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Ode to an ODE
Krzysztof Choromanski · Jared Quincy Davis · Valerii Likhosherstov · Xingyou Song · Jean-Jacques Slotine · Jacob Varley · Honglak Lee · Adrian Weller · Vikas Sindhwani

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #1104

We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the orthogonal group O(d). This nested system of two flows, where the parameter-flow is constrained to lie on the compact manifold, provides stability and effectiveness of training and solves the gradient vanishing-explosion problem which is intrinsically related to training deep neural network architectures such as Neural ODEs. Consequently, it leads to better downstream models, as we show on the example of training reinforcement learning policies with evolution strategies, and in the supervised learning setting, by comparing with previous SOTA baselines. We provide strong convergence results for our proposed mechanism that are independent of the width of the network, supporting our empirical studies. Our results show an intriguing connection between the theory of deep neural networks and the field of matrix flows on compact manifolds.

Author Information

Krzysztof Choromanski (Google Brain Robotics & Columbia University)
Jared Quincy Davis (DeepMind | Stanford)
Valerii Likhosherstov (University of Cambridge)
Xingyou Song (Google Brain)
Jean-Jacques Slotine (Massachusetts Institute of Technology)
Jacob Varley (Google)
Honglak Lee (Google Brain)
Adrian Weller (Cambridge, Alan Turing Institute)

Adrian Weller is Programme Director for AI at The Alan Turing Institute, the UK national institute for data science and AI, where he is also a Turing Fellow leading work on safe and ethical AI. He is a Principal Research Fellow in Machine Learning at the University of Cambridge, and at the Leverhulme Centre for the Future of Intelligence where he is Programme Director for Trust and Society. His interests span AI, its commercial applications and helping to ensure beneficial outcomes for society. He serves on several boards including the Centre for Data Ethics and Innovation. Previously, Adrian held senior roles in finance.

Vikas Sindhwani (Google)

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