English(EN) Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks

新框架统一了深度神经网络的表示成本

作者 PulseAugur 编辑部 · [3 个来源] · 2026-06-12 20:57

一篇新的研究论文介绍了一个统一的框架，用于分析参数化数据拟合方法的表示成本。该框架揭示了各种模型（包括核方法、小波和浅层神经网络）的诱导函数空间作为特例。对于具有ReLU激活的深度神经网络，该论文证明了它们的原生空间是拟Banach空间，其中归纳偏倚无法通过深度大于两层的范数来捕捉。 AI

影响这项研究为理解深度神经网络的归纳偏倚提供了理论基础，可能指导未来的模型设计。

排序理由该集群包含一篇在arXiv上发表的研究论文，详细介绍了理解神经网络的新理论框架。

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arXiv cs.LG TIER_1 English(EN) · Greg Ongie, Rahul Parhi · 2026-06-16 04:00

数据科学中的表示成本：基础与深度神经网络的准巴拿赫空间

arXiv:2606.14954v1 Announce Type: cross Abstract: We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers. From this abstract perspective, we define representation costs for arbitrary parametr…
arXiv stat.ML TIER_1 English(EN) · Rahul Parhi · 2026-06-12 20:57

数据科学中的表示成本：基础与深度神经网络的拟Banach空间

We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers. From this abstract perspective, we define representation costs for arbitrary parametric models and reveal their induced (native) functi…
arXiv stat.ML TIER_1 English(EN) · Rahul Parhi · 2026-06-12 20:57

数据科学中的表示成本：基础与深度神经网络的拟Banach空间

We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers. From this abstract perspective, we define representation costs for arbitrary parametric models and reveal their induced (native) functi…