Convolutional neural networks have been the cornerstone of FER due to their ability to capture local spatial features and hierarchical representations. Recent works have focused on improving CNN architectures to address challenges such as occlusions, pose variations, and subtle expression differences. Wang et al. [1] proposed a CNN-based uncertainty suppression framework for large-scale FER, demonstrating the effectiveness of CNNs in handling noisy and ambiguous data. Minaee et al. [2] introduced a multi-task learning framework using CNNs to jointly learn facial expressions and auxiliary attributes such as age and gender. Their work highlighted the robustness of CNNs in handling fine-grained feature extraction for FER. Li et al. [3] proposed a deep locality-preserving CNN that leverages crowd-sourced data to improve FER in real-world scenarios. Their approach demonstrated the effectiveness of CNNs in capturing local features while addressing dataset biases. Bodapati et al. [6] proposed a novel deep learning-based strategy for FER using a deep convolutional neural network model (FERNet). The model is designed to learn hidden nonlinearities from input facial images, which are crucial for accurately discriminating emotions. FERNet consists of a sequence of blocks, each containing multiple convolutional and sub-sampling layers. Febrian et al. [7] proposed a deep learning architecture to enhance FER performance by introducing a BiLSTM-CNN model, which combines CNN with a Bidirectional Long Short-Term Memory (BiLSTM) network. The study compares the proposed BiLSTM-CNN model with standalone CNN and LSTM-CNN models. Zou et al. [8] proposed a lightweight Multi-feature Fusion Based Convolutional Neural Network (MFF-CNN) for FER, designed to explore expression features at distinct abstract levels and regions. The model consists of two branches: the Image Branch, which extracts mid-level and high-level global features from the entire input image, and the Patch Branch, which extracts local features from sixteen image patches. Feature selection based on L2 norm is applied to enhance the discriminative power of local features, and joint tuning is used to integrate and fuse features from both branches.

Despite the significant advancements in CNN for FER, several limitations persist. While CNNs excel at capturing local spatial features and hierarchical representations, they often struggle to model long-range dependencies and global contextual information, which are crucial for distinguishing between subtle expressions. Additionally, CNNs require extensive computational resources and large datasets to achieve optimal performance, making them less efficient for real-time applications or scenarios with limited data.

Attention mechanisms have been integrated into FER frameworks to enhance the model’s ability to focus on discriminative facial regions. These methods aim to improve performance by dynamically weighting important features while suppressing irrelevant ones. Minaee et al. [2] introduced an attentional CNN architecture that combines spatial and channel attention to improve FER performance. Their work demonstrated the effectiveness of attention mechanisms in capturing subtle expression details. Zhang et al. [9] proposed a hybrid attention mechanism that integrates spatial and temporal attention for video-based FER. Their approach achieved state-of-the-art results by focusing on the most relevant frames and regions. Chen et al. [10] developed a self-supervised attention framework for FER, which leverages unlabeled data to improve the model’s ability to focus on discriminative facial regions. Zhang et al. [11] proposed a cross-fusion dual-attention network for FER in the wild, which integrates a grouped dual-attention mechanism and a novel C2 activation function. Their approach achieved state-of-the-art results by refining local features, capturing global information, and addressing challenges such as occlusion and blurring. Zhou et al. [12] proposed a cross-attention and hybrid feature weighting network for emotion recognition in video clips, which integrates a dual-branch encoding network and a hierarchical-attention encoding network. Their approach achieved state-of-the-art results by capturing complementary information between facial expressions and contextual cues, addressing challenges such as emotion confusion and misunderstanding. Le Ngwe et al. [13] proposed a lightweight patch and attention network (PAtt-Lite) for FER under challenging conditions, which integrates a patch extraction block and an attention classifier. Their approach achieved state-of-the-art results by enhancing local feature representation and improving feature learning, addressing challenges such as occlusion and blurring in real-world scenarios.

Despite the advancements in attention-based methods for FER, several limitations remain. While attention mechanisms have improved the ability of models to focus on discriminative facial regions, they often require significant computational resources and complex architectures, making them less suitable for real-time or resource-constrained applications. Additionally, attention mechanisms can struggle with occlusions and extreme pose variations, as they may incorrectly weight irrelevant or noisy regions. Hybrid approaches, while effective, often involve increased model complexity and training difficulty, limiting their practicality. Furthermore, lightweight attention-based models may still face challenges in generalizing to diverse and unconstrained environments due to their reliance on local feature extraction. These limitations highlight the need for more robust, efficient, and scalable attention mechanisms that can effectively handle real-world FER challenges while maintaining computational efficiency.

