Binary classification and numerical labels I am trying to create a sentiment analysis model using a dataset that have ~50000  positive tweets that i labeled as 1, ~50000 negative tweets that i have labeled as 0. Also i have acquired ~10000 tweets that are neutral.
Due to the low number of neutral tweets my thinking is to label neutral with 0.5 and train the model using binary crossentropy as loss function. My output layer is 1 neuron with sigmoid activation function so prediction value would be between (0,1) .
Is my thinking right or it will mess the accuracy?
If you’re going to have more than two labels, you need to go with a softmax activation and a loss for multi class classification, ie cross entropy loss.
Also, be cautious for multi-class versus multi-label (below).

Multi-class
One-of-many classification. Each sample can belong to ONE of $C$ classes. The model will have $C$ output neurons that can be gathered in a vector $s$ (Scores). The target (ground truth) vector $t$ will be a one-hot vector with a positive class and $C−1$ negative classes. This task is treated as a single classification problem of samples in one of $C$ classes.
Multi-label
Each sample can belong to more than one class. The model will have as well
$C$ output neurons. The target vector $t$ can have more than a positive class, so it will be a vector of 0s and 1s with $C$ dimensionality. This task is treated as $C$ different binary $(C′=2,t′=0 \ or \ t′=1)$ and independent classification problems, where each output neuron decides if a sample belongs to a class or not.
source: https://gombru.github.io/2018/05/23/cross_entropy_loss/