414 lines
14 KiB
Python
414 lines
14 KiB
Python
from enum import unique
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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 time
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N = 8
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M = 2
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def vec_to_int(x):
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global N
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z = 0
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for i in range(0, N + 1):
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z <<= 1
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z |= x[i]
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return z
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def timeit(f):
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def timed(*args, **kw):
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ts = time.time()
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result = f(*args, **kw)
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te = time.time()
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print('func:%r took: %2.4f sec' % (f.__name__, te-ts))
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return result
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return timed
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class Candidate:
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def __init__(self, layer):
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global N
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self.layer = layer
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self.node_count = layer
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self.offsets = np.zeros((self.node_count, N + 1)).astype(np.int32)
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class Probabilities:
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def __init__(self, layer):
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global N
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self.layer = layer
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self.node_count = layer
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self.p_offsets = np.zeros((self.node_count, N + 1))
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self.p_offsets.fill(0.5)
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self.offset_coherences = np.zeros((2, self.node_count, N + 1, 2, self.node_count, N + 1))
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self.offset_coherences.fill(-1)
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self.deltas = np.zeros((self.node_count, N + 1, 2, self.node_count, N + 1))
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def has_converged(self):
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global N
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for i in range(0,self.node_count):
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for j in range(0, N + 1):
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if self.p_offsets[i][j] > 0.05 and self.p_offsets[i][j] < 0.95:
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return False
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return True
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def flatten(self):
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global N
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candidate = Candidate(self.layer)
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for i in range(0, self.node_count):
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for j in range(0, N + 1):
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candidate.offsets[i][j] = 1 if self.p_offsets[i][j] >= 0.95 else 0
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return candidate
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def clamp(x, min_value = 0.01, max_value = 1):
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return min(max(x, min_value), max_value)
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def encode(v):
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global N
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byte_values = []
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for i in range(0, math.ceil(N / 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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# 00100111 x4
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# 00000110 x1
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def sha(v):
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global M
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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] % M
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def xor(x):
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num_one_bits = 0
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for i in range(0, len(x)):
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if i == 0:
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continue
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num_one_bits += x[i]
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return num_one_bits % 2
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# 0 ^ 1 ^ (2 ^ (4 * (5 ^ 0 * 7))) * (3 ^ 6 * 7)
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# 0 ^ 1 ^ 2 * 3 ^ 2 * 6 * 7 ^ 3 * 4 * (5 ^ 0 * 7)) ^ 4 * 6 * 7 * (5 ^ 0 * 7)
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# 0 ^ 1 ^ 2 * 3 ^ 2 * 6 * 7 ^ 3 * 4 * 5 ^ 0 * 3 * 4 * 7 ^ 4 * 5 * 6 * 7 ^ 0 * 4 * 6 * 7
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# 0 ^ 1 ^ 2*3 ^ 2*6*7 ^ 3*4*5 ^ 0*3*4*7 ^ 4*5*6*7 ^ 0*4*6*7
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def test_fn(x):
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# 0 1
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# 2 | 3
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# 4 | 5 | 6 | 7
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# | | 0 | 7 | | | |
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return x[0] ^ x[1] ^ ((x[2] ^ (x[4] * (x[5] ^ (x[0] * x[7])))) * (x[3] ^ (x[6] * x[7])))
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def candidate_fn(x):
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return x[0] ^ x[1] ^ (~(x[2] ^ x[3]) * x[2])
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def true_fn(x):
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return x[0] ^ x[1] ^ (x[3] * x[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 coherence(outputs, distances):
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coherences = []
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for i in range(0, len(outputs)):
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y_a = outputs[i]
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numerator = 0
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denominator = 0
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for j in range(0, len(outputs)):
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if i == j:
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continue
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y_b = outputs[j]
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weight = 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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return sum(coherences) / len(coherences)
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def random_sample(m, n):
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inputs = np.zeros((m, n + 1)).astype(np.int32)
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for i in range(0, m):
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for j in range(0, n):
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inputs[i][j] = random.randint(0, 1)
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inputs[i][n] = 1
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return inputs
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def populate_distances(inputs, distances, scratch):
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for i in range(0, len(inputs)):
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x_a = inputs[i]
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for j in range(0, len(inputs)):
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if i == j:
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continue
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x_b = inputs[j]
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distance = hamming_distance(x_a, x_b, scratch)
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distances[i][j] = 1.0 / (2 ** distance)
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def evaluate(layers, candidate, x, compute_scratch):
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global N
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z = evaluate_layers(layers, x, compute_scratch)
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z ^= evaluate_candidate(candidate, x, compute_scratch)
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return z
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def evaluate_layers(layers, x, compute_scratch):
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global N
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z = 0
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for layer in layers:
