Platonic Representations in the Human Brain: Unsupervised Recovery of Universal Geometry

Pablo Marcos-Manchón; Rishi Jha; Lluís Fuentemilla

Source-linked AI summary

Platonic Representations in the Human Brain: Unsupervised Recovery of Universal Geometry

Pablo Marcos-Manchón, Rishi Jha, Lluís Fuentemilla

arXiv:2605.20496v1May 19, 2026q-bio.NCcs.CV

TL;DR

The paper asks whether human brains share a translatable representational geometry despite independently learned fMRI spaces and no paired cross-subject training data. It learns subject-specific embeddings from repeated presentations, translates them with unsupervised orthogonal rotations, and synchronizes those rotations. The resulting shared space improves retrieval and supports approximately isometric shared neural geometry, while remaining dependent on high-quality repeated-presentation fMRI data.

Problem
The paper asks whether independently learned human fMRI representations can be translated across subjects using intrinsic geometry without paired data or external reference spaces.
Method
A self-supervised encoder learns subject-specific embeddings from repeated presentations, followed by unsupervised orthogonal brain-to-brain translation and global rotation synchronization.
Results
Synchronizing pairwise rotations into a shared latent space further improved retrieval, indicating that independently learned subject embeddings are mutually compatible with a common coordinate system.
Takeaways & Limitations
The results support an approximately isometric shared neural geometry in human visual cortex that can be recovered directly from fMRI data through geometric transformations.
Takeaways & Limitations
The approach relies on high-quality fMRI data with repeated stimulus presentations, and its applicability to lower-SNR modalities, smaller datasets, and higher-level cognitive tasks remains unclear.

Abstract

from arXiv · show

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without paired data. We ask whether an analogous geometry can be recovered across human brains. Using fMRI data from the Natural Scenes Dataset, we propose a self-supervised encoder that learns subject-specific embeddings from brain data alone by exploiting repeated stimulus presentations. We show that these independently learned spaces can be translated across subjects using unsupervised orthogonal rotations, without paired cross-subject samples or intermediate model representations. Synchronizing pairwise rotations into a single shared latent space further improves cross-subject retrieval, indicating that subject-specific spaces are mutually compatible with a common coordinate system. These results provide evidence for a shared neural geometry in the human visual cortex: subject-specific fMRI representations are approximately isometric across individuals and can be translated through purely geometric transformations.

1 Introduction

The paper extends the Strong Platonic Representation Hypothesis to human visual cortex, asking whether independently learned fMRI embedding spaces can be translated using intrinsic neural geometry. It reports approximately isometric subject spaces and a compatible shared coordinate system recovered without paired cross-subject data.

Evidence for strong representational convergence has largely come from artificial vision and language systems, motivating a test in human brains.
The study evaluates independently learned subject-specific fMRI embeddings on the Natural Scenes Dataset using only intrinsic neural-response geometry.
Subject-specific embeddings are learned from repeated stimulus presentations, without external model features or cross-subject supervision.
Unsupervised orthogonal rotations recover accurate instance-level cross-subject correspondences, indicating approximately isometric embeddings across brains.
Synchronizing pairwise rotations improves cross-subject retrieval and shows compatibility with a common coordinate system.

2 Problem Setup

The problem is to map independently observed subject-specific fMRI responses into a shared latent space without paired cross-subject training data. The method treats subject spaces as noisy instances of shared geometry and restricts translations to orthogonal maps.

The target is a common latent space in which independently observed embeddings align despite the absence of paired cross-subject data during training.
Subjects observe disjoint image sets, while shared held-out images are reserved solely for evaluating translation quality.
Each subject’s fMRI responses are mapped into a low-dimensional embedding using only that subject’s neural activity.
Orthogonal transformations are used because they preserve distances and inner products while preventing arbitrary geometric warping.

3 Method

The method learns repetition-invariant subject embeddings, estimates unsupervised orthogonal translations between subject pairs, and synchronizes them into one shared latent space. Its pipeline combines reliability-weighted dimensionality reduction, multiview representation learning, geometric matching, and global cycle-consistent synchronization.

