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We present a framework for compiling recurrence equations into native code. In our framework, users specify a system of recurrences, the types of data structures that store inputs and outputs, and scheduling commands for optimization. Our compiler then lowers these specifications into native code that respects the dependencies in the recurrence equations. Our compiler can generate code over both sparse and dense data structures, and determines if the recurrence system is solvable with the provided scheduling primitives. We evaluate the performance and correctness of the generated code on several recurrences, from domains as diverse as dense and sparse matrix solvers, dynamic programming, graph problems, and sparse tensor algebra. We demonstrate that the generated code has competitive performance to hand-optimized implementations in libraries. However, these handwritten libraries target specific recurrences, specific data structures, and specific optimizations. Our system, on the other hand, automatically generates implementations from recurrences, data formats, and schedules, giving our system more generality than library approaches. 

Historically, the database search algorithms have been the de facto standard for inferring peptides from mass spectrometry (MS) data. Database search algorithms deduce peptides by transforming theoretical peptides into theoretical spectra and matching them to the experimental spectra. Heuristic similarity-scoring functions are used to match an experimental spectrum to a theoretical spectrum. However, the heuristic nature of the scoring functions and the simple transformation of the peptides into theoretical spectra, along with noisy mass spectra for the less abundant peptides, can introduce a cascade of inaccuracies. In this paper, we design and implement a Deep Cross-Modal Similarity Network called SpeCollate , which overcomes these inaccuracies by learning the similarity function between experimental spectra and peptides directly from the labeled MS data. SpeCollate transforms spectra and peptides into a shared Euclidean subspace by learning fixed size embeddings for both. Our proposed deep-learning network trains on sextuplets of positive and negative examples coupled with our custom-designed SNAP-loss function. Online hardest negative mining is used to select the appropriate negative examples for optimal training performance. We use 4.8 million sextuplets obtained from the NIST and MassIVE peptide libraries to train the network and demonstrate that for closed search, SpeCollate is able to perform better than Crux and MSFragger in terms of the number of peptide-spectrum matches (PSMs) and unique peptides identified under 1% FDR for real-world data. SpeCollate also identifies a large number of peptides not reported by either Crux or MSFragger. To the best of our knowledge, our proposed SpeCollate is the first deep-learning network that can determine the cross-modal similarity between peptides and mass-spectra for MS-based proteomics. We believe SpeCollate is significant progress towards developing machine-learning solutions for MS-based omics data analysis. SpeCollate is available at https://deepspecs.github.io/ .