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.
Distributed deployment of large vision foundation models often partitions a ViT backbone and exchanges intermediate token features between computing nodes, making efficient feature compression critical under bandwidth and computation constraints. Existing ViT feature codecs typically flatten heterogeneous global and patch tokens into an L x C pseudo image, causing entropy models to mainly capture sequence-axis dependencies while overlooking the native two-dimensional patch-grid structure. In this paper, we show that ViT patch tokens retain strong local spatial correlations on the original grid. To exploit this structural prior, we propose the Visual Token Codec (VTC), a dual-path learned codec that separates global and patch tokens into dedicated coding paths. Global tokens are compressed with a lightweight factorized prior, whereas patch tokens are encoded on the patch-token grid using a spatial-channel context entropy model. To support intermediate-layer compression and practical rate adaptation, VTC further incorporates feature-matching supervision after subsequent ViT blocks and variable-rate modules within a single codec. Experiments on DINOv2 and SAM3 show that VTC consistently outperforms representative ViT feature coding baselines on classification, segmentation, and detection tasks. At 90% of uncompressed-feature performance, VTC reduces bitrate by 15.7x-37.4x across these tasks. We further provide intermediate-layer rate-utility analyses for practical transmission- and storage-oriented deployment scenarios.
Andriy Enttsel, Vincent Corlayeess.IV cs.CV cs.IT eess.SP
Visual data compression is shifting from human-centered reconstruction to machine-oriented representation coding. In this setting, an image is often mapped to a compact semantic embedding, which is then compressed and transmitted for downstream inference. We propose an adaptive transform-coding method for semantic-feature compression motivated by the conditional rate-distortion function of a Gaussian mixture model. The scheme uses mode-dependent transforms and quantizers selected according to the inferred source component, enabling more efficient coding of heterogeneous feature distributions. Evaluations on features from widely used vision backbones and foundation models show that the proposed method outperforms or is competitive with state-of-the-art neural compression methods while preserving flexibility and interpretability.