Title: Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking) Show Chinese title

Title: 位置：首先求解分层线性模型以理解神经动力学现象（神经坍缩、涌现、懒惰/丰富模式和领悟）

Abstract: In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural network dynamics. These models follow the dynamical feedback principle, which describes how layers mutually govern and amplify each other's evolution. This principle extends beyond the simplified models, successfully explaining a wide range of dynamical phenomena in deep neural networks, including neural collapse, emergence, lazy and rich regimes, and grokking. In this position paper, we call for the use of layerwise linear models retaining the core principles of neural dynamical phenomena to accelerate the science of deep learning. Show Chinese abstract

Abstract: 在物理学中，复杂系统通常被简化为仅保留核心原理的最小可解模型。 在机器学习中，逐层线性模型（例如，线性神经网络）作为神经网络动态的简化表示。 这些模型遵循动态反馈原理，该原理描述了各层如何相互控制并放大彼此的演化。 这一原理不仅限于简化模型，还成功解释了深度神经网络中的广泛动态现象，包括神经坍缩、出现、懒惰和丰富区域以及理解现象。 在本文中，我们呼吁使用保留神经动态现象核心原理的逐层线性模型，以加速深度学习科学的发展。