torch-sla: New Open-Source Library for Differentiable Sparse Linear Algebra in PyTorch
Researchers have released torch-sla, an open-source PyTorch library that provides differentiable sparse linear algebra solvers with multi-GPU support. The library addresses a gap in PyTorch's existing ecosystem, which currently offers only low-level kernels and a non-differentiable, CPU-only sparse solver. It is significant for scientific machine learning applications that require gradient-based optimization through sparse linear systems.
torch-sla is a newly released open-source library designed to bring differentiable sparse linear algebra capabilities to PyTorch, an area the framework has lacked a unified solution for. The library exposes a single autograd-aware API supporting direct, iterative, nonlinear, and eigenvalue solvers across five interchangeable backends: SciPy and Eigen on CPU, and cuDSS, CuPy, and a PyTorch-native iterative solver on GPU. Automatic dispatch selects the appropriate backend based on device and problem size, reducing the burden on users. torch-sla also supports batched solves over shared or distinct sparsity patterns and distributed multi-GPU execution through domain decomposition with halo exchange. Scalability is achieved via an O(1)-graph adjoint differentiation framework and an autograd-compatible distributed halo-exchange layer. The work was submitted to arXiv in January 2026 and has since been revised twice, with the latest version posted in June 2026.
What's missing
The preprint has not undergone formal peer review. No benchmark comparisons against alternative sparse differentiation approaches (e.g., custom adjoint implementations or other frameworks) are described in the abstract, leaving the library's performance advantages unquantified.
What different sources said
- arXiv cs.AICenter
torch-sla: Differentiable Sparse Linear Algebra with Adjoint Solvers and Sparse Tensor Parallelism for PyTorch
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