sigma-pi 0.2.1

A lightweight tool to calculate Predictive Integrity (PI) for PyTorch models.

ΣPI: Observe the Cognitive ability of Your AI Model

ΣPI is a lightweight, universal SDK to calculate Predictive Integrity (PI), a metric from the Integrated Predictive Workspace Theory (IPWT) of consciousness. It provides a powerful, real-time proxy for your model's "cognitive state" during training.

Stop just looking at loss. Start observing how your model learns.

What is Predictive Integrity (PI)?

PI is a score (0 to 1) reflecting a model's internal world model integrity, derived from prediction error (Epsilon), model uncertainty (Tau), and global gradient norm (Surprise). High PI indicates healthy learning; a drop can signal issues like overfitting before loss metrics do.

Why Use ΣPI?

• Early Warning for Training Instability: Detects subtle shifts in model "cognition" before loss metrics diverge.
• Insight into OOD Impact: Quantifies the "surprise" your model experiences when encountering out-of-distribution data.
• Understanding Model Overfitting: Reveals when your model's internal world becomes too rigid or too chaotic.
• Quantifying Cognitive Load: Provides a novel metric for the "effort" your model expends to integrate new information.

Model Zoo & Experiments

The complete model zoo, experimental framework (PILR-S), and all associated results have been migrated to a dedicated repository: dmf-archive/PILF.

This SigmaPI repository now contains only the core SDK for calculating Predictive Integrity. Please visit the PILF repository for all implementation examples, training scripts, and pre-trained models.

Installation

pip install sigma-pi

How to Use

The sigma-pi package provides the core SigmaPI monitor. Here is a basic integration example:

import torch
from sigma_pi import SigmaPI

# 1. Initialize the SigmaPI monitor once outside your training loop
sigma_pi = SigmaPI(device='cuda' if torch.cuda.is_available() else 'cpu')

# 2. Inside your training/validation loop:
#    (Ensure you are in a `with torch.enable_grad():` block for validation)

# Calculate loss
loss_epsilon = loss_fn(logits, target)

# Compute gradients (this is crucial)
model.zero_grad()
loss_epsilon.backward(create_graph=True) # Use create_graph=True if you need to backprop through PI metrics

# Calculate PI metrics
pi_metrics = sigma_pi.calculate(
    model=model,
    loss_epsilon=loss_epsilon,
    logits=logits
)

print(f"PI: {pi_metrics['pi_score']:.4f}, Surprise: {pi_metrics['surprise']:.4f}")

# Don't forget to step your optimizer after calculating PI
optimizer.step()

The returned pi_metrics dictionary contains:

• pi_score: The overall predictive integrity (0-1)
• surprise: Gradient norm indicating model adaptation
• normalized_error: Error scaled by model uncertainty
• cognitive_cost: Combined cost of error and surprise
• Additional component metrics for detailed analysis

Further Reading

PI is a concept derived from the Integrated Predictive Workspace Theory (IPWT), a computational theory of consciousness. To understand the deep theory behind this tool, please refer to https://github.com/dmf-archive/IPWT

Citation

If you wish to cite this work, please use the following BibTeX entry:

@misc{sigma_pi,
  author       = {Rui, L.},
  title        = {{ΣPI: Observe the Cognitive ability of Your AI Model}},
  year         = {2025},
  publisher    = {GitHub},
  url          = {https://github.com/dmf-archive/SigmaPI}
}

License

This project is licensed under the MIT License.