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Identifying the subset of events that influence events of interest from continuous time datasets is of great interest in various applications. Existing methods however often fail to produce accurate and interpretable results in a time-efficient manner. In this paper, we propose a neural model – Influence-Aware Attention for Multivariate Temporal Point Processes (IAA-MTPPs) – which leverages the powerful attention mechanism in transformers to capture temporal dynamics between event types, which is different from existing instance-to-instance attentions, using variational inference while maintaining interpretability. Given event sequences and a prior influence matrix, IAA-MTPP efficiently learns an approximate posterior by an Attention-to-Influence mechanism, and subsequently models the conditional likelihood of the sequences given a sampled influence through an Influence-to-Attention formulation. Both steps are completed efficiently inside a Bblock multi-head self-attention layer, thus our end-to-end training with parallelizable transformer architecture enables faster training compared to sequential models such as RNNs. We demonstrate strong empirical performance compared to existing baselines on multiple synthetic and real benchmarks, including qualitative analysis for an application in decentralized finance. 

ABSTRACT The merger of two or more galaxies can enhance the inflow of material from galactic scales into the close environments of active galactic nuclei (AGNs), obscuring and feeding the supermassive black hole (SMBH). Both recent simulations and observations of AGN in mergers have confirmed that mergers are related to strong nuclear obscuration. However, it is still unclear how AGN obscuration evolves in the last phases of the merger process. We study a sample of 60 luminous and ultra-luminous IR galaxies (U/LIRGs) from the GOALS sample observed by NuSTAR. We find that the fraction of AGNs that are Compton thick (CT; $$N_{\rm H}\ge 10^{24}\rm \, cm^{-2}$$) peaks at $$74_{-19}^{+14}{{\ \rm per\ cent}}$$ at a late merger stage, prior to coalescence, when the nuclei have projected separations (dsep) of 0.4–6 kpc. A similar peak is also observed in the median NH [$$(1.6\pm 0.5)\times 10^{24}\rm \, cm^{-2}$$]. The vast majority ($$85^{+7}_{-9}{{\ \rm per\ cent}}$$) of the AGNs in the final merger stages (dsep ≲ 10 kpc) are heavily obscured ($$N_{\rm H}\ge 10^{23}\rm \, cm^{-2}$$), and the median NH of the accreting SMBHs in our sample is systematically higher than that of local hard X-ray-selected AGN, regardless of the merger stage. This implies that these objects have very obscured nuclear environments, with the $$N_{\rm H}\ge 10^{23}\rm \, cm^{-2}$$ gas almost completely covering the AGN in late mergers. CT AGNs tend to have systematically higher absorption-corrected X-ray luminosities than less obscured sources. This could either be due to an evolutionary effect, with more obscured sources accreting more rapidly because they have more gas available in their surroundings, or to a selection bias. The latter scenario would imply that we are still missing a large fraction of heavily obscured, lower luminosity ($$L_{2-10}\lesssim 10^{43}\rm \, erg\, s^{-1}$$) AGNs in U/LIRGs.