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Factorization Machines (FMs) refer to a class of general predictors working with real valued feature vectors, which are well-known for their ability to estimate model parameters under significant sparsity and have found successful applications in many areas such as the click-through rate (CTR) prediction. However, standard FMs only produce a single fixed representation for each feature across different input instances, which may limit the CTR model’s expressive and predictive power. Inspired by the success of Input-aware Factorization Machines (IFMs), which aim to learn more flexible and informative representations of a given feature according to different input instances, we propose a novel model named Dual Input-aware Factorization Machines (DIFMs) that can adaptively reweight the original feature representations at the bit-wise and vector-wise levels simultaneously. Furthermore, DIFMs strategically integrate various components including Multi-Head Self-Attention, Residual Networks and DNNs into a unified end-to-end model. Comprehensive experiments on two real-world CTR prediction datasets show that the DIFM model can outperform several state-of-the-art models consistently.

The flow performance of a high-viscosity fluid in novel static mixers with multitwisted leaves was investigated numerically in the range of Re = 0.1−150. The effects of mixing-segment construction, Reynolds number, and aspect ratio on the chaotic mixing characteristics of different static mixers were evaluated based on the Lagrangian tracking method. The tracer particle distributions, G values, extensional efficiency characteristics, and stretching fields were used to evaluate the dispersion and distribution mixing performances in the new static mixers. Compared with the Kenics static mixer (KSM), the static mixers with three twisted leaves (TKSM) and four twisted leaves (FKSM) achieved chaotic mixing status much earlier and could also maintain this status by successive mixing-element groups. In contrast, there were large unmixed zones in the static mixer with double twisted leaves (DKSM). Stretching rates calculated from pathlines were found to be in good agreement with results reported in the literature. The particle trajectories revealed that the logarithm of the stretching rate increased linearly with the dimensionless axial length. For a given length of static mixer, a decrease in aspect ratio benefited an increasing stretching rate. When the number of multitwisted leaves in the cross section was greater than 2, the range of the probability density curve became larger than that of the KSM. All of the static mixers were found to have small groups of material points experiencing very high stretching. The TKSM and FKSM were found to have higher mixing efficiencies than the KSM, whereas the DKSM exhibited a worse micromixing ability.

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