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Despite recent advances in high-throughput combinatorial mutagenesis assays, the number of labeled sequences available to predict molecular functions has remained small for the vastness of the sequence space combined with the ruggedness of many fitness functions. While deep neural networks (DNNs) can capture high-order epistatic interactions among the mutational sites, they tend to overfit to the small number of labeled sequences available for training. Here, we developed Epistatic Net (EN), a method for spectral regularization of DNNs that exploits evidence that epistatic interactions in many fitness functions are sparse. We built a scalable extension of EN, usable for larger sequences, which enables spectral regularization using fast sparse recovery algorithms informed by coding theory. Results on several biological landscapes show that EN consistently improves the prediction accuracy of DNNs and enables them to outperform competing models which assume other priors. EN estimates the higher-order epistatic interactions of DNNs trained on massive sequence spaces-a computational problem that otherwise takes years to solve.

Summary We propose a new spectral framework for reliable training, scalable inference and interpretable explanation of the DNA repair outcome following a Cas9 cutting. Our framework, dubbed CRISPRL and, relies on an unexploited observation about the nature of the repair process: the landscape of the DNA repair is highly sparse in the (Walsh–Hadamard) spectral domain. This observation enables our framework to address key shortcomings that limit the interpretability and scaling of current deep-learning-based DNA repair models. In particular, CRISPRL and reduces the time to compute the full DNA repair landscape from a striking 5230 years to 1 week and the sampling complexity from 1012 to 3 million guide RNAs with only a small loss in accuracy (R2R2 ∼ 0.9). Our proposed framework is based on a divide-and-conquer strategy that uses a fast peeling algorithm to learn the DNA repair models. CRISPRL and captures lower-degree features around the cut site, which enrich for short insertions and deletions as well as higher-degree microhomology patterns that enrich for longer deletions. Availability and implementation The CRISPRL and software is publicly available at https://github.com/UCBASiCS/CRISPRLand.

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