This paper formalizes and systematically characterizes Aristotelian Manifolds, a generalized structural framework built upon the Platonic Representation Hypothesis. We position high-capacity foundation models as universal perceptual filters and conduct a comprehensive layer-wise investigation to map how knowledge is functionally synthesized within these latent subspaces. Across diverse architectural paradigms and multi-domain datasets, we rigorously chart the interplay between network depth, dimensionality reduction, and distance metrics. Our characterization reveals that semantic maturation does not follow a singular, monotonic path; instead, different data domains exhibit highly distinct geometric response profiles, characterized by intermediate mound-like peaks for specialized clinical modalities and sigmoidal plateaus for natural visual tasks. By profiling the exact coordinates where these manifolds achieve peak representational efficiency, we establish a predictable taxonomy for layer selection and feature compression. Ultimately, this systematic characterization demonstrates that mapping the internal geometry of frozen representations provides a robust, backpropagation-free, and interpretable framework for understanding and exploiting foundation model latent spaces.
Monocular depth estimation (MDE) is a fundamental yet inherently ill-posed task. Recent vision foundation models (VFMs), particularly DINO-based transformers, have significantly improved accuracy and generalization for dense prediction. Prior works generally follow a unified paradigm: sampling a fixed set of intermediate transformer layers at uniform intervals to build multi-scale features. This common practice implicitly assumes that geometric information is uniformly distributed across layers, which may underutilize the structural 3D cues encoded in VFMs. In this study, we present a systematic layer-wise analysis of DINOv3, revealing that 3D information is distributed non-uniformly: deeper layers exhibit stronger depth predictability and better capture inter-sample geometric variation. Motivated by this, we introduce a Last-Layer-Centric Feature Recombination (LFR) module to enhance geometric expressiveness. LFR treats the final layer as a geometric anchor and adaptively selects complementary intermediate layers according to a minimal-similarity criterion. Selected features are fused with the last-layer representation via compact linear adapters.Extensive experiments show that LFR module consistently improves MDE accuracy and achieves state-of-the-art performance. Our analysis sheds light on how geometric knowledge is organized within VFMs and offers an efficient strategy for unlocking their potential in dense 3D tasks.