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Quantization replaces floating point arithmetic with integer arithmetic in deep neural networks, enabling more efficient on-device inference with less power and memory. However, it also brings in loss of generalization and even potential errors to the models. In this work, we propose a parallelization technique for formally verifying the equivalence between quantized models and their original real-valued counterparts. In order to guarantee both soundness and completeness, mixed integer linear programming (MILP) is deployed as the baseline technique. Nevertheless, the incorporation of two networks as well as the mixture of integer and real number arithmetic make the problem much more challenging than verifying a single network, and thus using MILP alone is inadequate for the non-trivial cases. To tackle this, we design a distributed verification technique that can leverage hundreds of CPUs on high-performance computing clusters. We develop a two-tier parallel framework and propose property- and output-based partition strategies. Evaluated on perception networks quantized with PyTorch, our approach outperforms existing methods in successfully verifying many cases that are otherwise considered infeasible. 

Abstract The past decade has witnessed a rapid evolution in identifying more versatile clustered regularly interspaced short palindromic repeats (CRISPR)/CRISPR-associated protein (Cas) nucleases and their functional variants, as well as in developing precise CRISPR/Cas-derived genome editors. The programmable and robust features of the genome editors provide an effective RNA-guided platform for fundamental life science research and subsequent applications in diverse scenarios, including biomedical innovation and targeted crop improvement. One of the most essential principles is to guide alterations in genomic sequences or genes in the intended manner without undesired off-target impacts, which strongly depends on the efficiency and specificity of single guide RNA (sgRNA)-directed recognition of targeted DNA sequences. Recent advances in empirical scoring algorithms and machine learning models have facilitated sgRNA design and off-target prediction. In this review, we first briefly introduce the different features of CRISPR/Cas tools that should be taken into consideration to achieve specific purposes. Secondly, we focus on the computer-assisted tools and resources that are widely used in designing sgRNAs and analyzing CRISPR/Cas-induced on- and off-target mutations. Thirdly, we provide insights into the limitations of available computational tools that would help researchers of this field for further optimization. Lastly, we suggest a simple but effective workflow for choosing and applying web-based resources and tools for CRISPR/Cas genome editing.