Multimodal sentiment analysis (MSA) leverages information fusion from diverse modalities (e.g., text, audio, visual) to enhance sentiment prediction. However, simple fusion techniques often fail to account for variations in modality quality, such as those that are noisy, missing, or semantically conflicting. This oversight leads to suboptimal performance, especially in discerning subtle emotional nuances. To mitigate this limitation, we introduce a simple yet efficient \textbf{A}daptive \textbf{G}ated \textbf{F}usion \textbf{N}etwork that adaptively adjusts feature weights via a dual gate fusion mechanism based on information entropy and modality importance. This mechanism mitigates the influence of noisy modalities and prioritizes informative cues following unimodal encoding and cross-modal interaction. Experiments on CMU-MOSI and CMU-MOSEI show that AGFN significantly outperforms strong baselines in accuracy, effectively discerning subtle emotions with robust performance. Visualization analysis of feature representations demonstrates that AGFN enhances generalization by learning from a broader feature distribution, achieved by reducing the correlation between feature location and prediction error, thereby decreasing reliance on specific locations and creating more robust multimodal feature representations.

Recent research into solving vehicle routing problems (VRPs) has gained significant traction, particularly through the application of deep (reinforcement) learning for end-to-end solution construction. However, many current construction-based neural solvers predominantly utilize Transformer architectures, which can face scalability challenges and struggle to produce diverse solutions. To address these limitations, we introduce a novel framework beyond Transformer-based approaches, i.e., Adversarial Generative Flow Networks (AGFN). These models are trained alternately in an adversarial manner to improve the overall solution quality, followed by a proposed hybrid decoding method to construct the solution. We apply the AGFN framework to solve the capacitated vehicle routing problem (CVRP) and the travelling salesman problem (TSP), and our experimental results demonstrate that AGFN surpasses the popular construction-based neural solvers, showcasing strong generalization capabilities on synthetic and real-world benchmark instances. Our code is available at https://github.com/ZHANG-NI/AGFN . The vehicle routing problem (VRP) represents a fundamental and intricate combinatorial optimization challenge with extensive real-world implications (Toth & Vigo, 2014), including supply chain management (Lee et al., 2006), last-mile delivery services (Koc et al., 2020), and public transportation (Hassold & Ceder, 2014). Given its widespread occurrence across numerous domains, the VRPs have been the subject of extensive research for decades within the Operations Research (OR) community. Particularly, practitioners employ both exact and heuristic methods to tackle complex optimization problems including VRPs. Exact methods, such as branch-and-bound (Lawler & Wood, 1966), branch-and-cut (Tawarmalani & Sahinidis, 2005), and column generation (Barnhart et al., 1998), guarantee optimal solutions but often face computational limitations for large-scale instances.

Structure learning is the crux of causal inference. Notably, causal discovery (CD) algorithms are brittle when data is scarce, possibly inferring imprecise causal relations that contradict expert knowledge -- especially when considering latent confounders. To aggravate the issue, most CD methods do not provide uncertainty estimates, making it hard for users to interpret results and improve the inference process. Surprisingly, while CD is a human-centered affair, no works have focused on building methods that both 1) output uncertainty estimates that can be verified by experts and 2) interact with those experts to iteratively refine CD. To solve these issues, we start by proposing to sample (causal) ancestral graphs proportionally to a belief distribution based on a score function, such as the Bayesian information criterion (BIC), using generative flow networks. Then, we leverage the diversity in candidate graphs and introduce an optimal experimental design to iteratively probe the expert about the relations among variables, effectively reducing the uncertainty of our belief over ancestral graphs. Finally, we update our samples to incorporate human feedback via importance sampling. Importantly, our method does not require causal sufficiency (i.e., unobserved confounders may exist). Experiments with synthetic observational data show that our method can accurately sample from distributions over ancestral graphs and that we can greatly improve inference quality with human aid.