Exploring the Properties and Evolution of Neural Network Eigenspaces during Training

• URL: http://arxiv.org/abs/2106.09526v2
• Date: Fri, 18 Jun 2021 07:44:38 GMT
• Title: Exploring the Properties and Evolution of Neural Network Eigenspaces during Training
• Authors: Mats L. Richter, Leila Malihi, Anne-Kathrin Patricia Windler, Ulf Krumnack
• Abstract summary: We show that problem difficulty and neural network capacity affect the predictive performance in an antagonistic manner. We show that the observed effects are independent from previously reported pathological patterns like the tail pattern''
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work we explore the information processing inside neural networks using logistic regression probes \cite{probes} and the saturation metric \cite{featurespace_saturation}. We show that problem difficulty and neural network capacity affect the predictive performance in an antagonistic manner, opening the possibility of detecting over- and under-parameterization of neural networks for a given task. We further show that the observed effects are independent from previously reported pathological patterns like the ``tail pattern'' described in \cite{featurespace_saturation}. Finally we are able to show that saturation patterns converge early during training, allowing for a quicker cycle time during analysis

Related papers

• 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)
• Understanding Activation Patterns in Artificial Neural Networks by Exploring Stochastic Processes [0.0]
  We propose utilizing the framework of processes, which has been underutilized thus far. We focus solely on activation frequency, leveraging neuroscience techniques used for real neuron spike trains. We derive parameters describing activation patterns in each network, revealing consistent differences across architectures and training sets.
  arXiv  Detail & Related papers  (2023-08-01T22:12:30Z)
• Addressing caveats of neural persistence with deep graph persistence [54.424983583720675]
  We find that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence. We propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers. This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues.
  arXiv  Detail & Related papers  (2023-07-20T13:34:11Z)
• How neural networks learn to classify chaotic time series [77.34726150561087]
  We study the inner workings of neural networks trained to classify regular-versus-chaotic time series. We find that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models.
  arXiv  Detail & Related papers  (2023-06-04T08:53:27Z)
• Gradient Descent in Neural Networks as Sequential Learning in RKBS [63.011641517977644]
  We construct an exact power-series representation of the neural network in a finite neighborhood of the initial weights. We prove that, regardless of width, the training sequence produced by gradient descent can be exactly replicated by regularized sequential learning.
  arXiv  Detail & Related papers  (2023-02-01T03:18:07Z)
• Dense Hebbian neural networks: a replica symmetric picture of supervised learning [4.133728123207142]
  We consider dense, associative neural-networks trained by a teacher with supervision. We investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations.
  arXiv  Detail & Related papers  (2022-11-25T13:37:47Z)
• 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)
• Persistent Homology Captures the Generalization of Neural Networks Without A Validation Set [0.0]
  We suggest studying the training of neural networks with Algebraic Topology, specifically Persistent Homology. Using simplicial complex representations of neural networks, we study the PH diagram distance evolution on the neural network learning process. Results show that the PH diagram distance between consecutive neural network states correlates with the validation accuracy.
  arXiv  Detail & Related papers  (2021-05-31T09:17:31Z)
• 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)
• Bayesian Neural Networks [0.0]
  We show how errors in prediction by neural networks can be obtained in principle, and provide the two favoured methods for characterising these errors. We will also describe how both of these methods have substantial pitfalls when put into practice.
  arXiv  Detail & Related papers  (2020-06-02T09:43:00Z)

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.