tfp.math.soft_sorting_matrix
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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. Whentemperatureapproaches zero,
this will retrieve the exact permutation matrix corresponding to sorting
from largest to smallest.
</td>
</tr><tr>
<td>name<a id="name"></a>
</td>
<td>
Pythonstrname 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.
https://arxiv.org/abs/1903.08850
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Last updated 2023-11-21 UTC.
[null,null,["Last updated 2023-11-21 UTC."],[],[],null,["# tfp.math.soft_sorting_matrix\n\n\u003cbr /\u003e\n\n|-----------------------------------------------------------------------------------------------------------------------------------------|\n| [View source on GitHub](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/math/generic.py#L795-L844) |\n\nComputes a matrix representing a continuous relaxation of sorting. \n\n tfp.math.soft_sorting_matrix(\n x, temperature, name=None\n )\n\nGiven a vector `x`, there exists a permutation matrix `P_x`, when applied to\n`x` gives `x` sorted in decreasing order. Here, we compute a continuous\nrelaxation of `P_x`, parameterized by `temperature`. This continuous\nrelaxation satisfies the property that it is a unimodal row-stochastic matrix,\nmeaning that all entries are non-negative, all rows sum to 1., and there is a\nunique maximum entry in each column. The unique maximum entry will correspond\nto the location of a `1` in the exact sorting permutation.\n\nComplexity: Given a vector `x` of size `N`, this operation will take `O(N**2)`\ntime.\n\nThis is also known as a Neural sort in \\[1\\].\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Args ---- ||\n|---------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n| `x` | `float` `Tensor`. Argument to compute the relaxed sorting matrix with respect to. The relaxed permutation is computed with respect to the last axis. |\n| `temperature` | Positive `float` Tensor`. When`temperature`approaches zero, this will retrieve the exact permutation matrix corresponding to sorting from largest to smallest. \u003c/td\u003e \u003c/tr\u003e\u003ctr\u003e \u003ctd\u003e`name`\u003ca id=\"name\"\u003e\u003c/a\u003e \u003c/td\u003e \u003ctd\u003e Python`str`name prefixed to Ops created by this function. Default value:`None`(i.e.,`'soft_sorting_matrix'\\`). |\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Returns ------- ||\n|-------------|------------------------------------------------------------------------------------------------------------|\n| `soft_sort` | A unimodal row-stochastic matrix. Applying this matrix on x will in the limit of low temperature, sort it. |\n\n\u003cbr /\u003e\n\n#### References\n\n\\[1\\]: Aditya Grover, Eric Wang, Aaron Zweig, Stefano Ermon.\nStochastic Optimization of Sorting Networks via Continuous Relaxations.\n\u003chttps://arxiv.org/abs/1903.08850\u003e"]]
View source on GitHub