Optimizing 405B Parameter LLM Inference on Liquid-Cooled B200 Clusters

Serving frontier large language models with over 400 billion parameters poses acute memory bandwidth and inter-device communication challenges. In this deep dive, we detail our low-rank tensor factorization kernel implementations in CUDA and Triton, benchmarking them across 8-way and 16-way NVLink 5.0 Blackwell B200 topologies.

The Matrix Factorization Formulation

Standard dense linear projections require P = TSD2D1 parameters. By decomposing convolution and projection layers into factor matrices r(TS + D2D1), we reduce the memory footprint by up to 64% with negligible perplexity degradation.