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ARXIV:2605.13652 · LLM TRAINING · SUBMITTED 14 MAY · 20:10 UTC · FRESHNESS FRESH
ARXIV:2605.13652LLM TRAININGSUBMITTED 14 MAY · 20:10 UTCFRESHNESS FRESHNamrata Shivagunde · Vijeta Deshpande · Sherin Muckatira · Anna Rumshisky · arXiv
A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training.
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Pain A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training.
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A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly.
Pre-training large language models is dominated by the memory cost of storing full-rank weights, gradients, and optimizer states. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly.
ScienceToStartup currently rates this 3.0/10 on the public viability pass. We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. A public repository…
LLM Training moved forward this cycle; last verified May 2026. Public score 3.0/10. Implementation evidence is present through a linked repository.
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A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training.
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10.48550/arXiv.2605.13652A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training.
Abstract
Pre-training large language models is dominated by the memory cost of storing full-rank weights, gradients, and optimizer states. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly. A central question remains open: do low-rank methods produce models that generalize comparably to full-rank training, or does the rank constraint fundamentally alter the solutions reached? Existing comparisons rely almost entirely on validation perplexity from single-seed runs, often carried forward from prior literature. Yet perplexity is a poor proxy for solution quality; two methods can match on perplexity while converging to different loss landscape regions and internal representations. We close this gap by characterizing the solutions found by five low-rank pre-training methods, GaLore and Fira (memory-efficient optimizers), CoLA and SLTrain (architecture reparameterizations), and ReLoRA (adapter-style updates with periodic resets), against full-rank training at three model scales (60M, 130M, 350M). We evaluate each along 16 metrics across four dimensions: 1-D loss landscape along random/top-K PCA directions, 1-D interpolation between checkpoints, spectral structure of the weights and learned updates, and activation similarity to full-rank training. We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. Full-rank training settles into a sharper basin than low-rank methods along random directions, while the reverse holds for the top-1 PCA direction. Each method converges to a geometrically distinct basin. Low-rank activations diverge from full-rank in later layers as training progresses, with GaLore tracking full-rank most closely. Further, validation perplexity does not translate to downstream performance at every scale. Adding geometric and spectral metrics improves the prediction.
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PROBLEM
A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly.
METHOD
Pre-training large language models is dominated by the memory cost of storing full-rank weights, gradients, and optimizer states. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly.
RESULT
ScienceToStartup currently rates this 3.0/10 on the public viability pass. We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. A public repository is linked, so build verification can inspect imple...
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LLM Training moved forward this cycle; last verified May 2026. Public score 3.0/10. Implementation evidence is present through a linked repository.
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A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Pre-training large language models is dominated by the memory cost of storing full-rank weights, gradients, and optimizer states. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 3.0/10 on the public viability pass. We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. A public repository is linked, so build verification can inspect implementation evidence instead of treating the paper as PDF-only.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
LLM Training moved forward this cycle; last verified May 2026. Public score 3.0/10. Implementation evidence is present through a linked repository.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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A geometric and spectral study comparing low-rank pre-training methods for large language models against full-rank training.
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