Pairwise learning underpins implicit collaborative filtering, yet its effectiveness is often hindered by sparse supervision, noisy interactions, and popularity-driven exposure bias. In this paper, we propose Variational Bayesian Personalized Ranking (VarBPR), a tractable variational framework for implicit-feedback pairwise learning that offers principled exposure controllability and theoretical interpretability. VarBPR reformulates pairwise learning as variational inference over discrete latent indexing variables, explicitly modeling noise and indexing uncertainty, and divides training into two stages: variational inference, which solve variational posteriors, and variational learning, which updates model parameters based on these posteriors. In the variational inference stage, we develop a variational formulation that integrates preference alignment, denoising, and popularity debiasing under a unified ELBO/regularization objective, deriving closed-form posteriors with clear control semantics: the prior encodes a target exposure pattern, while temperature/regularization strength controls posterior-prior adherence. As a result, exposure controllability becomes an endogenous and interpretable outcome of variational inference. In the variational learning stage, we propose a posterior-compression objective that reduces the ideal ELBO's computational complexity from polynomial to linear, with the approximation justified by an explicit Jensen-gap upper bound. Theoretically, we provide interpretable generalization guarantees by identifying a structural error component and revealing the opportunity cost of prioritizing certain exposure patterns (e.g., long-tail), offering a concrete analytical lens for designing controllable recommender systems. Empirically, We validate VarBPR across popular backbones; it demonstrates consistent gains in ranking accuracy, enables controlled long-tail exposure, and preserves the linear-time complexity of BPR.

Over the recent years, multimodal named entity recognition has gained increasing attentions due to its wide applications in social media. The key factor of multimodal named entity recognition is to effectively fuse information of different modalities. Existing works mainly focus on reinforcing textual representations by fusing image features via the cross-modal attention mechanism. However, these works are limited in reinforcing the text modality at the token level. As a named entity usually contains several tokens, modeling token-level inter-modal interactions is suboptimal for the multimodal named entity recognition problem. In this work, we propose a multimodal named entity recognition approach dubbed Adaptive Multi-scale Language Reinforcement (AMLR) to implement entity-level language reinforcement. To this end, our model first expands token-level textual representations into multi-scale textual representations which are composed of language units of different lengths. After that, the visual information reinforces the language modality by modeling the cross-modal attention between images and expanded multi-scale textual representations. Unlike existing token-level language reinforcement methods, the word sequences of named entities can be directly interacted with the visual features as a whole, making the modeled cross-modal correlations more reasonable. Although the underlying entity is not given, the training procedure can encourage the relevant image contents to adaptively attend to the appropriate language units, making our approach not rely on the pipeline design. Comprehensive evaluation results on two public Twitter datasets clearly demonstrate the superiority of our proposed model.

In this paper, we propose a novel self-supervised Gaussian Restricted Boltzmann Machine with contrastive learning (CL-GRBM), which fuses contrastive representation learning and contrastive divergence to optimize and enhance the representation of GRBM. Built upon the concept of contrastive representation learning, CL-GRBM aims to enhance the representation capacity of the GRBM. Firstly, a pair of positive samples are constructed by one times Gibbs sampling with the original data. Then, the contrastive loss is used to pull the positive samples closer and push other samples further apart, making similar representations closer and different representations farther apart. In summary, during the training process of CL-GRBM using the CD algorithm, the objective is to align the sampling probability distribution of the visible layer in CL-GRBM as closely as possible with the empirical distribution of the original data. In the feature space of the sampling probabilities in the hidden layer, the distance between positive samples is minimized to capture the intrinsic structure of the data. According to the experimental verification, the proposed CL-GRBM shows better performance than contrastive models. As a shallow self-supervised model, it has even better performance than some excellent deep self-supervised models.

Feature learning is a crucial phase machine learning [1] – [3] . How to obtain appropriate features distribution without any background is still a hard problem in machine learning. In this paper, we present a novel unsupervised feature learning architecture (see Fig. 1 ), which consists of a multi-clustering integration module and a variant of RBM termed multi-clustering integration RBM (MIRBM). In the multi-clustering integration module, we choose three clusterers to obtain three different global clustering partitions (CPs). Then, an unanimous voting strategy is used to generate the local clustering partition (LCP) of visible layer data. Hence, the LCP only has partial visible layer data. The novel MIRBM model is a core feature encoding part of the proposed unsupervised feature learning architecture. The novelty of it is that the LCP as an unsupervised guidance is integrated into the CD 1 learning to guide the distribution of the hidden layer features. For the instance in the same LCP cluster, the hidden and reconstructed hidden layer features of the MIRBM model in the proposed architecture tend to constrict together in the training process. Meanwhile, each LCP center tends to disperse from each other as much as possible in the hidden and reconstructed hidden layer during training. This work has three main contributions: 1) A novel unsupervised feature learning architecture is proposed, which consists of a multi-clustering integration module and an MIRBM model. 2) In the multi-clustering integration module of the proposed architecture, three unsupervised algorithms are employed to obtain three different global CPs without any background knowledge or label. 3) The MIRBM model in the proposed architecture uses the LCP as an unsupervised guidance to guide the distribution of the hidden layer features by integrating the LCP into the CD 1 learning.

