DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Training
For practitioners seeking efficient pre-training of large language models, DLR offers a practical way to close the quality gap between low-rank and full-rank training with no overhead at inference.
DLR introduces a zero-inference-cost, parameter-free plug-in that improves low-rank pre-training quality by augmenting outputs with fixed structured residuals, achieving perplexity gains at 130M+ parameter scales without increasing deployment cost.
Large language models have driven recent progress in language and multimodal AI, yet pre-training them at scale is prohibitively expensive. Low-rank pre-training, which factorizes each weight matrix into a rank-r product to reduce both parameters and FLOPs, is a promising response but typically lags full-rank training in quality. We propose Duplicated Latent Residual (DLR), a training-only, parameter-free, foldable plug-in for low-rank pre-training. DLR augments the standard low-rank output Bz with a fixed structured residual alpha/sqrt(K) * Expand_K(z) that replicates each latent coordinate K = ceil(d_out/r) times across the output. With alpha fixed, DLR adds zero learnable parameters per layer; after training, it is absorbed into the up-projection in closed form, B* = B + alpha/sqrt(K) R^T, so deployment parameter count, FLOPs and memory match the underlying low-rank backbone exactly. Across LLaMA models from 60M to 7B parameters, DLR strengthens low-rank pre-training on C4 validation perplexity in most settings, with the clearest gains at 130M and above; folded checkpoints transfer cleanly to supervised fine-tuning on standard benchmarks.