On Multi-Stage Loss Dynamics in Neural Networks: Mechanisms of Plateau and Descent Stages

• URL: http://arxiv.org/abs/2410.20119v2
• Date: Wed, 06 Nov 2024 02:57:42 GMT
• Title: On Multi-Stage Loss Dynamics in Neural Networks: Mechanisms of Plateau and Descent Stages
• Authors: Zheng-An Chen, Tao Luo, GuiHong Wang,
• Abstract summary: We identify three distinct stages observed in the loss curve during training: the initial plateau stage, the initial descent stage, and the secondary plateau stage. Through rigorous analysis, we reveal the underlying challenges contributing to slow training during the plateau stages.
• Score: 1.5235340620594793
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The multi-stage phenomenon in the training loss curves of neural networks has been widely observed, reflecting the non-linearity and complexity inherent in the training process. In this work, we investigate the training dynamics of neural networks (NNs), with particular emphasis on the small initialization regime, identifying three distinct stages observed in the loss curve during training: the initial plateau stage, the initial descent stage, and the secondary plateau stage. Through rigorous analysis, we reveal the underlying challenges contributing to slow training during the plateau stages. While the proof and estimate for the emergence of the initial plateau were established in our previous work, the behaviors of the initial descent and secondary plateau stages had not been explored before. Here, we provide a more detailed proof for the initial plateau, followed by a comprehensive analysis of the initial descent stage dynamics. Furthermore, we examine the factors facilitating the network's ability to overcome the prolonged secondary plateau, supported by both experimental evidence and heuristic reasoning. Finally, to clarify the link between global training trends and local parameter adjustments, we use the Wasserstein distance to track the fine-scale evolution of weight amplitude distribution.

