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Energy-Based View of Softmax
The softmax function has roots in statistical physics, closely mirroring the Boltzmann distribution where the prevalence of a thermodynamic state with energy and temperature is proportional to . By treating the model's error (or negative logit) as energy, the softmax formulation naturally models a distribution over states, forming the conceptual basis for energy-based models in deep learning.
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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