arXiv AI
What Does the Rank Buy? A Spectral and Distributional Analysis of Low-Rank Adaptation
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
Related stories
arXiv Machine Learning
Jul 31
Tight Sample Complexity for Low-Rank Adaptation: Matching Bounds and Rank Selection
arXiv:2607. 27680v1 Announce Type: new Abstract: Low-Rank Adaptation (LoRA) has become the standard mechanism for fine-tuning large pretrained models, yet its statistical properties remain only partially understood.
arXiv Machine Learning
Oct 19
How Finite-Rank Bottlenecks Shape the Low-Rank Adaptation Landscape
arXiv:2610.23343v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) has become the standard method for parameter-efficient fine-tuning of large pretrained models, yet theoretical explanations...
arXiv Machine Learning
Sep 14
Rank-Efficient LoRA via Joint Tangent-Space Optimization under Isotropic Curvature
The paper introduces ISO-LoRA, an optimizer that improves rank utilization in Low‑Rank Adaptation (LoRA) by coupling factor updates through spectral descent on the induced tangent perturbation in weight space. Experiments on GPT‑2 adaptation show that standard optimizers like AdamW concentrate updates in a few singular directions, whereas ISO-LoRA distributes energy more evenly, leading to higher effective rank and better downstream performance across 0.1B‑7B models. The authors provide theoretical guarantees under a stylized spiked‑gradient model and demonstrate that ISO-LoRA consistently outperforms factor‑wise optimizers, especially at moderate‑to‑large LoRA ranks.
arXiv Machine Learning
Jul 28
The Entropic Bound for Transformers: Why Static Rank Fails and Attention-Native Rank Recovers
arXiv:2607. 23050v1 Announce Type: new Abstract: Neural scaling laws describe how loss decreases as models, data, and compute grow, but they do not answer a prior question: for a fixed task, what is the minimum model capacity required to solve it?
arXiv Machine Learning
Aug 27
How Much Rank Does LoRA Need? Rank-Error Bounds for Transformer Attention
arXiv:2608. 26052v1 Announce Type: new Abstract: Choosing the rank of a low-rank adaptation (LoRA) update is usually an empirical task.
arXiv Machine Learning
Aug 20
Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems
The paper proposes a new dimension‑reduction strategy for transfer‑operator models of dynamical systems that focuses on scoring the σ‑algebra generated by coordinates rather than the operator’s spectral span. By using a χ²‑divergence criterion between embedded present and future states, the method guarantees that twice the intrinsic system dimension suffices to capture the full operator spectrum, even for systems with weakly interacting components that would otherwise require exponentially many modes. Experiments on benchmark systems show that this algebraic approach recovers masked components missed by rank‑based methods and enables accurate prediction of those components from few labels.