Compiler-First State Space Duality and Portable $O(1)$ Autoregressive Caching for Inference

TL;DR

This paper introduces a hardware-agnostic, compiler-based approach for efficient autoregressive inference in state-space models, achieving $O(1)$ memory management and high performance across CPU, GPU, and TPU platforms.

Contribution

It presents a novel compiler-first method that maps state-space duality onto XLA optimizations, enabling portable, kernel-free inference with on-device caching.

Findings

Achieves near-peak FLOPS on TPU for large models.

Runs unmodified across CPU, GPU, and TPU from a single JAX source.

Matches reference decoding accuracy across platforms.

Abstract

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.