mlsanityData to 7 Oct 2026

CoLA: Compute-Efficient Pre-Training of LLMs via Low-Rank Activation

arXiv 2502.10940 ↗First posted 16 Feb 2025cs.LG cs.AIcited by 28

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Abstract (arXiv)

The full-size MLPs and the projection layers in attention introduce tremendous model sizes of large language models (LLMs), consuming extensive computational resources in pre-training. We empirically observe that the activations of pre-trained LLMs exhibit low-rank property. Motivated by such observations, we propose CoLA and its memory-efficient implementation, CoLA-M, to replace these full-size layers with compute-efficient auto-encoders that naturally enforce low-rank activations throughout training. This fundamental architectural change eliminates the activation redundancy and significantly boosts 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 2pmb× and improves training throughput by bf 1.86pmb× 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 2pmb× smaller, enabling faster inference with lower memory cost on resource-constrained platforms.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 35 of its 49 references that are in the map. First posted on arXiv 16 Feb 2025.

Builds on

35 of 49 references.

References · 35

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23 more
  1. 2024GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projectioncited by 447
  2. 2014Speeding up Convolutional Neural Networks with Low Rank Expansionscited by 283
  3. 2015Tensorizing Neural Networkscited by 246
  4. 2023ReLoRA: High-Rank Training Through Low-Rank Updatescited by 200
  5. 2014Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decompositioncited by 199
  6. 2024Scaling Laws for Fine-Grained Mixture of Expertscited by 166
  7. 2021The Low-Rank Simplicity Bias in Deep Networkscited by 150
  8. 2024Flora: Low-Rank Adapters Are Secretly Gradient Compressorscited by 103
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  13. 2024Fira: Can We Achieve Full-rank Training of LLMs Under Low-rank Constraint?cited by 39
  14. 2017Compressing Recurrent Neural Network with Tensor Traincited by 28
  15. 2024Accelerating Transformer Pre-training with 2:4 Sparsitycited by 18
  16. 2024SLoPe: Double-Pruned Sparse Plus Lazy Low-Rank Adapter Pretraining of LLMscited by 18
  17. 2024Training Neural Networks from Scratch with Parallel Low-Rank Adapterscited by 17
  18. 2024CompAct: Compressed Activations for Memory-Efficient LLM Trainingcited by 15
  19. 2024CoMERA: Computing- and Memory-Efficient Training via Rank-Adaptive Tensor Optimizationcited by 14
  20. 2019Active Subspace of Neural Networks: Structural Analysis and Universal Attackscited by 12
  21. 2023How Sparse Can We Prune A Deep Network: A Fundamental Limit Perspectivecited by 9
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 11; 2026: 17.

28 papers.

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  1. 2025AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mappingcited by 22
  2. 2026Muon2: Boosting Muon via Adaptive Second-Moment Preconditioningcited by 15
  3. 2025LOST: Low-rank and Sparse Pre-training for Large Language Modelscited by 10
  4. 2025RefLoRA: Refactored Low-Rank Adaptation for Efficient Fine-Tuning of Large Modelscited by 9
  5. 2025Greedy Low-Rank Gradient Compression for Distributed Learning with Convergence Guaranteescited by 9
  6. 2025Reparameterized LLM Training via Orthogonal Equivalence Transformationcited by 8
  7. 2025CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structurecited by 7
  8. 2025LaX: Boosting Low-Rank Training of Foundation Models via Latent Crossingcited by 6
  9. 2026Stabilizing Native Low-Rank LLM Pretrainingcited by 6
  10. 2026TEON: Tensorized Orthonormalization Beyond Layer-Wise Muon for Large Language Model Pre-Trainingcited by 5
  11. 2026MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-trainingcited by 5
  12. 2025Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarkingcited by 4
16 more
  1. 2026POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformationcited by 3
  2. 2025DiaBlo: Diagonal Blocks Are Sufficient For Finetuningcited by 2
  3. 2025Memory-Efficient Fine-Tuning via Low-Rank Activation Compressioncited by 2
  4. 2025BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Modelscited by 2
  5. 2026SALAAD: Sparse And Low-Rank Adaptation via ADMM for Large Language Model Inferencecited by 1
  6. 2026OASIS: Online Activation Subspace Learning for Memory-Efficient Trainingcited by 1
  7. 2026DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Trainingcited by 1
  8. 2026When Does Context Help? Error Dynamics of Contextual Information in Large Language Modelscited by 0
  9. 2026CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation with Non-linearity Retained at Inferencecited by 0
  10. 2026ELAS: Efficient Pre-Training of Low-Rank Large Language Models via 2:4 Activation Sparsitycited by 0
  11. 2026BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimizationcited by 0
  12. 2026Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Trainingcited by 0
  13. 2026Efficient Pre-Training of LLMs through Truncated SVD Representationscited by 0
  14. 2026GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuningcited by 0
  15. 2026MoARa: Module-Aware Rank Allocation and Structure-Preserving Decomposition for Low-Rank LLM Pre-trainingcited by 0
  16. 2026QuantWM: Temporally Consistent 2-Bit KV Cache Quantization for World Models and Video Generationcited by 0