The instability is shown in the existing methods of representation learning based on Euclidean distance under a broad set of conditions. Furthermore, the scarcity and high cost of labels prompt us to explore more expressive representation learning methods which depends on as few labels as possible. To address above issues, the small-perturbation ideology is firstly introduced on the representation learning model based on the representation probability distribution. The positive small-perturbation information (SPI) which only depend on two labels of each cluster is used to stimulate the representation probability distribution and then two variant models are proposed to fine-tune the expected representation distribution of Restricted Boltzmann Machine (RBM), namely, Micro-supervised Disturbance Gaussian-binary RBM (Micro-DGRBM) and Micro-supervised Disturbance RBM (Micro-DRBM) models. The Kullback-Leibler (KL) divergence of SPI is minimized in the same cluster to promote the representation probability distributions to become more similar in Contrastive Divergence (CD) learning. In contrast, the KL divergence of SPI is maximized in the different clusters to enforce the representation probability distributions to become more dissimilar in CD learning. To explore the representation learning capability under the continuous stimulation of the SPI, we present a deep Micro-supervised Disturbance Learning (Micro-DL) framework based on the Micro-DGRBM and Micro-DRBM models and compare it with a similar deep structure which has no external stimulation. Experimental results demonstrate that the proposed deep Micro-DL architecture shows better performance in comparison to the baseline method, the most related shallow models and deep frameworks for clustering.

In this paper, we present a novel unsupervised feature learning architecture, which consists of a multi-clustering integration module and a variant of RBM termed multi-clustering integration RBM (MIRBM). In the multi-clustering integration module, we apply three clusterers (K-means, affinity propagation and spectral clustering algorithms) to obtain three different clustering partitions (CPs) without any background knowledge or label. Then, an unanimous voting strategy is used to generate a local clustering partition (LCP). The novel MIRBM model is a core feature encoding part of the proposed unsupervised feature learning architecture. The novelty of it is that the LCP as an unsupervised guidance is integrated into one step contrastive divergence (${\mathtt{{CD}}}_{1}$) learning to guide the distribution of the hidden layer features. For the instance in the same LCP cluster, the hidden and reconstructed hidden layer features of the MIRBM model in the proposed architecture tend to constrict together in the training process. Meanwhile, each LCP center tends to disperse from each other as much as possible in the hidden and reconstructed hidden layer during training. The experiments demonstrate that the proposed unsupervised feature learning architecture has more powerful feature representation and generalization capability than the state-of-the-art models for clustering tasks in the Microsoft Research Asia Multimedia (MSRA-MM)2.0 dataset.

Restricted Boltzmann machines (RBMs) and their variants are usually trained by contrastive divergence (CD) learning, but the training procedure is an unsupervised learning approach, without any guidances of the background knowledge. To enhance the expression ability of traditional RBMs, in this paper, we propose pairwise constraints (PCs) RBM with Gaussian visible units (pcGRBM) model, in which the learning procedure is guided by PCs and the process of encoding is conducted under these guidances. The PCs are encoded in hidden layer features of pcGRBM. Then, some pairwise hidden features of pcGRBM flock together and another part of them are separated by the guidances. In order to deal with real-valued data, the binary visible units are replaced by linear units with Gaussian noise in the pcGRBM model. In the learning process of pcGRBM, the PCs are iterated transitions between visible and hidden units during CD learning procedure. Then, the proposed model is inferred by approximative gradient descent method and the corresponding learning algorithm is designed. In order to compare the availability of pcGRBM and traditional RBMs with Gaussian visible units, the features of the pcGRBM and RBMs hidden layer are used as input "data" for K -means, spectral clustering (SP) and affinity propagation (AP) algorithms, respectively. We also use tenfold cross-validation strategy to train and test pcGRBM model to obtain more meaningful results with PCs which are derived from incremental sampling procedures. A thorough experimental evaluation is performed with 12 image datasets of Microsoft Research Asia Multimedia. The experimental results show that the clustering performance of K -means, SP, and AP algorithms based on pcGRBM model are significantly better than traditional RBMs. In addition, the pcGRBM model for clustering tasks shows better performance than some semi-supervised clustering algorithms.

There are different models to characterize AGM belief revision framework. When the background language is finite propositional language, Katsuno and Mendelzon (KM) proposed in 1991 a representation model using total preorder on worlds. This ‘preorder’ model is very influential and has been extended to characterize epistemic state in iterated belief revision. KM showed an approach how to construct the preorder via a belief set and an AGM belif revision operator, however, this approach does not work well when the language is infinite. In this paper, we argue when the language is infinite propositional language, how to construct a preorder on world to model AGM belief revision framework, and then we generalize the representation theorem of KM over an infinite language.