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THEORY-794: In vision models, compositional generalization to unseen combinations of concepts is driven by the diversity of the combinations seen in training rather than by data volume, and arrives with representations that are linearly factored by concept, as Uselis, Dittadi and Oh propose

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Properties5
StatusProposed
Tagsrepresentation-learning, compositionality, learning-theory, anthology-candidate
SourceLIT-667 — Does Data Scaling Lead to Visual Compositional Generalization?
ExtendsTHEORY-117 — In Uselis, Dittadi and Oh's two-concept grids, ResNet-50s trained from scratch, with checkpoints chosen on the unseen pairs, reach unseen combinations as the share of combinations seen grows and not as up to four times more data of the same combinations is added; and when embeddings are exactly linearly factored, seen pairs that connect every value of both concepts, as two per value arranged in one cycle do, determine the embedding of every unseen pair
AnswersQUESTION-207 — Without choosing checkpoints on the unseen pairs, does coverage of combinations still beat volume for compositional generalization, in a second architecture or with more than two concepts?

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Source

LIT-667. Filed by the promotion audit’s narrowing-loss sweep (batch 066, ADR-047 v4) on 2026-10-20, to carry the wider claim that the narrowing of THEORY-117 dropped. THEORY-117 is Active and is this THEORY’s evidence; this one stays Proposed.

What was actually shown

In an n × n grid of two concepts with k combinations seen per value, ResNet-50s trained from scratch fit the seen pairs and fail on unseen ones; four times the data of the same combinations leaves 60–80% drops, while seeing a larger share of the combinations closes the gap, and the features pass from spurious to decodable to linearly factored as coverage grows. Pretrained DINO, DINOv2 and CLIP features are partly factored. THEORY-117 states the measured result, with its oracle checkpoint selection, and the re-derived theorem that exactly factored embeddings of every unseen pair are fixed by seen pairs connecting every value. The authors draw the general conclusion, about vision models and about what drives compositional generalization, from this one design.

What would settle it

The promote_when is inherited from THEORY-117’s before it was narrowed, and QUESTION-207 asks the same question.

What this does not say

It is not a claim about how much data a practitioner needs, and it says nothing about generative models. The measurements chose checkpoints on the test pairs, so they bound what is possible rather than what honest selection reaches; this THEORY’s general form needs that gap closed.

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