Subject encoder: Each subject encoder maps fMRI responses into a lower-dimensional embedding space using repeated presentations as self-supervision.The full pipeline has three stages: subject encoding, pairwise translation, and shared-space synchronization.
Subject encoder: Voxel responses are reliability-weighted across repetitions before PCA reduces them to a lower-dimensional subspace.
Subject encoder: MCCA extracts components shared across repetition views, after which view-specific projections are averaged and distilled into one linear mapping.
Subject encoder: A residual nonlinear refinement adds a learnable MLP correction to the frozen linear embedding and is trained with contrastive and cosine-pull objectives.
Pairwise translation: Pairwise subject translations use geometry-derived pseudocorrespondences and iterative nearest-neighbor refinement to estimate orthogonal rotations without paired samples.
Shared latent space: Pairwise rotations are symmetrized and globally synchronized to recover one orthogonal transformation per subject in a common coordinate system.
Shared latent space: Global synchronization maps each subject embedding into the shared space and denoises pairwise estimates by enforcing cycle consistency.

4 Experiments

Experiments evaluate repetition-trained fMRI encoders, unsupervised brain-to-brain translations, shared-space synchronization, and supervised model–brain mappings on held-out shared images. The results show stable within-subject embeddings, accurate cross-subject retrieval, further gains from global synchronization, and weaker model–brain alignment.

Dataset and evaluation: The Natural Scenes Dataset contains 8 participants viewing up to 10,000 images, with subject-specific images used for training and shared images held out for evaluation.Retrieval uses 515 candidates, with Mean Rank, R@1, and RSA reported across within- and across-subject settings.
Within-subject encoder evaluation: Repetition-based self-supervision produced stable within-subject embeddings, achieving an average Mean Rank of 5.28 across subjects.S1 and S2 were nearly perfectly matched across repetitions, while S3 and S8 achieved lower but still solid performance.
Within-subject encoder evaluation: The full encoder achieved the lowest Mean Rank and highest R@1 among encoder baselines, with RSA comparable to the strongest model-guided baselines.The comparison included direct neural, multiview self-supervised, and model-guided baselines.
Pairwise brain-to-brain translation: Pairwise unsupervised orthogonal translations achieved Mean Rank 2.56 ± 1.71 and R@1 0.78 ± 0.14 across 515 held-out shared images.The method outperformed baselines on retrieval metrics and performed comparably to external-reference baselines on RSA.
Shared-space translation: Global synchronization improved average Mean Rank from 2.47 to 1.97 and R@1 from 0.79 to 0.83 across ordered off-diagonal subject pairs.One orthogonal transformation per subject maps all embeddings into a coherent shared latent space.
Model–brain alignment: Supervised model–brain mappings were weaker than shared-space brain-to-brain translation, with best semi-orthogonal performance of Mean Rank 13.33 and R@1 0.29.Ridge regression improved retrieval and RSA, but remained below the shared-space results of Mean Rank 1.97 and R@1 0.83.

5 Related work

Related work motivates the paper through convergent geometries in artificial networks and partially preserved neural representations across people. It positions the study as testing whether the Strong Platonic Representation Hypothesis extends to biological neural representations.

Universal geometry in machine learning: Deep neural networks trained with different architectures, objectives, and modalities often develop similar representational spaces, motivating the Platonic Representation Hypothesis.The paper frames its question as whether the constructive strong form also applies to biological neural representations.
Shared representations in neuroscience: Neuroscience studies report that neural response structure is partly preserved across subjects, while hyperalignment typically uses shared stimuli to establish common spaces.This motivates testing cross-subject translation from intrinsic geometry without shared-stimulus correspondences for learning.
Model–brain alignment: Model–brain alignment studies reveal systematic correspondences between cortical processing stages and model layers, supporting encoding, decoding, and benchmarking efforts.The paper distinguishes these model-mediated approaches from recovering shared neural geometry directly across subjects.

6 Discussion

The study finds that brain-derived subject spaces can be translated without paired cross-subject data, while highlighting methodological and scope limitations. Residualized NSD fMRI responses support this analysis, but transferability beyond high-quality repeated-measures visual data remains unresolved.

