Aristotelian Manifolds: Leveraging Platonic Perceptual Features for Backpropagation Free Rapid Concept Learning

Michael Karnes; Alper Yilmaz

cs.CVAug 21, 2026

Aristotelian Manifolds: Leveraging Platonic Perceptual Features for Backpropagation Free Rapid Concept Learning

Authors: Michael Karnes, Alper Yilmaz

Organizations: Photogrammetric Computer Vision Lab The Ohio State University Columbus, OH, USA

Abstract

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.

Figures & tables

Category	Parameter / Stage	Specification / Search Grid
Evaluation Setup	Unsupervised Training	1000 random images
	Supervised Training	64 images/class
	Test Evaluation	200 random images
	Inference Classifier	$k\text{NN}$ ( $k=3$ ), Mahalanobis distance
Sweep Stages	Stage 1: Raw Encoding	Uncompressed sweep across all backbone layers.
	Stage 2: Component Encoding	Layer sweep with PCA: $A\in\{64,128,256,512\}$ .

Table 1: Experimental Protocol and Hyperparameter Sweep Stages

Metric	MedMNIST Paradigm	FSL Benchmark Paradigm
Backbone Model	DINOv2 ViT-Large/14	ViT-Large/16
Evaluation Style	All-Way (All classes jointly)	Episodic $N$ -Way (5-Way)
Data Regime	512-Shot Fixed Target	1-Shot and 5-Shot Regimes
Statistical Depth	5 random support trials	600 episodes ( $\text{Seed}=42$ )
Query Pool	Full Test Split ( $n_{\text{eval}}=-1$ )	15 samples/class/episode
Unsupervised Pool	$\leq$ 5,000 samples/class	500 unlabeled background images

Table 2: Structural Comparison Between Evaluation Protocols

Figure 1: Model performance comparison collapsed across all experimental stages, isolating the single best accuracy achieved by each specific model-dataset pairing across all three stages and layers. Bar heights represent the mean of these peak configurations across the constituent datasets in each group: solid bars denote the FSL Benchmarks group, while hatched bars denote the MedMNIST group. Error bars denote the standard deviation ( $\pm$ SD) calculated across the datasets within each model group.

Figure 2: Model performance decomposed by operational stage across benchmark groups. Bar heights represent the mean of the peak layer-wise accuracies computed across all constituent datasets within a given group for each specific (model, group, stage) cell. Error bars denote the standard deviation ( $\pm$ SD) of these best-layer configurations across the respective datasets within that specific stage and model cluster.

Figure 3: Layer-wise accuracy trends across the complete transformer hierarchy broken down by encoding stages. Each data point represents a hierarchical aggregation: hyperparameter sweeps ( $A\in\{64,128,256,512\}$ principal components in Stage 2; $V\in\{64,128,256,512\}$ vocabulary clusters in Stage 3) are condensed into a single mean layer score per dataset, and the final line coordinates plot the group-level mean across all constituent datasets. Vertical error bars represent the standard deviation ( $\pm$ SD) of the mean accuracies averaged across the hyperparameters across datasets within that evaluation group.

Figure 4: Mean all-way 512-shot classification accuracy across 11 MedMNIST v2 datasets (excluding multi-label ChestMNIST) evaluated using a frozen DINOv2 ViT-L/14 backbone. Performance is broken down across the three encoding stages (Stage 1: Raw, Stage 2: Components , Stage 3: Full) and three distance metrics (Mahalanobis, Euclidean, Cosine). Bar heights show the unweighted mean computed across the 11 individual dataset accuracy scores (where each dataset score represents an underlying 5-trial randomized execution average). Error bars denote the standard deviation ( $\pm$ SD) across the dataset cohort, capturing macro-level domain/modality variability rather than intra-trial fluctuations. The A-ROM Full shows the performance with 512 Few-Shot from [ Karnes and Yilmaz(2026a) ] .

Method	Backbone	MiniImageNet		TieredImageNet
		5-way 1-shot	5-way 5-shot	5-way 1-shot	5-way 5-shot
SYNTRANS [ Tang et al.(2025)Tang, He, and Qin ]	ResNet-12	76.20 $\pm$ 0.69	86.12 $\pm$ 0.54	79.69 $\pm$ 0.81	87.78 $\pm$ 0.60
SYNTRANS [ Tang et al.(2025)Tang, He, and Qin ]	ViT-S	81.30 $\pm$ 0.61	89.96 $\pm$ 0.42	84.31 $\pm$ 0.54	91.73 $\pm$ 0.44
RGEE-Raw [ Karnes and Yilmaz(2026b) ]	DINOv2-L	83.36 $\pm$ 0.75	96.51 $\pm$ 0.24	83.61 $\pm$ 0.84	94.96 $\pm$ 0.40
RGEE-PCA 512 [ Karnes and Yilmaz(2026b) ]	DINOv2-L	84.11 $\pm$ 0.74	96.18 $\pm$ 0.26	84.01 $\pm$ 0.81	94.50 $\pm$ 0.42
RGEE-PCA 256 [ Karnes and Yilmaz(2026b) ]	DINOv2-L	84.16 $\pm$ 0.78	95.34 $\pm$ 0.31	82.23 $\pm$ 0.81	93.09 $\pm$ 0.46

Table 3: Comparative results on MiniImageNet and TieredImageNet datasets. Average accuracy (%) with 95% confidence intervals.

