LoRDO: Distributed Low-Rank Optimization with Infrequent Communication

Distributed training of foundation models via DDP is limited by interconnect bandwidth. While infrequent communication strategies reduce synchronization frequency, they remain bottlenecked by the memory and communication requirements of optimizer states. Low-rank optimizers can alleviate these constraints; however, in the localupdate regime, workers lack access to the fullbatch gradients required to compute low-rank projections, which degrades performance. We propose LoRDO, a principled framework unifying low-rank optimization with infrequent synchronization. We first demonstrate that, while global projections based on pseudo-gradients are theoretically superior, they permanently restrict the optimization trajectory to a low-rank subspace. To restore subspace exploration, we introduce a fullrank quasi-hyperbolic update. LoRDO achieves near-parity with low-rank DDP in language modeling and downstream tasks at model scales of 125M-720M, while reducing communication by ≈ 10×. Finally, we show that LoRDO improves performance even more in very low-memory settings with small rank/batch size. However, the deployment of such methods faces two critical constraints. First, for large-scale training (Brown et al.,