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Unbalanced Soft-Matching Distance For Neural Representational Comparison With Partial Unit Correspondence

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.7Download Report PDF
Optimal TransportNeural TuningRepresentational SimilarityDeep Neural Networks
Abstract:

Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that allows some neurons to remain unmatched, yielding rotation-sensitive but robust correspondences. This unbalanced soft-matching distance provides theoretical advantages---relaxing strict mass conservation while maintaining interpretable transport costs---and practical benefits through efficient neuron ranking in terms of cross-network alignment without costly iterative recomputation. In simulations, it preserves correct matches under outliers and reliably selects the correct model in noise-corrupted identification tasks. On fMRI data, it automatically excludes low-reliability voxels and produces voxel rankings by alignment quality that closely match computationally expensive brute-force approaches. It achieves higher alignment precision across homologous brain areas than standard soft-matching, which is forced to match all units regardless of quality. In deep networks, highly matched units exhibit similar maximally exciting images, while unmatched units show divergent patterns. This ability to partition by match quality enables focused analyses, \emph{e.g.,} testing whether networks have privileged axes even within their most aligned subpopulations. Overall, unbalanced soft-matching provides a principled and practical method for representational comparison under partial correspondence.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes an unbalanced soft-matching distance that extends optimal transport to allow partial neuron correspondences, addressing robustness to outliers and noise in neural representation comparison. It resides in the 'Partial and Unbalanced Optimal Transport for Neural Comparison' leaf, which currently contains only this paper as a sibling. This indicates a relatively sparse research direction within the broader optimal transport branch, suggesting the work occupies a niche position in the taxonomy where explicit unbalanced transport formulations for neural alignment are not yet densely populated.

The taxonomy reveals neighboring leaves focused on partial point cloud registration (PRNet, RORNet) and hierarchical correspondence matching, which address partial overlap in geometric or semantic domains but do not explicitly formulate unbalanced transport for neural units. The broader 'Representation Learning and Convergence' branch explores whether networks learn similar codes but lacks the algorithmic machinery for partial matching. The paper's contribution bridges classical optimal transport theory with practical neural comparison challenges, diverging from rigid one-to-one matching (e.g., Inexact Neural Matching) and complementing geometric registration methods by targeting neuron-level alignment with explicit mass relaxation.

Among the three contributions analyzed, the core unbalanced soft-matching distance examined ten candidates with zero refutable prior work, suggesting novelty within the limited search scope. The L-curve heuristic for regularization selection examined four candidates with one refutable match, indicating some overlap with existing parameter selection methods. Efficient neuron ranking examined two candidates with one refutable match, pointing to prior work on alignment-based ranking. The statistics reflect a modest search scale (sixteen total candidates), so these findings characterize novelty relative to top semantic matches rather than exhaustive coverage of the field.

Given the limited search scope and sparse taxonomy leaf, the work appears to introduce a principled extension of soft-matching to unbalanced settings, a direction not densely explored in the examined literature. The core transport formulation shows novelty among the candidates reviewed, while auxiliary contributions (L-curve heuristic, ranking) have more substantial prior work. The analysis covers top semantic matches and does not claim exhaustive field coverage, leaving open the possibility of related work outside the examined set.

Taxonomy

Core-task Taxonomy Papers
19
3
Claimed Contributions
16
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: comparing neural representations with partial unit correspondence. This field addresses the challenge of aligning and comparing learned or biological neural representations when units (neurons or features) do not correspond one-to-one across systems. The taxonomy organizes work into four main branches. Optimal Transport and Matching Methods develop algorithmic frameworks—often rooted in optimal transport or graph matching—to find correspondences between representations even when they are incomplete or unbalanced. Representation Learning and Convergence Across Networks examines how different architectures or training regimes produce similar or divergent internal codes, exploring questions of convergence and generalization. Neural Coding and Representational Mechanisms in Biological Systems investigates how real neurons encode information, including population codes and sensory integration. Decoding Neural Representations Through Statistics, Intervention, and Behavior focuses on extracting interpretable structure from neural activity via statistical analysis, causal interventions, or behavioral readouts. Together, these branches span computational, theoretical, and empirical perspectives on understanding and comparing neural codes. A particularly active line of work within Optimal Transport and Matching Methods tackles partial and unbalanced scenarios where not all units have counterparts, a setting that arises naturally when comparing networks of different sizes or biological recordings with missing data. Unbalanced Soft Matching[0] contributes to this direction by proposing methods that relax strict one-to-one constraints, allowing flexible alignment even when correspondence is incomplete. This contrasts with earlier exact matching approaches like Inexact Neural Matching[18], which assumed more rigid structure, and complements recent geometric methods such as PRNet Partial Registration[5] and RORNet Partial Registration[14] that handle partial overlaps in spatial or feature domains. Meanwhile, works like Understanding Learning Representations[4] and Convergent Learning[8] explore whether different training procedures yield aligned codes, raising questions about when and why representations converge. Situating the original paper within this landscape, Unbalanced Soft Matching[0] fits squarely in the optimal transport branch, emphasizing robustness to imbalance and offering a principled framework that bridges classical matching theory with modern representation comparison challenges.

Claimed Contributions

Unbalanced soft-matching distance for partial neural correspondence

The authors extend the soft-matching distance to a partial optimal transport framework that permits some neurons to remain unmatched rather than forcing all units into correspondence. This relaxes strict mass conservation constraints while maintaining interpretable transport costs and enables rotation-sensitive but robust alignments between neural populations.

10 retrieved papers
L-curve heuristic for automatic regularization selection

The authors introduce an L-curve method to automatically determine the optimal fraction of mass to transport between neural populations. This heuristic identifies the point of maximal positive curvature in the cost-regularization tradeoff curve, enabling principled selection of how many units should be matched without requiring prior knowledge of noise levels.

4 retrieved papers
Can Refute
Efficient neuron ranking by alignment quality

The method provides a computationally efficient approach to rank neurons by their cross-population alignment quality. A single optimization at an appropriate regularization value achieves results nearly identical to exhaustive brute-force ranking while requiring substantially fewer operations, making it practical for identifying highly-aligned or poorly-aligned neural subpopulations.

2 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Unbalanced soft-matching distance for partial neural correspondence

The authors extend the soft-matching distance to a partial optimal transport framework that permits some neurons to remain unmatched rather than forcing all units into correspondence. This relaxes strict mass conservation constraints while maintaining interpretable transport costs and enables rotation-sensitive but robust alignments between neural populations.

Contribution

L-curve heuristic for automatic regularization selection

The authors introduce an L-curve method to automatically determine the optimal fraction of mass to transport between neural populations. This heuristic identifies the point of maximal positive curvature in the cost-regularization tradeoff curve, enabling principled selection of how many units should be matched without requiring prior knowledge of noise levels.

Contribution

Efficient neuron ranking by alignment quality

The method provides a computationally efficient approach to rank neurons by their cross-population alignment quality. A single optimization at an appropriate regularization value achieves results nearly identical to exhaustive brute-force ranking while requiring substantially fewer operations, making it practical for identifying highly-aligned or poorly-aligned neural subpopulations.

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