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LIT-1807: AvAtar: Learning to Align via Active Optimal Transport

2 min read

Properties5
StatusActive — read in full 2026-10-29 (NOTE-1327), from the arXiv v2; worth reading as a precise case of budgeted question choice within a fixed vocabulary: which object's correspondence to ask about, scored by an exact derivative through entropic transport of a coherence proxy, and evaluated on accuracy.
Version2
Tagsmathematics, network-science, anthology-candidate
Cited as “paper” byNOTE-1327 — Yu et al. — AvAtar active OT alignment
Cited as “source” byTHEORY-1147 — For entropy-regularized optimal transport with a fixed cost, the gradient of any differentiable function of the optimal plan with respect to the cost is obtained exactly from one linear system of size n + m whose matrix [​[diag µ, T], [Tᵀ, diag ν]] is positive semidefinite and singular only along the gauge direction (1, −1), which does not affect the gradient; so the first-order effect of supervising any candidate pair on a utility of the whole alignment can be computed without forming the (nm)² Jacobian, THEORY-1160 — Choosing which source objects to have an oracle match, by the derivative of a proxy utility of the entropic transport plan (its nearness to a permutation, or its consistency with the graphs) with respect to supervising each candidate match, averaged over matches by the current plan, raises held-out alignment accuracy more than uncertainty, centrality and matching-sampling query rules at the same label budget, by up to about three points on network alignment and less on image–text tasks; the gain depends on weighting by the current plan, without which the rule does worse than random

Graph View

Yu, Q., Qiu, R., Zeng, Z., Thai, M. T., Liu, H., & Tong, H. (2026). AvAtar: Learning to align via active optimal transport. ICML 2026, PMLR 306, 151023–151044.

Read in full in NOTE-1327.

Key takeaways

  • What is chosen is a source object; the oracle names its match; the question form, object sets, cost and utility are fixed. It allocates a label budget among questions already askable.
  • The score is an exact first-order derivative through entropic OT (THEORY-1147), of a coherence proxy, not of accuracy.
  • Its gains are small and reported without variances (THEORY-1160); without weighting by the current plan the rule does worse than random.

Why this is here

A7’s highest-priority connection, to the inquiry frontier (TERM-092, CLAIM-475): establishing a correspondence is a budgeted choice of which question to ask. A7’s distinction is kept: AvAtar chooses a query within a fixed vocabulary, while TERM-092 also asks how the vocabulary in which new questions become askable is extended.

The reading confirms A7’s distinction exactly. One refinement: the budget counts answers only. The cost of choosing is measured as query time but not charged, and formulating costs nothing because the questions are given, so the paper bears on neither of CLAIM-475’s defeaters (NOTE-1327).

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