A simple sequence processing model generates an output vector, (y_i), for each input vector, (x_i), in a sequence. The output (y_i) is a weighted sum of all input vectors up to and including (x_i). The weights are determined by a three-step process:

1. Scoring: A score is calculated between the current input (x_i) and each preceding input (x_j) (where (j \le i)) using a dot product: (score(x_i, x_j) = x_i \cdot x_j).
2. Normalization: These scores are converted into weights, (\alpha_{ij}), by applying a softmax function across all (j \le i).
3. Output Calculation: The output (y_i) is calculated as the weighted sum: (y_i = \sum_{j \le i} \alpha_{ij} x_j).

Your task is to apply this process to calculate the final output vector, (y_3), for the given sequence.