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deepmind.google·6d ago
AI Engineering
Lobsters·10d ago·5 min read
Keeping Futhark off the GPU
TL;DR
Elias Smedegaard's BSc thesis explores efficient computation of sparse Jacobian matrices using a distance-2 graph coloring algorithm, but challenges arise when integrating CPU and GPU processing in Futhark.
✦ Why It Matters
Consider using a hybrid CPU-GPU approach for tasks requiring both sequential and parallel processing.
Key Takeaways
- Explore efficient algorithms for graph coloring in matrix computations.
- Investigate hybrid CPU-GPU processing for complex workflows.
- Understand the limitations of Futhark's memory management.
- Consider alternative frameworks if Futhark's design constraints hinder performance.
Full Summary
Elias Smedegaard's thesis focuses on computing sparse Jacobian matrices through automatic differentiation, which is crucial for various applications in machine learning and optimization. A key part of his solution involves coloring a graph that represents the sparsity pattern of the matrix.
While optimal graph coloring is NP-hard, Elias implemented a fast greedy algorithm for distance-2 coloring, which is inherently sequential. This presents a challenge when trying to leverage Futhark's capabilities for parallel processing on GPUs, as Futhark's design requires all arrays to reside in GPU memory for efficient execution.
Consequently, the first step of the process, which involves coloring, must be executed on the CPU, complicating the overall workflow. The blog post discusses the limitations of Futhark's implementation and the decision to use a workaround rather than a more principled solution.