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arxiv: 2605.20030 · v1 · pith:KVNW7V7Qnew · submitted 2026-05-19 · 💻 cs.LG · math.OC

Take It or Leave It: Intent-Controlled Partial Optimal Transport

Salil Parth Tripathi , Bertrand Chapron , Fabrice Collard , Nicolas Courty , Ronan Fablet This is my paper

Pith reviewed 2026-05-20 06:55 UTC · model grok-4.3

classification 💻 cs.LG math.OC
keywords optimal transportpartial optimal transportpositive-unlabeled learningdomain adaptationside informationKantorovich formulationsatellite ocean data
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The pith

Intent-controlled partial optimal transport replaces global mass rejection with pointwise costs derived from side information.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces intent-controlled partial optimal transport as a way to relax the exact matching requirement of optimal transport in a more structured manner than standard partial variants allow. Instead of a single global budget or uniform rule for leaving mass unmatched, it assigns individual rejection costs to points in both measures based on reliability, geometry, or external signals. This change yields a dual formulation based on local acceptance thresholds and reduces the problem to a standard balanced optimal transport task on an enlarged support. The approach is shown to improve performance when plugged into positive-unlabeled learning and open-partial domain adaptation pipelines. A geophysical example with satellite ocean data illustrates how physical sensor priors can directly shape the rejection decisions.

Core claim

IC-POT replaces the global rejection paradigm with pointwise rejection costs over both measures. The resulting optimization problem admits a dual interpretation in terms of local acceptance thresholds and can be solved by recasting it as a balanced Kantorovich OT problem on an augmented support. In applications where rejection is driven by side information, incorporating these pointwise rules improves fixed baseline pipelines in positive-unlabeled learning and open-partial domain adaptation, and it enables retrieval of comparable signal information from multi-modal satellite ocean measurements.

What carries the argument

intent-controlled partial optimal transport (IC-POT), which encodes side-specific information as pointwise rejection costs over the two measures rather than a global unmatched-mass budget

If this is right

  • In positive-unlabeled learning, pointwise rejection rules that encode statistical structure improve fixed baseline pipelines.
  • In open-partial domain adaptation, the same pointwise mechanism yields measurable gains over global-rejection baselines.
  • For multi-modal satellite ocean measurements, physical and sensor priors can be directly translated into rejection costs to define the retrieved comparable signal.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The dual view with local thresholds may allow practitioners to inspect and tune acceptance decisions per data point rather than adjusting one global parameter.
  • Because the method reduces to ordinary balanced OT on an augmented space, existing fast solvers can be reused without new algorithmic machinery.

Load-bearing premise

Meaningful pointwise rejection costs can be supplied from side-specific reliability, support geometry, or external information and produce a well-behaved optimization problem whose solution remains useful in downstream tasks.

What would settle it

A direct comparison experiment in which standard partial OT and IC-POT receive identical side information yet IC-POT fails to improve accuracy or stability on the positive-unlabeled or domain-adaptation benchmarks.

Figures

Figures reproduced from arXiv: 2605.20030 by Bertrand Chapron, Fabrice Collard, Nicolas Courty, Ronan Fablet, Salil Parth Tripathi.

Figure 1
Figure 1. Figure 1: Controlled PU selection-bias test on a representative seed. The top row is homogeneous [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of partial OT for SWIM-SAR ocean-wave spectra. (a) Real co-location: [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Construction of the side-specific unmatched costs for the synthetic SWIM/SAR case used [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Constant-cost partial-W trade-off on the synthetic SWIM/SAR case from Figure 2(b). The [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Representative synthetic SWIM/SAR cases. Each row follows the same layout as Fig [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Supplementary selective transfer examples under fixed transport geometry. (a) Bilateral [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Pairing ablation for the bilateral fruit example. The source-target pair, color cost matrix, [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Source-side participation signals used in the cat selective-transfer comparison. The two [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Continuous selection-bias sweep. The x-axis measures the strength of the selection bias [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Sensitivity to the negative geometry. We vary only the vertical offset of the negative [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Additional qualitative comparison on a heterogeneous PU selection-bias seed. From left [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
read the original abstract