Transformers have gained popularity in computer vision tasks due to their ability to model long-range dependencies and global contextual information. However, their application to FER is still evolving, with challenges such as high computational costs and the need for large datasets. Liu et al. [14] proposed a facial muscle movement-aware representation learning framework for FER, which integrates a discriminative feature generation module and a muscle relationship mining module. Their approach achieved state-of-the-art results by learning semantic relationships of facial muscle movements and addressing challenges such as occlusion, arbitrary orientations, and illumination in real-world scenarios. Xue et al. [15] proposed a novel approach for FER in the wild by introducing two attentive pooling (AP) modules, Attentive Patch Pooling (APP) and Attentive Token Pooling (ATP), to address the limitations of Vision Transformers (ViT) in FER tasks. While ViTs often underperform compared to CNNs due to difficulties in convergence and a tendency to focus on occluded or noisy areas, the proposed AP modules aim to pool noisy features directly, emphasizing the most discriminative features while reducing the impact of less relevant ones. APP selects the most informative patches from CNN features, and ATP discards unimportant tokens in ViT, both of which are simple to implement, parameter-free, and computationally efficient. Li et al. [16] proposed a multimodal supervision-steering transformer for FER in the wild, referred to as FER-former, to address the limitations of narrow receptive fields and homogenous supervisory signals in existing methods. The FER-former introduces a hybrid feature extraction pipeline that cascades CNNs and transformers to expand receptive fields, along with a heterogeneous domain-steering supervision module that incorporates text-space semantic correlations to enhance image features. Additionally, a FER-specific transformer encoder is designed to process both conventional one-hot label-focused tokens and CLIP-based text-oriented tokens in parallel, enabling the capture of global receptive fields with multimodal semantic cues. Chen et al. [17] proposed a privacy-preserving few-shot FER system using a self-supervised vision transformer (SSF-ViT) to address challenges such as privacy concerns, insufficient labeled data, and class imbalance in real-world FER tasks. The system integrates self-supervised learning (SSL) and few-shot learning (FSL) to train a deep learning model with limited labeled samples. The SSF-ViT framework involves pretraining a ViT encoder using four self-supervised pretext tasks—image denoising and reconstruction, image rotation prediction, jigsaw puzzle, and masked patch prediction—followed by fine-tuning on a lab-controlled FER dataset to extract spatiotemporal features. For few-shot classification, prototypes are constructed from support sets, and query samples are classified by computing Euclidean distances to these prototypes.

Despite the growing popularity of transformers in FER, several limitations hinder their widespread adoption. Transformers, while effective at modeling long-range dependencies and global contextual information, often require large amounts of data and significant computational resources, making them less practical for real-time or resource-constrained applications. Additionally, transformers can struggle with fine-grained feature extraction, which is critical for distinguishing subtle facial expressions, as they tend to focus on global patterns rather than local details. Although hybrid approaches, such as those combining CNNs and transformers, have shown promise in addressing these challenges, they often introduce increased model complexity and training difficulty. Furthermore, transformers are susceptible to overfitting when trained on small datasets, limiting their effectiveness in scenarios with limited labeled data. These limitations highlight the need for more efficient and scalable transformer-based architectures that can balance global and local feature extraction while maintaining computational efficiency and generalization capabilities in FER tasks.

Recent hybrid approaches have emerged that combine CNNs with Transformers to leverage their complementary strengths. Liang et al. [18] proposed CT-DBN, which uses a dual-branch network with CNN and Transformer, achieving promising results through feature concatenation. Similarly, other methods have explored various fusion strategies to combine local and global features. However, these methods typically fuse features at the global or feature level, without explicitly modeling spatial-level relationships between samples. Our work differs by introducing spatial-level similarity learning that operates before global aggregation, providing fine-grained supervision that is particularly beneficial for capturing subtle expression differences.

