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Article overview
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CoNSoLe: Convex Neural Symbolic Learning | | Haoran Li
; Yang Weng
; Hanghang Tong
; | | Date: |
1 Jun 2022 | | Abstract: | 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. | | Source: | arXiv, 2206.00257 | | Services: | Forum | Review | PDF | Favorites | |
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