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    def forward(self, output_logits, target, extra_info=None):
        if extra_info is None:
            return self.base_loss(output_logits, target)  # output_logits indicates the final prediction
 
        loss = 0
        temperature_mean = 1
        temperature = 1  
        # Obtain logits from each expert
        epoch = extra_info['epoch']
        num = int(target.shape[0] / 2)
 
        expert1_logits = extra_info['logits'][0] + torch.log(torch.pow(self.prior, -0.5) + 1e-9)      #head
 
        expert2_logits = extra_info['logits'][1] + torch.log(torch.pow(self.prior, 1) + 1e-9)         #medium
 
        expert3_logits = extra_info['logits'][2] + torch.log(torch.pow(self.prior, 2.5) + 1e-9)       #few
 
        teacher_expert1_logits = expert1_logits[:num, :]  # view1
        student_expert1_logits = expert1_logits[num:, :]  # view2
 
        teacher_expert2_logits = expert2_logits[:num, :]  # view1
        student_expert2_logits = expert2_logits[num:, :]  # view2
 
        teacher_expert3_logits = expert3_logits[:num, :]  # view1
        student_expert3_logits = expert3_logits[num:, :]  # view2
 
        teacher_expert1_softmax = F.softmax((teacher_expert1_logits) / temperature, dim=1).detach()
        student_expert1_softmax = F.log_softmax(student_expert1_logits / temperature, dim=1)
 
        teacher_expert2_softmax = F.softmax((teacher_expert2_logits) / temperature, dim=1).detach()
        student_expert2_softmax = F.log_softmax(student_expert2_logits / temperature, dim=1)
 
        teacher_expert3_softmax = F.softmax((teacher_expert3_logits) / temperature, dim=1).detach()
        student_expert3_softmax = F.log_softmax(student_expert3_logits / temperature, dim=1)
 
        teacher1_max, teacher1_index = torch.max(F.softmax((teacher_expert1_logits), dim=1).detach(), dim=1)
        student1_max, student1_index = torch.max(F.softmax((student_expert1_logits), dim=1).detach(), dim=1)
 
        teacher2_max, teacher2_index = torch.max(F.softmax((teacher_expert2_logits), dim=1).detach(), dim=1)
        student2_max, student2_index = torch.max(F.softmax((student_expert2_logits), dim=1).detach(), dim=1)
 
        teacher3_max, teacher3_index = torch.max(F.softmax((teacher_expert3_logits), dim=1).detach(), dim=1)
        student3_max, student3_index = torch.max(F.softmax((student_expert3_logits), dim=1).detach(), dim=1)
 
        # distillation
        partial_target = target[:num]
        kl_loss = 0
        if torch.sum((teacher1_index == partial_target)) > 0:
            kl_loss = kl_loss + F.kl_div(student_expert1_softmax[(teacher1_index == partial_target)],
                                         teacher_expert1_softmax[(teacher1_index == partial_target)],
                                         reduction='batchmean') * (temperature ** 2)
 
        if torch.sum((teacher2_index == partial_target)) > 0:
            kl_loss = kl_loss + F.kl_div(student_expert2_softmax[(teacher2_index == partial_target)],
                                         teacher_expert2_softmax[(teacher2_index == partial_target)],
                                         reduction='batchmean') * (temperature ** 2)
 
        if torch.sum((teacher3_index == partial_target)) > 0:
            kl_loss = kl_loss + F.kl_div(student_expert3_softmax[(teacher3_index == partial_target)],
                                         teacher_expert3_softmax[(teacher3_index == partial_target)],
                                         reduction='batchmean') * (temperature ** 2)
 
        loss = loss + 0.6 * kl_loss * min(extra_info['epoch'] / self.warmup, 1.0)
 
        # expert 1
        loss += self.base_loss(expert1_logits, target)
 
        # expert 2
        loss += self.base_loss(expert2_logits, target)
 
        # expert 3
        loss += self.base_loss(expert3_logits, target)
 
        return loss