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Measuring the Higgs trilinear self-coupling $\lambda_{hhh}$ is experimentallydemanding but fundamental for understanding the shape of the Higgs potential.We present a comprehensive analysis strategy for the HL-LHC using di-Higgsevents in the four $b$-quark channel ($hh \to 4b$), extending current methodsin several directions. We perform deep learning to suppress the formidablemultijet background with dedicated optimisation for BSM $\lambda_{hhh}$scenarios. We compare the $\lambda_{hhh}$ constraining power of events usingdifferent multiplicities of large radius jets with a two-prong structure thatreconstruct boosted $h \to bb$ decays. We show that current uncertainties inthe SM top Yukawa coupling $y_t$ can modify $\lambda_{hhh}$ constraints by$\sim 20\%$. For SM $y_t$, we find prospects of $-0.8 < \lambda_{hhh} /\lambda_{hhh}^\text{SM} < 6.6$ at 68% CL under simplified assumptions for3000~fb$^{-1}$ of HL-LHC data. Our results provide a careful assessment ofdi-Higgs identification and machine learning techniques for all-hadronicmeasurements of the Higgs self-coupling and sharpens the requirements forfuture improvement.

Higgs self-coupling measurements using deep learning in the $b\bar{b}b\bar{b}$ final state