January 04, 2023
Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is the ability to incorporate domain knowledge of invariances, e.g., translational invariance of images. Kernels based on the maximum similarity over a group of transformations are not generally positive definite. Perhaps it is for this reason that they have not been studied theoretically. We address this lacuna and show that positive definiteness indeed holds with high probability for kernels based on the maximum similarity in the small training sample set regime of interest, and that they do yield the best results in that regime. We also show how additional properties such as their ability to incorporate local features at multiple spatial scales, e.g., as done in CNNs through max pooling, and to provide the benefits of composition through the architecture of multiple layers, can also be embedded into SVMs. We verify through experiments on widely available image sets that the resulting SVMs do provide superior accuracy in comparison to well-established deep neural network benchmarks for small sample sizes.
Written by
Xi Liu
Panganamala Kumar
Ruida Zhou
Tao Liu
Publisher
NeurIPS
July 23, 2024
Zecheng He, Bo Sun, Felix Xu, Haoyu Ma, Ankit Ramchandani, Vincent Cheung, Siddharth Shah, Anmol Kalia, Ning Zhang, Peizhao Zhang, Roshan Sumbaly, Peter Vajda, Animesh Sinha
July 23, 2024
July 23, 2024
Llama team
July 23, 2024
July 21, 2024
Ouail Kitouni, Niklas Nolte, Samuel Pérez Díaz, Sokratis Trifinopoulos, Mike Williams
July 21, 2024
July 08, 2024
Antonio Orvieto, Lin Xiao
July 08, 2024
Product experiences
Foundational models
Product experiences
Latest news
Foundational models