Structured Inverse-Free Natural Gradient: Memory-Efficient & Numerically-Stable KFAC

Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such meth...

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Hauptverfasser:	Lin, Wu, Dangel, Felix, Eschenhagen, Runa, Neklyudov, Kirill, Kristiadi, Agustinus, Turner, Richard E, Makhzani, Alireza
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Schlagworte:	Computer Science - Learning Statistics - Machine Learning
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creator	Lin, Wu Dangel, Felix Eschenhagen, Runa Neklyudov, Kirill Kristiadi, Agustinus Turner, Richard E Makhzani, Alireza
description	Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such methods unpopular for modern mixed-precision training. We address them by (i) formulating an inverse-free KFAC update and (ii) imposing structures in the Kronecker factors, resulting in structured inverse-free natural gradient descent (SINGD). On modern neural networks, we show that SINGD is memory-efficient and numerically robust, in contrast to KFAC, and often outperforms AdamW even in half precision. Our work closes a gap between first- and second-order methods in modern low-precision training.
doi_str_mv	10.48550/arxiv.2312.05705
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title	Structured Inverse-Free Natural Gradient: Memory-Efficient & Numerically-Stable KFAC
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