End-to-End Kernel Learning with Supervised Convolutional Kernel Networks

By Julien Mairal. 2016

133 citations recorded by the source corpus.

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We show that our method achieves reasonably competitive performance for image classification on some standard "deep learning" datasets such as CIFAR-10 and SVHN, and also for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Structured Convolutional Kernel Networks for Airline Crew Scheduling (2021, methodology): “1 5: (Optional) Center and rescale these representations to have unit `2-norm on average 6: Infer probabilities by providing image map as input to structured predictor 7: Train the structured predictor using the feature map as an input for nEp epochs 8: Use the inferred probabilities to compute the ”
Biological Sequence Modeling with Convolutional Kernel Networks (2017, positive): “A major advantage of the Nyström method is that it may be extended to produce lower-dimensional task-dependent mappings [Mairal, 2016] and it admits a model interpretation in terms of sequence logos (see Section 3).”
Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice (2017, methodology): “ion application. MNIST and CIFAR-10 are two image classication datasets involving 10 classes. The feature representation of each image was computed using an unsupervised convolutional kernel network Mairal (2016). We focus here on the the task of classifying class #1 vs. the rest of the dataset. 30 ”
Locality defeats the curse of dimensionality in convolutional teacher–student scenarios (2021, methodology): “In [8] the effects of the architecture’s locality are studied from a kernel perspective, using a class of deep convolutional kernels introduced in [26, 27] and characterising their reproducing kernel Hilbert space (RKHS).”
Generalizing the Convolution Operator in Convolutional Neural Networks (2017, unknown): “In convolutional kernel networks (CKN), Mairal et al (2014) considered a special kernel function for measuring the similarity between two complete images and showed that its associated feature map can be approximated by a Gaussian-convolution followed by pooling.”
Local Group Invariant Representations via Orbit Embeddings (2016, background): “Kernel convolutional networks introduced in [27], [26], considers the composition of multilayer kernels, where local image patches are represented as points in a reproducing kernel.”
A Kernel Perspective for Regularizing Deep Neural Networks (2018, unknown): “The construction of hierarchical kernels and the study of neural networks in the corresponding RKHS was studied by Mairal (2016); Zhang et al. (2016; 2017); Bi-etti & Mairal (2019).”
Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations (2017, unknown): “However, values of ρ larger than one typically lead to better empirical performance for classiﬁcation (Mairal, 2016), and the stability results of Section 3 are still valid with an additional factor ρ n (with n = 2 here) in Eq.”
On Regularization and Robustness of Deep Neural Networks (2018, methodology): “The construction of hierarchical kernels and the study of neural networks in the corresponding RKHS was studied by Mairal (2016); Zhang et al. (2016; 2017); Bietti & Mairal (2018).”
Neural Kernels Without Tangents (2020, background): “More recent work Mairal et al. (2014); Mairal (2016) proposes a multi-layer “convolutional kernel network” (CKN) for image classification that iterates convolutional and nonlinear operations in kernel space.”