## 1 Introduction
The study in [14] proposed an identity-aware convolutional neural network using two convolutional neural networks for training, one for training features related to facial expressions and the other for training features related to identity, which improved the accuracy of expression recognition for different faces. [PERSON] et al. [15] increased the width and depth of the network based on the Inception layer and achieved good results on datasets such as CK+. Study [16] proposed a fused convolutional neural network to improve the accuracy and robustness of facial expression recognition by extracting facial features through improved LeNet and ResNet, respectively, and then connecting the two feature vectors for classification. [PERSON] et al. [17] designed a dual-stream coding network that extracts features from face and background regions, respectively, and combines them with scenarios for expression recognition so that reduces the ambiguity of network and improves the accuracy of emotion recognition. Study [18] proposed a self-cure network (SCN) that mitigates the problem of inaccurate labeling of large-scale facial expression datasets by weighting each sample in training through ranked regularization. [PERSON] et al. [19] proposed an Identity-Expression Dual Branch Network (IE-DBN) that can force the network to generate expression-guided identity-related features while suppressing negative identity factors and outperforms most current techniques. [PERSON] et al. [20] proposed a novel three-phase hybrid feature selection method that leverages the strengths of filter, wrapper, and embedded algorithms. [PERSON] et al. [21] presents a new facial expressions detection method by exploiting textural image features such as local binary patterns (LBP), local ternary patterns (LTP) and completed local binary pattern (CLBP). [PERSON] et al. [22] first propose a deeply-supervised attention network (DSAN) to recognize human emotions based on facial images automatically. Based on DSAN, a two-stage training scheme is designed, taking full advantage of the race/gender/age-related information. [PERSON] et al. [23] adopt an Adaptive Confidence Margin (Ada-CM) to fully leverage all unlabeled data for semi-supervised deep facial expression recognition. All unlabeled samples are partitioned into two subsets by comparing their confidence scores with the adaptively learned confidence margin at each training epoch: (1) subset I including samples whose confidence scores are no lower than the margin; (2) subset II including samples whose confidence scores are lower than the margin. For samples in subset I, the predictions are constrained to match pseudo labels. Meanwhile, samples in subset II participate in the feature-level contrastive objective to learn effective facial expression features. Ada-CM is evaluated extensively on four challenging datasets, showing that the method achieves state-of-the-art performance, especially surpassing fully supervised baselines in a semi-supervised manner. The study of ablation further proves the effectiveness of the method. With the continuous development and application of deep neural network models, the key indicators of network continue to improve, such as the depth, the width, the parameters number, the computation amount and so on. As neural networks become increasingly complex, deploying them on mobile and embedded devices becomes challenging. However, with the increasing demand for real-time, on-device facial expression recognition in mobile and embedded environments, there is an urgent need to develop lightweight FER models that offer competitive accuracy with significantly lower computational cost. The necessity for lightweight FER models is driven by the rapid proliferation of edge computing and ubiquitous devices such as smartphones, smartwatches, AR/VR headsets, and in-vehicle monitoring systems. In such settings, computational resources, power availability, and memory capacity are often constrained.