Related papers

• Dichotomy of Feature Learning and Unlearning: Fast-Slow Analysis on Neural Networks with Stochastic Gradient Descent [5.5165579223151795]
  In this study, we consider the infinite-width limit of a two-layer neural network updated with a large-batch gradient, then derive differential equations with different time scales.<n>The direction of a flow on a critical manifold, determined by the slow dynamics, decides whether feature unlearning occurs.<n>Our results yield the following insights: (i) the strength of the primary nonlinear term in data induces the feature unlearning, and (ii) an initial scale of the second-layer weights mitigates the feature unlearning.
  arXiv  Detail & Related papers  (2026-02-07T05:50:44Z)
• Emergence of Superposition: Unveiling the Training Dynamics of Chain of Continuous Thought [64.43689151961054]
  We theoretically analyze the training dynamics of a simplified two-layer transformer on the directed graph reachability problem.<n>Our analysis reveals that during training using continuous thought, the index-matching logit will first increase and then remain bounded under mild assumptions.
  arXiv  Detail & Related papers  (2025-09-27T15:23:46Z)
• The Butterfly Effect: Neural Network Training Trajectories Are Highly Sensitive to Initial Conditions [51.68215326304272]
  We show that even small perturbations reliably cause otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time.<n>Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.
  arXiv  Detail & Related papers  (2025-06-16T08:35:16Z)
• New Evidence of the Two-Phase Learning Dynamics of Neural Networks [59.55028392232715]
  We introduce an interval-wise perspective that compares network states across a time window.<n>We show that the response of the network to a perturbation exhibits a transition from chaotic to stable.<n>We also find that after this transition point the model's functional trajectory is confined to a narrow cone-shaped subset.
  arXiv  Detail & Related papers  (2025-05-20T04:03:52Z)
• Enlightenment Period Improving DNN Performance [7.374268326712801]
  In the early stage of deep neural network training, the loss decreases rapidly before gradually leveling off. Existing studies suggest that the introduction of noise during early training can degrade model performance. We identify a critical "enlightenment period" encompassing up to the first 4% of the training cycle.
  arXiv  Detail & Related papers  (2025-04-02T13:49:31Z)
• On the Cone Effect in the Learning Dynamics [57.02319387815831]
  We take an empirical perspective to study the learning dynamics of neural networks in real-world settings. Our key findings reveal a two-phase learning process: i) in Phase I, the eNTK evolves significantly, signaling the rich regime, and ii) in Phase II, the eNTK keeps evolving but is constrained in a narrow space.
  arXiv  Detail & Related papers  (2025-03-20T16:38:25Z)
• In-Context Linear Regression Demystified: Training Dynamics and Mechanistic Interpretability of Multi-Head Softmax Attention [52.159541540613915]
  We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution.
  arXiv  Detail & Related papers  (2025-03-17T02:00:49Z)
• Training Dynamics of Transformers to Recognize Word Co-occurrence via Gradient Flow Analysis [97.54180451650122]
  We study the dynamics of training a shallow transformer on a task of recognizing co-occurrence of two designated words. We analyze the gradient flow dynamics of simultaneously training three attention matrices and a linear layer. We prove a novel property of the gradient flow, termed textitautomatic balancing of gradients, which enables the loss values of different samples to decrease almost at the same rate and further facilitates the proof of near minimum training loss.
  arXiv  Detail & Related papers  (2024-10-12T17:50:58Z)
• Non-asymptotic Convergence of Training Transformers for Next-token Prediction [48.9399496805422]
  Transformers have achieved extraordinary success in modern machine learning due to their excellent ability to handle sequential data. This paper provides a fine-grained non-asymptotic analysis of the training dynamics of a one-layer transformer. We show that the trained transformer presents non-token prediction ability with dataset shift.
  arXiv  Detail & Related papers  (2024-09-25T20:22:06Z)
• Universal Sharpness Dynamics in Neural Network Training: Fixed Point Analysis, Edge of Stability, and Route to Chaos [6.579523168465526]
  In descent dynamics of neural networks, the top eigenvalue of the Hessian of the loss (sharpness) displays a variety of robust phenomena throughout training. We demonstrate that a simple $2$-layer linear network (UV model) trained on a single training example exhibits all of the essential sharpness phenomenology observed in real-world scenarios.
  arXiv  Detail & Related papers  (2023-11-03T17:59:40Z)
• Phase Diagram of Initial Condensation for Two-layer Neural Networks [4.404198015660192]
  We present a phase diagram of initial condensation for two-layer neural networks. Our phase diagram serves to provide a comprehensive understanding of the dynamical regimes of neural networks.
  arXiv  Detail & Related papers  (2023-03-12T03:55:38Z)
• Catapult Dynamics and Phase Transitions in Quadratic Nets [10.32543637637479]
  We will prove that the catapult phase exists in a large class of models, including quadratic models and two-layer, homogenous neural nets. We show that for a certain range of learning rates the weight norm decreases whenever the loss becomes large. We also empirically study learning rates beyond this theoretically derived range and show that the activation map of ReLU nets trained with super-critical learning rates becomes increasingly sparse as we increase the learning rate.
  arXiv  Detail & Related papers  (2023-01-18T19:03:48Z)
• Critical Learning Periods for Multisensory Integration in Deep Networks [112.40005682521638]
  We show that the ability of a neural network to integrate information from diverse sources hinges critically on being exposed to properly correlated signals during the early phases of training. We show that critical periods arise from the complex and unstable early transient dynamics, which are decisive of final performance of the trained system and their learned representations.
  arXiv  Detail & Related papers  (2022-10-06T23:50:38Z)
• Multi-scale Feature Learning Dynamics: Insights for Double Descent [71.91871020059857]
  We study the phenomenon of "double descent" of the generalization error. We find that double descent can be attributed to distinct features being learned at different scales.
  arXiv  Detail & Related papers  (2021-12-06T18:17:08Z)
• Gradient Starvation: A Learning Proclivity in Neural Networks [97.02382916372594]
  Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks.
  arXiv  Detail & Related papers  (2020-11-18T18:52:08Z)
• Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel [41.79250783277419]
  We study the relationship between the training dynamics of nonlinear deep networks, the geometry of the loss landscape, and the time evolution of a data-dependent NTK. In multiple neural architectures and datasets, we find these diverse measures evolve in a highly correlated manner, revealing a universal picture of the deep learning process.
  arXiv  Detail & Related papers  (2020-10-28T17:53:01Z)
• Phase diagram for two-layer ReLU neural networks at infinite-width limit [6.380166265263755]
  We draw the phase diagram for the two-layer ReLU neural network at the infinite-width limit. We identify three regimes in the phase diagram, i.e., linear regime, critical regime and condensed regime. In the linear regime, NN training dynamics is approximately linear similar to a random feature model with an exponential loss decay. In the condensed regime, we demonstrate through experiments that active neurons are condensed at several discrete orientations.
  arXiv  Detail & Related papers  (2020-07-15T06:04:35Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)

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.