Self-supervised contrastive learning frameworks have progressed rapidly over the last few years. In this paper, we propose a novel mutual information optimization-based loss function for contrastive learning. We model our pre-training task as a binary classification problem to induce an implicit contrastive effect and predict whether a pair is positive or negative. We further improve the n\"aive loss function using the Majorize-Minimizer principle and such improvement helps us to track the problem mathematically. Unlike the existing methods, the proposed loss function optimizes the mutual information in both positive and negative pairs. We also present a closed-form expression for the parameter gradient flow and compare the behavior of the proposed loss function using its Hessian eigen-spectrum to analytically study the convergence of SSL frameworks. The proposed method outperforms the SOTA contrastive self-supervised frameworks on benchmark datasets like CIFAR-10, CIFAR-100, STL-10, and Tiny-ImageNet. After 200 epochs of pre-training with ResNet-18 as the backbone, the proposed model achieves an accuracy of 86.2\%, 58.18\%, 77.49\%, and 30.87\% on CIFAR-10, CIFAR-100, STL-10, and Tiny-ImageNet datasets, respectively, and surpasses the SOTA contrastive baseline by 1.23\%, 3.57\%, 2.00\%, and 0.33\%, respectively.

翻译：近年来，自监督对比学习框架取得了快速发展。本文提出一种基于互信息优化的新型损失函数，用于对比学习。我们将预训练任务建模为二分类问题，以诱导隐式对比效应，并预测样本对为正例或负例。通过应用Majorize-Minimizer原理改进朴素损失函数，该改进有助于从数学角度追踪问题。与现有方法不同，所提损失函数同时优化正负样本对的互信息。我们还给出了参数梯度流的闭式表达式，并利用损失函数的Hessian特征谱比较其行为，以解析研究自监督学习框架的收敛性。所提方法在CIFAR-10、CIFAR-100、STL-10和Tiny-ImageNet等基准数据集上优于最先进的自监督对比学习框架。以ResNet-18为骨干网络进行200轮预训练后，模型在CIFAR-10、CIFAR-100、STL-10和Tiny-ImageNet数据集上分别达到86.2%、58.18%、77.49%和30.87%的准确率，较最先进对比基线分别提升1.23%、3.57%、2.00%和0.33%。