## 5 Experimental Result and Analysis
### Performance Comparison with the Existing Methods  
The scheme proposed in this paper is evaluated using four different steganographic datasets. The experimental results for four steganographic techniques are illustrated in Figure 5.  
Figure 5 presents the performance comparison of various methods. The DST-based approach [24] exhibited the lowest accuracy, around 75% on the Geiser dataset and be \begin{table}
\begin{tabular}{c c} \hline \hline
**Steganography Method** & **Average MSE Value** \\ \hline [PERSON]’s method [17] & 0.0206 \\ [PERSON]’s (\(\eta=1\)) method [18] & 0.0341 \\ [PERSON]’s (\(\eta=2\)) method [18] & 0.0224 \\ [PERSON]’s (\(\eta=4\)) method [18] & 0.0101 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average MSE result for multiple steganography methods. Figure 4: Impact of joint optimization coefficient on detection accuracy across multiple steganography methods. low 80% on others. SVM-MSDA [25] and XGBoost-MSDA [25] demonstrated moderate improvements, with SVM achieving 87.1% on Geiser and XGBoost slightly surpassing it at 88.3%. The Kmeans-XGBoost [25] method outperformed these baselines, reaching nearly 90% on Geiser and maintaining stable performance across datasets. Our proposed method achieved the highest detection accuracy, reaching 92.45% on Geiser and 94.75% on Miao (\(\eta=4\)), consistently surpassing all baselines. While Kmeans-XGBoost [25] attained a 5% FNR on Geiser, our approach further reduced it to 3.5% on Miao (\(\eta=4\)), demonstrating superior detection capability, especially at low embedding rates. Additionally, our method maintained competitive FPR values, effectively minimizing false positives across all datasets. DST-based methods [24] encounter significant limitations, particularly at low embedding rates. Their dependence on fixed embedding rate classifiers restricts their ability to accurately identify steganographic samples, often misclassifying low embedding rate instances as cover samples. This results in high FNR values and reduced overall accuracy. While these methods achieve relatively low FPR by correctly classifying most cover samples, their reliance on manual feature extraction and inability to adapt to embedding rate variations constrain their effectiveness. SVM-MSDA and XGBoost-MSDA [25] rely on handcrafted features and suffer from underfitting due to their training strategies. By merging steganographic samples with different embedding rates into a single training set, they fail to capture the distinct patterns of low embedding rate steganography. This leads to the frequent misclassification of low-rate steganographic samples as cover samples, increasing FNR values. Additionally, their inability to model relationships between different embedding rates further limits detection performance. The Kmeans-XGBoost detection method [25] achieves competitive performance by utilizing a clustering mechanism. It assigns samples to clusters based on distance measures and applies a classifier within each cluster for detection. Its multi-class training strategy, which treats each embedding rate as a separate class, helps address data imbalance and enhance detection accuracy. However, its reliance on handcrafted features and lack of modeling for embedding rate interdependencies limits its adaptability to highly diverse embedding rates, leading to slightly higher FPR values. In contrast, our approach addresses these limitations by replacing handcrafted feature reliance with a hierarchical transformer architecture that captures both local and global dependencies across embedding rates. Unlike traditional methods [24; 25], which overlook embedding rate correlations, our model employs a multi-task learning framework that integrates classification and regression. This design enables explicit modeling of embedding rate interdependencies, enhancing sensitivity to low embedding rate steganography. As a result, it significantly reduces FNR values while improving overall detection accuracy. Figure 5: The accuracy results on different steganography methods.