BitSparse: Compact Activation Storage for ReLU Feed-Forward Networks

Lossless tensor compression could reduce memory usage during training, but training requires tensors to be repeatedly re-encoded. We introduce Losslessly Compressed Tensors (LCT), a GPU execution framework designed for this repeated encode-decode regime. LCT exploits the natural redundancy in floating point data to reduce storage for weights, activations and optimizer states. Highly optimized GPU kernels implement Huffman coding with precomputed codebooks for low compression and decompression overhead, essential for training. Our analysis characterizes LCT's storage costs and adaptation to magnitude shifts. LCT achieves a compression ratio of up to $1.455\times$, and is demonstrated in training and finetuning settings. On a 162M-parameter NanoGPT, LCT reduces memory usage by $24.6\%$ for a $7.2\%$ step-time increase. In Qwen3-4B fine-tuning, LCT saves up to $23.8\%$ of peak memory, enabling a $3.5\times$ larger context length in training on the same GPU.

Training large language models (LLMs) is highly memory-intensive, as training must store not only weights and optimizer states but also intermediate activations for backpropagation. While existing memory-efficient methods largely focus on gradients and optimizer states, activation compression is less well established due to the lack of LLM-tailored theory and guarantees. In this work, we develop a theoretical framework showing that activation compression is safe for linear operators when activation compression is unbiased, but problematic for nonlinear ones. We further derive gradient variance bound and establish convergence guarantees for applying activation compression to all linear operators under the standard $L$-smoothness assumption, showing that it does not change the convergence rate. Guided by the theory, we propose an activation-gradient co-compression method that reuses low-rank activation factors to compress linear-layer gradients without extra computation or additional gradient error. We conduct extensive experiments on Qwen and LLaMA models using a pretraining benchmark and multiple fine-tuning benchmarks to validate our theory and demonstrate competitive performance of our method in both accuracy and compression efficiency. We provide our code in the supplementary material for reproducibility.

Activations have become the primary memory bottleneck in large-batch LLM training. However, existing compression methods fail to exploit the spectral structure of activations, resulting in slow convergence or limited compression. To address this, we bridge the relationship between the algorithm's fast convergence and the requirements for subspace projection, and show that an effective compression should yield an unbiased estimate of the original activation with low variance. We propose Principal-Random Subspace for LLM Activation Compression (PRAC), which novelly decomposes activations into two components: a principal subspace captured via SVD to retain dominant information, and a random subspace sampled from the orthogonal complement to approximate the tail. By introducing a precise scaling factor, we prove that PRAC yields an unbiased gradient estimator with minimum variance under certain conditions. Extensive experiments on pre-training and fine-tuning tasks demonstrate that PRAC achieves up to 36% total memory reduction with negligible performance degradation and minimal computational cost.