Adaptive Nonlinear Compression for Large Foundation Models

Despite achieving superior performance, large foundation models (LFMs) have substantial memory requirements, leading to a growing demand for model compression methods. While low-rank approximation presents a promising hardware-friendly solution, existing linear methods suffer significant information losses due to rank truncation. Nonlinear kernels can enhance expressiveness by operating in higher-dimensional spaces, yet most kernels introduce prohibitive overhead and struggle to support adaptive rank allocation across heterogeneous matrices. In this paper, we propose a compression method called Nonlinear Low-Rank Approximation with Adaptive Budget Allocation (NLA). Instead of relying on linear products, we employ piecewise-linear kernels with a forward-pass optimization operator to approximate weight matrices, enhancing the recovery of high-rank weight matrices from low-rank matrices. Moreover, considering the heterogeneous representation abilities and dynamic sensitivities of different weight matrices, we adaptively allocate the compression ratio of each weight matrix during the re-training process by cubic sparsity scheduling. Through evaluations on large language models and vision models across various datasets, NLA demonstrates superior performance while achieving a higher compression ratio compared to existing methods.