nsa-flow 0.5.0

Non-negative Stiefel Approximating Flow for interpretable representation learning

🧠 NSA-Flow: Non-negative Stiefel Approximating Flow

NSA-Flow is a general-purpose optimization framework for interpretable representation learning.
It unifies sparse matrix factorization, orthogonalization, and manifold constraints into a single, differentiable algorithm that operates near the Stiefel manifold.

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✨ Overview

Interpretable representation learning remains a core challenge in high-dimensional domains such as neuroimaging, genomics, and text analysis.
NSA-Flow provides a smooth geometric mechanism for balancing reconstruction fidelity and column-wise decorrelation, producing sparse, stable, and interpretable representations.

NSA-Flow enforces structured sparsity via a single tunable weight parameter, combining:

• Continuous orthogonality control via manifold retraction (e.g., soft-polar, polar)
• Non-negativity via proximal updates
• Adaptive gradient scaling and learning-rate control

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🧩 Key Features

• ⚙️ Continuous flow near the Stiefel manifold
• 🧮 Non-negative and orthogonal constraints
• 🧠 Interpretable latent representations
• 🚀 Compatible with PyTorch optimization routines
• 🧬 Validated on neuroimaging and genomics datasets

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📦 Installation

Install from PyPI (once published):

pip install nsa_flow

Or install the latest development version directly from GitHub:

pip install git+https://github.com/stnava/nsa_flow.git

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🧰 Dependencies • Python ≥ 3.9 • PyTorch ≥ 2.0 • NumPy ≥ 1.23 • Matplotlib (for optional visualization)

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🚀 Quick Start

import torch
import nsa_flow
from nsa_flow import nsa_flow, invariant_orthogonality_defect

torch.manual_seed(42)

# Random initialization
Y = torch.randn(50, 10)
X0 = torch.randn_like(Y)

# Run NSA-Flow optimization
result = nsa_flow(
    Y,
    X0=X0,
    w=0.8,
    retraction="soft_polar",
    optimizer="sgdp",
    max_iter=50,
    record_every=1,
    tol=1e-8,
    initial_learning_rate=1e-2,
    verbose=True,
)

print("Initial orthogonality defect:", invariant_orthogonality_defect(Y))
print("Final orthogonality defect:", invariant_orthogonality_defect(result["Y"]))

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📖 Documentation

NSA-Flow exposes a small set of high-level functions:

Function Description

• nsa_flow() Main optimization loop balancing fidelity and orthogonality

• nsa_flow_retract_auto() Retraction operator enforcing manifold constraints

• invariant_orthogonality_defect() Computes orthogonality defect measure

• defect_fast() Fast approximate defect metric

• nsa_flow_autograd() Autograd-compatible variant for joint optimization

• get_torch_optimizer() Returns a configured PyTorch optimizer

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🧪 Validation

NSA-Flow has been validated in:

•	Golub leukemia gene expression dataset

•	Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset

NSA-Flow constraints maintain or improve performance while simplifying latent representations and improving interpretability.

There is also a layer that can be included (potentially) in deep learning tools. See tests/test_nsaf_layer.py. This has not been used tested. ⸻

🧑‍💻 Citation

If you use NSA-Flow in research, please cite:

Stnava et al. (2025). NSA-Flow: Non-negative Stiefel Approximating Flow for Interpretable Representation Learning.

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⚖️ License

MIT License © 2025

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📫 Contact

For issues, feature requests, or contributions, open an issue on GitHub.

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