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We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…

Numerical Analysis · Mathematics 2020-10-02 Weinan E , Chao Ma , Lei Wu

A well-trained Convolutional Neural Network can easily be pruned without significant loss of performance. This is because of unnecessary overlap in the features captured by the network's filters. Innovations in network architecture such as…

Computer Vision and Pattern Recognition · Computer Science 2019-02-26 Aaditya Prakash , James Storer , Dinei Florencio , Cha Zhang

In recent years, new regularization methods based on (deep) neural networks have shown very promising empirical performance for the numerical solution of ill-posed problems, e.g., in medical imaging and imaging science. Due to the…

Numerical Analysis · Mathematics 2024-06-07 Tim Jahn , Bangti Jin

This paper introduces versatile filters to construct efficient convolutional neural networks that are widely used in various visual recognition tasks. Considering the demands of efficient deep learning techniques running on cost-effective…

Computer Vision and Pattern Recognition · Computer Science 2021-09-23 Kai Han , Yunhe Wang , Chang Xu , Chunjing Xu , Enhua Wu , Dacheng Tao

Continual learning is an emerging topic in the field of deep learning, where a model is expected to learn continuously for new upcoming tasks without forgetting previous experiences. This field has witnessed numerous advancements, but few…

Computer Vision and Pattern Recognition · Computer Science 2026-03-24 Aupendu Kar , Krishnendu Ghosh , Prabir Kumar Biswas

Pre-trained representation is one of the key elements in the success of modern deep learning. However, existing works on continual learning methods have mostly focused on learning models incrementally from scratch. In this paper, we explore…

Machine Learning · Computer Science 2022-08-18 Hyounguk Shon , Janghyeon Lee , Seung Hwan Kim , Junmo Kim

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Machine Learning · Computer Science 2016-03-01 Yixuan Li , Jason Yosinski , Jeff Clune , Hod Lipson , John Hopcroft

In this paper we propose integrating a priori knowledge into both design and training of convolutional neural networks (CNNs) to learn object representations that are invariant to affine transformations (i.e., translation, scale, rotation).…

Computer Vision and Pattern Recognition · Computer Science 2019-09-04 Xenju Xu , Guanghui Wang , Alan Sullivan , Ziming Zhang

Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We…

We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…

Machine Learning · Computer Science 2019-10-04 Wonpyo Park , Paul Hongsuck Seo , Bohyung Han , Minsu Cho

Rehearsal is one of the key techniques for mitigating catastrophic forgetting and has been widely adopted in continual learning algorithms due to its simplicity and practicality. However, the theoretical understanding of how rehearsal scale…

Machine Learning · Computer Science 2026-02-25 JinLi He , Liang Bai , Xian Yang

This paper proposes a novel regularization approach to bias Convolutional Neural Networks (CNNs) toward utilizing edge and line features in their hidden layers. Rather than learning arbitrary kernels, we constrain the convolution layers to…

Computer Vision and Pattern Recognition · Computer Science 2024-10-23 Christoph Linse , Beatrice Brückner , Thomas Martinetz

In this work we study the problem of network morphism, an effective learning scheme to morph a well-trained neural network to a new one with the network function completely preserved. Different from existing work where basic morphing types…

Machine Learning · Computer Science 2017-01-13 Tao Wei , Changhu Wang , Chang Wen Chen

Modern deep neural networks require a tremendous amount of data to train, often needing hundreds or thousands of labeled examples to learn an effective representation. For these networks to work with less data, more structure must be built…

Computer Vision and Pattern Recognition · Computer Science 2019-03-06 Reuben Feinman , Brenden M. Lake

Sequential Bayesian inference over predictive functions is a natural framework for continual learning from streams of data. However, applying it to neural networks has proved challenging in practice. Addressing the drawbacks of existing…

Machine Learning · Statistics 2023-12-29 Tim G. J. Rudner , Freddie Bickford Smith , Qixuan Feng , Yee Whye Teh , Yarin Gal

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In…

Computer Vision and Pattern Recognition · Computer Science 2020-02-07 Ivan Sosnovik , Michał Szmaja , Arnold Smeulders

Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired…

Recent work in neural networks for image classification has seen a strong tendency towards increasing the spatial context. Whether achieved through large convolution kernels or self-attention, models scale poorly with the increased spatial…

Computer Vision and Pattern Recognition · Computer Science 2024-05-16 Julia Grabinski , Janis Keuper , Margret Keuper

Denoising is a fundamental imaging problem. Versatile but fast filtering has been demanded for mobile camera systems. We present an approach to multiscale filtering which allows real-time applications on low-powered devices. The key idea is…

Computer Vision and Pattern Recognition · Computer Science 2018-02-20 Sungjoon Choi , John Isidoro , Pascal Getreuer , Peyman Milanfar

Convolutional neural networks have many hyperparameters such as the filter size, number of filters, and pooling size, which require manual tuning. Though deep stacked structures are able to create multi-scale and hierarchical…

Computer Vision and Pattern Recognition · Computer Science 2018-03-02 Ilker Cam , F. Boray Tek