Adaptive Circular Manifold (ACM) Optimiser

Official PyTorch implementation of the Adaptive Circular Manifold (ACM) optimiser, as presented at the 8th International Congress on Human-Computer Interaction, Optimization and Robotic Applications (ICHORA 2026).

Paper: Adaptive Circular Manifold (ACM): A Density-Dependent Geometric Metric for Robust Gradient Descent (Accepted at ICHORA 2026)

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📖 Abstract

Standard optimisation methods, such as basic Gradient Descent and adaptive variants like Adam, typically rely on fixed geometries or sub-Riemannian scaling metrics. This rigidity causes major failures in AI training: aggressive overshooting in steep, dense regions and stagnation on flat plateaus.

The Adaptive Circular Manifold (ACM) is an $\mathcal{O}(N)$ approximation of Natural Gradient Descent that incorporates decoupled weight decay. ACM abandons the variance square-root scaling of Adam in favour of a strictly Tikhonov-regularised diagonal Riemannian metric tensor. By measuring the density of the local gradient, ACM dynamically shrinks or expands its manifold trust region, inherently preventing geometric collapse while guaranteeing $\mathcal{O}(1/\sqrt{T})$ convergence.

Key Features

• Riemannian Metric Tensor: Replaces the flawed square-root denominator of Adam with a mathematically bounded geometric constraint ($G^{-1}_t = 1 / (1 + \kappa \rho_t)$).
• Decoupled Weight Decay: Natively supports $\lambda$ regularisation, achieving state-of-the-art parity with AdamW.
• Massive Variance Reduction: Empirically proven to reduce statistical variance by over 3$\times$ compared to Adam on heavily imbalanced datasets.
• Structural Immunity to Noise: Safely navigates extreme (40%) label noise environments without catastrophic overfitting.

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🛠 Installation

You can install the dependencies and use the optimiser directly from this repository:

git clone https://github.com/Mopheshi/ACM-Optimiser.git
cd ACM-Optimiser
pip install -r requirements.txt

(Optional: If you have configured the setup.py, you can install it as a package using pip install -e .)

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🚀 Quick Start

ACM acts as a direct, drop-in replacement for any standard PyTorch optimiser (e.g., torch.optim.Adam).

import torch
from acm.optimiser import ACM

# 1. Initialise your model
model = MyNeuralNetwork()

# 2. Drop in the ACM optimiser
# Note: ACM requires a slightly higher learning rate than Adam due to its strict geometric braking.
# The 'kappa' parameter controls the manifold sensitivity (default: 10.0, optimal for ResNet: 5.0).
optimiser = ACM(
    model.parameters(), 
    lr=0.005,           # Base learning rate
    kappa=5.0,          # Manifold boundary strictness
    beta1=0.9,          # Momentum decay
    beta2=0.99,         # Density decay
    weight_decay=0.01   # Decoupled weight decay
)

# 3. Standard PyTorch training loop
loss = criterion(model(inputs), targets)
loss.backward()
optimiser.step()
optimiser.zero_grad()

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📂 Repository Structure

acm-optimiser/
│
├── acm/                        # Main Python package
│   ├── __init__.py             
│   └── optimiser.py            # Contains the core ACM class definition
│
├── experiments/                # Scripts to reproduce ICHORA 2026 benchmarks
│   ├── utils.py                # Training engines and reproducibility utilities
│   ├── run_rosenbrock.py       # Geometric trajectory mapping on Rosenbrock
│   ├── run_fashionmnist.py     # 40% label noise overfitting tests
│   ├── run_cora.py             # GCN stability on non-Euclidean topologies
│   └── run_cassava.py          # ResNet-18 statistical variance and hardware scaling
│
├── notebooks/                  
│   └── acm_demo.ipynb          # Interactive Jupyter notebook for getting started
│
├── tests/                      
│   └── test_optimiser.py       # PyTest suite for mathematical bounds and gradient checks
│
├── CITATION.cff                # GitHub integration for automated citations
├── LICENSE                     # MIT License
├── README.md                   
└── requirements.txt            # Project dependencies

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🔬 Reproducing the Paper Experiments

To guarantee full reproducibility of the claims made in the ICHORA 2026 paper, run the benchmark scripts located in the experiments/ directory. All scripts are configured with deterministic seeding (seed=42, 100, 2026).

# Example: Run the Rosenbrock Topography Test
python experiments/run_rosenbrock.py

# Example: Run the ResNet-18 Statistical Validation (Requires Kaggle Cassava Dataset)
python experiments/run_cassava.py

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📜 Citation

If you find this code or the ACM framework useful in your research, please consider citing our ICHORA 2026 paper:

@inproceedings{edward2026acm,
  title={Adaptive Circular Manifold (ACM): A Density-Dependent Geometric Metric for Robust Gradient Descent},
  author={Edward, Ndachimya Magaji and Daniel, Jibrailu and Dauda, Yohanna},
  booktitle={8th International Congress on Human-Computer Interaction, Optimization and Robotic Applications (ICHORA)},
  year={2026},
  organization={IEEE}
}

📄 License

This project is licensed under the MIT Licence - see the LICENCE file for details.