With alpha = 1.5 and normalizing sparse transform (a la softmax).
Arguments
- dim
The dimension along which to apply 1.5-entmax.
- k
The number of largest elements to partial-sort input over. For optimal performance, should be slightly bigger than the expected number of non-zeros in the solution. If the solution is more than k-sparse, this function is recursively called with a 2*k schedule. If
NULL, full sorting is performed from the beginning.
Value
The projection result P of the same shape as input, such that \(P$sum(dim=dim) == 1\) elementwise.
Details
Solves the optimization problem: \(\max_p <input, P> - H_{1.5}(P) \text{ s.t. } P \geq 0, \sum(P) == 1\) where \(H_{1.5}(P)\) is the Tsallis alpha-entropy with \(\alpha=1.5\).
Examples
input <- torch::torch_randn(10,5, requires_grad = TRUE)
# create a top3 alpha=1.5 entmax on last input dimension
nn_entmax <- entmax15(dim=-1L, k = 3)
result <- nn_entmax(input)