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"""Analyze and visualize scaling law experiment results
This script aggregates results from multiple scaling law runs and generates
comprehensive visualizations showing how model performance scales with data size.
Usage:
python analyze_scaling_law.py [results_dir]
# Default: analyzes results/scaling_law/
python analyze_scaling_law.py
# Custom directory:
python analyze_scaling_law.py results/my_scaling_experiment/
"""
import json
import sys
from pathlib import Path
from typing import Any
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
def load_scaling_results(results_dir: Path) -> pd.DataFrame:
"""Load all scaling law results into a DataFrame"""
results = []
# Find all summary.json files
for summary_file in results_dir.rglob('summary.json'):
with open(summary_file) as f:
data = json.load(f)
results.append(data)
if not results:
raise ValueError(f"No summary.json files found in {results_dir}")
df = pd.DataFrame(results)
return df
def plot_scaling_curves(df: pd.DataFrame, output_dir: Path) -> None:
"""Plot performance metrics vs. data fraction"""
# Aggregate across seeds
agg_df = df.groupby('data_fraction').agg({
'num_train_samples': 'mean',
'test_acc': ['mean', 'std'],
'test_f1': ['mean', 'std'],
'test_precision': ['mean', 'std'],
'test_recall': ['mean', 'std'],
'training_time_seconds': ['mean', 'std'],
}).reset_index()
# Flatten column names
agg_df.columns = ['_'.join(col).strip('_') if col[1] else col[0]
for col in agg_df.columns]
# Sort by data fraction
agg_df = agg_df.sort_values('data_fraction')
# Create figure with subplots
fig, axes = plt.subplots(2, 2, figsize=(14, 10))
fig.suptitle('Scaling Law: Model Performance vs. Training Data Size',
fontsize=16, fontweight='bold')
# Plot 1: Accuracy vs. Data Fraction
ax = axes[0, 0]
ax.errorbar(agg_df['data_fraction'] * 100,
agg_df['test_acc_mean'],
yerr=agg_df['test_acc_std'],
marker='o', capsize=5, capthick=2, linewidth=2,
label='Test Accuracy')
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('Accuracy', fontsize=12)
ax.set_title('Accuracy vs. Data Size', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3)
ax.legend()
ax.set_ylim([0, 1])
# Plot 2: F1 Score vs. Data Fraction
ax = axes[0, 1]
ax.errorbar(agg_df['data_fraction'] * 100,
agg_df['test_f1_mean'],
yerr=agg_df['test_f1_std'],
marker='o', capsize=5, capthick=2, linewidth=2,
color='green', label='Test F1')
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('F1 Score', fontsize=12)
ax.set_title('F1 Score vs. Data Size', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3)
ax.legend()
ax.set_ylim([0, 1])
# Plot 3: Precision & Recall vs. Data Fraction
ax = axes[1, 0]
ax.errorbar(agg_df['data_fraction'] * 100,
agg_df['test_precision_mean'],
yerr=agg_df['test_precision_std'],
marker='s', capsize=5, capthick=2, linewidth=2,
label='Precision')
ax.errorbar(agg_df['data_fraction'] * 100,
agg_df['test_recall_mean'],
yerr=agg_df['test_recall_std'],
marker='^', capsize=5, capthick=2, linewidth=2,
label='Recall')
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('Score', fontsize=12)
ax.set_title('Precision & Recall vs. Data Size', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3)
ax.legend()
ax.set_ylim([0, 1])
# Plot 4: Training Time vs. Data Fraction
ax = axes[1, 1]
ax.errorbar(agg_df['data_fraction'] * 100,
agg_df['training_time_seconds_mean'] / 60,
yerr=agg_df['training_time_seconds_std'] / 60,
marker='o', capsize=5, capthick=2, linewidth=2,
color='red', label='Training Time')
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('Training Time (minutes)', fontsize=12)
ax.set_title('Training Time vs. Data Size', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3)
ax.legend()
plt.tight_layout()
plt.savefig(output_dir / 'scaling_curves.png', dpi=300, bbox_inches='tight')
print(f"Saved: {output_dir / 'scaling_curves.png'}")
plt.close()
def plot_scaling_curves_logscale(df: pd.DataFrame, output_dir: Path) -> None:
"""Plot performance metrics vs. number of samples (log scale)"""
agg_df = df.groupby('data_fraction').agg({
'num_train_samples': 'mean',
'test_acc': ['mean', 'std'],
'test_f1': ['mean', 'std'],
}).reset_index()
agg_df.columns = ['_'.join(col).strip('_') if col[1] else col[0]
for col in agg_df.columns]
agg_df = agg_df.sort_values('num_train_samples')
fig, axes = plt.subplots(1, 2, figsize=(14, 5))
