in range(0, len(self.raw_inputs)):
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self.expected_outputs[i] = xor(self.raw_inputs[i])
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def compute_base_outputs(self):
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if self.base is None:
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self.base_outputs.fill(0)
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return
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for i in range(0, len(self.inputs)):
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self.base_outputs[i] = self.base(self.inputs[i])
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def mat_coherence(self):
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np.abs(self.output_xor, self.mask)
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np.subtract(self.output_xor, self.mask, self.mask)
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np.divide(self.mask, 2.0, self.mask)
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np.add(1.0, self.mask, self.mask)
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self.xor_square.fill(0)
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np.copyto(self.masked_distances, self.distances)
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masked_distances_t = self.masked_distances.transpose()
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for i in range(0, len(self.xor_square)):
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self.xor_square[i] = self.output_xor
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np.multiply(self.masked_distances[i], self.mask, self.masked_distances[i])
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np.multiply(masked_distances_t[i], self.mask, masked_distances_t[i])
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np.sum(self.masked_distances, axis=0, out=self.denominators)
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self.xor_square = self.xor_square.transpose()
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np.logical_xor(self.xor_square, self.output_xor, self.xor_square)
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np.multiply(self.xor_square, self.masked_distances, self.xor_square)
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np.sum(self.xor_square, axis=0, out=self.numerators)
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np.divide(self.numerators, self.denominators, self.coherences)
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mean = np.nanmean(self.coherences)
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if isnan(mean):
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mean = 1.0
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return 1.0 - mean
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def coherence(self, outputs=None):
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if outputs is None:
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outputs = self.outputs
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np.logical_xor(outputs, self.expected_outputs, self.output_xor)
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return self.mat_coherence()
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coherences = []
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for i in range(0, len(self.output_xor)):
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y_a = self.output_xor[i]
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numerator = 0
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denominator = 0
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for j in range(0, len(self.output_xor)):
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if i == j:
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continue
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y_b = self.output_xor[j]
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weight = self.distances[i][j]
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denominator += weight
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if y_a == 0 and y_b == 0 or y_a == 1 and y_b == 1:
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numerator += weight
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coherence = numerator / denominator if denominator > 0 else 0
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coherences.append(coherence)
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raw_coherence = sum(coherences) / len(coherences)
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check_coherence = self.mat_coherence()
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return raw_coherence
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def div_coherence(self):
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coherences = []
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for i in range(0, len(self.output_xor)):
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y_a = self.output_xor[i]
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if y_a < 0:
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continue
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numerator = 0
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denominator = 0
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for j in range(0, len(self.output_xor)):
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if i == j:
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continue
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y_b = self.output_xor[j]
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if y_b < 0:
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continue
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weight = self.distances[i][j]
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denominator += weight
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if y_a == 0 and y_b == 0 or y_a == 1 and y_b == 1:
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numerator += weight
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# if y_a < 0 or y_b < 0:
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# numerator += weight
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coherence = numerator / denominator if denominator > 0 else 0
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coherences.append(coherence)
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if len(coherences) == 0:
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return 1.0
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return sum(coherences) / len(coherences)
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def normalize_p(self):
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check = self.knowns[:]
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for i in range(0, len(self.p)):
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if self.p[i] < 0:
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self.p[i] = 0
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for i in range(0, len(self.p)):
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if i in self.knowns:
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flip = i ^ 0b1
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self.p[i] = 0.0
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self.p[flip] = 0.0
