LCSB: Layer-Cyclic Selective Backpropagation for Memory-Efficient On-Device LLM Fine-Tuning

Abstract: Memory-efficient backpropagation (MeBP) has enabled first-order fine-tuning of LLMs on mobile devices with less than 1GB memory. However, MeBP requires backward computation through all transformer layers at every step, where weight decompression alone accounts for 32--42% of backward time. We propose Layer-Cyclic Selective Backpropagation (LCSB), which computes gradients for only a subset of layers per step. Our key insight is that residual connections guarantee gradient flow through identity paths, while AdamW momentum provides implicit updates for non-selected layers. We interpret LCSB as Block Coordinate Descent on the LoRA parameter space, providing theoretical justification for convergence. LCSB achieves up to 1.40$\times$ speedup with less than 2\% quality degradation across five models and three tasks. Surprisingly, in 4-bit quantized settings, LCSB exhibits superior stability: a 3B model that completely diverges under full backpropagation converges smoothly with LCSB, suggesting an implicit regularization effect from selective gradient computation.