The production of multiple Higgs bosons at the CERN LHC provides a direct way to measure the trilinear and quartic Higgs self-interaction strengths as well as potential access to beyond the standard model effects that can enhance production at large transverse momentum $p_{\mathrm{T}}$. The largest event fraction arises from the fully hadronic final state in which every Higgs boson decays to a bottom quark-antiquark pair ($b\bar{b}$). This introduces a combinatorial challenge known as the \emph{jet assignment problem}: assigning jets to sets representing Higgs boson candidates. Symmetry-preserving attention networks (SPA-Nets) have been been developed to address this challenge. However, the complexity of jet assignment increases when simultaneously considering both $H\rightarrow b\bar{b}$ reconstruction possibilities, i.e., two "resolved" small-radius jets each containing a shower initiated by a $b$-quark or one "boosted" large-radius jet containing a merged shower initiated by a $b\bar{b}$ pair. The latter improves the reconstruction efficiency at high $p_{\mathrm{T}}$. In this work, we introduce a generalization to the SPA-Net approach to simultaneously consider both boosted and resolved reconstruction possibilities and unambiguously interpret an event as "fully resolved'', "fully boosted", or in between. We report the performance of baseline methods, the original SPA-Net approach, and our generalized version on nonresonant $HH$ and $HHH$ production at the LHC. Considering both boosted and resolved topologies, our SPA-Net approach increases the Higgs boson reconstruction purity by 57--62\% and the efficiency by 23--38\% compared to the baseline method depending on the final state.

Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these approaches are evaluated on the same two datasets. We find that all techniques are capable of accurately reproducing the particle-level spectra across complex observables. Given that these approaches are conceptually diverse, they offer an exciting toolkit for a new class of measurements that can probe the Standard Model with an unprecedented level of detail and may enable sensitivity to new phenomena.

High-energy collisions at the Large Hadron Collider (LHC) provide valuable insights into open questions in particle physics. However, detector effects must be corrected before measurements can be compared to certain theoretical predictions or measurements from other detectors. Methods to solve this \textit{inverse problem} of mapping detector observations to theoretical quantities of the underlying collision are essential parts of many physics analyses at the LHC. We investigate and compare various generative deep learning methods to approximate this inverse mapping. We introduce a novel unified architecture, termed latent variation diffusion models, which combines the latent learning of cutting-edge generative art approaches with an end-to-end variational framework. We demonstrate the effectiveness of this approach for reconstructing global distributions of theoretical kinematic quantities, as well as for ensuring the adherence of the learned posterior distributions to known physics constraints. Our unified approach achieves a distribution-free distance to the truth of over 20 times less than non-latent state-of-the-art baseline and 3 times less than traditional latent diffusion models.