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Softmax Function Definition
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Foundations of Large Language Models Course
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Softmax Function Definition
A vector of raw, unnormalized scores
[1000, 1002, 999]is passed as input to a computational function that converts these scores into a probability distribution. A common technique to prevent numerical errors is to first subtract the maximum value of the vector from every element before applying the main transformation (exponentiation). Why is this subtraction step crucial for handling large input values?Calculating Output Probabilities from Model Scores
A model outputs the following raw, unnormalized scores for three classes:
[2.0, 1.0, 0.1]. If a constant value of 5.0 is added to each of these scores, resulting in a new score vector of[7.0, 6.0, 5.1], how will the resulting probability distribution calculated by the function that converts these scores to probabilities change?Order Preservation of the Softmax Function
Energy-Based View of Softmax
Output Layer of Softmax Regression
Partition Function in Softmax
Vectorized Minibatch Softmax Regression
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Calculating a Probability Distribution
Consider a vector of scores x = [x₁, x₂, ..., xₙ]. A new vector y is created by adding a constant value C to every element of x, such that yᵢ = xᵢ + C for all i. How does the output of the softmax function for y compare to the output for x?
In the context of converting a vector of raw numerical scores into a probability distribution, what is the primary role of the denominator (the summation term
Σ exp(x_j)) in the softmax functionsoftmax(x)_i = exp(x_i) / Σ exp(x_j)?True or False: For any given non-empty vector of real numbers x, the sum of all the components of the resulting vector y = softmax(x) will always be equal to 1. The function is defined as:
softmax(x)_i = exp(x_i) / Σ exp(x_j).