A search is presented for an extended Higgs sector with two new particles, X and ϕ, in the process X→ϕϕ→(γγ)(γγ). Novel neural networks classify events with diphotons that are merged and determine the diphoton masses. The search uses LHC proton-proton collision data at sqrt[s]=13 TeV collected with the CMS detector, corresponding to an integrated luminosity of 138 fb^{-1}. No evidence of such resonances is seen. Upper limits are set on the production cross section for m_{X} between 300 and 3000 GeV and m_{ϕ}/m_{X} between 0.5% and 2.5%, representing the most sensitive search in this channel.
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