fig.suptitle('Scaling Law: Performance vs. Number of Training Samples (Log Scale)',
fontsize=16, fontweight='bold')
# Accuracy
ax = axes[0]
ax.errorbar(agg_df['num_train_samples'],
agg_df['test_acc_mean'],
yerr=agg_df['test_acc_std'],
marker='o', capsize=5, capthick=2, linewidth=2,
label='Test Accuracy')
ax.set_xlabel('Number of Training Samples', fontsize=12)
ax.set_ylabel('Accuracy', fontsize=12)
ax.set_title('Accuracy vs. Sample Count', fontsize=13, fontweight='bold')
ax.set_xscale('log')
ax.grid(True, alpha=0.3, which='both')
ax.legend()
ax.set_ylim([0, 1])
# F1 Score
ax = axes[1]
ax.errorbar(agg_df['num_train_samples'],
agg_df['test_f1_mean'],
yerr=agg_df['test_f1_std'],
marker='o', capsize=5, capthick=2, linewidth=2,
color='green', label='Test F1')
ax.set_xlabel('Number of Training Samples', fontsize=12)
ax.set_ylabel('F1 Score', fontsize=12)
ax.set_title('F1 vs. Sample Count', fontsize=13, fontweight='bold')
ax.set_xscale('log')
ax.grid(True, alpha=0.3, which='both')
ax.legend()
ax.set_ylim([0, 1])
plt.tight_layout()
plt.savefig(output_dir / 'scaling_curves_logscale.png', dpi=300, bbox_inches='tight')
print(f"Saved: {output_dir / 'scaling_curves_logscale.png'}")
plt.close()
def plot_overfitting_analysis(df: pd.DataFrame, output_dir: Path) -> None:
"""Plot train-val gap (overfitting indicators)"""
agg_df = df.groupby('data_fraction').agg({
'train_val_acc_gap': ['mean', 'std'],
'train_val_f1_gap': ['mean', 'std'],
}).reset_index()
agg_df.columns = ['_'.join(col).strip('_') if col[1] else col[0]
for col in agg_df.columns]
agg_df = agg_df.sort_values('data_fraction')
fig, axes = plt.subplots(1, 2, figsize=(14, 5))
fig.suptitle('Overfitting Analysis: Train-Val Gap vs. Data Size',
fontsize=16, fontweight='bold')
# Accuracy gap
ax = axes[0]
ax.errorbar(agg_df['data_fraction'] * 100,
agg_df['train_val_acc_gap_mean'],
yerr=agg_df['train_val_acc_gap_std'],
marker='o', capsize=5, capthick=2, linewidth=2,
color='orange', label='Train-Val Acc Gap')
ax.axhline(y=0, color='red', linestyle='--', alpha=0.5, label='No Gap')
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('Train - Val Accuracy', fontsize=12)
ax.set_title('Accuracy Gap (Higher = More Overfitting)', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3)
ax.legend()
# F1 gap
ax = axes[1]
ax.errorbar(agg_df['data_fraction'] * 100,
agg_df['train_val_f1_gap_mean'],
yerr=agg_df['train_val_f1_gap_std'],
marker='o', capsize=5, capthick=2, linewidth=2,
color='purple', label='Train-Val F1 Gap')
ax.axhline(y=0, color='red', linestyle='--', alpha=0.5, label='No Gap')
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('Train - Val F1', fontsize=12)
ax.set_title('F1 Gap (Higher = More Overfitting)', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3)
ax.legend()
plt.tight_layout()
plt.savefig(output_dir / 'overfitting_analysis.png', dpi=300, bbox_inches='tight')
print(f"Saved: {output_dir / 'overfitting_analysis.png'}")
plt.close()
def plot_variance_analysis(df: pd.DataFrame, output_dir: Path) -> None:
"""Plot variance across seeds for each data fraction"""
fig, axes = plt.subplots(1, 2, figsize=(14, 5))
fig.suptitle('Variance Analysis Across Seeds', fontsize=16, fontweight='bold')
# Box plot for accuracy
ax = axes[0]
df_sorted = df.sort_values('data_fraction')
df_sorted['data_fraction_pct'] = df_sorted['data_fraction'] * 100
sns.boxplot(data=df_sorted, x='data_fraction_pct', y='test_acc', ax=ax)
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('Test Accuracy', fontsize=12)
ax.set_title('Accuracy Distribution Across Seeds', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3, axis='y')
# Box plot for F1
ax = axes[1]
sns.boxplot(data=df_sorted, x='data_fraction_pct', y='test_f1', ax=ax)
ax.set_xlabel('Training Data (%)', fontsize=12)
ax.set_ylabel('Test F1 Score', fontsize=12)
ax.set_title('F1 Distribution Across Seeds', fontsize=13, fontweight='bold')
ax.grid(True, alpha=0.3, axis='y')
plt.tight_layout()
plt.savefig(output_dir / 'variance_analysis.png', dpi=300, bbox_inches='tight')
print(f"Saved: {output_dir / 'variance_analysis.png'}")
plt.close()
def generate_summary_table(df: pd.DataFrame, output_dir: Path) -> None:
"""Generate a summary table of results"""
summary = df.groupby('data_fraction').agg({
'num_train_samples': 'mean',
'test_acc': ['mean', 'std'],
'test_f1': ['mean', 'std'],
