# SO(3)-equivariant point-cloud regression on SO(3) point-cloud (test) Source: [SO(3)-equivariant point-cloud regression on SO(3) point-cloud (test)]() Collection index: [llms.txt]() Data updated: 2026-05-11T08:07:15.446Z Evaluation of SO(3)-equivariant point-cloud regression performance on the test split of the SO(3) point-cloud dataset, reporting metrics such as mean test MSE, Δ(P−M), and paired t-statistic. 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 | SO(3)-equivariant point-cloud regression | | Dataset (including any stated split) | SO(3) point-cloud (test) | | Metric | Mean Test MSE | | Unit | SCALAR | | Direction | Lower is better | | Results loaded | 12 of 12 | | 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 - [Mean Test MSE](): Lower is better; unit: SCALAR. - [Delta (P-M)](): Lower is better; unit: SCALAR. - [Paired t-statistic](): Higher is better; unit: SCALAR. ## Recorded results | Method | Mean Test MSE | Result date | Report paper | | --- | --- | --- | --- | | Muon | 0.0049 | Not recorded | 6a016297dbc836b87d82315c | | Muon | 0.0055 | Not recorded | 6a016297dbc836b87d82315c | | PolarAdamW | 0.0063 | Not recorded | 6a016297dbc836b87d82315c | | Muon | 0.0064 | Not recorded | 6a016297dbc836b87d82315c | | Muon | 0.0067 | Not recorded | 6a016297dbc836b87d82315c | | PolarAdamW | 0.0067 | Not recorded | 6a016297dbc836b87d82315c | | PolarAdamW | 0.0074 | Not recorded | 6a016297dbc836b87d82315c | | PolarAdamW | 0.0074 | Not recorded | 6a016297dbc836b87d82315c | | AdamW | 0.0099 | Not recorded | 6a016297dbc836b87d82315c | | AdamW | 0.0102 | Not recorded | 6a016297dbc836b87d82315c | | AdamW | 0.0103 | Not recorded | 6a016297dbc836b87d82315c | | AdamW | 0.0104 | Not recorded | 6a016297dbc836b87d82315c | ### Muon Mean Test MSE: 0.0049. Result ID: 6a018e1e47f34ce924e33d1e. [Reporting paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"128","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### Muon Mean Test MSE: 0.0055. Result ID: 6a018e1e47f34ce924e33d1b. [Reporting paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"64","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### PolarAdamW Mean Test MSE: 0.0063. Result ID: 6a018e1e47f34ce924e33d1f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"128","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### Muon Mean Test MSE: 0.0064. Result ID: 6a018e1e47f34ce924e33d18. [Reporting paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"32","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### Muon Mean Test MSE: 0.0067. Result ID: 6a018e1e47f34ce924e33d15. [Reporting paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"16","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### PolarAdamW Mean Test MSE: 0.0067. Result ID: 6a018e1e47f34ce924e33d1c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"64","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### PolarAdamW Mean Test MSE: 0.0074. Result ID: 6a018e1e47f34ce924e33d16. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"16","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### PolarAdamW Mean Test MSE: 0.0074. Result ID: 6a018e1e47f34ce924e33d19. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"32","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### AdamW Mean Test MSE: 0.0099. Result ID: 6a018e1e47f34ce924e33d14. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"16","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### AdamW Mean Test MSE: 0.0102. Result ID: 6a018e1e47f34ce924e33d17. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"32","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### AdamW Mean Test MSE: 0.0103. Result ID: 6a018e1e47f34ce924e33d1a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"64","number of seeds (n)":"100"}. This record does not assert independent reproduction. ### AdamW Mean Test MSE: 0.0104. Result ID: 6a018e1e47f34ce924e33d1d. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"hidden-channel width (hc)":"128","number of seeds (n)":"100"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.