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LIT-937: Post-Hoc Concept Disentanglement: From Correlated to Isolated Concept Representations

2 min read

Properties5
StatusActive — read 2026-10-14 (NOTE-816) in full; worth reading as a clean case where concept directions for correlated attributes align only because each is fitted alone: a joint fit with an orthogonality penalty finds mutually orthogonal directions that still separate each concept with AUROC largely preserved, at the last convolutional layer of VGG16 and ResNet18 on CelebA and FunnyBirds. Read it knowing that every result is in a figure with no values or error bars, that AUROC is the only check that a direction keeps its meaning, and that the attributes are correlated, not hierarchical. Registered for QUESTION-025, where it bears on the correlated branch only; THEORY-292 is filed from it.
Version2
Tagsrepresentation-learning, anthology-candidate
Cited as “paper” byNOTE-816 — Erogullari et al. — Post-Hoc Concept Disentanglement
Cited as “source” byTHEORY-292 — In CNN image classifiers, concept directions fitted one concept at a time align for attributes that co-occur in the labels, yet a joint fit finds mutually orthogonal directions that still separate each concept with little loss of AUROC, so the alignment is a property of the separate fits and not forced by the representation

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Eren Erogullari, Sebastian Lapuschkin, Wojciech Samek, Frederik Pahde (2025), arXiv:2503.05522.

Key takeaways

From the reading, NOTE-816.

  • Separate fits align. Pattern-CAVs, argmin ‖Z − t wᵀ − b‖² fitted per concept, give a cosine matrix whose blocks match the label correlation matrix. CelebA shows two blocks, which the paper calls female- and male-associated. FunnyBirds shows its injected 70% beak–tail correlation. Anti-correlated concepts point in opposite directions.
  • Orthogonal directions exist. Adding α‖CCᵀ − I‖²_F to the objective and fine-tuning for 300 epochs reaches near-perfect orthogonality in every dataset–model pair. AUROC is “largely preserved”. Per-concept relative changes fall within about ±20%, with gains and losses in both blocks. For α between 10⁻⁴ and 10⁰, average AUROC is slightly above the unpenalised fit.
  • So the alignment is in the fit. By the reader’s derivation, Eq. 2 gives w_c ∝ Cov(z, t_c), which mixes the directions of correlated concepts in proportion to their label covariance.
  • Steering. Moving a diffusion autoencoder’s latent along the baseline “necktie” direction also adds a mustache and eyeglasses, and the orthogonal direction does not. In a controlled shortcut experiment, removing the orthogonal “timestamp” direction costs less clean accuracy. Both are shown in figures only.
  • Limits. There are no values, seeds or error bars in the text, and AUROC is the only check of meaning. The paper tests two small CNNs, one layer, and correlated (not hierarchical) attributes.

Standing in the record

Filed on 2026-10-12 for QUESTION-025, and read on 2026-10-14 in NOTE-816. It was registered as “a measured case of correlated attributes yielding non-orthogonal, entangled concept directions”. The reading corrects that. What is measured is the alignment of separately fitted directions. The paper’s own result is that orthogonal directions separating each concept about as well exist. So, in supervised CNN features, correlated attributes keep linear directions. That is filed as THEORY-292, which partially answers the correlated branch of QUESTION-025. It does not reach hierarchical attributes or the lattice. It sits beside THEORY-185’s case of correlated attributes in a PMI embedding and THEORY-117’s passage from entangled to factored features. The steering results are ML practice, hence the anthology-candidate flag.

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