Orthogonal Transforms in Neural Networks Amount to Effective Regularization

• URL: http://arxiv.org/abs/2305.06344v2
• Date: Thu, 8 Feb 2024 17:31:40 GMT
• Title: Orthogonal Transforms in Neural Networks Amount to Effective Regularization
• Authors: Krzysztof Zaj\k{a}c and Wojciech Sopot and Pawe{\l} Wachel
• Abstract summary: We consider applications of neural networks in nonlinear system identification. We show that such a structure is a universal approximator. We empirically show in particular, that such a structure, using the Fourier transform, outperforms equivalent models without orthogonality support.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider applications of neural networks in nonlinear system identification and formulate a hypothesis that adjusting general network structure by incorporating frequency information or other known orthogonal transform, should result in an efficient neural network retaining its universal properties. We show that such a structure is a universal approximator and that using any orthogonal transform in a proposed way implies regularization during training by adjusting the learning rate of each parameter individually. We empirically show in particular, that such a structure, using the Fourier transform, outperforms equivalent models without orthogonality support.

Related papers

• Generalization emerges from local optimization in a self-organized learning network [0.0]
  We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Our network stores new knowledge in the nodes accurately and instantaneously, in the form of a lookup table. We show on numerous examples of classification tasks that the networks generated by our algorithm systematically reach such a state of perfect generalization when the number of learned examples becomes sufficiently large. We report on the dynamics of the change of state and show that it is abrupt and has the distinctive characteristics of a first order phase transition, a phenomenon already observed for traditional learning networks and known as grokking.
  arXiv  Detail & Related papers  (2024-10-03T15:32:08Z)
• Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
  We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs) Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators. Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
  arXiv  Detail & Related papers  (2024-05-22T17:23:15Z)
• Joint Group Invariant Functions on Data-Parameter Domain Induce Universal Neural Networks [14.45619075342763]
  We present a systematic method to induce a generalized neural network and its right inverse operator, called the ridgelet transform. Since the ridgelet transform is an inverse, it can describe the arrangement of parameters for the network to represent a target function. We present a new simple proof of the universality by using Schur's lemma in a unified manner covering a wide class of networks.
  arXiv  Detail & Related papers  (2023-10-05T13:30:37Z)
• TANGOS: Regularizing Tabular Neural Networks through Gradient Orthogonalization and Specialization [69.80141512683254]
  We introduce Tabular Neural Gradient Orthogonalization and gradient (TANGOS) TANGOS is a novel framework for regularization in the tabular setting built on latent unit attributions. We demonstrate that our approach can lead to improved out-of-sample generalization performance, outperforming other popular regularization methods.
  arXiv  Detail & Related papers  (2023-03-09T18:57:13Z)
• Simple initialization and parametrization of sinusoidal networks via their kernel bandwidth [92.25666446274188]
  sinusoidal neural networks with activations have been proposed as an alternative to networks with traditional activation functions. We first propose a simplified version of such sinusoidal neural networks, which allows both for easier practical implementation and simpler theoretical analysis. We then analyze the behavior of these networks from the neural tangent kernel perspective and demonstrate that their kernel approximates a low-pass filter with an adjustable bandwidth.
  arXiv  Detail & Related papers  (2022-11-26T07:41:48Z)
• Entangled Residual Mappings [59.02488598557491]
  We introduce entangled residual mappings to generalize the structure of the residual connections. An entangled residual mapping replaces the identity skip connections with specialized entangled mappings. We show that while entangled mappings can preserve the iterative refinement of features across various deep models, they influence the representation learning process in convolutional networks.
  arXiv  Detail & Related papers  (2022-06-02T19:36:03Z)
• Implicit Bias of Linear Equivariant Networks [2.580765958706854]
  Group equivariant convolutional neural networks (G-CNNs) are generalizations of convolutional neural networks (CNNs) We show that $L$-layer full-width linear G-CNNs trained via gradient descent converge to solutions with low-rank Fourier matrix coefficients.
  arXiv  Detail & Related papers  (2021-10-12T15:34:25Z)
• Lattice gauge equivariant convolutional neural networks [0.0]
  We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications. We show that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.
  arXiv  Detail & Related papers  (2020-12-23T19:00:01Z)
• Neural Subdivision [58.97214948753937]
  This paper introduces Neural Subdivision, a novel framework for data-driven coarseto-fine geometry modeling. We optimize for the same set of network weights across all local mesh patches, thus providing an architecture that is not constrained to a specific input mesh, fixed genus, or category. We demonstrate that even when trained on a single high-resolution mesh our method generates reasonable subdivisions for novel shapes.
  arXiv  Detail & Related papers  (2020-05-04T20:03:21Z)
• Fiedler Regularization: Learning Neural Networks with Graph Sparsity [6.09170287691728]
  We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. We propose to use the Fiedler value of the neural network's underlying graph as a tool for regularization.
  arXiv  Detail & Related papers  (2020-03-02T16:19:33Z)
• Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data [52.78581260260455]
  We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group. We apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems.
  arXiv  Detail & Related papers  (2020-02-25T17:40:38Z)

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.