Scaling Neural Network Verification with Tensor Parallelism and Fully Sharded Data Parallelism

Abstract: Formal neural network verification -- proving that a network satisfies safety properties for \emph{all} inputs in a specified domain -- is bounded in practice by GPU memory: standard implementations of bound-propagation algorithms (IBP, CROWN, $α$-CROWN) require weight and relaxation-coefficient matrices to reside entirely on one accelerator. We adapt two parallelism techniques originally developed for large-scale model training to the \texttt{auto_LiRPA}\,/\,$α,β$-CROWN verification framework. \textbf{Tensor Parallelism (TP)} shards both weight and $A$-matrices across GPUs, achieving ${\approx}2\times$ peak-memory reduction at $P{=}2$; soundness is confirmed on VNN-COMP 2022 MNIST-FC benchmarks, though bound tightness degrades with the number of sharded zones due to forced IBP substitution for intermediate bounds inside sharded zones. \textbf{Fully Sharded Data Parallelism (FSDP)} shards only weight matrices with a per-layer \texttt{AllGather}, producing bounds that are \emph{bitwise identical} to the single-GPU baseline: baseline memory drops by 80--90\%, peak memory by 34--39\% on wide MLPs. FSDP integrates cleanly with complete verification ($β$-CROWN + Branch-and-Bound) and with convolutional layers (\texttt{BoundConv}); a complete \emph{unsat} result is obtained for CIFAR-100 ResNet-large (VNN-COMP 2024) under FSDP. Across all experiments the memory bottleneck in $α$-CROWN+BaB mode proves to be per-neuron alpha tensors, not weight matrices, pointing to the key direction for future work.