TY - GEN
T1 - CONSOLE
T2 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
AU - Li, Haoran
AU - Weng, Yang
AU - Tong, Hanghang
N1 - Funding Information:
This work is partially supported by NSF (1947135, 2134079, 1939725, ECCS-1810537, and ECCS-2048288), DARPA (HR001121C0165), ARO (W911NF2110088), DOE (DE-AR00001858-1631 and DE-EE0009355) and AFOSR FA9550-22-1-0294.
Publisher Copyright:
© 2022 Neural information processing systems foundation. All rights reserved.
PY - 2022
Y1 - 2022
N2 - Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of NNs. In this paper, we propose Convex Neural Symbolic Learning (CONSOLE) to seek convexity under mild conditions. The main idea is to decompose the recovering process into two steps and convexify each step. In the first step of searching for right symbols, we convexify the deep Q-learning. The key is to maintain double convexity for both the negative Q-function and the negative reward function in each iteration, leading to provable convexity of the negative optimal Q function to learn the true symbol connections. Conditioned on the exact searching result, we construct a Locally-Convex equation Learner (LOCAL) neural network to convexify the estimation of symbol coefficients. With such a design, we quantify a large region with strict convexity in the loss surface of LOCAL for commonly used physical functions. Finally, we demonstrate the superior performance of the CONSOLE framework over the state-of-the-art on a diverse set of datasets.
AB - Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of NNs. In this paper, we propose Convex Neural Symbolic Learning (CONSOLE) to seek convexity under mild conditions. The main idea is to decompose the recovering process into two steps and convexify each step. In the first step of searching for right symbols, we convexify the deep Q-learning. The key is to maintain double convexity for both the negative Q-function and the negative reward function in each iteration, leading to provable convexity of the negative optimal Q function to learn the true symbol connections. Conditioned on the exact searching result, we construct a Locally-Convex equation Learner (LOCAL) neural network to convexify the estimation of symbol coefficients. With such a design, we quantify a large region with strict convexity in the loss surface of LOCAL for commonly used physical functions. Finally, we demonstrate the superior performance of the CONSOLE framework over the state-of-the-art on a diverse set of datasets.
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M3 - Conference contribution
AN - SCOPUS:85150654272
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
A2 - Koyejo, S.
A2 - Mohamed, S.
A2 - Agarwal, A.
A2 - Belgrave, D.
A2 - Cho, K.
A2 - Oh, A.
PB - Neural information processing systems foundation
Y2 - 28 November 2022 through 9 December 2022
ER -