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GaLore 2: Large-Scale LLM Pre-Training by Gradient Low-Rank Projection
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GaLore 2: Large-Scale LLM Pre-Training by Gradient Low-Rank Projection
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Large language models (LLMs) have revolutionized natural language understanding and generation but face significant memory bottlenecks during training. GaLore, Gradient Low-Rank Projection, addresses this issue by leveraging the inherent low-rank structure of weight gradients, enabling substantial memory savings without sacrificing performance. Recent works further extend GaLore from various aspects, including low-bit quantization and higher-order tensor structures. However, there are several remaining challenges for GaLore, such as the computational overhead of SVD for subspace updates and the integration with state-of-the-art training parallelization strategies (e.g., FSDP). In this paper, we present GaLore 2, an efficient and scalable GaLore framework that addresses these challenges and incorporates recent advancements. In addition, we demonstrate the scalability of GaLore 2 by pre-training Llama 7B from scratch using up to 500 billion training tokens, highlighting its potential impact on real LLM pre-training scenarios.
Forward citations
Cited by 6 Pith papers
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No Subspace to Track: Non-Identifiability and Optimizer State in Low-Rank Training
The top-r gradient subspace in GaLore-family optimizers is statistically non-identifiable beyond ~39 of 128 directions, and the fix is to transport optimizer state across refreshes rather than stabilize the basis.
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Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers
Proposes equivariant optimizers matched to the symmetry groups of embeddings, SwiGLU projections and MoE routers, with experiments showing consistent gains over AdamW on language model pre-training.
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Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training
Low-rank pre-training methods converge to geometrically and spectrally distinct basins from full-rank training and from each other, even at similar validation perplexity.
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Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training
Low-rank pre-training methods converge to geometrically and spectrally distinct basins and show diverging activations compared to full-rank training at 60M-350M scales.
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Gradient Clipping Beyond Vector Norms: A Spectral Approach for Matrix-Valued Parameters
Spectral clipping of leading singular values in gradient matrices stabilizes SGD for non-convex problems with heavy-tailed noise and achieves the optimal convergence rate O(K^{(2-2α)/(3α-2)}).
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Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers
Proposes equivariant optimizer updates matched to layer symmetries for embeddings, SwiGLU MLPs, and MoE routers, with reported gains in validation loss and training stability on several language model architectures.
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