From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

• URL: http://arxiv.org/abs/2409.14623v1
• Date: Sun, 22 Sep 2024 23:19:04 GMT
• Title: From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks
• Authors: Clémentine C. J. Dominé, Nicolas Anguita, Alexandra M. Proca, Lukas Braun, Daniel Kunin, Pedro A. M. Mediano, Andrew M. Saxe,
• Abstract summary: In artificial networks, the effectiveness of these models relies on their ability to build task specific representation. Prior studies highlight that different initializations can place networks in either a lazy regime, where representations remain static, or a rich/feature learning regime, where representations evolve dynamically. These solutions capture the evolution of representations and the Neural Kernel across the spectrum from the rich to the lazy regimes.
• Score: 47.13391046553908
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Biological and artificial neural networks develop internal representations that enable them to perform complex tasks. In artificial networks, the effectiveness of these models relies on their ability to build task specific representation, a process influenced by interactions among datasets, architectures, initialization strategies, and optimization algorithms. Prior studies highlight that different initializations can place networks in either a lazy regime, where representations remain static, or a rich/feature learning regime, where representations evolve dynamically. Here, we examine how initialization influences learning dynamics in deep linear neural networks, deriving exact solutions for lambda-balanced initializations-defined by the relative scale of weights across layers. These solutions capture the evolution of representations and the Neural Tangent Kernel across the spectrum from the rich to the lazy regimes. Our findings deepen the theoretical understanding of the impact of weight initialization on learning regimes, with implications for continual learning, reversal learning, and transfer learning, relevant to both neuroscience and practical applications.

Related papers

• Artificial Neural Network and Deep Learning: Fundamentals and Theory [0.0]
  This book lays a solid groundwork for understanding data and probability distributions. The book delves into multilayer feed-forward neural networks, explaining their architecture, training processes, and the backpropagation algorithm. The text covers various learning rate schedules and adaptive algorithms, providing strategies to optimize the training process.
  arXiv  Detail & Related papers  (2024-08-12T21:06:59Z)
• Coding schemes in neural networks learning classification tasks [52.22978725954347]
  We investigate fully-connected, wide neural networks learning classification tasks. We show that the networks acquire strong, data-dependent features. Surprisingly, the nature of the internal representations depends crucially on the neuronal nonlinearity.
  arXiv  Detail & Related papers  (2024-06-24T14:50:05Z)
• Dynamical stability and chaos in artificial neural network trajectories along training [3.379574469735166]
  We study the dynamical properties of this process by analyzing through this lens the network trajectories of a shallow neural network. We find hints of regular and chaotic behavior depending on the learning rate regime. This work also contributes to the cross-fertilization of ideas between dynamical systems theory, network theory and machine learning.
  arXiv  Detail & Related papers  (2024-04-08T17:33:11Z)
• How connectivity structure shapes rich and lazy learning in neural circuits [14.236853424595333]
  We investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Our research highlights the pivotal role of initial weight structures in shaping learning regimes.
  arXiv  Detail & Related papers  (2023-10-12T17:08:45Z)
• The Neural Race Reduction: Dynamics of Abstraction in Gated Networks [12.130628846129973]
  We introduce the Gated Deep Linear Network framework that schematizes how pathways of information flow impact learning dynamics. We derive an exact reduction and, for certain cases, exact solutions to the dynamics of learning. Our work gives rise to general hypotheses relating neural architecture to learning and provides a mathematical approach towards understanding the design of more complex architectures.
  arXiv  Detail & Related papers  (2022-07-21T12:01:03Z)
• Data-driven emergence of convolutional structure in neural networks [83.4920717252233]
  We show how fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs. By carefully designing data models, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs.
  arXiv  Detail & Related papers  (2022-02-01T17:11:13Z)
• What can linearized neural networks actually say about generalization? [67.83999394554621]
  In certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization. We show that the linear approximations can indeed rank the learning complexity of certain tasks for neural networks. Our work provides concrete examples of novel deep learning phenomena which can inspire future theoretical research.
  arXiv  Detail & Related papers  (2021-06-12T13:05:11Z)
• Learning Contact Dynamics using Physically Structured Neural Networks [81.73947303886753]
  We use connections between deep neural networks and differential equations to design a family of deep network architectures for representing contact dynamics between objects. We show that these networks can learn discontinuous contact events in a data-efficient manner from noisy observations. Our results indicate that an idealised form of touch feedback is a key component of making this learning problem tractable.
  arXiv  Detail & Related papers  (2021-02-22T17:33:51Z)
• Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
  We propose a topological perspective to represent a network into a complete graph for analysis. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
  arXiv  Detail & Related papers  (2020-08-19T04:53:31Z)
• Deep learning of contagion dynamics on complex networks [0.0]
  We propose a complementary approach based on deep learning to build effective models of contagion dynamics on networks. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks.
  arXiv  Detail & Related papers  (2020-06-09T17:18:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.