Conservation Spectral SDK — OpenCL

Cross-Vendor GPU Compute for Spectral Graph Analysis

The OpenCL implementation of the Conservation Spectral framework. Laplacian construction, power-iteration eigendecomposition, conservation ratios, Fiedler vector, and anomaly detection — all accelerated on GPU. Runs on NVIDIA, AMD, Intel, and Apple Silicon via OpenCL.

The Aha Moment

OpenCL is the United Nations of GPU compute. It doesn't care if you're running NVIDIA, AMD, Intel, or Apple — the same kernels compile and run everywhere. This matters for conservation analysis because the real world doesn't have homogeneous hardware. A researcher analyzing food web conservation on their MacBook (Apple Silicon), a data center running AMD MI300X, and a workstation with an RTX 4090 should all get the same answers. OpenCL guarantees that. The laplacian, power_iteration, conservation, fiedler, and anomaly kernels are pure data-parallel compute — exactly what GPUs were born to do. Spectral graph analysis on a 10,000-node graph that takes seconds on CPU completes in milliseconds on GPU.

How to Use

# Install OpenCL headers and ICD loader
sudo apt install opencl-headers ocl-icd-opencl-dev

# Build
make

# Run tests
make test

Expected output: a 5-node chord graph analysis showing eigenvalues, spectral gap, Cheeger constant, conservation ratios, and anomaly detection.

Architecture

• OpenCL kernels (kernels/*.cl): laplacian, power_iteration, conservation, fiedler, anomaly
• C host code (src/): Platform/device detection, kernel compilation, data marshalling
• Zero dependencies beyond OpenCL ICD + standard C math/string

Key Kernels

Kernel	Purpose
laplacian	Build L = D - W from adjacency matrix
power_iteration	Find dominant eigenvector via iterative GPU multiply
conservation	Compute α(G,a) = (a^T L a) / (λ_max ‖a‖²)
fiedler	Compute the Fiedler vector (eigenvector of λ₂)
anomaly	Detect conservation anomalies via residual analysis

Connection to the Conservation Spectral Framework

This is the cross-vendor GPU implementation. It implements the same conservation ratio α(G,a) pipeline as the Vulkan, PTX, and WebGPU versions, but prioritizes portability over peak performance. Where Vulkan gives you the lowest-level cross-platform control and PTX lets you hand-write GPU assembly, OpenCL gives you write once, run on any GPU.

Related Repos

• conservation-spectral-vulkan — Lowest-level cross-platform GPU
• conservation-spectral-ptx — Hand-written NVIDIA GPU assembly
• conservation-spectral-webgpu — Browser-based spectral analysis
• conservation-spectral-v2 — Reference Python implementation
• conservation-spectral-asm — CPU AVX2 assembly

License

MIT

Part of the SuperInstance OpenConstruct ecosystem.