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Poster
Neural Kernels Without Tangents
Vaishaal Shankar · Alex Fang · Wenshuo Guo · Sara Fridovich-Keil · Jonathan Ragan-Kelley · Ludwig Schmidt · Benjamin Recht

Thu Jul 16 12:00 PM -- 12:45 PM & Fri Jul 17 12:00 AM -- 12:45 AM (PDT) @ None #None

We investigate the connections between neural networks and simple building blocks in kernel space. In particular, using well established feature space tools such as direct sum, averaging, and moment lifting, we present an algebra for creating “compositional” kernels from bags of features. We show that these operations correspond to many of the building blocks of “neural tangent kernels (NTK)”. Experimentally, we show that there is a correlation in test error between neural network architectures and the associated kernels. We construct a simple neural network architecture using only 3x3 convolutions, 2x2 average pooling, ReLU, and optimized with SGD and MSE loss that achieves 96% accuracy on CIFAR10, and whose corresponding compositional kernel achieves 90% accuracy. We also use our constructions to investigate the relative performance of neural networks, NTKs, and compositional kernels in the small dataset regime. In particular, we find that compositional kernels outperform NTKs and neural networks outperform both kernel methods.

Author Information

Vaishaal Shankar (UC Berkeley)
Alex Fang (UC Berkeley)
Wenshuo Guo (UC Berkeley)
Sara Fridovich-Keil (UC Berkeley)
Jonathan Ragan-Kelley (UC Berkeley)
Ludwig Schmidt (University of California, Berkeley)
Benjamin Recht (Berkeley)

Benjamin Recht is an Associate Professor in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. Ben's research group studies the theory and practice of optimization algorithms with a focus on applications in machine learning, data analysis, and controls. Ben is the recipient of a Presidential Early Career Awards for Scientists and Engineers, an Alfred P. Sloan Research Fellowship, the 2012 SIAM/MOS Lagrange Prize in Continuous Optimization, the 2014 Jamon Prize, the 2015 William O. Baker Award for Initiatives in Research, and the 2017 NIPS Test of Time Award.

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