---
language: en
license: mit
library_name: pytorch
tags:
- continual-learning
- catastrophic-forgetting
- information-geometry
- spectral-methods
- computer-vision
metrics:
- accuracy
---

# Anastrophic Regularization CNN (Split-MNIST)

This model card hosts the weights for a CNN trained using **Anastrophic Regularization ($\mathcal{R}_{ana}$)**, a novel approach to mitigate catastrophic forgetting in sequential learning tasks.

## Model Description
Anastrophic Regularization is derived from **Anastrophic Theory**, a mathematical framework for analyzing discrete periodic systems. Unlike standard $L_2$ decay or EWC, this method preserves the structural "Harmonic Memory" of the network by guiding weight evolution along Fisher-Rao geodetic paths.

### Key Advantages
* **Maximum Plasticity**: Weights adapt to new tasks while maintaining the global periodic functional invariants of previous ones.
* **100% Data-Free**: Operates strictly in the spectral domain via Fast Fourier Transforms (FFT). No access to previous training data is required.
* **Privacy Preserving**: Ideal for environments with data-retention constraints where EWC or Replay buffers are not feasible.

## Intended Use
This specific model serves as a benchmark for **Continual Learning**. It was trained on the Split-MNIST dataset:
1. **Task A**: Digits 0-4
2. **Task B**: Digits 5-9 (Trained using $\mathcal{R}_{ana}$ to prevent forgetting Task A).

## Evaluation Results
The model achieves the following performance:
* **Task B (Current) Accuracy**: ~86.69%
* **Task A (Retained) Accuracy**: ~71.16%

## Mathematical Formulation
The weights were optimized using the following objective:

$$\mathcal{R}_{ana}(W) = \lambda(1 - \Phi(Spec(W))) + \eta BB(W, W_{prev})$$

## Citation and Full Paper
For the complete theoretical framework, proof of the Fisher-Rao geodetic paths, and the original publication, please refer to:

**Zenodo Repository:** [https://zenodo.org/records/18699347]

**GitHub Implementation:** [https://github.com/MituMath/Anastrophic-Regularization-PyTorch]