Visual Language Hypothesis

Abstract: We study visual representation learning from a structural and topological perspective. We begin from a single hypothesis: that visual understanding presupposes a semantic language for vision, in which many perceptual observations correspond to a small number of discrete semantic states. Together with widely assumed premises on transferability and abstraction in representation learning, this hypothesis implies that the visual observation space must be organized in a fiber bundle like structure, where nuisance variation populates fibers and semantics correspond to a quotient base space. From this structure we derive two theoretical consequences. First, the semantic quotient $X/G$ is not a submanifold of $X$ and cannot be obtained through smooth deformation alone, semantic invariance requires a non-homeomorphic, discriminative target, for example, supervision via labels, cross instance identification, or multimodal alignment that supplies explicit semantic equivalence. Second, we show that approximating the quotient also places structural demands on the model architecture. Semantic abstraction requires not only an external semantic target, but a representation mechanism capable of supporting topology change: an expand-and-snap process in which the manifold is first geometrically expanded to separate structure and then collapsed to form discrete semantic regions. We emphasize that these results are interpretive rather than prescriptive: the framework provides a topological lens that aligns with empirical regularities observed in large-scale discriminative and multimodal models, and with classical principles in statistical learning theory.