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else:
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check.append(i)
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stop_id = index_hash(check)
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check.pop()
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if stop_id in self.stops:
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self.p[i] = 0.0
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total = np.sum(self.p)
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if total > 0:
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for i in range(0, len(self.p)):
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self.p[i] = self.p[i] / total
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def reset_p(self):
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self.p.fill(1.0)
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self.normalize_p()
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def threshold(self):
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# return (1.0 / (self.num_terms - len(self.knowns))) - (self.epoch / 100)
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return 1.0 - (self.epoch / 1000)
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def get_converged_index(self):
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for i in range(0, len(self.p)):
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if self.p[i] > self.threshold():
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return i
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return None
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def add_layer(self):
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self.has_added_layer = True
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self.add_stop()
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layer = Candidate(self.knowns)
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self.layers.append(layer)
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self.base = self.cache_layers()
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self.knowns.pop()
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self.reset_p()
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def random_sample(self):
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self.randomize_inputs()
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self.populate_distances()
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self.compute_expected_outputs()
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self.compute_base_outputs()
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return self.coherence(self.base_outputs)
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def random_candidate(self):
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indices = self.knowns[:]
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np.copyto(self.p_temp, self.p)
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self.p_temp[self.actual_N] = 0
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total = np.sum(self.p_temp)
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if total == 0:
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return None
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np.divide(self.p_temp, total, self.p_temp)
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for _ in range(0, self.num_terms - len(self.knowns)):
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index = np.random.choice(len(self.p_temp), 1, p=self.p_temp)[0]
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indices.append(index)
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flip = index ^ 0b1
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self.p_temp[index] = 0
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self.p_temp[flip] = 0
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for i in range(0, len(self.p_temp)):
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if i not in indices:
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indices.append(i)
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stop_id = index_hash(indices)
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indices.pop()
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if stop_id in self.stops:
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self.p_temp[i] = 0.0
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total = np.sum(self.p_temp)
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if total == 0:
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return None
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np.divide(self.p_temp, total, self.p_temp)
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return Candidate(indices)
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def seed_candidate_pool(self):
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for _ in range(0, self.num_candidates):
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candidate = self.random_candidate()
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if candidate is None:
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continue
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candidate_id = candidate.id()
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if candidate_id in self.candidate_ids:
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continue
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self.candidate_pool.append(candidate)
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self.candidate_ids.add(candidate_id)
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def add_stop(self):
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stop_id = index_hash(self.knowns)
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self.stops.add(stop_id)
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def get_distribution(self, candidate, half = 1):
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count = 0
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for i in range(0, len(self.inputs)):
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value = candidate.evaluate(self.inputs[i])
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if value == half:
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self.output_xor[i] = self.base_outputs[i] ^ self.expected_outputs[i]
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count += 1
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else:
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self.output_xor[i] = -1
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return (count, self.mat_coherence())
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def update(self):
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sample = self.epoch
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self.epoch += 1
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base_coherence = self.random_sample()
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self.base_coherence_samples[sample] = base_coherence - 0.5
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candidate = Candidate(self.knowns[:])
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for i in range(0, self.actual_N):
