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Displacement Geometry Captures Platonic Shared Reality Across Models and Modalities

NeurIPS 2026 · Large language models › Instruction and fine-tuning · approach: Fine-tuning for reasoning data · 0 citations (OpenAlex)

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Shows that independently trained vision and language encoders share displacement-vector geometry under rigid Procrustes alignment, explains it via within-model concept orthogonality, and uses a cached-forward-pass transfer (Shadow Casting, ShadowCLIP) to import capabilities.

Problem

Platonic Representation Hypothesis claims cross-model convergence, but pointwise neighborhood/position-based measures show weak or degrading similarity; the paper asks whether models share directions between samples rather than positions.

Approach

Measure cross-model agreement via cosine similarity of displacement vectors between input pairs after a single orthogonal Procrustes alignment; decompose representations into a linearly-aligned shared semantic component and a nonlinearly-entangled private capability component; transfer capabilities via a cached forward pass (Shadow Casting).

Key results

• Concept-level Cross-Model similarity is 0.73 (vision-vision), 0.91 (language-language), 0.49 (vision-language), versus pointwise 0.41, 0.36, 0.25.
• ShadowCLIP (ViT-Large) reaches 29.6 on MMVP vs 20.0 for CLIP-Large, and 92.5 on Food101 vs 90.1 for CLIP-Large in zero-shot.
• ShadowCLIP training takes about 0.5 hours on 8 RTX Pro 6000 GPUs and trains about 20M parameters versus 400M for full CLIP-Large fine-tuning.

Surprising findings

• Cross-Object similarity is high (0.87-0.96) even for randomly initialized models, so it is an architectural baseline rather than evidence of learned convergence.
• Fine-tuning CLIP projections on CC12M degrades performance across all three evaluation suites.

Limitations

• Analysis does not reach the largest frontier models; scale effects at extreme size are untested.
• Uniqueness of the shared geometry is not established; the 'Anna Karenina' scenario is not excluded.
• Only the simplest cosine-of-difference-vectors under rigid alignment is studied; richer directional decompositions are unexplored.

Experimental setup

Datasets: Flickr30k ImageNet-22k CommonWords79k WordNet CC12M ImageNet-1k

Benchmarks: Food101 CIFAR10 CIFAR100 SUN397 Stanford Cars FGVC Aircraft DTD Oxford Pets Caltech101 Flowers102 ImageNet-1k MSCOCO

Metrics: cosine similarity (pointwise, cross-object, cross-model) zero-shot accuracy recall@1 Wilcoxon signed-rank p-value linear probe accuracy HSIC

Baselines: CLIP DreamLIP LiT ShareLock SAIL CLIP-FT

Builds on: Platonic Representation Hypothesis linear representation hypothesis relational knowledge distillation LLM2Vec DreamLIP

Closest papers by meaning

• Position: The Platonic Representation Hypothesis (ICML 2024 · similarity 0.91)
• Platonic Representations in the Human Brain: Unsupervised Recovery of Universal Geometry (NeurIPS 2026 · similarity 0.87)
• Platonic Task Arithmetic (NeurIPS 2026 · similarity 0.87)
• Bridging Critical Gaps in Convergent Learning: How Representational Alignment Evolves Across Layers, Training, and Distribution Shifts (NeurIPS 2025 · similarity 0.87)
• Objective drives the consistency of representational similarity across datasets (ICML 2025 · similarity 0.85)
• Vision Language Models Cannot Reason About Physical Transformation (ICML 2026 · similarity 0.85)