CoLA: Compute-Efficient Pre-Training of LLMs via Low-Rank Activation
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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
- 2024GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projectioncited by 447
- 2014Speeding up Convolutional Neural Networks with Low Rank Expansionscited by 283
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Citing papers per year: 2025: 11; 2026: 17.
28 papers.
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- 2025AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mappingcited by 22
- 2026Muon2: Boosting Muon via Adaptive Second-Moment Preconditioningcited by 15
- 2025LOST: Low-rank and Sparse Pre-training for Large Language Modelscited by 10
- 2025RefLoRA: Refactored Low-Rank Adaptation for Efficient Fine-Tuning of Large Modelscited by 9
- 2025Greedy Low-Rank Gradient Compression for Distributed Learning with Convergence Guaranteescited by 9
- 2025Reparameterized LLM Training via Orthogonal Equivalence Transformationcited by 8
- 2025CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structurecited by 7
- 2025LaX: Boosting Low-Rank Training of Foundation Models via Latent Crossingcited by 6
- 2026Stabilizing Native Low-Rank LLM Pretrainingcited by 6
- 2026TEON: Tensorized Orthonormalization Beyond Layer-Wise Muon for Large Language Model Pre-Trainingcited by 5
- 2026MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-trainingcited by 5
- 2025Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarkingcited by 4
16 more
- 2026POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformationcited by 3
- 2025DiaBlo: Diagonal Blocks Are Sufficient For Finetuningcited by 2
- 2025Memory-Efficient Fine-Tuning via Low-Rank Activation Compressioncited by 2
- 2025BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Modelscited by 2
- 2026SALAAD: Sparse And Low-Rank Adaptation via ADMM for Large Language Model Inferencecited by 1
- 2026OASIS: Online Activation Subspace Learning for Memory-Efficient Trainingcited by 1
- 2026DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Trainingcited by 1
- 2026When Does Context Help? Error Dynamics of Contextual Information in Large Language Modelscited by 0
- 2026CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation with Non-linearity Retained at Inferencecited by 0
- 2026ELAS: Efficient Pre-Training of Low-Rank Large Language Models via 2:4 Activation Sparsitycited by 0
- 2026BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimizationcited by 0
- 2026Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Trainingcited by 0
- 2026Efficient Pre-Training of LLMs through Truncated SVD Representationscited by 0
- 2026GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuningcited by 0
- 2026MoARa: Module-Aware Rank Allocation and Structure-Preserving Decomposition for Low-Rank LLM Pre-trainingcited by 0
- 2026QuantWM: Temporally Consistent 2-Bit KV Cache Quantization for World Models and Video Generationcited by 0
- 2026QuantWM: Temporally Consistent 2-Bit KV Cache Quantization for World Models and Video Generation22 Sep 2026
- 2026MoARa: Module-Aware Rank Allocation and Structure-Preserving Decomposition for Low-Rank LLM Pre-training14 Sep 2026
- 2026DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Training27 Jun 2026
- 2026GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuning1 Jun 2026
- 2026Efficient Pre-Training of LLMs through Truncated SVD Representations27 May 2026
- 2026Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training13 May 2026
- 2026BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization11 May 2026
- 2026ELAS: Efficient Pre-Training of Low-Rank Large Language Models via 2:4 Activation Sparsity5 May 2026
- 2026Muon2: Boosting Muon via Adaptive Second-Moment Preconditioning11 Apr 2026
- 2026OASIS: Online Activation Subspace Learning for Memory-Efficient Training10 Apr 2026
- 2026POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation5 Mar 2026
- 2026CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation with Non-linearity Retained at Inference26 Feb 2026
16 more
- 2026MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training25 Feb 2026
- 2026Stabilizing Native Low-Rank LLM Pretraining12 Feb 2026
- 2026When Does Context Help? Error Dynamics of Contextual Information in Large Language Models9 Feb 2026
- 2026SALAAD: Sparse And Low-Rank Adaptation via ADMM for Large Language Model Inference1 Feb 2026
- 2026TEON: Tensorized Orthonormalization Beyond Layer-Wise Muon for Large Language Model Pre-Training30 Jan 2026
- 2025BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Models13 Dec 2025
- 2025Memory-Efficient Fine-Tuning via Low-Rank Activation Compression27 Sep 2025
- 2025CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structure23 Sep 2025
- 2025LOST: Low-rank and Sparse Pre-training for Large Language Models4 Aug 2025
- 2025Greedy Low-Rank Gradient Compression for Distributed Learning with Convergence Guarantees11 Jul 2025
- 2025Reparameterized LLM Training via Orthogonal Equivalence Transformation9 Jun 2025
- 2025DiaBlo: Diagonal Blocks Are Sufficient For Finetuning3 Jun 2025
- 2025Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarking28 May 2025
- 2025LaX: Boosting Low-Rank Training of Foundation Models via Latent Crossing27 May 2025
- 2025RefLoRA: Refactored Low-Rank Adaptation for Efficient Fine-Tuning of Large Models24 May 2025
- 2025AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mapping24 May 2025
- 2025AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mappingcited by 22
- 2026Muon2: Boosting Muon via Adaptive Second-Moment Preconditioningcited by 15
- 2025LOST: Low-rank and Sparse Pre-training for Large Language Modelscited by 10
- 2025RefLoRA: Refactored Low-Rank Adaptation for Efficient Fine-Tuning of Large Modelscited by 9
- 2025Greedy Low-Rank Gradient Compression for Distributed Learning with Convergence Guaranteescited by 9
- 2025Reparameterized LLM Training via Orthogonal Equivalence Transformationcited by 8
- 2025CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structurecited by 7
- 2025LaX: Boosting Low-Rank Training of Foundation Models via Latent Crossingcited by 6
- 2026Stabilizing Native Low-Rank LLM Pretrainingcited by 6
- 2026TEON: Tensorized Orthonormalization Beyond Layer-Wise Muon for Large Language Model Pre-Trainingcited by 5
- 2026MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-trainingcited by 5
- 2025Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarkingcited by 4
12 most cited of 27 All 27 (JSON)
- 2026MoARa: Module-Aware Rank Allocation and Structure-Preserving Decomposition for Low-Rank LLM Pre-training14 Sep 2026
- 2026DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Training27 Jun 2026
- 2026GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuning1 Jun 2026
- 2026Efficient Pre-Training of LLMs through Truncated SVD Representations27 May 2026
- 2026Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training13 May 2026
- 2026BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization11 May 2026
- 2026ELAS: Efficient Pre-Training of Low-Rank Large Language Models via 2:4 Activation Sparsity5 May 2026
- 2026Muon2: Boosting Muon via Adaptive Second-Moment Preconditioning11 Apr 2026
- 2026OASIS: Online Activation Subspace Learning for Memory-Efficient Training10 Apr 2026
- 2026POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation5 Mar 2026
- 2026CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation with Non-linearity Retained at Inference26 Feb 2026
- 2026MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training25 Feb 2026
12 newest of 27 All 27 (JSON)