## 2 Methodology
### From Discrete to Continuous Meta-Prediction  
In the KAIST dataset, the data falls into two distinct categories, daytime and nighttime. However, in a real-world deployment, the system would observe a gradual change between daytime and nighttime, which is not accurately represented by such a binary grouping. However, in the LTD dataset [1], each clip has an extensive, highly granular set of metadata. This allows us to evaluate the impact of auxiliary task conditioning in real-world scenarios with more diverse samples. Furthermore, the distillation of this knowledge through conditioning could serve to make the model weather-aware, thus allowing it to adjust to weather-induced visual changes. In [2], the authors proposed guiding the conditioning branch with a binary classification head (i.e., classifying day or night). However, to perform fine-grained, continuous weather prediction, the auxiliary optimization task and loss must be adjusted accordingly. The problem with binary classification is that it treats all false positives equally, regardless of the magnitude of the error. For continuous classifications, however, the severity of the misclassification can be assessed by determining the absolute difference between the prediction and the ground truth. Naively, an \(L1\) loss can be used to punish/reward the network based on the difference in absolute distance. However, due to the data being captured by a relative thermal camera, identical visual appearance cannot be guaranteed between calibrations. During the capture of the data for the LTD dataset, the camera would routinely undergo automatic calibration, thus resulting in an inconsistent profile over time. This induces a noise signal that could result in the optimization converging toward a global mean rather than an acceptable guess. We combat this by employing an exponential \(L1\) that is tuned to allow a pre-determined degree of deviation, and this is conducted before approaching the values of the primary task loss or losses. We employed a variation of an exponential \(L1\) loss, inspired by a naive exponential \(L1\) loss [53], with a novel exponent-based soft reduction for losses lower than a specified deviation. Denoted as \(k\), the accepted variance reduces the punishment as long as the absolute \(L1\) distance to the ground truth is closer than \(k\). \[L1_{e}(x,y)\equiv L\equiv\{l_{1},\ldots,\ l_{N}\},l_{n}\equiv|x_{n}-y_{n}|^{ \frac{k}{|x_{n}-y_{n}|}} \tag{1}\]  
\(L1_{e}(x,y)\) denotes the total loss \(L\) given the prediction \(x\) and ground truth \(y\). The sum of losses in a given batch of size \(N\) is the sum of the individual loss' \(l_{n}\) at each position \(n\). The individual losses \(l_{n}\) are normalized with respect to \(k\) over the absolute \(L1\) distance, thus resulting in an exponent \(<\)1 for samples within the accepted deviation and an exponent \(>\)1 for samples exceeding the accepted deviation. When establishing the baseline performance for each model, the minimum, maximum, and standard deviation of the primary loss was noted down for the final epoch. A corresponding \(k\) that would approach the expected loss values of the primary task was selected. This is where the resulting weighting of the auxiliary in the optimization process would be approximately equal to that of the primary task at the border of the desired deviation \(k\), all the while exponentially increasing when deviating further from the allowed \(k\). Due to the thermal images of the LTD dataset being recorded with a relative thermal camera, the visual appearance of a scene might be slightly different, even under similar meta-conditions. Thus, predicting the exact values from visual data would be an ill-posed problem, as any given state inherits some degree of variance from the calibration of the relative thermograph. To evaluate the accuracy of the auxiliary module, we reported the Mean Average Error (MAE), Mean Average Percentage Error (MAPE), and Standard Deviation (Std.)