Эксперимент: Partial Gromov-Wasserstein Cross-Attention (#582)

{ "worked": true, "confidence": 8, "verdict": "Built a readable partial GW cross-attention MVP with cosine feature cost, relational GW cost, entropic kernels, and alternating clipped row/column upper-bound projections. Quantitative checks matched predictions: beta=0 relative invariance error was 0, convex linearity error was 3.33e-16, beta logit shifts scaled exactly from 0 to 21.13, and maximum feasibility violations were 0 for all tested shapes. In the synthetic benchmark, increasing beta improved matched mass from 0.717 to 0.882 and reduced distractor mass from 0.151 to 0.090, while accuracy stayed 1.0; however, partial GW did not beat softmax accuracy and assigned slightly more distractor fraction than softmax, so no general performance win is established.", "metrics": { "baseline": "Softmax: accuracy 1.000, matched_mass_fraction 0.748, distractor_mass_fraction 0.106, transported_mass 12.0, entropy 0.769", "idea": "Partial GW: accuracy 1.000, matched_mass_fraction 0.800, distractor_mass_fraction 0.123, transported_mass 0.684, entropy 3.416; beta sweep matched mass 0.717->0.882 and distractor fraction 0.151->0.090 for beta 0->3" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small synthetic feature-matching benchmark was tested; no learned neural network, backpropagation, variable padding masks, learned masses, runtime/FLOP profiling, or larger/noisier real-world correspondence task was evaluated. The beta linearity and feasibility checks validate algebraic properties directly and are not evidence of end-to-end accuracy gains." }