在论文中，作者提到这个损失函数可能会导致专家网络之间的强烈耦合，因为一个专家网络的权重变化会影响到其他专家网络的loss。这种耦合可能会导致多个专家网络被用于处理每条样本，而不是专注于它们各自擅长的子任务。为了解决这个问题，论文提出了重新定义损失函数的方法，以鼓励专家网络之间的相互竞争。

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总共有 个 cores，其中 ， 代表数据并行维度上的分割因子， 代表模型并行维度上的分割因子。现在每个 Main 处理的是 个 token 以及 个权重。

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对于一个样本 ，第 个 expert 的输出为 ，期望的输出向量为 ，那么损失函数就这么计算：

论文指出，门控网络倾向于收敛到一种状态，总是为相同的几个专家产生大的权重。这种不平衡是自我强化的，因为受到青睐的专家训练得更快，因此被门控网络更多地选择。这种不平衡可能导致训练效率低下，因为某些专家可能从未被使用过。

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