Study E — Impact of \(p_e\) under larger batch size¶
Reproduces the sweep of Study A (\(p_e \in [0.001, 0.1]\), \(N=100\), \(\alpha=0.1\)) under a larger batch size, to assess the robustness of the convergence behaviour with respect to the Bernoulli probability of ones \(p_e\).
Run with:
python studies/run_study_E.py
Results are visualised in Study E — Impact of p_e on Convergence (Large Batch).
studies/run_study_E.py¶
#
# Software Name : learning-parities-with-product-networks
# SPDX-FileCopyrightText: Copyright (c) 2026 Orange S.A.
# SPDX-License-Identifier: MIT
#
# This software is distributed under the MIT License .,
# see the "LICENSE.md" file for more details or https://opensource.org/licenses/MIT
#
# Author: Guillaume Larue, guillaume.larue@orange.com
# Software description: Source code of the paper "Learning High-Dimensional Parity Functions with Product Networks"
#
"""
Study E: Impact of p_e on convergence under larger batch size
=============================================================
Same sweep as Study A but with a larger batch size.
Fixed parameters:
N = 100
alpha = 0.1
n_outputs = 1000
p_w = 0.5
batch_size = 1000
max_steps = 10000
Swept parameter:
p_e in [0.001, 0.1] (50 values, log-spaced)
Outputs (saved to studies/results/E_p_e_impact_large_batch_<timestamp>/):
p_e_values.npy – array of tested p_e values
p_diff_matrix.npy – average distance history matrix (n_p_e x max_len), padded
steps_to_convergence.npy – steps to convergence per p_e (max_steps if not converged)
metadata.txt – summary of parameters
"""
import torch
import numpy as np
import os
import sys
from datetime import datetime
# ---------------------------------------------------------------------------
# Path setup
# ---------------------------------------------------------------------------
sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
from training.training import create_and_train_model
# ---------------------------------------------------------------------------
# Device setup
# ---------------------------------------------------------------------------
if torch.cuda.is_available():
device = torch.device("cuda:0")
elif torch.backends.mps.is_available():
device = torch.device("mps")
else:
device = torch.device("cpu")
print(f"Using device: {device}")
# ---------------------------------------------------------------------------
# Results directory
# ---------------------------------------------------------------------------
timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
results_dir = f"studies/results/E_p_e_impact_large_batch_{timestamp}"
os.makedirs(results_dir, exist_ok=True)
print(f"Results directory: {results_dir}/")
# ---------------------------------------------------------------------------
# Study parameters
# ---------------------------------------------------------------------------
n_inputs = 100
n_outputs = 1_000
learning_rate = 0.1
max_steps = 10_000
convergence_threshold = 0.01
stagnation_window = 100
stagnation_threshold = 1e-6
batch_size = 1_000
p_w = 0.5
p_e_values = np.logspace(-3, -1, 50) # [0.001, 0.1]
print(f"\n{'='*80}")
print(f"STUDY E: Impact of p_e under larger batch size")
print(f"{'='*80}")
print(f"N = {n_inputs}")
print(f"alpha = {learning_rate}")
print(f"p_e range: {p_e_values[0]:.4f} to {p_e_values[-1]:.4f} ({len(p_e_values)} values)")
print(f"batch size = {batch_size}")
print(f"{'='*80}\n")
# ---------------------------------------------------------------------------
# Storage
# ---------------------------------------------------------------------------
p_diff_matrix = []
steps_to_convergence = []
# ---------------------------------------------------------------------------
# Training loop – sweep over p_e
# ---------------------------------------------------------------------------
torch.manual_seed(42)
for i, p_e in enumerate(p_e_values):
print(f"Training {i+1}/{len(p_e_values)}: p_e={p_e:.4f}", end="")
result = create_and_train_model(
n_inputs=n_inputs,
n_outputs=n_outputs,
learning_rate=learning_rate,
batch_size=batch_size,
max_steps=max_steps,
convergence_threshold=convergence_threshold,
p_e=p_e,
device=device,
seed=42,
verbose=False,
record_history=True,
p_w=p_w,
stagnation_window=stagnation_window,
stagnation_threshold=stagnation_threshold,
)
training_result = result['training_results']
history = training_result['history']
# Store results
p_diff_matrix.append(history['p_diff'])
steps = training_result['steps'] if training_result['converged'] else max_steps
steps_to_convergence.append(steps)
status = "OK" if training_result['converged'] else "NOK"
print(f" -> {status} steps={steps}, p_diff={training_result['final_p_diff']:.4f}")
# ---------------------------------------------------------------------------
# Pad histories and convert to numpy
# ---------------------------------------------------------------------------
max_len = max(len(h) for h in p_diff_matrix)
p_diff_matrix_padded = []
for hist in p_diff_matrix:
padded = list(hist) + [hist[-1]] * (max_len - len(hist))
p_diff_matrix_padded.append(padded)
p_diff_matrix_padded = np.array(p_diff_matrix_padded, dtype=float)
steps_to_convergence = np.array(steps_to_convergence)
# ---------------------------------------------------------------------------
# Save results
# ---------------------------------------------------------------------------
np.save(f"{results_dir}/p_e_values.npy", p_e_values)
np.save(f"{results_dir}/p_diff_matrix.npy", p_diff_matrix_padded)
np.save(f"{results_dir}/steps_to_convergence.npy", steps_to_convergence)
# ---------------------------------------------------------------------------
# Save metadata
# ---------------------------------------------------------------------------
with open(f"{results_dir}/metadata.txt", 'w') as f:
f.write(f"Study E: Impact of p_e (large batch size)\n")
f.write(f"Timestamp: {timestamp}\n")
f.write(f"N = {n_inputs}\n")
f.write(f"alpha = {learning_rate}\n")
f.write(f"p_e range: {p_e_values[0]:.4f} to {p_e_values[-1]:.4f}\n")
f.write(f"Number of p_e values: {len(p_e_values)}\n")
f.write(f"Max steps: {max_steps}\n")
f.write(f"Convergence threshold: {convergence_threshold}\n")
f.write(f"p_w: {p_w}\n")
print(f"\n{'='*80}")
print(f"Study completed!")
print(f"Results saved to: {results_dir}/")
print(f"{'='*80}")