[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127477-en":3,"doc-seo-127477-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},127477,962084925290,"Ophelia","https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Chemical machine learning with kernels - The key impact of loss functions","Chemical machine learning with kernels for materials discovery is presented as a study of how learning formulations, especially loss functions, shape prediction outcomes from limited reference calculations. The work directly optimizes loss functions aligned with common prediction-error metrics such as mean absolute error and worst-case error. Statistical learning theoretic foundations are developed, followed by numerical evidence using atomization-energy prediction for small organic molecules, showing improved performance in the target metric at the cost of additional training computation.","View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE  \nprovided by Infoscience- École polytechnique fédérale de Lausanne  \nChemical machine learning with kernels: The key impact of loss functions Quang Van Nguyen,1, a) Sandip De,2, 3 Junhong Lin,1 and Volkan Cevher1  \n1) Laboratory for Information and Inference Systems (LIONS)  \n􀀓  \nEcole Polytechnique F􀀓ed􀀓erale de Lausanne, Switzerland  \n2) Laboratory of Computational Science and Modelling (COSMO), Institute of Materials,  \n􀀓  \nEcole Polytechnique F􀀓ed􀀓erale de Lausanne, Switzerland  \n3) National Center for Computational Design and Discovery of Novel Materials (MARVEL)  \nMachine learning promises to accelerate materials discovery by allowing computational e􀀎cient property predictions from a small number of reference calculations. As a result, the literature spent a considerable e􀀋ort in designing representations that capture basic physical properties so far. In stark contrast, our work focuses on the less-studied learning formulations in this context in order to exploit inner structures in the prediction errors. In particular, we propose to directly optimize basic loss functions of the prediction error metrics typically used in the literature, such as the mean absolute error or the worst case error. We show that a proper choice of the loss function can directly improve the prediction performance in the desired metric, albeit at the cost of additional computations during training. To support this claim, we describe the statistical learning theoretic foundations and provide numerical evidence with the prediction of atomization energies fora database of small organic molecules.  \nI. INTRODUCTION  \nEstimating the ground state energy of molecules and crystals is one of the most fundamental topics in computational quantum mechanics. The traditional approach is to use the density functional theory (DFT) 1,2 which solves Schro¨dinger’s equations with extremely expensive calculations. Recently, there is a great deal of interest in the materials design using machine learning at quantum chemistry level based DFT data. This research vein has been supported with strong preliminary evidence that we can simulate relatively large systems, containing thousands of atoms with accurate prediction performance.  \nAs a result, a considerable e􀀋ort has gone into building machine learning models for purpose of representing the atomic data. In particular, the existing literature, to out knowledge, mainly focuses on the design of kernels along with the so-called “descriptors” or “􀀌ngerprints”, e.g., bond lengths, bond angles, etc, to tailor the machine learning procedures to capture subtle di􀀋erencesin atomic environments. The resulting machine learning frameworks often use a kernel ridge regression or neural networks with impressive prediction performance.  \nIn stark contrast, our work emphasizes the learning formulations, i.e., the loss functions, which have received very little attention in the same context. To go beyond the root mean squared error (RMSE) metric, we provide learning theoretic arguments to motivate loss functions to improve predictions in the mean absolute error (MAE) and max absolute error (MaxAE) metrics.  \nMAE had been cited in the very early forecasting literature as a primary measure of performance for forecasting models3 and has recently come to our attention due to its robustness. MaxAE, on the other hand, is an upper bound for both RMSE and MAE and re􀀍ects the  \na) Electronic mail: quang.nguyen@ep􀀍.ch  \nprediction with the highest inaccuracy.  \nIn the sequel, we represent the state of a molecule by a sequence { (rk , zk)}, where rk ∈ R3 is the position of k-th nuclei and zk is its charge. This physical state is translated into a vector-like representation x ∈ Rn , which is usually required to be invariant with respect to permutational, rotational, re􀀍ectional and translational symmetries4 .  \nThe pape","cbCaimbS8cd3xvEe","https://ap.wps.com/l/cbCaimbS8cd3xvEe","pdf",1597101,1,9,"English","en",105,"# Introduction\n## Learning theory basics for regression\n### Regression for atomization energies\n# Learning formulations and loss functions\n## Optimization and numerical methods\n# Numerical evidence and results","[{\"question\":\"How does the paper connect loss functions to improved prediction metrics?\",\"answer\":\"It argues that different learning formulations introduce different structures into prediction errors. Choosing a loss function aligned with the desired metric can optimize that metric’s performance during training.\"},{\"question\":\"What loss functions are highlighted in this work?\",\"answer\":\"The study focuses on directly optimizing basic loss functions of prediction-error metrics, including mean absolute error (MAE) and worst-case-style errors such as max absolute error (MaxAE).\"},{\"question\":\"What evidence does the paper provide to support its claims?\",\"answer\":\"Numerical experiments are presented for atomization-energy prediction on a database of small organic molecules. Results show improved prediction in the desired metric, with additional computation during training.\"}]","Chemical machine learning with kernels - The key impact of loss functions | PDF",1785939180,23,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"chemical-machine-learning-with-kernels-the-key-impact-of-loss-functions","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/chemical-machine-learning-with-kernels-the-key-impact-of-loss-functions/127477/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the paper connect loss functions to improved prediction metrics?","Question",{"text":75,"@type":76},"It argues that different learning formulations introduce different structures into prediction errors. Choosing a loss function aligned with the desired metric can optimize that metric’s performance during training.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What loss functions are highlighted in this work?",{"text":80,"@type":76},"The study focuses on directly optimizing basic loss functions of prediction-error metrics, including mean absolute error (MAE) and worst-case-style errors such as max absolute error (MaxAE).",{"name":82,"@type":73,"acceptedAnswer":83},"What evidence does the paper provide to support its claims?",{"text":84,"@type":76},"Numerical experiments are presented for atomization-energy prediction on a database of small organic molecules. 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