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import numpy as np
from dataclasses import dataclass
@dataclass
class Hyperparameters:
num_intervals: int = 200
learning_rate: float = 0.005
num_steps: int = 20000
penalty_strength: float = 1000000.0
class ErdosOptimizer:
"""
Finds a step function h that minimizes the maximum overlap integral.
"""
def __init__(self, hypers: Hyperparameters):
self.hypers = hypers
self.domain_width = 2.0
self.dx = self.domain_width / self.hypers.num_intervals
def compute_c5(self, h: np.ndarray) -> float:
"""Compute C5 bound via cross-correlation of h with (1-h)."""
j = 1.0 - h
correlation = np.correlate(h, j, mode="full") * self.dx
return float(np.max(correlation))
def run_optimization(self):
"""Simple optimization using random restarts and local perturbation."""
N = self.hypers.num_intervals
best_h = None
best_c5 = float("inf")
for trial in range(5):
np.random.seed(42 + trial)
# Initialize h so that integral is 1
h = np.random.uniform(0.3, 0.7, N)
h = h / (np.sum(h) * self.dx) # Normalize integral to 1
h = np.clip(h, 0, 1)
# Re-normalize after clipping
current_integral = np.sum(h) * self.dx
if current_integral > 0:
h = h * (1.0 / current_integral)
h = np.clip(h, 0, 1)
# Simple perturbation-based local search
for step in range(self.hypers.num_steps):
c5 = self.compute_c5(h)
# Random perturbation
idx = np.random.randint(0, N)
delta = np.random.uniform(-0.02, 0.02)
h_new = h.copy()
h_new[idx] = np.clip(h_new[idx] + delta, 0, 1)
# Re-normalize integral
current_integral = np.sum(h_new) * self.dx
if current_integral > 0:
h_new = h_new * (1.0 / current_integral)
h_new = np.clip(h_new, 0, 1)
c5_new = self.compute_c5(h_new)
if c5_new < c5:
h = h_new
c5 = self.compute_c5(h)
if c5 < best_c5:
best_c5 = c5
best_h = h.copy()
print(f"Optimization complete. Final C5 upper bound: {best_c5:.8f}")
return best_h, best_c5
def run():
hypers = Hyperparameters()
optimizer = ErdosOptimizer(hypers)
final_h_values, c5_bound = optimizer.run_optimization()
return final_h_values, c5_bound, hypers.num_intervals
# EVOLVE-BLOCK-END
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