differentiable_permutations.md

Notes on differentiable permutations

labels: experimental, interpretability, regularization, differentiable_permutation

since this is apparently something I've been thinking about on and off in the context of learning functional regions for interpretability and evolutionary strategies

• Learning Representations of Sets through Optimized Permutations - Has a cost function for scoring permutations matrices
  • https://github.com/Cyanogenoid/perm-optim/blob/master/permutation.py
• Learning Permutations with Sinkhorn Policy Gradient - "Sinkhorn layer produces continuous relaxations of permutation matrices"
• https://paperswithcode.com/paper/git-re-basin-merging-models-modulo
• Learning Latent Permutations with Gumbel-Sinkhorn Networks

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1. assign a learnable parameter that will serve as a permutation matrix
2. segment weights into (non overlapping?) tiles, post-permutation
3. compute per-tile activation variances (sampled tiles?)
4. define the permutation score as a statistic over the per-tile variances (e.g. sum, mean, p90...)
5. learn the permutation matrix which minimizes the permutation score