The Butterfly Effect: Neural Network Training Trajectories Are Highly Sensitive to Initial Conditions

• URL: http://arxiv.org/abs/2506.13234v1
• Date: Mon, 16 Jun 2025 08:35:16 GMT
• Title: The Butterfly Effect: Neural Network Training Trajectories Are Highly Sensitive to Initial Conditions
• Authors: Devin Kwok, Gül Sena Altıntaş, Colin Raffel, David Rolnick,
• Abstract summary: 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.
• Score: 51.68215326304272
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i) $L^2$ distance between parameters, (ii) the loss barrier when interpolating between networks, (iii) $L^2$ and barrier between parameters after permutation alignment, and (iv) representational similarity between intermediate activations; revealing how perturbations across different hyperparameter or fine-tuning settings drive training trajectories toward distinct loss minima. Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.

Related papers

• 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)
• ConsistentFeature: A Plug-and-Play Component for Neural Network Regularization [0.32885740436059047]
  Over- parameterized neural network models often lead to significant performance discrepancies between training and test sets.<n>We introduce a simple perspective on overfitting: models learn different representations in different i.i.d. datasets.<n>We propose an adaptive method, ConsistentFeature, that regularizes the model by constraining feature differences across random subsets of the same training set.
  arXiv  Detail & Related papers  (2024-12-02T13:21:31Z)
• GD doesn't make the cut: Three ways that non-differentiability affects neural network training [5.439020425819001]
  This paper critically examines the distinctions between methods applied to non-differentiable functions (NGDMs) and classical gradient descents (GDs) for differentiable functions.<n>Our work identifies critical misunderstandings of algorithms in influential literature, stemming from an overreliance on strong assumptions.
  arXiv  Detail & Related papers  (2024-01-16T15:11:29Z)
• Connecting NTK and NNGP: A Unified Theoretical Framework for Wide Neural Network Learning Dynamics [6.349503549199403]
  We provide a comprehensive framework for the learning process of deep wide neural networks.<n>By characterizing the diffusive phase, our work sheds light on representational drift in the brain.
  arXiv  Detail & Related papers  (2023-09-08T18:00:01Z)
• Latent State Models of Training Dynamics [51.88132043461152]
  We train models with different random seeds and compute a variety of metrics throughout training. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.
  arXiv  Detail & Related papers  (2023-08-18T13:20:08Z)
• Early Stage Convergence and Global Convergence of Training Mildly Parameterized Neural Networks [3.148524502470734]
  We show that the loss is decreased by a significant amount in the early stage of the training, and this decrease is fast. We use a microscopic analysis of the activation patterns for the neurons, which helps us derive more powerful lower bounds for the gradient.
  arXiv  Detail & Related papers  (2022-06-05T09:56:50Z)
• Imitating Deep Learning Dynamics via Locally Elastic Stochastic Differential Equations [20.066631203802302]
  We study the evolution of features during deep learning training using a set of differential equations (SDEs) that each corresponds to a training sample. Our results shed light on the decisive role of local elasticity in the training dynamics of neural networks.
  arXiv  Detail & Related papers  (2021-10-11T17:17:20Z)
• 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)
• Feature Purification: How Adversarial Training Performs Robust Deep Learning [66.05472746340142]
  We show a principle that we call Feature Purification, where we show one of the causes of the existence of adversarial examples is the accumulation of certain small dense mixtures in the hidden weights during the training process of a neural network. We present both experiments on the CIFAR-10 dataset to illustrate this principle, and a theoretical result proving that for certain natural classification tasks, training a two-layer neural network with ReLU activation using randomly gradient descent indeed this principle.
  arXiv  Detail & Related papers  (2020-05-20T16:56:08Z)
• The large learning rate phase of deep learning: the catapult mechanism [50.23041928811575]
  We present a class of neural networks with solvable training dynamics. We find good agreement between our model's predictions and training dynamics in realistic deep learning settings. We believe our results shed light on characteristics of models trained at different learning rates.
  arXiv  Detail & Related papers  (2020-03-04T17:52:48Z)
• The Break-Even Point on Optimization Trajectories of Deep Neural Networks [64.7563588124004]
  We argue for the existence of the "break-even" point on this trajectory. We show that using a large learning rate in the initial phase of training reduces the variance of the gradient. We also show that using a low learning rate results in bad conditioning of the loss surface even for a neural network with batch normalization layers.
  arXiv  Detail & Related papers  (2020-02-21T22:55:51Z)

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.