MC$^2$A: Enabling Algorithm-Hardware Co-Design for Efficient Markov Chain Monte Carlo Acceleration

2025-07-17

AI Summary

To address the high computational overhead of Markov Chain Monte Carlo (MCMC) algorithms in large-scale machine learning and the limited flexibility and system-level efficiency of existing hardware accelerators, this paper proposes MC²A, an algorithm–hardware co-design framework. Its key contributions are: (1) a three-dimensional extension of the roofline model to jointly optimize computation, sampling, and memory; (2) a programmable ISA-based tree-structured processing unit, a reconfigurable Gumbel sampler that avoids expensive exponential and normalization operations, and a crossbar interconnect architecture; and (3) efficient support for irregular memory access patterns and diverse MCMC kernels. End-to-end evaluation demonstrates that MC²A achieves 307.6×, 1.4×, 2.0×, and 84.2× speedups over CPU, GPU, TPU, and the state-of-the-art MCMC accelerator, respectively—significantly enhancing the practicality and scalability of MCMC for planning, optimization, and probabilistic inference.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Security and privacy of machine learning and AI applications

Abstract

An increasing number of applications are exploiting sampling-based algorithms for planning, optimization, and inference. The Markov Chain Monte Carlo (MCMC) algorithms form the computational backbone of this emerging branch of machine learning. Unfortunately, the high computational cost limits their feasibility for large-scale problems and real-world applications, and the existing MCMC acceleration solutions are either limited in hardware flexibility or fail to maintain efficiency at the system level across a variety of end-to-end applications. This paper introduces extbf{MC$^2$A}, an algorithm-hardware co-design framework, enabling efficient and flexible optimization for MCMC acceleration. Firstly, extbf{MC$^2$A} analyzes the MCMC workload diversity through an extension of the processor performance roofline model with a 3rd dimension to derive the optimal balance between the compute, sampling and memory parameters. Secondly, extbf{MC$^2$A} proposes a parametrized hardware accelerator architecture with flexible and efficient support of MCMC kernels with a pipeline of ISA-programmable tree-structured processing units, reconfigurable samplers and a crossbar interconnect to support irregular access. Thirdly, the core of extbf{MC$^2$A} is powered by a novel Gumbel sampler that eliminates exponential and normalization operations. In the end-to-end case study, extbf{MC$^2$A} achieves an overall {$307.6 imes$, $1.4 imes$, $2.0 imes$, $84.2 imes$} speedup compared to the CPU, GPU, TPU and state-of-the-art MCMC accelerator. Evaluated on various representative MCMC workloads, this work demonstrates and exploits the feasibility of general hardware acceleration to popularize MCMC-based solutions in diverse application domains.

Problem

• High computational cost limits MCMC for large-scale applications
• Existing MCMC accelerators lack flexibility or system-level efficiency
• Need for algorithm-hardware co-design to optimize MCMC acceleration

Innovation

• Algorithm-hardware co-design for MCMC acceleration
• Parametrized hardware accelerator with flexible MCMC support
• Novel Gumbel sampler eliminates exponential operations