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z ^= evaluate_candidate(layer, x, compute_scratch)
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return z
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def evaluate_candidate(candidate, x, compute_scratch):
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y = 1
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for j in range(0, candidate.node_count):
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value = 0
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np.multiply(candidate.offsets[j], x, compute_scratch)
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value ^= np.sum(compute_scratch) % 2
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y &= value
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return y
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@timeit
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def compute_scores(probabilities, candidates, num_candidates, layers, scores, distances, inputs, outputs, output_xor, expected_outputs, sample_size, int_scratch):
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global M, N
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for i in range(0, sample_size):
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outputs[0][i] = evaluate_layers(layers, inputs[i], int_scratch)
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for j in range(1, num_candidates):
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np.copyto(outputs[j], outputs[0])
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np.subtract(outputs[0], expected_outputs, output_xor)
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np.mod(output_xor, M, output_xor)
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base_score = coherence(output_xor, distances)
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scores.fill(0)
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unique_candidates = {}
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for j in range(0, num_candidates):
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create_candidate(probabilities, candidates[j])
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unique_candidates[candidate_str(candidates[j])] = j
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for i in range(0, sample_size):
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for _, j in unique_candidates.items():
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candidate = candidates[j]
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outputs[j][i] ^= evaluate_candidate(candidate, inputs[i], int_scratch)
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for _, j in unique_candidates.items():
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candidate = candidates[j]
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np.subtract(outputs[j], expected_outputs, output_xor)
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np.mod(output_xor, M, output_xor)
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score = coherence(output_xor, distances)
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scores[j] = score
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return base_score
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def compute_uplift(candidate, layers, distances, inputs, outputs, output_xor, expected_outputs, sample_size, int_scratch):
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global M, N
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for i in range(0, sample_size):
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outputs[0][i] = evaluate_layers(layers, inputs[i], int_scratch)
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np.subtract(outputs[0], expected_outputs, output_xor)
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np.mod(output_xor, M, output_xor)
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base_score = coherence(output_xor, distances)
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for i in range(0, sample_size):
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outputs[0][i] ^= evaluate_candidate(candidate, inputs[i], int_scratch)
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np.subtract(outputs[0], expected_outputs, output_xor)
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np.mod(output_xor, M, output_xor)
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score = coherence(output_xor, distances)
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return (base_score, score)
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@timeit
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def update_probabilities(probabilities, candidates, inputs, base_score, scores, scale):
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global N
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num_candidates = len(candidates)
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probabilities.offset_coherences.fill(-1)
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for p in range(0, num_candidates):
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candidate = candidates[p]
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if scores[p] == 0:
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continue
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# score = max(scores[p], base_score)
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score = scores[p]
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for j in range(0, probabilities.node_count):
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for k in range(0, N + 1):
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i = candidate.offsets[j][k]
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for m in range(0, probabilities.node_count):
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for n in range(0, N + 1):
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l = candidate.offsets[m][n]
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probabilities.offset_coherences[i][j][k][l][m][n] = max(score, probabilities.offset_coherences[i][j][k][l][m][n])
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p_offsets_next = np.zeros((probabilities.node_count, N + 1))
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inertia = 0
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for j in range(0, probabilities.node_count):
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for k in range(0, N + 1):
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delta = 0
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count = 0
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for m in range(0, probabilities.node_count):
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for n in range(0, N + 1):
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# if j == m and k == n:
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# continue
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p_j1_if_m0 = probabilities.offset_coherences[1][j][k][0][m][n]
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p_j0_if_m0 = probabilities.offset_coherences[0][j][k][0][m][n]
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p_j1_if_m1 = probabilities.offset_coherences[1][j][k][1][m][n]
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p_j0_if_m1 = probabilities.offset_coherences[0][j][k][1][m][n]
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if p_j1_if_m0 >= 0 and p_j0_if_m0 >= 0:
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# delta_if_m0 = (p_j1_if_m0 - base_score) - (p_j0_if_m0 - base_score)
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delta_if_m0 = p_j1_if_m0 - p_j0_if_m0
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delta += delta_if_m0 * (1.0 - probabilities.p_offsets[m][n]) * scale
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count += 1
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if p_j1_if_m1 >= 0 and p_j0_if_m1 >= 0:
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# delta_if_m1 = (p_j1_if_m1 - base_score) - (p_j0_if_m1 - base_score)
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delta_if_m1 = p_j1_if_m1 - p_j0_if_m1
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delta += delta_if_m1 * probabilities.p_offsets[m][n] * scale
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count += 1
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if count > 0:
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delta /= count
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p_offsets_next[j][k] = clamp(probabilities.p_offsets[j][k] + delta, 0, 1)
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inertia += abs(p_offsets_next[j][k] - probabilities.p_offsets[j][k])
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for j in range(0, probabilities.node_count):
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for k in range(0, N + 1):
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p_offset_next = 0.9 * probabilities.p_offsets[j][k] + 0.1 * p_offsets_next[j][k]
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# if p_offset_next <= 0.05:
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# p_offset_next = 0.0
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# elif p_offset_next >= 0.95:
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# p_offset_next = 1.0
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probabilities.p_offsets[j][k] = p_offset_next
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return inertia
