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FMMformer: Efficient and Flexible Transformer via Decomposed Near-field and Far-field Attention
Tan Nguyen · Vai Suliafu · Stanley Osher · Long Chen · Bao Wang

Tue Dec 07 04:30 PM -- 06:00 PM (PST) @
We propose FMMformers, a class of efficient and flexible transformers inspired by the celebrated fast multipole method (FMM) for accelerating interacting particle simulation. FMM decomposes particle-particle interaction into near-field and far-field components and then performs direct and coarse-grained computation, respectively. Similarly, FMMformers decompose the attention into near-field and far-field attention, modeling the near-field attention by a banded matrix and the far-field attention by a low-rank matrix. Computing the attention matrix for FMMformers requires linear complexity in computational time and memory footprint with respect to the sequence length. In contrast, standard transformers suffer from quadratic complexity. We analyze and validate the advantage of FMMformers over the standard transformer on the Long Range Arena and language modeling benchmarks. FMMformers can even outperform the standard transformer in terms of accuracy by a significant margin. For instance, FMMformers achieve an average classification accuracy of $60.74\%$ over the five Long Range Arena tasks, which is significantly better than the standard transformer's average accuracy of $58.70\%$.

Author Information

Tan Nguyen (UCLA)

I am currently a postdoctoral scholar in the Department of Mathematics at the University of California, Los Angeles, working with Dr. Stanley J. Osher. I have obtained my Ph.D. in Machine Learning from Rice University, where I was advised by Dr. Richard G. Baraniuk. My research is focused on the intersection of Deep Learning, Probabilistic Modeling, Optimization, and ODEs/PDEs. I gave an invited talk in the Deep Learning Theory Workshop at NeurIPS 2018 and organized the 1st Workshop on Integration of Deep Neural Models and Differential Equations at ICLR 2020. I also had two awesome long internships with Amazon AI and NVIDIA Research, during which he worked with Dr. Anima Anandkumar. I am the recipient of the prestigious Computing Innovation Postdoctoral Fellowship (CIFellows) from the Computing Research Association (CRA), the NSF Graduate Research Fellowship, and the IGERT Neuroengineering Traineeship. I received his MSEE and BSEE from Rice in May 2018 and May 2014, respectively.

Vai Suliafu (University of Utah)
Stanley Osher (UCLA)
Long Chen (University of California, Irvine)
Bao Wang (University of Utah)

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