Progressive Feedforward Collapse of ResNet Training

• URL: http://arxiv.org/abs/2405.00985v1
• Date: Thu, 2 May 2024 03:48:08 GMT
• Title: Progressive Feedforward Collapse of ResNet Training
• Authors: Sicong Wang, Kuo Gai, Shihua Zhang,
• Abstract summary: We study the relationship of the last-layer features to the data and intermediate layers during training. We derive a model for the well-trained ResNet according to that ResNet with weight decay approximates the geodesic curve in Wasserstein space at the terminal phase. This study extends NC to PFC to model the collapse phenomenon of intermediate layers and its dependence on the input data, shedding light on the theoretical understanding of ResNet in classification problems.
• Score: 7.824226954174748
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Neural collapse (NC) is a simple and symmetric phenomenon for deep neural networks (DNNs) at the terminal phase of training, where the last-layer features collapse to their class means and form a simplex equiangular tight frame aligning with the classifier vectors. However, the relationship of the last-layer features to the data and intermediate layers during training remains unexplored. To this end, we characterize the geometry of intermediate layers of ResNet and propose a novel conjecture, progressive feedforward collapse (PFC), claiming the degree of collapse increases during the forward propagation of DNNs. We derive a transparent model for the well-trained ResNet according to that ResNet with weight decay approximates the geodesic curve in Wasserstein space at the terminal phase. The metrics of PFC indeed monotonically decrease across depth on various datasets. We propose a new surrogate model, multilayer unconstrained feature model (MUFM), connecting intermediate layers by an optimal transport regularizer. The optimal solution of MUFM is inconsistent with NC but is more concentrated relative to the input data. Overall, this study extends NC to PFC to model the collapse phenomenon of intermediate layers and its dependence on the input data, shedding light on the theoretical understanding of ResNet in classification problems.

Related papers

• Wide Neural Networks Trained with Weight Decay Provably Exhibit Neural Collapse [32.06666853127924]
  Deep neural networks (DNNs) at convergence consistently represent the training data in the last layer via a symmetric geometric structure referred to as neural collapse. Here, the features of the penultimate layer are free variables, which makes the model data-agnostic and, hence, puts into question its ability to capture training. We first prove generic guarantees on neural collapse that assume (i) low training error and balancedness of the linear layers, and (ii) bounded conditioning of the features before the linear part.
  arXiv  Detail & Related papers  (2024-10-07T10:16:40Z)
• Neural Collapse in Deep Linear Networks: From Balanced to Imbalanced Data [12.225207401994737]
  We show that complex systems with massive amounts of parameters exhibit the same structural properties when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of vectors.
  arXiv  Detail & Related papers  (2023-01-01T16:29:56Z)
• Understanding and Improving Transfer Learning of Deep Models via Neural Collapse [37.483109067209504]
  This work investigates the relationship between neural collapse (NC) and transfer learning for classification problems. We find strong correlation between feature collapse and downstream performance. Our proposed fine-tuning methods deliver good performances while reducing fine-tuning parameters by at least 90%.
  arXiv  Detail & Related papers  (2022-12-23T08:48:34Z)
• Measurement-Consistent Networks via a Deep Implicit Layer for Solving Inverse Problems [0.0]
  End-to-end deep neural networks (DNNs) have become state-of-the-art (SOTA) for solving inverse problems. These networks are sensitive to minor variations in the training pipeline and often fail to reconstruct small but important details. We propose a framework that transforms any DNN for inverse problems into a measurement-consistent one.
  arXiv  Detail & Related papers  (2022-11-06T17:05:04Z)
• On Feature Learning in Neural Networks with Global Convergence Guarantees [49.870593940818715]
  We study the optimization of wide neural networks (NNs) via gradient flow (GF) We show that when the input dimension is no less than the size of the training set, the training loss converges to zero at a linear rate under GF. We also show empirically that, unlike in the Neural Tangent Kernel (NTK) regime, our multi-layer model exhibits feature learning and can achieve better generalization performance than its NTK counterpart.
  arXiv  Detail & Related papers  (2022-04-22T15:56:43Z)
• Extended Unconstrained Features Model for Exploring Deep Neural Collapse [59.59039125375527]
  Recently, a phenomenon termed "neural collapse" (NC) has been empirically observed in deep neural networks. Recent papers have shown that minimizers with this structure emerge when optimizing a simplified "unconstrained features model" In this paper, we study the UFM for the regularized MSE loss, and show that the minimizers' features can be more structured than in the cross-entropy case.
  arXiv  Detail & Related papers  (2022-02-16T14:17:37Z)
• Non-Gradient Manifold Neural Network [79.44066256794187]
  Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent. We propose a novel manifold neural network based on non-gradient optimization.
  arXiv  Detail & Related papers  (2021-06-15T06:39:13Z)
• Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path [11.181590224799224]
  Recent work discovered a phenomenon called Neural Collapse (NC) that occurs pervasively in today's deep net training paradigm. In this work, we establish the empirical reality of MSE-NC by reporting experimental observations for three prototypical networks and five canonical datasets. We produce closed-form dynamics that predict full Neural Collapse in an unconstrained features model.
  arXiv  Detail & Related papers  (2021-06-03T18:31:41Z)
• Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks [54.27962244835622]
  This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs) In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit. We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
  arXiv  Detail & Related papers  (2020-07-03T01:37:16Z)
• Revisiting Initialization of Neural Networks [72.24615341588846]
  We propose a rigorous estimation of the global curvature of weights across layers by approximating and controlling the norm of their Hessian matrix. Our experiments on Word2Vec and the MNIST/CIFAR image classification tasks confirm that tracking the Hessian norm is a useful diagnostic tool.
  arXiv  Detail & Related papers  (2020-04-20T18:12:56Z)
• 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.