Various Riemannian optimization tasks, such as Riemannian metaoptimization (RMO) and Riemannian metalearning, can be formulated as Riemannian bilevel optimization problems (i.e., the inner-level and outer-level optimization). Implicit differentiation has shown effectiveness in solving RMO, which decouples the computation of outer gradients from the inner-level process, avoiding huge computational burdens. However, extending implicit differentiation to other Riemannian bilevel optimization tasks is nontrivial because it requires much expert involvement for case-by-case derivations. In this article, we propose a Riemannian implicit differentiation method that provides a unified expression for outer gradients, leading to flexible application to other tasks with less expert involvement. Specifically, we formulate the inner-level optimization as a root-finding process of a fixed-point equation, through which the inner-level optimization among different tasks is formulated in a unified way. By differentiating the fixed-point equation, we derive a unified expression for outer gradients, circumventing the case-by-case derivations for different tasks. Then, we present convergence analysis and approximation error analysis, which guarantee the effectiveness of our method in various Riemannian optimization tasks. We further conduct experiments on multiple Riemannian optimization tasks, and the experimental results confirm the effectiveness.

Compositional generalization is the capability of a model to understand novel compositions composed of seen concepts. There are multiple levels of novel compositions including phrase-phrase level, phrase-word level, and word-word level. Existing methods achieve promising compositional generalization, but the consistency of compositional generalization across multiple levels of novel compositions remains unexplored. The consistency refers to that a model should generalize to a phrase-phrase level novel composition, and phrase-word/word-word level novel compositions that can be derived from it simultaneously. In this paper, we propose a meta-learning based framework, for achieving consistent compositional generalization across multiple levels. The basic idea is to progressively learn compositions from simple to complex for consistency. Specifically, we divide the original training set into multiple validation sets based on compositional complexity, and introduce multiple meta-weight-nets to generate sample weights for samples in different validation sets. To fit the validation sets in order of increasing compositional complexity, we optimize the parameters of each meta-weight-net independently and sequentially in a multilevel optimization manner. We build a GQA-CCG dataset to quantitatively evaluate the consistency. Experimental results on visual question answering and temporal video grounding, demonstrate the effectiveness of the proposed framework.

Open-vocabulary learning requires modeling the data distribution in open environments, which consists of both seen-class and unseen-class data. Existing methods estimate the distribution in open environments using seen-class data, where the absence of unseen classes makes the estimation error inherently unidentifiable. Intuitively, learning beyond the seen classes is crucial for distribution estimation to bound the estimation error. We theoretically demonstrate that the distribution can be effectively estimated by generating unseen-class data, through which the estimation error is upper-bounded. Building on this theoretical insight, we propose a novel open-vocabulary learning method, which generates unseen-class data for estimating the distribution in open environments. The method consists of a class-domain-wise data generation pipeline and a distribution alignment algorithm. The data generation pipeline generates unseen-class data under the guidance of a hierarchical semantic tree and domain information inferred from the seen-class data, facilitating accurate distribution estimation. With the generated data, the distribution alignment algorithm estimates and maximizes the posterior probability to enhance generalization in open-vocabulary learning. Extensive experiments on 11 datasets demonstrate that our method outperforms baseline approaches by up to 14%, highlighting its effectiveness and superiority.

Smart agricultural decision support systems (DSS) leverage big data technology to generate efficient decision recommendations. However, missing values in sensor data can lead to cumulative errors and reduced accuracy in data analysis, compromising the precision of these decision systems. To address this issue, we propose an intelligent multi-factor prediction framework for smart agriculture environments. This framework utilizes fuzzy Bayesian data imputation to minimize filling errors and provide a reliable data foundation for decision systems. The framework includes a fuzzy Bayesian module for imputing missing data, resulting in complete datasets and enhancing interpretability. Additionally, a multi-factor prediction model is established within an encode-decode framework, incorporating dimension-temporal cross-attention layers to capture and extract correlations among multiple factors. Extensive experiments demonstrate that our proposed model outperforms single-factor prediction, achieving a 13.6% increase in correlation. These results validate the effectiveness of the imputation module in enhancing forecasting precision and reliability, thereby assisting agricultural DSS in meeting evolving demands.

