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Stochastic Optimization of Sorting Networks via Continuous Relaxations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace non-differentiable sorting with the NeuralSort relaxation | sorting models · Large-MNIST sorting, n=3–15 | permutation accuracy: 0.093 -> 0.837 (n=5; Vanilla RS -> Deterministic NeuralSort) | Helped |
| Use Stochastic NeuralSort instead of Deterministic NeuralSort | sorting models · Large-MNIST sorting, n=3–15 | permutation accuracy: 0.930 vs 0.927 (n=3); 0.386 vs 0.418 (n=15) | Mixed |
| Use NeuralSort-based differentiable ordering for median prediction | quantile regression models · Large-MNIST quantile regression, n=5, 9, 15 | MSE (× 10^-4): 343.60 -> 45.50 (n=5; Sinkhorn -> Deterministic NeuralSort) | Helped |
| Use Stochastic NeuralSort rather than Deterministic NeuralSort | quantile regression models · Large-MNIST quantile regression, n=5, 9, 15 | MSE (× 10^-4): 45.50 -> 33.80 (n=5); 34.98 -> 31.43 (n=9); 34.78 -> 29.34 (n=15) | Helped |
| Use Deterministic NeuralSort rather than Stochastic NeuralSort | quantile regression models · Large-MNIST quantile regression, n=5, 9, 15 | R²: 0.94 -> 0.95 (n=5); 0.93 -> 0.94 (n=9); 0.90 -> 0.92 (n=15) | Helped |
| Learn the representation end-to-end with NeuralSort-based kNN | kNN classifier · MNIST test | accuracy: 97.6% -> 99.5% (kNN+AE -> kNN + Deterministic NeuralSort) | Helped |
| Learn the representation end-to-end with NeuralSort-based kNN | kNN classifier · Fashion-MNIST test | accuracy: 87.5% -> 93.5% (kNN+AE -> kNN + Deterministic NeuralSort) | Helped |
| Learn the representation end-to-end with NeuralSort-based kNN | kNN classifier · CIFAR-10 test | accuracy: 44.2% -> 90.7% (kNN+AE -> kNN + Deterministic NeuralSort) | Helped |
| Compare differentiable kNN with a standalone CNN | CIFAR-10 classifier · CIFAR-10 test | accuracy: 90.7% vs 95.1% | Hurt |
| Increase the relaxation temperature (ablation) | NeuralSort gradient estimation · Large-MNIST sorting | gradient-estimate variance | Helped |
| Use REINFORCE gradient estimation instead of reparameterized NeuralSort gradients | stochastic permutation optimization · Experiments across tasks | experimental performance | Hurt |
Closest papers by meaning
- Monotonic Differentiable Sorting Networks (ICLR 2022 · similarity 0.89)
- SoftSort: A Continuous Relaxation for the argsort Operator (ICML 2020 · similarity 0.89)
- Generalized Neural Sorting Networks with Error-Free Differentiable Swap Functions (ICLR 2024 · similarity 0.87)
- LapSum - One Method to Differentiate Them All: Ranking, Sorting and Top-k Selection (ICML 2025 · similarity 0.84)
- Differentiable extensions with rounding guarantees for combinatorial optimization over permutations (NeurIPS 2025 · similarity 0.84)
- OT4P: Unlocking Effective Orthogonal Group Path for Permutation Relaxation (NeurIPS 2024 · similarity 0.84)
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