|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/math/generic.py#L795-L844) | Computes a matrix representing a continuous relaxation of sorting. tfp.math.soft_sorting_matrix( x, temperature, name=None ) Given a vector `x`, there exists a permutation matrix `P_x`, when applied to `x` gives `x` sorted in decreasing order. Here, we compute a continuous relaxation of `P_x`, parameterized by `temperature`. This continuous relaxation satisfies the property that it is a unimodal row-stochastic matrix, meaning that all entries are non-negative, all rows sum to 1., and there is a unique maximum entry in each column. The unique maximum entry will correspond to the location of a `1` in the exact sorting permutation. Complexity: Given a vector `x` of size `N`, this operation will take `O(N**2)` time. This is also known as a Neural sort in \[1\].


| ## Args || |---|---| | `x` | `float` `Tensor`. Argument to compute the relaxed sorting matrix with respect to. The relaxed permutation is computed with respect to the last axis. | | `temperature` | Positive `float` Tensor`. When`temperature`approaches zero, this will retrieve the exact permutation matrix corresponding to sorting from largest to smallest. `name` Python`str`name prefixed to Ops created by this function. Default value:`None`(i.e.,`'soft_sorting_matrix'\`). |



| ## Returns || |---|---| | `soft_sort` | A unimodal row-stochastic matrix. Applying this matrix on x will in the limit of low temperature, sort it. |
#### References \[1\]: Aditya Grover, Eric Wang, Aaron Zweig, Stefano Ermon. Stochastic Optimization of Sorting Networks via Continuous Relaxations.