Accurate traffic flow prediction, a hotspot for intelligent transportation research, is the prerequisite for traffic flow prediction for making travel plans. The speed of traffic flow can be affected by roads condition, weather, holidays, etc. Moreover, sensors to catch the information about traffic flow will be interfered with by environmental factors such as illumination, collection time, occlusion, etc. Therefore, the traffic flow in the practical transportation system is complicated, uncertain, and challenging to predict accurately. Motivated from the aforementioned issues and challenges, in this paper, we propose a deep encoder-decoder prediction framework based on variational Bayesian inference. A Bayesian neural network is designed by combining variational inference with Gated Recurrent Units (GRU) which is used as the deep neural network unit of the encoder-decoder framework to mine the intrinsic dynamics of traffic flow. Then, the variational inference is introduced into the multi-head attention mechanism to avoid noise-induced deterioration of prediction accuracy. The proposed model achieves superior prediction performance on the Guangzhou urban traffic flow dataset over the benchmarks, particularly when the long-term prediction.

Livestream e-commerce integrates live streaming and online shopping, allowing viewers to make purchases while watching. However, effective marketing strategies remain a challenge due to limited empirical research and subjective biases from the absence of quantitative data. Current tools fail to capture the interdependence between live performances and feedback. This study identified computational features, formulated design requirements, and developed LiveRetro, an interactive visual analytics system. It enables comprehensive retrospective analysis of livestream e-commerce for streamers, viewers, and merchandise. LiveRetro employs enhanced visualization and time-series forecasting models to align performance features and feedback, identifying influences at channel, merchandise, feature, and segment levels. Through case studies and expert interviews, the system provides deep insights into the relationship between live performance and streaming statistics, enabling efficient strategic analysis from multiple perspectives.

Many learning tasks are modeled as optimization problems with nonlinear constraints, such as principal component analysis and fitting a Gaussian mixture model. A popular way to solve such problems is resorting to Riemannian optimization algorithms, which yet heavily rely on both human involvement and expert knowledge about Riemannian manifolds. In this paper, we propose a Riemannian meta-optimization method to automatically learn a Riemannian optimizer. We parameterize the Riemannian optimizer by a novel recurrent network and utilize Riemannian operations to ensure that our method is faithful to the geometry of manifolds. The proposed method explores the distribution of the underlying data by minimizing the objective of updated parameters, and hence is capable of learning task-specific optimizations. We introduce a Riemannian implicit differentiation training scheme to achieve efficient training in terms of numerical stability and computational cost. Unlike conventional meta-optimization training schemes that need to differentiate through the whole optimization trajectory, our training scheme is only related to the final two optimization steps. In this way, our training scheme avoids the exploding gradient problem, and significantly reduces the computational load and memory footprint. We discuss experimental results across various constrained problems, including principal component analysis on Grassmann manifolds, face recognition, person re-identification, and texture image classification on Stiefel manifolds, clustering and similarity learning on symmetric positive definite manifolds, and few-shot learning on hyperbolic manifolds.

Promotions are commonly used by e-commerce merchants to boost sales. The efficacy of different promotion strategies can help sellers adapt their offering to customer demand in order to survive and thrive. Current approaches to designing promotion strategies are either based on econometrics, which may not scale to large amounts of sales data, or are spontaneous and provide little explanation of sales volume. Moreover, accurately measuring the effects of promotion designs and making bootstrappable adjustments accordingly remains a challenge due to the incompleteness and complexity of the information describing promotion strategies and their market environments. We present PromotionLens, a visual analytics system for exploring, comparing, and modeling the impact of various promotion strategies. Our approach combines representative multivariant time-series forecasting models and well-designed visualizations to demonstrate and explain the impact of sales and promotional factors, and to support "what-if" analysis of promotions. Two case studies, expert feedback, and a qualitative user study demonstrate the efficacy of PromotionLens.

To solve optimization problems with nonlinear constrains, the recently developed Riemannian meta-optimization methods show promise, which train neural networks as an optimizer to perform optimization on Riemannian manifolds. A key challenge is the heavy computational and memory burdens, because computing the meta-gradient with respect to the optimizer involves a series of time-consuming derivatives, and stores large computation graphs in memory. In this paper, we propose an efficient Riemannian meta-optimization method that decouples the complex computation scheme from the meta-gradient. We derive Riemannian implicit differentiation to compute the meta-gradient by establishing a link between Riemannian optimization and the implicit function theorem. As a result, the updating our optimizer is only related to the final two iterations, which in turn speeds up our method and reduces the memory footprint significantly. We theoretically study the computational load and memory footprint of our method for long optimization trajectories, and conduct an empirical study to demonstrate the benefits of the proposed method. Evaluations of three optimization problems on different Riemannian manifolds show that our method achieves state-of-the-art performance in terms of the convergence speed and the quality of optima.