While our work shares conceptual similarities with metric learning methods, it differs fundamentally in how similarity is computed and applied. Traditional metric learning approaches, including triplet loss and quadruplet loss, operate on holistic feature representations extracted after global pooling operations. Given a feature map F∈R∧(C×H×W), these methods first compute a global descriptor g = GlobalPool(F) ∈R∧C, then enforce distance constraints in this C-dimensional embedding space. This formulation produces a single global constraint that treats the entire face as a holistic entity. In contrast, our Spatial Quad-Similarity (SQS) module operates at the spatial level before any global aggregation. For each spatial location (i, j), we independently compute similarity constraints across the anchor-positive-negative quad, yielding H × W independent local similarity constraints rather than a single global constraint. Why This Matters for FER: Facial expressions are characterized by localized muscle movements, a smile involves the mouth corners (AU12: lip corner puller), while surprise involves the eyebrows and eyes (AU1 + 2: brow raiser, AU5: upper lid raiser). Global pooling in standard metric learning destroys the spatial correspondence between, for example, mouth regions across different images information that is essential for distinguishing between a smile and a neutral expression. By computing similarity at each spatial location independently, SQS preserves these fine-grained spatial relationships throughout the learning process. Furthermore, unlike pairwise (triplet) or triple (quadruplet) comparisons in standard metric learning, our quad-based formulation with two negative samples provides richer contrastive supervision. This is particularly beneficial for FER where multiple expressions may share similar global appearance but differ in subtle local details (e.g., fear vs. surprise both involve wide eyes, but differ in mouth shape and eyebrow position).

Comparison with Recent Hybrid FER Methods: Recent works have explored CNN-Transformer fusion for FER, such as FER-former [16], MMATrans [14], and CF-DAN [11]. However, these methods typically fuse features at the global level using concatenation, addition, or standard cross-attention mechanisms. For instance, FER-former employs cross-attention between CNN and Transformer features but operates on sequence-level representations after spatial pooling. MMATrans fuses multi-scale features but does not explicitly model spatial-level similarity relationships between samples. Our SQS module is unique in enforcing spatial-level similarity constraints across multiple instances during training, providing fine-grained supervision that guides the network to learn more discriminative spatial features. Fig. 1 illustrates the fundamental architectural differences between these approaches.

In this section, we present SQSNet, a hybrid framework for robust facial expression recognition. SQSNet combines the local feature extraction capabilities of convolutional neural networks and the global contextual modeling of Swin Transformers into a unified feature space. To further refine feature representations, we introduce the Spatial Quad-Similarity module, which adaptively enhances discriminative features and suppresses redundant ones through fine-grained spatial interactions across multiple instances. The overall architecture consists of three main components: (1) a hybrid CNN-Transformer backbone for feature extraction, (2) the Spatial Quad-Similarity module for feature refinement, and (3) classification heads optimized with advanced regularization techniques. Fig. 2 illustrates the complete pipeline of SQSNet.

The backbone network of SQSNet integrates two complementary architectures: EfficientNet-B6 [19] and Swin Transformer [20]. EfficientNet-B6 is used to capture detailed local features with strong inductive biases, while Swin Transformer models long-range dependencies and global structures through hierarchical window-based self-attention. The output features from both branches are concatenated to form a comprehensive multi-scale representation, preserving both spatial detail and global context necessary for effective FER.

To enhance the discriminative quality of feature representations for facial expression recognition, we introduce the Spatial Quad-Similarity module. This module is designed to refine features by explicitly modeling spatial-level relationships across four instances: an anchor image A, a positive sample P from the same class, and two negative samples N1 and N2 from different classes. Unlike conventional cross-attention or metric learning methods, which often use holistic features or pairwise comparisons, SQS operates at a spatial granularity, allowing the model to better exploit fine-grained differences and similarities within facial regions.

The model is optimized using a combination of cross-entropy loss across multiple branches and a Kullback-Leibler (KL) divergence loss for residual distillation between the base classifier and the cross-enhanced classifier. Data augmentation techniques such as Mixup and label smoothing are applied to improve generalization. An adaptive learning rate scheduler based on Cosine Annealing Warm Restarts is employed to stabilize training. Early stopping is triggered if validation performance does not improve over a set number of epochs. This comprehensive training strategy enables SQSNet to achieve robust convergence and strong generalization across different FER benchmarks.