Method	Backbone	CIFAR-FS		FC100
		5-way 1-shot	5-way 5-shot	5-way 1-shot	5-way 5-shot
SYNTRANS [ Tang et al.(2025)Tang, He, and Qin ]	ResNet-12	82.58 $\pm$ 0.75	89.42 $\pm$ 0.56	52.30 $\pm$ 0.75	64.91 $\pm$ 0.59
SYNTRANS [ Tang et al.(2025)Tang, He, and Qin ]	ViT-S	84.64 $\pm$ 0.65	90.81 $\pm$ 0.41	56.38 $\pm$ 0.69	69.45 $\pm$ 0.54
RGEE-Raw [ Karnes and Yilmaz(2026b) ]	DINOv2-L	90.92 $\pm$ 0.58	97.66 $\pm$ 0.19	56.01 $\pm$ 0.92	77.67 $\pm$ 0.71
RGEE-PCA 512 [ Karnes and Yilmaz(2026b) ]	DINOv2-L	91.35 $\pm$ 0.57	97.53 $\pm$ 0.20	55.34 $\pm$ 0.89	76.00 $\pm$ 0.71
RGEE-PCA 256 [ Karnes and Yilmaz(2026b) ]	DINOv2-L	90.71 $\pm$ 0.61	97.14 $\pm$ 0.23	53.56 $\pm$ 0.86	73.20 $\pm$ 0.72

Table 4: Few-shot classification performance on CIFAR-FS and FC100 datasets. Results report average accuracy (%) with 95% confidence intervals.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Heatmap visualization mapping the optimal feature extraction layer selected per dataset across the three operational encoding stages. The analysis evaluates the ViT-Large/16 (left) and the DINOv2 ViT-L/14 (right). Cell labels explicitly denote the specific transformer block index that yielded peak accuracy for that configuration. Cell shading corresponds to layer depth along a continuous gradient from the initial layers.

Figure 6: Per-dataset peak accuracies evaluated at the best-performing layer across the three encoding stages. The top row tracks a standard, supervised/self-supervised ViT-Large/16 backbone, while the bottom row tracks the self-supervised DINOv2 ViT-L/14 architecture. Evaluation is split side-by-side between the open-domain FSL Benchmarks (left) and the specialized MedMNIST v2 suite (right).

Figure 7: Mean all-way 512-shot classification accuracy across MedMNIST v2 (excluding multi-label ChestMNIST) evaluated using a frozen DINOv2 ViT-L/14 backbone. Performance is broken down across the three encoding stages and distance metrics. Bar heights show the mean computed across the 11 individual dataset accuracy scores across the 5-trials. Error bars denote the standard deviation ( $\pm$ SD) across the 5-trials.

Figure 8: Layer-wise classification accuracy of VGG architectures on FSL benchmarks.

Figure 9: Layer-wise classification accuracy of ResNet architectures on FSL benchmarks.

Figure 10: Layer-wise classification accuracy of ViT architectures on FSL benchmarks.

Figure 11: Layer-wise classification accuracy of DINOv2 architectures on FSL benchmarks.

Figure 12: Layer-wise classification accuracy of VGG architectures on MedNIST v2.

Figure 13: Layer-wise classification accuracy of ResNet architectures on MedNIST v2.

Figure 14: Layer-wise classification accuracy of ViT architectures on MedNIST v2.

Figure 15: Layer-wise classification accuracy of DINOv2 architectures on MedNIST v2.

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The Platonic Representation Hypothesis suggests that representations from neural networks are converging to a common statistical model of reality. We show that the existing metrics used to measure representational similarity are confounded by network scale: increasing model depth or width can systematically inflate representational similarity scores. To correct these effects, we introduce a permutation-based null-calibration framework that transforms any representational similarity metric into a calibrated score with statistical guarantees. We revisit the Platonic Representation Hypothesis with our calibration framework, which reveals a nuanced picture: the apparent convergence reported by global spectral measures largely disappears after calibration, while local neighborhood similarity, but not local distances, retains significant agreement across different modalities. Based on these findings, we propose the Aristotelian Representation Hypothesis: representations in neural networks are converging to shared local neighborhood relationships.

Abstract

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