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candidate.indices.append(i)
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try:
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count_0, subspace_coherence_0 = self.get_distribution(candidate, 0)
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count_1, subspace_coherence_1 = self.get_distribution(candidate, 1)
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# delta = (subspace_coherence_0 - base_coherence) * count_0 / self.sample_size
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# delta = subspace_coherence_0 - subspace_coherence_1
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self.subspace_uplift_left_samples[i][sample] = subspace_coherence_0 - 0.5
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self.subspace_uplift_right_samples[i][sample] = subspace_coherence_1 - 0.5
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# if index_hash(candidate.indices) in self.stops:
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# continue
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for j in range(0, len(self.inputs)):
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self.outputs[j] = self.base_outputs[j] ^ candidate.evaluate(self.inputs[j])
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coherence = self.coherence()
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self.coherence_samples[i][sample] = coherence - 0.5
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finally:
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candidate.indices.pop()
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if self.epoch >= self.samples:
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# for i in range(0, self.actual_N):
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# parameters = stats.norm.fit(self.uplift_samples[i])
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# print(i, parameters)
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# print(i, stats.kstest(self.uplift_samples[i], "norm", parameters))
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added = False
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# parameters = stats.norm.fit(self.base_coherence_samples)
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# (base_mu, _) = parameters
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try:
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index = -1
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lowest_pvalue = -1
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is_subspace = False
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for i in range(0, self.actual_N):
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if i in self.knowns:
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continue
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result = stats.kstest(self.base_coherence_samples, self.coherence_samples[i], alternative='greater')
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print(i, result)
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# value = result.pvalue * (1 - result.statistic)
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if index < 0 or result.pvalue < lowest_pvalue:
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# if index < 0 or value < lowest_pvalue:
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index = i
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lowest_pvalue = result.pvalue
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for i in range(0, self.actual_N):
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if i in self.knowns:
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continue
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result = stats.kstest(self.base_coherence_samples, self.subspace_uplift_left_samples[i], alternative='greater')
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# result = stats.kstest(self.subspace_uplift_left_samples[i], self.subspace_uplift_right_samples[i], alternative='greater')
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print(i, result)
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# value = result.pvalue * (1 - result.statistic)
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if index < 0 or result.pvalue < lowest_pvalue:
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# if index < 0 or value < lowest_pvalue:
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index = i
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lowest_pvalue = result.pvalue
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is_subspace = True
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# if result.pvalue > 0.95:
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# index = i
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# parameters = stats.norm.fit(self.subspace_uplift_samples[i])
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# (mu, _) = parameters
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# if mu > base_mu:
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# if index < 0 or mu > highest_mu:
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# index = i
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# highest_mu = mu
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if index >= 0:
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if is_subspace:
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# print('subspace')
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self.knowns.append(index)
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print(self.knowns, lowest_pvalue)
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else:
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# print('flat')
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self.knowns.append(index)
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# self.layer_confidence[index_hash(self.knowns)] = confidence
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# num_terms = len(self.knowns)
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print(self.knowns, lowest_pvalue)
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print(base_coherence)
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self.add_layer()
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# if num_terms > self.num_terms:
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# self.stops = set()
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# self.num_terms = num_terms
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self.knowns = []
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return
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# if len(self.knowns) > 0:
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# # self.add_stop()
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# self.knowns = []
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finally:
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fig, axs = plt.subplots(4, 4)
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for i in range(0, 4):
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for j in range(0, 4):
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axs[i][j].hist(self.base_coherence_samples, 50, density=True, facecolor='r', alpha=0.5)