The proposed SQSNet framework is evaluated on three widely used benchmark datasets for FER: RAF-DB [3], FERPlus [21], and AffectNet [22]. RAF-DB (Real-world Affective Faces Database) contains approximately 30,000 facial images with seven basic emotions, labeled through crowd-sourcing to ensure diversity and realism. FERPlus is an extension of the FER2013 dataset, featuring around 28,000 images with eight emotion categories, including an additional “neutral” class, and provides more accurate labels through crowd-sourced annotations. AffectNet is one of the largest FER datasets, with over 1 million facial images collected from the web, annotated for eight discrete emotions and continuous valence-arousal values. These datasets are chosen for their diversity in expression intensity, pose variations, lighting conditions, and occlusions, making them ideal for evaluating the robustness and generalization capabilities of the SQSNet framework.

Dataset Split Details and Protocols

RAF-DB: We follow the standard protocol with 12,271 training images and 3068 test images across 7 emotion categories. No validation split is provided; hyperparameters are tuned on a 10% held-out portion of the training set, then the full training set is used for final model training.

FERPlus: We use the official split with 28,709 training images, 3589 validation images, and 3589 test images across 8 emotion categories. The validation set is used for hyperparameter tuning and early stopping.

AffectNet: Following standard practice for 8-class discrete emotion recognition, we use the manually annotated subset containing 283,901 training images and 3500 validation images. We report results on the validation set as the test set annotations are not publicly available. This protocol is consistent with recent FER literature [14,16].

The SQSNet framework is implemented using PyTorch and leverages the timm library for pre-trained models. The CNN backbone is based on EfficientNet-B6, while the Swin Transformer backbone uses Swin-Small with a patch size of 8 and a window size of 7. The model is trained on two NVIDIA GPU with a batch size of 64 and optimized using AdamW with a learning rate of 3e−4 and weight decay of 1e−5. The learning rate is scheduled using cosine annealing with warm restarts, with an initial cycle length of 50 epochs. Data augmentation techniques, including Mixup (α = 0.4), CutMix (α = 0.4), and Random Erasing (p = 0.5), are applied to improve generalization. The loss function is cross-entropy loss and KL-Divergence with label smoothing (α = 0.1) to handle class imbalance and noisy labels. The training process runs for 50 epochs, and the best model is selected based on validation accuracy. For evaluation, Test-Time Augmentation (TTA) is applied with 5 augmentations per image to enhance robustness. To ensure reproducibility and assess result stability, all SQSNet experiments are repeated 5 times with different random seeds. We report mean accuracy with standard deviation across runs.

Table 1 presents a comprehensive comparison of SQSNet against existing state-of-the-art methods on three benchmark datasets: RAF-DB, FERPlus, and AffectNet. The results demonstrate that SQSNet outperforms all competing approaches, achieving the highest accuracy across all datasets (91.90% on RAF-DB, 91.11% on FERPlus, and 67.15% on AffectNet). Notably, SQSNet surpasses strong baselines such as HALNet (90.29%, 90.04%, 61.75%), AGT (89.52%, 89.40%), and LRN (88.91%, 89.53%, 60.83%), confirming its robustness and generalizability. The consistent improvement over existing methods, ranging from 1.61% on RAF-DB to 5.40% on AffectNet validates the effectiveness of our proposed strategy and architectural innovations.

SQSNet results represent mean ± standard deviation across 5 runs with different random seeds: RAF-DB: 91.90% ± 0.28%, FERPlus: 91.11% ± 0.31%, AffectNet: 67.15% ± 0.42%. All improvements over previous best methods are statistically significant (paired t-test, p < 0.05). Baseline results are taken from original publications.

The lower absolute accuracies on AffectNet (67.15%) compared to RAF-DB (91.90%) and FERPlus (91.11%) reflect the substantially greater challenges inherent to this dataset. AffectNet comprises over 1 million web-collected images with extreme diversity in pose, lighting, occlusion, and image quality—far exceeding the controlled conditions of RAF-DB and laboratory-based FERPlus. Additional challenges include higher annotation noise from automated collection, severe class imbalance, and domain shift from in-the-wild capture conditions. Notably, SQSNet achieves the largest relative improvement on AffectNet (+5.40% over previous best), compared to +1.61% on RAF-DB and +1.07% on FERPlus. This demonstrates that our spatial quad-similarity mechanism provides superior robustness precisely under the most challenging real-world conditions where traditional methods struggle. The spatial-level refinement proves especially valuable when dealing with occlusions, extreme poses, and noisy annotations characteristic of unconstrained environments.

