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# tfp.math.soft_sorting_matrix

Computes a matrix representing a continuous relaxation of sorting.

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].

`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. </td> </tr><tr> <td>```name```</td> <td> Python```str```name prefixed to Ops created by this function. Default value:```None`(i.e.,`'soft_sorting_matrix'`).

`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. https://arxiv.org/abs/1903.08850

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