aiqbench analysis
This research investigates the theoretical mechanisms behind scaling laws in large language models, specifically demonstrating how nonlinearity in attention mechanisms alters depth scaling behavior compared to linear-attention baselines. By enabling selective focus on relevant tokens, nonlinear attention allows parallel learning of spectral directions and connects layer aggregation dynamics to the central limit theorem. These findings provide critical insight into why deeper architectures succeed and suggest that global covariance structures may be less dominant than previously thought in nonlinear regimes.
Emergent Inverse-Depth Scaling From Nonlinearity In Attention
arXiv:2610.11063v1 Announce Type: cross Abstract: Scaling laws describe power-law improvements in model performance with dataset size and parameter count, yet their underlying mechanisms are not fully understood. To explain the parameter count scaling, existing theory posits power-law scaling with model depth. In linear-attention models, this scaling is tied to a power-law data spectrum: unable to selectively attend to relevant tokens, these models learn according to global spectral strength, with stronger directions learned before weaker ones. Large language models, however, can be strongly nonlinear. Here, we show that nonlinear attention yields inverse-depth decay of loss across all tested data spectra. Nonlinearity enables attention to focus selectively on relevant tokens, allowing strong and weak spectral directions to be learned in parallel. Similar focusing across layers motivates a connection to the central limit theorem: shared error across layers sets the loss plateau, while aggregation turns layer-specific differences into continued gains with depth. Our findings suggest that depth scaling may arise from nonlinearity in attention, which allows large language models to focus locally and may make the global covariance structure less relevant.
Abstract:Scaling laws describe power-law improvements in model performance with dataset size and parameter count, yet their underlying mechanisms are not fully understood. To explain the parameter count scaling, existing theory posits power-law scaling with model depth. In linear-attention models, this scaling is tied to a power-law data spectrum: unable to selectively attend to relevant tokens, these models learn according to global spectral strength, with stronger directions learned before weaker ones. Large language models, however, can be strongly nonlinear. Here, we show that nonlinear attention yields inverse-depth decay of loss across all tested data spectra. Nonlinearity enables attention to focus selectively on relevant tokens, allowing strong and weak spectral directions to be learned in parallel. Similar focusing across layers motivates a connection to the central limit theorem: shared error across layers sets the loss plateau, while aggregation turns layer-specific differences into continued gains with depth. Our findings suggest that depth scaling may arise from nonlinearity in attention, which allows large language models to focus locally and may make the global covariance structure less relevant.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.11063 [cs.LG]
(or arXiv:2610.11063v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.11063 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 270 words