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def create_candidate(probabilities, candidate):
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global N
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for i in range(0, probabilities.node_count):
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for j in range(0, N + 1):
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candidate.offsets[i][j] = 1 if random.random() < probabilities.p_offsets[i][j] else 0
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def copy_candidate(src, dest):
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global N
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for i in range(0, src.node_count):
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for j in range(0, N + 1):
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dest.offsets[i][j] = src.offsets[i][j]
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def p(x):
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return math.ceil(x * 100) / 100
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def p_a(x):
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return [p(z) for z in x]
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def print_probabilities(probabilities):
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print('=====================')
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for i in range(0, probabilities.node_count):
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print(i, p_a(probabilities.p_offsets[i]))
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print('=====================')
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def candidate_str(candidate):
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global N
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build_str = ''
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for i in range(0, candidate.node_count):
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for j in range(0, N + 1):
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build_str += str(candidate.offsets[i][j])
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return build_str
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def main():
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global N, M
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sample_size = 64
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num_candidates = 100
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num_survivors = 1
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uplift_sample_size = 100
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output_xor = np.zeros(sample_size,)
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scratch = np.zeros((N + 1,))
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int_scratch = np.zeros((N + 1,)).astype(np.int32)
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g = test_fn
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expected_outputs = np.zeros((sample_size,))
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inputs = random_sample(sample_size, N)
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distances = np.zeros((sample_size, sample_size))
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populate_distances(inputs, distances, scratch)
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for i in range(0, sample_size):
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expected_outputs[i] = g(inputs[i])
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outputs = np.zeros((num_candidates + num_survivors, sample_size,)).astype(np.int32)
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scores = np.zeros((num_candidates + num_survivors,))
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layers = []
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layer = 1
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np.subtract(outputs[0], expected_outputs, output_xor)
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np.mod(output_xor, M, output_xor)
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score = coherence(output_xor, distances)
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while score < 1:
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probabilities = Probabilities(layer)
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candidates = [Candidate(layer) for _ in range(0, num_candidates + num_survivors)]
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inertia = 1
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epoch = 1
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while inertia > 0.001 and epoch < 1000 and not probabilities.has_converged():
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base_score = compute_scores(probabilities, candidates, num_candidates, layers, scores, distances, inputs, outputs, output_xor, expected_outputs, sample_size, int_scratch)
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round_inertia = update_probabilities(probabilities, candidates, inputs, base_score, scores, 1 + 0.01 * epoch)
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inertia = 0.9 * inertia + 0.1 * round_inertia
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print_probabilities(probabilities)
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for candidate in layers:
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print(candidate.offsets)
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max_score = np.max(scores)
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print(base_score, max_score,round_inertia, inertia)
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top_n = sorted(range(len(scores)), key=lambda i: scores[i])[-num_survivors:]
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for i in range(0, num_survivors):
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src_index = top_n[i]
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dest_index = num_candidates + i
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if src_index == dest_index:
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continue
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src = candidates[src_index]
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dest = candidates[dest_index]
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candidates[dest_index] = src
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candidates[src_index] = dest
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inputs = random_sample(sample_size, N)
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populate_distances(inputs, distances, scratch)
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for i in range(0, sample_size):
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expected_outputs[i] = g(inputs[i])
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epoch += 1
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candidate = probabilities.flatten()
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print(candidate.offsets)
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for j in range(0, sample_size):
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outputs[0][j] = evaluate(layers, candidate, inputs[j], int_scratch)
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np.subtract(outputs[0], expected_outputs, output_xor)
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np.mod(output_xor, M, output_xor)
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score = coherence(output_xor, distances)
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average_base_score = 0
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average_score = 0
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for i in range(0, uplift_sample_size):
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inputs = random_sample(sample_size, N)
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populate_distances(inputs, distances, scratch)
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for i in range(0, sample_size):
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expected_outputs[i] = g(inputs[i])
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(base_score, score) = compute_uplift(candidate, layers, distances, inputs, outputs, output_xor, expected_outputs, sample_size, int_scratch)
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average_base_score += base_score
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average_score += score
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average_base_score /= uplift_sample_size
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average_score /= uplift_sample_size
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uplift = average_score - average_base_score
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print(uplift)
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if uplift <= 0:
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layer += 1
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continue
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layers.insert(0, candidate)
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if layer == 1:
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layer += 1
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for candidate in layers:
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print(candidate.offsets)
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if __name__ == "__main__":
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main() |