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.
Galore 2: Large-scale llm pre-training by gradient low-rank projection.ArXiv, abs/2504.20437
3 Pith papers cite this work. Polarity classification is still indexing.
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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)}).
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.
citing papers explorer
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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.