Softmaxitauzi

Softmaxitauzi is a mathematical function that combines the properties of the softmax function and the tauzi function. The softmax function is commonly used in machine learning and statistics to convert a vector of real numbers into a probability distribution. It is defined as:

softmax(x_i) = exp(x_i) / Σ exp(x_j)

where x_i is an element of the input vector x, and the denominator is the sum of the exponentials of all elements in the vector.

The tauzi function, on the other hand, is a generalization of the softmax function that includes an additional parameter tau, which controls the sharpness of the distribution. It is defined as:

tauzi(x_i, tau) = exp(x_i / tau) / Σ exp(x_j / tau)

When tau is set to 1, the tauzi function reduces to the softmax function.

The softmaxitauzi function is a hybrid of these two functions, defined as:

softmaxitauzi(x_i, tau) = softmax(x_i) * tauzi(x_i, tau)

This function inherits the properties of both the softmax and tauzi functions, allowing for a more flexible and tunable probability distribution. It has been used in various applications, including reinforcement learning and neural networks, where the ability to control the sharpness of the distribution is beneficial.