$σ^2$R Loss: a Weighted Loss by Multiplicative Factors using Sigmoidal Functions
This work addresses a specific issue in deep learning for computer vision by proposing an incremental improvement to loss functions for better model generalization.
The paper tackles the problem of intra-class variance in neural networks by introducing the $σ^2$R loss, a weighted loss function that uses sigmoidal functions to adjust errors per instance, resulting in reduced intra-class variance and improved performance over center loss and soft nearest neighbor functions on benchmark datasets.
In neural networks, the loss function represents the core of the learning process that leads the optimizer to an approximation of the optimal convergence error. Convolutional neural networks (CNN) use the loss function as a supervisory signal to train a deep model and contribute significantly to achieving the state of the art in some fields of artificial vision. Cross-entropy and Center loss functions are commonly used to increase the discriminating power of learned functions and increase the generalization performance of the model. Center loss minimizes the class intra-class variance and at the same time penalizes the long distance between the deep features inside each class. However, the total error of the center loss will be heavily influenced by the majority of the instances and can lead to a freezing state in terms of intra-class variance. To address this, we introduce a new loss function called sigma squared reduction loss ($σ^2$R loss), which is regulated by a sigmoid function to inflate/deflate the error per instance and then continue to reduce the intra-class variance. Our loss has clear intuition and geometric interpretation, furthermore, we demonstrate by experiments the effectiveness of our proposal on several benchmark datasets showing the intra-class variance reduction and overcoming the results obtained with center loss and soft nearest neighbour functions.