HPD: Hybrid Projection Decomposition for Robust State Space Models on Analog CIM Hardware

Abstract: State Space Models (SSMs) are efficient alternatives to traditional sequence models, excelling at processing long sequences with lower computational complexity. Their reliance on matrix multiplications makes them ideal for compute-in-memory (CIM) architectures, which improve energy efficiency by computing within memory arrays. However, device non-idealities in CIM introduce weight perturbations that can degrade inference accuracy. In this paper, we systematically analyze the robustness of SSMs under noisy conditions, identifying that the final block and output projection layers are more susceptible to perturbations compared to other components. Building on these insights, we propose HPD, a Hybrid Projection Decomposition strategy for the last output projection layer. We replace the original weight matrix with the multiplication of U and {\Sigma} in its SVD to ensure compatibility with existing hardware architectures, while offloading V> to digital hardware for precise and robust correction. Comprehensive tests on Mamba models show that our method reduces perplexity by up to 99.57% under various noise conditions compared to baseline models, with accuracy gains of up to 96.67% on the PIQA benchmark for commonsense reasoning.