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arXiv 2205.13624cs.LGmath.OCphysics.comp-ph
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基于神经网络参数化的稀疏图快速优化

Faster Optimization on Sparse Graphs via Neural Reparametrization

IBM Research(IBM研究院);Northeastern University(东北大学);UCSD(加州大学圣迭戈分校)

Nima Dehmamy, Csaba Both, Jianzhi Long, Rose Yu

摘要:

在数学优化中,二阶牛顿法通常比一阶牛顿法收敛得更快,但它们需要海森的逆,因此计算量很大。然而,我们发现在稀疏图上,图神经网络(GNN)可以实现一种有效的拟牛顿方法,可以将优化速度提高10- 100倍。我们的方法,神经重新参数化,修改优化参数作为GNN的输出,以重塑优化景观。使用预先计算的Hessian作为传播规则,GNN可以有效地利用二阶信息,达到与自适应梯度方法相似的效果。由于我们的方法通过架构设计来解决优化问题,因此可以与Adam和RMSProp等任何优化器结合使用。我们展示了我们的方法在科学相关问题上的应用,包括热扩散,同步和持久同源性。

英文摘要:

In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs, graph neural networks (GNN) can implement an efficient Quasi-Newton method that can speed up optimization by a factor of 10-100x. Our method, neural reparametrization, modifies the optimization parameters as the output of a GNN to reshape the optimization landscape. Using a precomputed Hessian as the propagation rule, the GNN can effectively utilize the second-order information, reaching a similar effect as adaptive gradient methods. As our method solves optimization through architecture design, it can be used in conjunction with any optimizers such as Adam and RMSProp. We show the application of our method on scientifically relevant problems including heat diffusion, synchronization and persistent homology.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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