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n, bins, patches = axs[i][j].hist(self.coherence_samples[i * 4 + j], 50, density=True, facecolor='g', alpha=0.5)
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n, bins, patches = axs[i][j].hist(self.subspace_uplift_left_samples[i * 4 + j], 50, density=True, facecolor='b', alpha=0.5)
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# n, bins, patches = axs[i][j].hist(self.subspace_uplift_right_samples[i * 4 + j], 50, density=True, facecolor='b', alpha=0.5)
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plt.show()
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self.epoch = 0
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return
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# print('=====' + str(base_coherence))
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# print(self.uplifts)
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# print(self.uplift_means)
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# print(self.uplift_medians)
|
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# print(self.uplift_stddevs)
|
|
# print(self.uplift_ranges)
|
|
# print(self.uplift_convergences)
|
|
# print(self.subspace_uplifts)
|
|
|
|
if index >= 0:
|
|
self.knowns.append(index)
|
|
print(base_coherence)
|
|
print(self.knowns, self.epoch)
|
|
# print(self.uplift_medians)
|
|
# print(self.uplifts)
|
|
# print(self.subspace_uplifts)
|
|
self.add_layer()
|
|
self.uplifts.fill(0)
|
|
self.subspace_uplifts.fill(0)
|
|
self.uplift_medians.fill(0)
|
|
self.uplift_convergences.fill(0)
|
|
self.uplift_samples = [[] for _ in range(0, self.actual_N)]
|
|
self.epoch = 0
|
|
return
|
|
|
|
if subspace_index >= 0:
|
|
self.knowns.append(subspace_index)
|
|
print(self.knowns, self.epoch)
|
|
# print(self.uplifts)
|
|
# print(self.subspace_uplifts)
|
|
self.uplifts.fill(0)
|
|
self.subspace_uplifts.fill(0)
|
|
self.uplift_medians.fill(0)
|
|
self.uplift_convergences.fill(0)
|
|
self.uplift_samples = [[] for _ in range(0, self.actual_N)]
|
|
self.epoch = 0
|
|
return
|
|
|
|
# print('======')
|
|
# print(self.epoch, base_coherence)
|
|
# print('======')
|
|
|
|
# if len(self.candidate_pool) == 0:
|
|
# print(self.p)
|
|
|
|
# for i in range(0, min(5, len(self.candidate_pool))):
|
|
# candidate = self.candidate_pool[i]
|
|
# print(candidate.id(), candidate.uplift)
|
|
|
|
# if self.epoch < 15:
|
|
# return
|
|
|
|
if self.candidate_pool[0].uplift > 0.3:
|
|
candidate = self.candidate_pool[0]
|
|
candidate_id = candidate.id()
|
|
self.candidate_ids.remove(candidate_id)
|
|
print(candidate_id)
|
|
self.knowns = candidate.indices
|
|
self.add_layer()
|
|
self.knowns = []
|
|
self.reset_p()
|
|
self.epoch = 0
|
|
self.candidate_pool = []
|
|
self.candidate_ids = set()
|
|
elif self.candidate_pool[0].uplift < -0.3 or self.epoch > 200:
|
|
self.epoch = 0
|
|
self.num_terms += 1
|
|
self.candidate_pool = []
|
|
self.candidate_ids = set()
|
|
self.knowns = []
|
|
self.stops = set()
|
|
self.reset_p()
|
|
return
|
|
|
|
# np.copyto(self.next_p, self.p)
|
|
for _ in range(0, self.num_candidates):
|
|
candidate = self.random_candidate()
|
|
if candidate is None:
|
|
continue
|
|
candidate_id = candidate.id()
|
|
if candidate_id in visited:
|
|
continue
|
|
visited.add(candidate_id)
|
|
if self.actual_N in candidate.indices:
|
|
continue
|
|
has_candidate = True
|
|
for i in range(0, len(self.inputs)):
|
|
self.outputs[i] = self.base_outputs[i] ^ candidate.evaluate(self.inputs[i])
|
|
# coherence = self.ring_coherence()
|
|
coherence = self.coherence()
|
|
# if coherence <= base_coherence:
|
|
# continue
|
|
# for index in candidate.indices:
|
|
# self.next_p[index] += (coherence - base_coherence) * (1 / 1000.0)
|
|
# self.p_temp[index] += 0
|
|
for index in candidate.indices:
|
|
if coherence > self.max_coherences[index]:
|
|
self.max_coherences[index] = coherence
|
|
self.max_candidates[index] = candidate
|
|
# self.max_coherences[index] = max(self.max_coherences[index], coherence)
|
|
# np.copyto(self.p, self.next_p)
|
|
|
|
# np.copyto(self.p_temp, self.p)
|
|
for i in range(0, self.actual_N):
|
|
candidate = self.max_candidates[i]
|
|
if candidate is None:
|
|
continue
|
|
for index in candidate.indices:
|
|
self.p[index] += (self.max_coherences[index] - base_coherence) * (1 / 1000.0)
|
|
# print(i, self.max_coherences[i] - base_coherence, self.max_candidates[i].id())
|
|
self.normalize_p()
|
|
# print(self.p)
|
|
|
|
# np.subtract(self.p_temp, self.p, self.p_temp)
|
|
# np.abs(self.p_temp, self.p_temp)
|
|
# delta = np.sum(self.p_temp) / len(self.p_temp)
|
|
# print(delta, np.argmax(self.p))
|
|
# np.copyto(self.p_temp, self.p)
|
|
# for i in range(0, len(self.p_temp)):
|
|
# self.p_temp[i] = round(self.p_temp[i] * 100) / 100
|
|
# print(self.p_temp)
|
|
|
|
index = np.argmax(self.p)
|
|
delta_over_null = self.p[index] - self.p[self.actual_N]
|
|
if self.epoch == 0:
|
|
self.average_delta_over_null = delta_over_null
|
|
else:
|
|
self.average_delta_over_null = 0.9 * self.average_delta_over_null + 0.1 * delta_over_null
|
|
diff = self.num_terms - len(self.knowns)
|
|
|
|
print(self.average_delta_over_null, np.argpartition(self.p, -diff)[-diff:], np.argmax(self.p))
|
|
|
|
# Always iterate for a minimum number of epochs
|
|
if self.epoch < 15:
|
|
return
|
|
if self.average_delta_over_null > 0.00001 and self.average_delta_over_null < 0.001 and self.epoch < 300:
|
|
return
|
|
if self.average_delta_over_null < 0.001:
|
|
index = self.actual_N
|
|
else:
|
|
index = np.argmax(self.p)
|
|
|
|
# index = np.argmax(self.p)
|
|
# if index == self.last_value:
|
|
# self.rounds += 1
|
|
# else:
|
|
# self.rounds = 0
|
|
# self.last_value = index
|
|
|
|
# if self.rounds < 10 and self.epoch < 100:
|
|
# return
|
|
|
|
# if self.epoch < 5 or (delta > 0.001 and self.epoch < 50):
|
|
# return
|
|
|
|
# index = np.argmax(self.p)
|
|
|
|
# print(self.p)
|
|
# print(self.threshold())
|
|
# print(self.p)
|
|
# index = self.get_converged_index()
|
|
if not index is None or not has_candidate:
|
|
# print(index, delta, np.argmax(self.p))
|
|
self.epoch = 0
|
|
if index == self.actual_N or not has_candidate:
|
|
if len(self.knowns) > 0:
|
|
self.add_stop()
|
|
self.knowns.pop()
|
|
print('Backtrack: ' + str(self.knowns))
|
|
self.reset_p()
|
|
return
|
|
self.num_terms += 1
|
|
self.knowns = []
|
|
self.stops = set()
|
|
self.reset_p()
|
|
print(self.num_terms)
|
|
return
|
|
self.knowns.append(index)
|
|
# bisect.insort(self.knowns, index)
|
|
if len(self.knowns) == self.num_terms:
|
|
print('Add layer: ' + str(self.knowns))
|
|
self.add_layer()
|
|
else:
|
|
print('Found term: ' + str(self.knowns))
|
|
self.reset_p()
|
|
print(base_coherence)
|
|
return
|
|
|
|
def cache_layers(self):
|
|
expr = 'def f(x):\n\tresult=0\n'
|
|
for layer in self.layers:
|
|
expr += '\tresult^=' + layer.eval_str() + '\n'
|
|
expr += '\treturn result\n'
|
|
scope = {}
|
|
exec(expr, scope)
|
|
return scope['f']
|
|
|
|
def main():
|
|
probabilities = Probabilities()
|
|
# probabilities.knowns = [14]
|
|
# probabilities.add_layer()
|
|
# probabilities.knowns = [8]
|
|
# probabilities.add_layer()
|
|
# probabilities.knowns = [4]
|
|
# probabilities.add_layer()
|
|
while probabilities.num_terms <= probabilities.N:
|
|
probabilities.update()
|
|
|
|
if __name__ == "__main__":
|
|
main() |