# Optimal Transport on Quad (Quadratic potential synthetic data)

Source: [Optimal Transport on Quad (Quadratic potential synthetic data)](<https://www.sota2.com/research/sota/optimal-transport-on-quad-quadratic-potential-synthetic-data>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-02-26T05:42:08.739Z

Evaluation of algorithms solving Optimal Transport problems on the synthetic Quad dataset, measured using metrics such as ϵμ(f\_i0), ϵμ(f\_i1), and Rank.

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

| Scope | Recorded value |
| --- | --- |
| Task | Optimal Transport |
| Dataset (including any stated split) | Quad (Quadratic potential synthetic data) |
| Metric | Epsilon Mu (f\_i0) |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 5 of 5 |
| Coverage | All results currently returned for this benchmark |

Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol.

## Metrics

- [Epsilon Mu (f\_i0)](<https://www.sota2.com/research/sota/optimal-transport-on-quad-quadratic-potential-synthetic-data.md?metric=Epsilon%20Mu%20(f_i0)>): Lower is better; unit: SCALAR.

- [Epsilon Mu (f\_i1)](<https://www.sota2.com/research/sota/optimal-transport-on-quad-quadratic-potential-synthetic-data.md?metric=Epsilon%20Mu%20(f_i1)>): Lower is better; unit: SCALAR.

- [Rank](<https://www.sota2.com/research/sota/optimal-transport-on-quad-quadratic-potential-synthetic-data.md?metric=Rank>): Lower is better; unit: SCALAR.

- [Number of Parameters](<https://www.sota2.com/research/sota/optimal-transport-on-quad-quadratic-potential-synthetic-data.md?metric=Number%20of%20Parameters>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Epsilon Mu (f\_i0) | Result date | Report paper |
| --- | --- | --- | --- |
| Selection via semi-dual Brenier objective | 0.014 | Not recorded | 68fa59fe1e209131ce9bc1d9 |
| SSNB | 0.014 | Not recorded | 68fa59fe1e209131ce9bc1d9 |
| Sinkhorn | 0.047 | Not recorded | 68fa59fe1e209131ce9bc1d9 |
| ICNN | 12.23 | Not recorded | 68fa59fe1e209131ce9bc1d9 |

### Selection via semi-dual Brenier objective

Epsilon Mu (f\_i0): 0.014. Result ID: 698bab3f7a967eddb77075b8.

[Reporting paper](<https://www.sota2.com/research/paper/68fa59fe1e209131ce9bc1d9.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa59fe1e209131ce9bc1d9.md>)

[Implementation](<https://github.com/AmirTag/OT-ICNN>)

Recorded evaluation configuration: {"Selection Criterion":"Semi-dual Brenier objective","Number of candidate models":"64"}. This record does not assert independent reproduction.

### SSNB

Epsilon Mu (f\_i0): 0.014. Result ID: 698c613a37894ef7d9cdf349.

[Reporting paper](<https://www.sota2.com/research/paper/68fa59fe1e209131ce9bc1d9.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa59fe1e209131ce9bc1d9.md>)

[Implementation](<https://github.com/AmirTag/OT-ICNN>)

Recorded evaluation configuration: {"Parameter selection criterion":"semi-dual Brenier objective"}. This record does not assert independent reproduction.

### Sinkhorn

Epsilon Mu (f\_i0): 0.047. Result ID: 698c613a37894ef7d9cdf348.

[Reporting paper](<https://www.sota2.com/research/paper/68fa59fe1e209131ce9bc1d9.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa57171e209131ce9a2661.md>)

Recorded evaluation configuration: {"Parameter selection criterion":"semi-dual Brenier objective"}. This record does not assert independent reproduction.

### ICNN

Epsilon Mu (f\_i0): 12.23. Result ID: 698c613a37894ef7d9cdf347.

[Reporting paper](<https://www.sota2.com/research/paper/68fa59fe1e209131ce9bc1d9.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa53f21e209131ce987ade.md>)

Recorded evaluation configuration: {"Parameter selection criterion":"semi-dual Brenier objective"}. This record does not assert independent reproduction.

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