'test_precision': ['mean', 'std'],
'test_recall': ['mean', 'std'],
'train_val_acc_gap': ['mean', 'std'],
'training_time_seconds': ['mean', 'std'],
'best_epoch': ['mean', 'std'],
}).reset_index()
# Flatten and rename
summary.columns = ['_'.join(col).strip('_') if col[1] else col[0]
for col in summary.columns]
summary = summary.sort_values('data_fraction')
# Format for display
summary['num_train_samples'] = summary['num_train_samples'].round(0).astype(int)
summary['data_fraction_pct'] = (summary['data_fraction'] * 100).round(1)
# Reorder columns
display_cols = [
'data_fraction_pct',
'num_train_samples',
'test_acc_mean', 'test_acc_std',
'test_f1_mean', 'test_f1_std',
'test_precision_mean', 'test_precision_std',
'test_recall_mean', 'test_recall_std',
'train_val_acc_gap_mean', 'train_val_acc_gap_std',
'training_time_seconds_mean', 'training_time_seconds_std',
'best_epoch_mean', 'best_epoch_std',
]
summary_display = summary[display_cols]
# Save to CSV
summary_display.to_csv(output_dir / 'summary_table.csv', index=False)
print(f"Saved: {output_dir / 'summary_table.csv'}")
# Create formatted text table
with open(output_dir / 'summary_table.txt', 'w') as f:
f.write("="*100 + "\n")
f.write("SCALING LAW SUMMARY TABLE\n")
f.write("="*100 + "\n\n")
for _, row in summary.iterrows():
f.write(f"Training Data: {row['data_fraction']*100:.1f}% ({row['num_train_samples']:.0f} samples)\n")
f.write("-" * 80 + "\n")
f.write(f" Test Accuracy: {row['test_acc_mean']:.4f} ± {row['test_acc_std']:.4f}\n")
f.write(f" Test F1: {row['test_f1_mean']:.4f} ± {row['test_f1_std']:.4f}\n")
f.write(f" Test Precision: {row['test_precision_mean']:.4f} ± {row['test_precision_std']:.4f}\n")
f.write(f" Test Recall: {row['test_recall_mean']:.4f} ± {row['test_recall_std']:.4f}\n")
f.write(f" Train-Val Gap: {row['train_val_acc_gap_mean']:+.4f} ± {row['train_val_acc_gap_std']:.4f}\n")
f.write(f" Training Time: {row['training_time_seconds_mean']/60:.2f} ± {row['training_time_seconds_std']/60:.2f} min\n")
f.write(f" Best Epoch: {row['best_epoch_mean']:.1f} ± {row['best_epoch_std']:.1f}\n")
f.write("\n")
print(f"Saved: {output_dir / 'summary_table.txt'}")
# Print to console
print("\n" + "="*100)
print("SCALING LAW SUMMARY")
print("="*100)
print(summary_display.to_string(index=False))
print("="*100 + "\n")
def main():
"""Main analysis function"""
# Get results directory from command line or use default
if len(sys.argv) > 1:
results_dir = Path(sys.argv[1])
else:
results_dir = Path('results/scaling_law')
if not results_dir.exists():
print(f"Error: Results directory not found: {results_dir}")
print(f"Usage: python {sys.argv[0]} [results_dir]")
sys.exit(1)
print(f"\nAnalyzing scaling law results from: {results_dir}")
print("="*80)
# Load all results
df = load_scaling_results(results_dir)
print(f"\nLoaded {len(df)} experiment runs")
print(f"Data fractions: {sorted(df['data_fraction'].unique())}")
print(f"Seeds: {sorted(df['seed'].unique())}")
# Create analysis output directory
analysis_dir = results_dir / 'analysis'
analysis_dir.mkdir(exist_ok=True)
print(f"\nSaving analysis to: {analysis_dir}")
# Generate all visualizations and summaries
print("\nGenerating visualizations...")
plot_scaling_curves(df, analysis_dir)
plot_scaling_curves_logscale(df, analysis_dir)
plot_overfitting_analysis(df, analysis_dir)
plot_variance_analysis(df, analysis_dir)
print("\nGenerating summary tables...")
generate_summary_table(df, analysis_dir)
# Save raw aggregated data
df.to_csv(analysis_dir / 'all_results.csv', index=False)
print(f"Saved: {analysis_dir / 'all_results.csv'}")
print("\n" + "="*80)
print("✓ Analysis complete!")
print(f"All results saved to: {analysis_dir}")
print("="*80 + "\n")
# Key insights
print("KEY INSIGHTS:")
print("-" * 80)
# Find minimum data fraction with >90% of max performance
agg_df = df.groupby('data_fraction')['test_f1'].mean().sort_values(ascending=False)
max_f1 = agg_df.iloc[0]
threshold_90 = max_f1 * 0.9
for frac in sorted(df['data_fraction'].unique()):
mean_f1 = df[df['data_fraction'] == frac]['test_f1'].mean()
if mean_f1 >= threshold_90:
num_samples = df[df['data_fraction'] == frac]['num_train_samples'].mean()
print(f"Minimum data for 90% of max F1: {frac*100:.1f}% ({num_samples:.0f} samples)")
print(f" F1 at {frac*100:.1f}%: {mean_f1:.4f} (max: {max_f1:.4f})")
break
print("-" * 80 + "\n")
if __name__ == '__main__':
main()