l1 loss와 l2 loss의 차이와 활용 방법에 대해 chatGPT 선생님의 답변..
Q) why advantage l1loss better than l2loss aspect of mathmetical for blurring
ChatGPT
The advantages of L1 loss (mean absolute error) over L2 loss (mean squared error) in a mathematical sense are primarily related to its robustness and characteristics in optimization. Here's a more mathematical explanation of why L1 loss can be preferable in some cases:
Robustness to Outliers: L1 loss is less sensitive to outliers in the data. When you calculate the mean absolute error, you take the absolute difference between the predicted and actual values. As a result, extremely large errors (outliers) have a linear influence on the loss. In contrast, L2 loss squares the errors, which gives more weight to large errors. This means that L2 loss can be heavily influenced by outliers, leading to less robust results.
Mathematically:
L1 Loss: |x - y|
L2 Loss: (x - y)^2
Sparsity-Promoting: L1 loss promotes sparse solutions. This means that the optimization process tends to produce solutions where many coefficients are exactly zero. In the context of image-to-image translation, this can be desirable when you want some regions of the image to be transparent or contain no information. L2 loss does not naturally encourage sparsity in the same way.
Mathematically, for a vector w:
L1 Regularization: ||w||_1 = Σ |w_i|
L2 Regularization: ||w||_2 = √(Σ w_i^2)
Less Smoothing: L1 loss tends to result in less smoothing of the output. When you minimize L1 loss, it encourages the model to produce predictions with absolute differences close to the ground truth. This leads to crisper, more detailed results. In contrast, L2 loss can encourage the model to produce smoother (blurrier) outputs because it heavily penalizes large errors.
In summary, the mathematical advantages of L1 loss over L2 loss are its robustness to outliers, sparsity-promoting properties, and the tendency to produce sharper, less smoothed results. These characteristics can make it a better choice for certain applications, such as image-to-image translation, where preserving detail, handling noisy data, and encouraging sparse solutions are important factors. However, the choice between L1 and L2 loss should depend on the specific problem and the desired characteristics of the output.
