This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematics, 44(2), 141-183]. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extension, called BCR-Net, by replacing each linear sub-network with a deeper and more powerful nonlinear one. Numerical results demonstrate the efficiency of the new architecture by approximating nonlinear maps that arise in homogenization theory and stochastic computation.

Our work seeks to transform how new and emergent variants of pandemic causing viruses, specially SARS-CoV-2, are identified and classified. By adapting large language models (LLMs) for genomic data, we build genome-scale language models (GenSLMs) which can learn the evolutionary landscape of SARS-CoV-2 genomes. By pre-training on over 110 million prokaryotic gene sequences, and then finetuning a SARS-CoV-2 specific model on 1.5 million genomes, we show that GenSLM can accurately and rapidly identify variants of concern. Thus, to our knowledge, GenSLM represents one of the first whole genome scale foundation models which can generalize to other prediction tasks. We demonstrate the scaling of GenSLMs on both GPU-based supercomputers and AI-hardware accelerators, achieving over 1.54 zettaflops in training runs. We present initial scientific insights gleaned from examining GenSLMs in tracking the evolutionary dynamics of SARS-CoV-2, noting that its full potential on large biological data is yet to be realized.

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