The Platonic Representation Hypothesis suggests that increasingly capable models converge toward shared representations. Recent work narrows this claim to shared local neighborhood relationships, finding that capacity-dependent trends in several global similarity measures largely disappear after calibration. We challenge this interpretation by showing that prior local-global comparisons confound structural scale (local versus global) with what is compared: relational structure, defined by which samples are related, versus metric geometry, characterized by quantitative relations such as distances, similarities, or correlations. To disentangle these factors, we construct a controlled 2×2 framework that evaluates both relational structure and metric geometry at local and global scales. We introduce H0 skeleton overlap as a global counterpart to mutual k-nearest neighbors, together with matched distance-aware variants. Across vision-language models, relational structure exhibits robust representational convergence at both scales after calibration, whereas increasingly stringent distance agreement substantially weakens alignment and progressively flattens the capacity-dependent trend. We further extend the analysis beyond ambient Euclidean geometry by evaluating distance agreement under a Riemannian metric approximation and recover the same structure-geometry pattern. The pattern is also reproduced in video-text representations. Together, these results show that relational convergence extends beyond local neighborhoods to global spanning structure, whereas metric geometry exhibits substantially weaker convergence.
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.
The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent work finds only weak pointwise similarity between models. In this paper, we show that what models share is not the location of samples in representation space, but the directions (displacement vectors) between them. Under a single orthogonal alignment--rotation and reflection only--these displacement vectors are substantially preserved across 44 independently trained vision and language encoders spanning modalities and asymmetric capability pairs, consistent with the PRH evidence. The samples' absolute positions are not, consistent with recent counter-evidence. Both arise from a single decomposition: representations split into a shared semantic component that is linearly aligned across models, and a private capability component that is not. We trace this geometry to concept-level structure: within a model, parent concepts are orthogonal to their child variation vectors; across models, concept displacements are parallel. Our theory falsifiably predicts (and experiments confirm) that fine-tuning preserves pointwise similarity but collapses displacement, and that relational distillation does the opposite. A major implication is that, because semantics align linearly but capabilities do not, capabilities can be imported from one model to another using a single cached forward pass through the source. We call this Shadow Casting. As a proof of concept, our SHADOWCLIP instantiation outperforms strong fine-tuned baselines at orders of magnitude less compute. A cache can be released alongside open model weights, letting one model's capabilities be downloaded and imported into any number of other models without fine-tuning.
The Platonic Representation Hypothesis suggests that neural networks trained on different modalities (e.g., text and images) align and eventually converge toward the same representation of reality. If true, this has significant implications for whether modality choice matters at all. We show that the experimental evidence for this hypothesis is fragile and depends critically on the evaluation regime. Alignment is measured using mutual nearest neighbors on small datasets (≈1K samples) and degrades substantially as the dataset is scaled to millions of samples. The same behavior is observed beyond text-image, for text-audio and text-video alignment. The alignment that remains between model representations reflects coarse semantic overlap rather than consistent fine-grained structure. Moreover, the evaluations in Huh et al. are done in a one-to-one image-caption setting, a constraint that breaks down in realistic many-to-many settings and further reduces measured alignment. We also find that the reported trend of stronger language models increasingly aligning with vision does not appear to hold for newer models. Overall, our findings suggest that the current evidence for cross-modal representational convergence is considerably weaker than subsequent works have taken it to be. Models trained on different modalities may learn equally rich representations of the world, just not the same one.