Table 2 presents a comprehensive comparison of SQSNet against various state-of-the-art deep learning architectures on three widely used facial expression recognition datasets: RAF-DB, FERPlus, and AffectNet. The results clearly demonstrate the superior performance of SQSNet, which achieves the highest accuracy across all datasets 91.90% on RAF-DB, 91.11% on FERPlus, and 67.15% on AffectNet. Compared to baseline models such as EfficientNet, ResNet, and Transformer-based methods like ViT and Swin Transformer, SQSNet consistently outperforms both individual and hybrid architectures. Notably, even combinations of strong backbones such as SeResNeXt50 with Swin Transformer fall short of SQSNet’s performance. These results highlight the effectiveness of the proposed SQSNet in learning discriminative features for facial expression recognition across diverse and challenging datasets. All SQSNet architecture results represent mean ± standard deviation across 5 independent runs. SQSNet achieves: RAF-DB: 91.90% ± 0.28%, FERPlus: 91.11% ± 0.31%, AffectNet: 67.15% ± 0.42%.

To assess the computational efficiency of SQSNet, we report its FLOPs, inference time, and parameter count in Table 3. Compared to MobileNetV2 and EfficientNet-Lite, SQSNet achieves superior accuracy with only a modest increase in computational cost, demonstrating its suitability for real-time or edge-based FER applications.

To assess the robustness of our approach to hyperparameter choices, we conducted sensitivity analysis on all SQS parameters. Table 4 presents the accuracy range across different parameter values on RAF-DB. The results demonstrate that SQSNet maintains stable performance (within ±1% variation) across reasonable hyperparameter ranges, indicating robustness to parameter selection. For new FER datasets, we recommend: (1) Start with default values (τ = 1.0, α = 1.0, β = 0.5, γ = 0.5, m = 0.5, λ = 0.5); (2) First tune λ on validation set to balance task objectives; (3) Adjust margin m if optimization is unstable; (4) Fine-tune α, β only if class distribution is highly imbalanced. Temperature τ and scaling γ typically transfer well across datasets.

Table 5 reports the statistical significance analysis comparing SQSNet with a strong baseline (HALNet) across three benchmark datasets. Results are reported as mean ± standard deviation over multiple runs. SQSNet achieves consistently higher accuracy on RAF-DB, FERPlus, and AffectNet, with all improvements being statistically significant (p < 0.01), confirming that the observed performance gains are robust and not due to random variation.

Table 6 presents a comprehensive evaluation of SQSNet using multiple metrics beyond accuracy, including Macro-F1, Weighted-F1, and Balanced Accuracy. On RAF-DB and FERPlus, SQSNet achieves consistently high and well-balanced performance across all metrics, indicating stable recognition across expression classes. On AffectNet, while overall accuracy remains competitive, the lower Macro-F1 and wider per-class F1 range reflect the dataset’s severe class imbalance and higher intra-class variability, highlighting the importance of spatial-level modeling under challenging real-world conditions.

Table 7 presents an ablation study analyzing the contribution of each module in SQSNet by removing key components: the CNN backbone (w/o CNN), Swin Transformer (w/o Swin), and Spatial Quad-Similarity (w/o SQS). The results demonstrate that all modules are essential for optimal performance, with the largest drop occurring when removing the CNN (−4.75% on RAF-DB), highlighting its role in modeling local dependencies. Disabling the Swin Transformer backbone significantly reduces accuracy on RAF-DB (−2.96%), emphasizing its importance for local feature extraction, while removing SQS leads to moderate declines (−3.01% on RAF-DB), confirming its effectiveness in feature fusion. The full SQSNet model achieves the highest accuracy across all datasets, proving the necessity of integrating all three components for state-of-the-art performance.

Confusion Matrix Comparison

Fig. 3: Confusion matrices for SQSNet on RAF-DB, FERPlus, and AffectNet datasets. The confusion matrices illustrate the class-wise performance of SQSNet across three benchmark datasets. SQSNet demonstrates strong predictive consistency on RAF-DB and FERPlus, achieving high accuracies of 91.90% and 91.11%, respectively, with minimal confusion between emotion classes. Particularly, the “Happy” and “Neutral” categories show robust recognition performance. In contrast, performance on AffectNet (67.15%) reveals greater inter-class confusion, especially among similar expressions such as “Fear,” “Sad,” and “Disgust.” This disparity highlights the increased complexity and imbalance in AffectNet, underscoring the challenges of emotion recognition in large-scale, real-world datasets. Overall, the visualizations confirm that SQSNet generalizes well on controlled datasets while maintaining competitive performance in more challenging environments.