Low-rank architectures have become increasingly important for efficient large language model (LLM) pre-training, providing substantial reductions in both parameter complexity and memory/computational demands. Despite these advantages, current low-rank methods face three critical shortcomings: (1) compromised model performance, (2) considerable computational overhead, and (3) limited activation memory savings. To address these limitations, we propose Cross-layer Low-Rank residual Network (CR-Net), an innovative parameter-efficient framework inspired by our discovery that inter-layer activation residuals possess low-rank properties. CR-Net implements this insight through a dual-path architecture that efficiently reconstructs layer activations by combining previous-layer outputs with their low-rank differences, thereby maintaining high-rank information with minimal parameters. We further develop a specialized activation recomputation strategy tailored for CR-Net that dramatically reduces memory requirements. Extensive pre-training experiments across model scales from 60M to 7B parameters demonstrate that CR-Net consistently outperforms state-of-the-art low-rank frameworks while requiring fewer computational resources and less memory.

Large language models (LLMs) are revolutionizing many science and engineering fields. However, their huge model sizes impose extremely demanding needs of computational resources in the pre-training stage. Although low-rank factorizations can reduce model parameters, their direct application in LLM pre-training often lead to non-negligible performance loss. To address this fundamental challenge, we introduce CoLA and its memory-efficient implementation, CoLA-M. We leverage the low-rank structure observed widely in model activations, enforcing non-linear transformations between factorized weight matrices to reduce model size, boost model capacity and training efficiency. Experiments on LLaMA models with 60 million to 7 billion parameters show that CoLA reduces the computing cost by $\bf 2\pmb{\times}$ and improves training throughput by $\bf 1.86\pmb{\times}$ while maintaining full-rank level performance. CoLA-M further squeezes memory cost without sacrificing throughput, offering a pre-training approach with collectively superior parameter, computing, and memory efficiency. The LLMs produced are also $\bf 2\pmb{\times}$ smaller, enabling faster inference with lower memory cost on resource-constrained platforms

Low-rank training has emerged as a promising approach for reducing memory usage in training Large Language Models (LLMs). Previous methods either rely on decomposing weight matrices (e.g., LoRA), or seek to decompose gradient matrices (e.g., GaLore) to ensure reduced memory consumption. However, both of them constrain the training in a low-rank subspace, thus inevitably leading to sub-optimal performance. This raises a question: whether it is possible to consistently preserve the low-rank constraint for memory efficiency, while achieving full-rank training (i.e., training with full-rank gradients of full-rank weights) to avoid inferior outcomes? In this paper, we propose a new plug-and-play training framework for LLMs called Fira, as the first attempt to achieve this goal. First, we observe an interesting phenomenon during LLM training: the scaling impact of adaptive optimizers (e.g., Adam) on the gradient norm remains similar from low-rank to full-rank training. Based on this observation, we propose a norm-based scaling method, which utilizes the scaling impact of low-rank optimizers as substitutes for that of original full-rank optimizers to enable full-rank training. In this way, we can preserve the low-rank constraint in the optimizer while achieving full-rank training for better performance. Moreover, we find that there are sudden gradient rises during the optimization process, potentially causing loss spikes. To address this, we further put forward a norm-growth limiter to smooth the gradient via regulating the relative increase of gradient norms. Extensive experiments on the pre-training and fine-tuning of LLMs show that Fira outperforms both LoRA and GaLore, achieving performance that is comparable to or even better than full-rank training.

In the era of large language models, the demand for efficient use of computational resources has become critically important. Although parameter-efficient fine-tuning techniques have achieved results comparable to full fine-tuning, their application during the pre-training phase poses significant challenges. Specifically, employing parameter-efficient strategies at the onset of pre-training can severely compromise efficiency, especially in larger models. In this paper, building upon the fine-tuning method LoRA, we introduce a novel parameter-efficient training technique that frequently alters trainable part of parameters, facilitating effective pre-training. Our method not only achieves memory reductions and computational overhead comparable to current state-of-the-art parameter-efficient algorithms during the pre-training phase but also maintains accuracy levels comparable to those of full pre-training. We provide both theoretical analyses and empirical evidence to demonstrate the effectiveness of our approach.

The growing computational demands posed by increasingly number of neural network's parameters necessitate low-memory-consumption training approaches. Previous memory reduction techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, suffer from the limitation of low rank and saddle point issues, particularly during intensive tasks like pre-training. In this paper, we propose Sparse Spectral Training (SST), an advanced training methodology that updates all singular values and selectively updates singular vectors of network weights, thereby optimizing resource usage while closely approximating full-rank training. SST refines the training process by employing a targeted updating strategy for singular vectors, which is determined by a multinomial sampling method weighted by the significance of the singular values, ensuring both high performance and memory reduction. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, including natural language generation, machine translation, node classification and link prediction, SST demonstrates its capability to outperform existing memory reduction training methods and is comparable with full-rank training in some cases. On OPT-125M, with rank equating to 8.3% of embedding dimension, SST reduces the perplexity gap to full-rank training by 67.6%, demonstrating a significant reduction of the performance loss with prevalent low-rank methods. This approach offers a strong alternative to traditional training techniques, paving the way for more efficient and scalable neural network training solutions.

Despite the dominance and effectiveness of scaling, resulting in large networks with hundreds of billions of parameters, the necessity to train overparameterized models remains poorly understood, while training costs grow exponentially. In this paper, we explore parameter-efficient training techniques as an approach to training large neural networks. We introduce a novel method called ReLoRA, which utilizes low-rank updates to train high-rank networks. We apply ReLoRA to training transformer language models with up to 1.3B parameters and demonstrate comparable performance to regular neural network training. ReLoRA saves up to 5.5Gb of RAM per GPU and improves training speed by 9-40% depending on the model size and hardware setup. Our findings show the potential of parameter-efficient techniques for large-scale pre-training.