# Support Operation Factorization: Compositional Readout of Frozen Vision Encoders under Controlled Interventions

arXiv: https://arxiv.org/abs/2608.06174 · HTML: https://mlsanity.com/paper/2608.06174/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Measuring Compositional Generalization: A Comprehensive Method on Realistic Data](https://mlsanity.com/paper/1912.09713/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Simple Unsupervised Object-Centric Learning for Complex and Naturalistic Videos](https://mlsanity.com/paper/2205.14065/) (2022)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [Visual Representation Learning Does Not Generalize Strongly Within the Same Domain](https://mlsanity.com/paper/2107.08221/) (2021)
- [Subspace-Decomposed JEPAs: Disentangling Progression and Content in Latent World Models](https://mlsanity.com/paper/2605.31111/) (2026)

## Abstract (arXiv)

Compositional analysis of frozen vision encoders should determine both what changed and where it changed. Standard factor probes score these axes separately, however, and can reward multiple operations that reuse the same predicted slot. We call this failure operation laundering. We introduce an injectively aligned leave-one-cell-out protocol over support x operation grids and SO-OPF, a readout that factors cell energy into support salience and a competitive operation posterior. This formulation separates two questions that aggregate scores conflate: whether the carrier composes held-out bindings when the grid is known, and whether that grid can be recovered from flat cell labels. With frozen DINOv3 features, known factorial assignment reaches 0.874 injective accuracy on Shapes3D-Extended and 0.799 on globally image-disjoint COCO; learning the assignment from flat labels reaches 0.769 and 0.762, respectively. Under matched-axis-aware supervision on Shapes3D, the factored carrier improves learned-assignment accuracy from 0.653 to 0.841 over a dense carrier and eliminates its laundering gap. SigLIP2 replicates the COCO separation. A rebuilt MuJoCo substrate exposes a boundary: learned-assignment accuracy is 0.569 with DINOv3 and 0.484 with SigLIP2, with substantial slot collapse. Thus factored readout and injective evaluation recover held-out bindings on two substrates while exposing, rather than hiding, a renderer-specific failure boundary; they do not establish universal recovery from flat labels.