Tensor programs quantify neural network convergence to Gaussian limits
Researchers have formalized quantitative bounds on how finite neural networks converge to their infinite-width Gaussian-process limits using tensor programs, establishing inverse square-root error rates in Wasserstein distance. This theoretical advance matters because it bridges the gap between practical finite networks and their mathematical idealization, with implications spanning feed-forward, recurrent, and transformer architectures. The architecture-agnostic framework provides rigorous guarantees that practitioners can use to reason about network behavior at scale, strengthening the theoretical foundations underlying modern deep learning.
Modelwire context
ExplainerThe paper quantifies not just that finite networks converge to Gaussian processes, but establishes concrete error rates (inverse square-root in Wasserstein distance). Prior work showed convergence happens; this work puts numbers on how fast and how tight those bounds are.
This sits in direct tension with the NTK dichotomy paper from the same day. While that work showed neural tangent kernels fail on compositional tasks relative to learned representations, this paper formalizes when finite networks actually behave like their kernel approximations (at infinite width). The two papers are asking opposite questions: one proves kernels break down; this one proves when they're valid. Together they clarify a critical boundary: tensor programs give you rigorous guarantees about network behavior, but only in regimes where architectural depth and compositionality don't dominate the learning problem.
If follow-up work applies these quantitative bounds to the compositional learning tasks from the NTK paper (e.g., proving finite-width networks still fail on those problems despite the Gaussian-process convergence guarantees), that confirms the bounds are tight enough to be practically informative. If the bounds remain too loose to rule out learning on structured tasks, the theoretical advance stays mostly academic.
Coverage we drew on
This analysis is generated by Modelwire’s editorial layer from our archive and the summary above. It is not a substitute for the original reporting. How we write it.
MentionsGaussian processes · Tensor programs · Transformers · Recurrent neural networks
Modelwire Editorial
This synthesis and analysis was prepared by the Modelwire editorial team. We use advanced language models to read, ground, and connect the day’s most significant AI developments, providing original strategic context that helps practitioners and leaders stay ahead of the frontier.
Modelwire summarizes, we don’t republish. arXiv cs.LG originally reported this story as “Quantitative Gaussian-Process limits of Tensor Programs”. The full content lives on arxiv.org. If you’re a publisher and want a different summarization policy for your work, see our takedown page.