Deep learning with kernels through RKHM and the Perron-Frobenius operator
Dec 10, 2023
Speakers
Yuka Hashimoto
Speaker · 1 follower
Masahiro Ikeda
Speaker · 0 followers
Hachem Kadri
Speaker · 0 followers
About
Reproducing kernel Hilbert C^*-module (RKHM) is a generalization of reproducing kernel Hilbert space (RKHS) by means of C^*-algebra, and the Perron-Frobenius operator is a linear operator related to the composition of functions. Combining these two concepts, we present deep RKHM, a deep learning framework for kernel methods. We derive a new Rademacher generalization bound in this setting and provide a theoretical interpretation of benign overfitting by means of Perron-Frobenius operators. By virtue of C^*-algebra, the dependency of the bound on output dimension is milder than existing bounds. We show that C^*-algebra is a suitable tool for deep learning with kernels, enabling us to take advantage of the product structure of operators and to provide a clear connection with convolutional neural networks. Our theoretical analysis provides a new lens through which one can design and analyze deep kernel methods.Reproducing kernel Hilbert C^*-module (RKHM) is a generalization of reproducing kernel Hilbert space (RKHS) by means of C^*-algebra, and the Perron-Frobenius operator is a linear operator related to the composition of functions. Combining these two concepts, we present deep RKHM, a deep learning framework for kernel methods. We derive a new Rademacher generalization bound in this setting and provide a theoretical interpretation of benign overfitting by means of Perron-Frobenius operators. By vir…
Organizer
NeurIPS 2023
Account · 617 followers
Like the format? Trust SlidesLive to capture your next event!
Professional recording and live streaming, delivered globally.
Sharing
Recommended Videos
Presentations on similar topic, category or speaker
Learning Mask-aware CLIP Representations for Zero-Shot Segmentation
Watch later
Siyu Jiao, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Minimax Optimal Rate for Parameter Estimation in Multivariate Deviated Models
Watch later
Dat Do, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Bandit Social Learning under Myopic Behavior
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
Let the Flows Tell: Solving Graph Combinatorial Problems with GFlowNets
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
NCDL: A Framework for Deep Learning on non-Cartesian Lattices
Watch later
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%
SyncDiffusion: Coherent Montage via Synchronized Joint Diffusions
Watch later
Yuseung Lee, …
Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%