## 2 BiCA-LSTM-Informer Framework
### Uncertainty-Aware Dynamic Loss Weighting  
In multi-task learning (MTL) frameworks, sub-tasks often differ significantly in terms of optimization difficulty and objective scale. Adopting a uniform static loss weighting strategy can lead to imbalanced training dynamics and hinder overall model performance. To address this issue, we introduce an uncertainty-aware dynamic loss weighting method [15; 16] that enables adaptive adjustment of task importance during training. Building upon the probabilistic formulation proposed by [PERSON] et al. [17], task uncertainty can be interpreted as a measure of the model's confidence in its predictions. Based on this principle, the total loss function \(\mathcal{L}_{\text{total}}\) is defined as  
\[\mathcal{L}_{\text{total}}=\sum_{i=1}^{M}\left(\frac{1}{2\sigma_{i}^{2}} \mathcal{L}_{i}+\log\sigma_{i}\right) \tag{16}\]  
where \(M\) denotes the number of tasks, \(\mathcal{L}_{i}\) is the original loss for the \(i\)-th task, and \(\sigma_{i}^{2}\) represents the observation noise variance associated with that task. As shown in Equation (16), as the uncertainty \(\sigma_{i}\) increases, the corresponding task weight \(\frac{1}{\sigma_{i}^{2}}\) decreases, effectively reducing the influence of noisy or difficult tasks during training. Additionally, the \(\log\sigma_{i}\) term acts as a regularizer that prevents \(\sigma_{i}\) from growing unbounded, ensuring numerical stability. By minimizing \(\mathcal{L}_{\text{total}}\), the model automatically learns appropriate weights for each task throughout training, achieving adaptive balancing of optimization objectives across tasks. To illustrate, consider a regression task where prediction errors are assumed to follow a Gaussian distribution:  
\[p(y\mid\hat{y},\sigma)=\frac{1}{\sqrt{2\pi\sigma^{2}}}\exp\left(-\frac{(y-\hat {y})^{2}}{2\sigma^{2}}\right) \tag{17}\]  
Taking the negative log-likelihood and simplifying yields the corresponding regression loss:  
\[\mathcal{L}_{\text{reg}}=-\log p(y\mid\hat{y},\sigma)=\frac{1}{2\sigma^{2}}(y -\hat{y})^{2}+\log\sigma \tag{18}\]  
Similarly, for classification tasks, incorporating Bayesian uncertainty modeling leads to the following form:\[\mathcal{L}_{\text{cls}}=\frac{1}{\sigma^{2}}\cdot\text{CrossEntropy}(\hat{y},y)+ \log\sigma \tag{19}\]  
To implement this framework in practice, we introduce two types of learnable log-variance parameters:  
Task-level uncertainties \(\log\sigma_{i}\): Each uncertainty parameter is represented as a scalar torch.nn.Parameter, initialized to moderate values. In our experiments, we set \(\log\sigma_{\text{reg}}=\log(0.5)\) for regression and \(\log\sigma_{\text{cls}}=\log(1.0)\) for classification. These parameters are jointly optimized with network weights. During forward propagation, the loss for task \(i\) is scaled by \(\exp(-\log\sigma_{i})\), and the regularization term \(\log\sigma_{i}\) is added directly, aligning with Equation (16) up to a constant absorbed into the parameter. Sample-level regression uncertainty \(\log\sigma_{\text{reg}}(x)\): The regression head outputs both a predicted mean \(\hat{y}\) and a raw log-variance value per sample. A Hardtanh(min=-5, max=5) activation is applied to constrain \(\log\sigma_{\text{reg}}\in[-5,5]\), thereby bounding the variance within \([\exp(-5),\exp(5)]\), preventing collapse or explosion. Through the above formulation, it becomes evident that uncertainty \(\sigma\) not only modulates the magnitude of each task's loss but also embeds interpretable noise modeling. This mechanism realizes an adaptive optimization process grounded in Bayesian inference principles. It eliminates the need for manual presetting of task weights, allowing the model to autonomously learn optimal loss scaling from data. Furthermore, it mitigates conflicts among sub-task gradients and prevents any single task from dominating the training process. Importantly, the learned \(\sigma_{i}\) values offer a quantitative estimate of the noise level associated with each sub-task, enhancing model interpretability.