$σ^2$ R损失：一种使用Sigmoidal函数的乘因子加权损失
$σ^2$R Loss: a Weighted Loss by Multiplicative Factors using Sigmoidal Functions
摘要：
在神经网络中，损失函数表示学习过程的核心，该学习过程引导优化器逼近最优收敛误差。卷积神经网络（CNN）使用损失函数作为监督信号来训练深度模型，并为实现人工视觉某些领域的最新技术做出了重大贡献。交叉熵和中心损失函数通常用于提高学习函数的鉴别能力，并提高模型的泛化性能。中心损失最小化类内方差，同时惩罚每个类内部深层特征之间的长距离。然而，中心损失的总误差将受到大多数实例的严重影响，并可能导致类内方差的冻结状态。为了解决这个问题，我们引入了一个新的损失函数，称为sigma squared reduction loss（$σ^2$ R loss），它由sigmoid函数调节，以增加/减少每个实例的错误，然后继续减少类内方差。我们的损失具有清晰的直观性和几何解释，此外，我们通过实验证明了我们的建议在几个基准数据集上的有效性，这些数据集显示了类内方差的减少，并克服了中心损失和软最近邻函数所获得的结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
