Two different machine learning models, Model A and Model B, use a parameterized function to convert a vector of raw scores into a probability distribution. Model A uses the function denoted as $\text{Softmax}_{\mathbf{w}_A}(\cdot)$, and Model B uses $\text{Softmax}_{\mathbf{w}_B}(\cdot)$. When given the exact same input vector, Model A produces the output [0.7, 0.2, 0.1] and Model B produces [0.3, 0.6, 0.1]. What is the most logical conclusion that can be drawn from this observation?

Interpreting Function Notation

Consider two distinct machine learning models that both utilize a function denoted as $\text{Softmax}_\mathbf{w}(\cdot)$. If both models are configured with the exact same weight vector $\mathbf{w}$, they are guaranteed to produce identical output probability distributions when given the same input vector.