Compiler-First State Space Duality and Portable $O(1)$ Autoregressive Caching for Inference
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908876976160768 |
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| author | Santoni, Cosmo |
| author_facet | Santoni, Cosmo |
| contents | State-space model releases are typically coupled to fused CUDA and Triton kernels, inheriting a hard dependency on NVIDIA hardware. We show that Mamba-2's state space duality algorithm -- diagonal state structure, chunkable recurrence, and einsum-dominated compute with static control flow -- maps cleanly onto what XLA's fusion and tiling passes actually optimise, making custom kernels optional rather than required. We implement the full inference path (prefill, cached autoregressive decoding) as shaped standard primitives under XLA, without hand-written kernels, and realise the architecture's theoretical $O(1)$ state management as a compiled on-device cache requiring no host synchronisation during generation. The implementation runs unmodified on CPU, NVIDIA GPU, and Google Cloud TPU from a single JAX source. On TPU v6e across five model scales (130M--2.7B parameters), XLA-generated code reaches approximately 140 TFLOPS on single-stream prefill ($15%$ MFU) and up to $64%$ bandwidth utilisation on decode. Greedy decoding matches the PyTorch/CUDA reference token-for-token across 64 steps, with hidden-state agreement within float32 rounding tolerance. The pattern transfers to any SSM recurrence satisfying the same structural conditions, on any platform with a mature XLA backend. The implementation is publicly available at https://github.com/CosmoNaught/mamba2-jax and merged into the Bonsai JAX model library. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09555 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compiler-First State Space Duality and Portable $O(1)$ Autoregressive Caching for Inference Santoni, Cosmo Machine Learning Artificial Intelligence Distributed, Parallel, and Cluster Computing Performance State-space model releases are typically coupled to fused CUDA and Triton kernels, inheriting a hard dependency on NVIDIA hardware. We show that Mamba-2's state space duality algorithm -- diagonal state structure, chunkable recurrence, and einsum-dominated compute with static control flow -- maps cleanly onto what XLA's fusion and tiling passes actually optimise, making custom kernels optional rather than required. We implement the full inference path (prefill, cached autoregressive decoding) as shaped standard primitives under XLA, without hand-written kernels, and realise the architecture's theoretical $O(1)$ state management as a compiled on-device cache requiring no host synchronisation during generation. The implementation runs unmodified on CPU, NVIDIA GPU, and Google Cloud TPU from a single JAX source. On TPU v6e across five model scales (130M--2.7B parameters), XLA-generated code reaches approximately 140 TFLOPS on single-stream prefill ($15%$ MFU) and up to $64%$ bandwidth utilisation on decode. Greedy decoding matches the PyTorch/CUDA reference token-for-token across 64 steps, with hidden-state agreement within float32 rounding tolerance. The pattern transfers to any SSM recurrence satisfying the same structural conditions, on any platform with a mature XLA backend. The implementation is publicly available at https://github.com/CosmoNaught/mamba2-jax and merged into the Bonsai JAX model library. |
| title | Compiler-First State Space Duality and Portable $O(1)$ Autoregressive Caching for Inference |
| topic | Machine Learning Artificial Intelligence Distributed, Parallel, and Cluster Computing Performance |
| url | https://arxiv.org/abs/2603.09555 |