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Traditional crowd counting networks suffer from information loss when feature maps are downsized through pooling layers, leading to inaccuracies in counting crowds at a distance. Existing methods often assume correct annotations during training, disregarding the impact of noisy annotations, especially in crowded scenes. Furthermore, the use of a fixed Gaussian kernel fails to account for the varying pixel distribution with respect to the camera distance. To overcome these challenges, we propose a Scale-Aware Crowd Counting Network (SACC-Net) that introduces a ``scale-aware'' architecture with error-correcting capabilities of noisy annotations. For the first time, we {\bf simultaneously} model labeling errors (mean) and scale variations (variance) by spatially-varying Gaussian distributions to produce fine-grained heat maps for crowd counting. Furthermore, the proposed adaptive Gaussian kernel variance enables the model to learn dynamically with a low-rank approximation, leading to improved convergence efficiency with comparable accuracy. The performance of SACC-Net is extensively evaluated on four public datasets: UCF-QNRF, UCF CC 50, NWPU, and ShanghaiTech A-B. Experimental results demonstrate that SACC-Net outperforms all state-of-the-art methods, validating its effectiveness in achieving superior crowd counting accuracy.