FusionRCG: Orchestrating Recursive Computation Graphs across GPU Memory Hierarchies

2026-05-11

AI Summary

This work addresses the severe memory bottleneck in GPU-based high-dimensional integral computations, where explosive growth of intermediate variables often leads to out-of-memory errors. To overcome this challenge, the authors propose a joint optimization approach that integrates lifetime-aware recursive computational graph restructuring to minimize live intermediates, algebraic dimensionality reduction via coordinate transformation from Cartesian to spherical systems, and an adaptive multi-level memory scheduling scheme coupled with a tailored parallel kernel architecture to exploit the GPU memory hierarchy efficiently. Evaluated on an A100 GPU, the method achieves up to 3.09× acceleration over GPU4PySCF in self-consistent field (SCF) iterations and demonstrates 75% parallel efficiency across 64 GPUs, substantially enhancing both scalability and performance for high-dimensional integrals.

Abstract

Evaluating high-dimensional integrals via deep hierarchical recurrences is a dominant cost in quantum chemistry. While CPUs manage these efficiently, GPUs suffer a critical mismatch: limited per-thread memory is quickly overwhelmed by an explosion of simultaneously live intermediate variables. As recurrence scales, this forces massive data spilling to global memory, collapsing performance into a severe memory-bound regime. We present FusionRCG, a framework that jointly optimizes computation graph structure and GPU memory mapping. Exploiting the inherent topological flexibility of recurrence graphs, using electron repulsion integrals as an example, we contribute: (1) liveness-aware graph orchestration to minimize peak live intermediates; (2) algebraic dimensionality reduction via stepwise Cartesian-to-spherical fusion, shrinking intermediate footprints by up to $7.7\times$; and (3) an adaptive multi-tier kernel architecture routing graphs across the memory hierarchy. Evaluated on NVIDIA A100 GPUs, FusionRCG achieves up to $3.09\times$ end-to-end SCF speedup over GPU4PySCF and maintains $75\%$ parallel efficiency at 64~GPUs, successfully rescuing these workloads from memory-bound limits.

Problem

• GPU memory hierarchy
• high-dimensional integrals
• quantum chemistry
• memory-bound performance
• intermediate variables

Innovation

• Recursive Computation Graphs
• GPU Memory Hierarchy
• Liveness-aware Orchestration
• Dimensionality Reduction
• Adaptive Kernel Architecture