While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or uniform rejection rule. However, many applications call for more structured, pointwise rejection mechanisms, where the decision to leave mass unmatched depends on side-specific reliability, support geometry, or external information about which components should participate in the comparison. We introduce \emph{intent-controlled partial optimal transport} (IC-POT), a targeted generalization of partial transport that replaces the global rejection paradigm with pointwise rejection costs over both measures. We show that the resulting optimization problem admits a dual interpretation in terms of local acceptance thresholds and can be solved by recasting it as a balanced Kantorovich OT problem on an augmented support. Beyond theoretical analysis, we demonstrate the practical relevance of IC-POT in settings where rejection is driven by side information. In positive-unlabeled learning and open-partial domain adaptation, incorporating pointwise rejection rules that encode statistical structure improves fixed baseline pipelines. Finally, we motivate the use of IC-POT with a geophysical practical case: multi-modal satellite ocean measurements, for which physical and sensors priors naturally inform the rejection mechanism and define the retrieved comparable signal information.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript introduces intent-controlled partial optimal transport (IC-POT), a generalization of partial optimal transport that replaces global rejection mechanisms with pointwise rejection costs defined over both measures. These costs are intended to encode side-specific information such as reliability, geometry, or external priors. The authors establish that the resulting problem admits a dual formulation in terms of local acceptance thresholds and can be exactly reduced to a standard balanced Kantorovich optimal transport problem on an augmented support. They demonstrate the approach on positive-unlabeled learning and open-partial domain adaptation tasks, reporting improvements over fixed baselines, and motivate its use with a geophysical case involving multi-modal satellite ocean measurements where physical and sensor priors inform rejection.

Significance. If the claimed dual and reduction results hold under standard assumptions on the cost function and finite rejection costs, IC-POT supplies a practical and theoretically grounded way to incorporate heterogeneous rejection preferences into transport problems. The reduction to balanced OT on augmented support is a clear implementation advantage, allowing reuse of existing solvers. The applications in PU learning and domain adaptation, together with the geophysical motivation, indicate that pointwise control can improve alignment when side information is available. This could be relevant for ML pipelines that must handle variable data quality or structured priors.

minor comments (3)
  1. §4 (Reduction to balanced OT): the construction of the augmented support and the precise mapping of the original pointwise rejection costs to the new cost matrix should be stated with an explicit equation or algorithm box to facilitate direct implementation.
  2. §5.2 (PU learning experiments): the procedure for deriving the pointwise rejection costs from the unlabeled data statistics is only sketched; adding a short paragraph or pseudocode would improve reproducibility.
  3. Figure 4 (geophysical case): the caption and surrounding text should clarify which physical/sensor priors were used to set the rejection costs and how the baseline partial OT was configured for fair comparison.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript on intent-controlled partial optimal transport (IC-POT). The recognition of the dual formulation with local acceptance thresholds, the exact reduction to balanced Kantorovich OT on augmented support, and the practical relevance in PU learning, open-partial domain adaptation, and geophysical satellite data is appreciated. We will prepare a revised version addressing the minor revision recommendation.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines IC-POT by replacing global rejection with pointwise rejection costs and then derives its dual form (local acceptance thresholds) plus exact reduction to a balanced Kantorovich problem on an augmented support. These steps are standard linear-penalty constructions for unbalanced/partial OT and rely only on the usual Kantorovich duality and lower-semicontinuity assumptions; they do not redefine any quantity in terms of itself, fit a parameter and relabel it a prediction, or rest on a load-bearing self-citation. The abstract and claimed results remain independent of the new pointwise costs once those costs are supplied, so the central theoretical claims are self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard optimal transport theory and the assumption that side information can be turned into valid pointwise rejection costs; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • standard math Standard assumptions of Kantorovich optimal transport (non-negative finite measures, existence of optimal plans).
    Invoked implicitly when the problem is recast as balanced OT on augmented support.
  • domain assumption Existence of side information that can be encoded as pointwise rejection costs without destroying convexity or duality.
    Central to the claim that IC-POT is practically relevant in PU learning and satellite data.

pith-pipeline@v0.9.0 · 5768 in / 1443 out tokens · 43404 ms · 2026-05-20T06:55:34.259387+00:00 · methodology

discussion (0)

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Reference graph

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