Unsupervised orthogonal rotations translate subject-specific brain embeddings across individuals without paired cross-subject samples or intermediate model representations.
Synchronizing pairwise rotations into one shared latent space further improves retrieval and indicates mutual compatibility with a common coordinate system.
Brain-derived shared spaces may help identify representational dimensions shared, distorted, or missing in artificial models, because model decodability does not imply geometric equivalence.
The analysis depends on high-quality fMRI data with repeated stimulus presentations to isolate stable stimulus-related signal from trial-level noise.
Similar isometries remain untested in lower-SNR modalities, smaller datasets, higher-level cognitive tasks, more distant stimulus distributions, task contexts, and clinical datasets.
Residualization removes acquisition-related confound components by fitting nuisance models on training trials and applying them to all responses, partially mitigating run/session block structure.The main analyses use these residualized responses as input.

A.2 Brain region selection

The analysis uses the NSDGeneral ROI because it includes reliable visually responsive voxels across visual and high-level associative cortex. Expanding the cortical mask improves within-subject retrieval and RSA, with NSDGeneral performing best.

NSDGeneral includes visually responsive voxels across visual and high-level associative cortex selected using stimulus-related reliability.
Performance improves as the cortical mask expands from V1 to V1–V4 and NSDGeneral, with NSDGeneral yielding the best retrieval and RSA.
Table S1 compares within-subject retrieval across cortical regions and volumetric or surface-based preprocessing spaces; lower Mean Rank and higher R@1 or RSA are better.

B.1 Encoder implementation details

The encoder uses a fixed 128-dimensional configuration with PCA and nonlinear residual refinement. Training settings are selected using within-subject retrieval across repeated presentations.

The encoder uses 768 PCA components, 128-dimensional embeddings, and a one-hidden-layer MLP with hidden size 768.The learned residual scaling parameter converges to approximately α ≈ 0.4 across subjects.
The MLP is optimized with Adam for 2000 steps using λNCE = 1 and λpull = 0.5.Hyperparameters were selected by within-subject retrieval, balancing Mean Rank and R@1.
Table S2 evaluates encoder-component ablations using within-subject retrieval across repeated presentations, with lower Mean Rank and higher R@1 or RSA preferred.

B.2 Encoder component ablation.

Ablation and sensitivity analyses evaluate how encoder components, dimensionality, and model-guided baselines affect within-subject retrieval. The full encoder is reported as strongest, while per-subject tables extend the evaluation across subjects and baselines.

Encoder component ablation: The full encoder gives the best retrieval performance, with nonlinear refinement contributing strongly to RSA and retrieval.
Encoder component ablation: The best Mean Rank and R@1 come from combining reliability weighting, PCA, MCCA, and nonlinear refinement.
Encoder dimensionality sensitivity: Mean Rank is evaluated across PCA dimensionalities 512, 768, 1024, and 1280, embedding dimensions from 64 to 384, hidden sizes, and MLP depths from 1 to 3.
Encoder dimensionality sensitivity: Figure S2 plots Mean Rank against embedding dimensionality, with curves for PCA dimensionality and panels for MLP depth; each point uses the best hidden size.Lower Mean Rank is better.
Per-subject evaluation: Table S3 reports Mean Rank separately for every subject across within-subject encoder baselines, using chance Mean Rank 258.
Model-guided baselines: Model-guided baselines fit ridge regressions from 768-component PCA-reduced fMRI responses to pretrained vision or language representations before measuring repeated-presentation retrieval.
Model-guided baselines: Table S4 reports per-subject Mean Rank for ridge mappings from fMRI responses to pretrained vision-model embeddings, with chance Mean Rank 258.

C.2 Pairwise rotation selection

Pairwise translation is initialization-sensitive, so the main experiments use multiple random seeds and select the best-performing candidate for each ordered subject pair.

Pairwise rotation selection: The procedure’s initialization sensitivity is amplified by limited unpaired training samples and measurement noise in the neural embeddings.
Pairwise rotation selection: 10 random seeds were run for each ordered subject pair, with the best-performing candidate reported in the main experiments.The procedure uses unsupervised centroid matching and iterative nearest-neighbor refinement to obtain pseudocorrespondences.
Pairwise rotation selection: Averaging the 10 rotation matrices and projecting the result back onto O(d) provides an additional candidate for comparison.
Pairwise rotation selection: 2.56 ± 1.71 Mean Rank was achieved by the best-performing seed across ordered subject pairs on 515 held-out shared images.This is the protocol used for the main results.
Pairwise rotation selection: Training one subject’s linear encoder takes approximately 2 minutes on CPU, while estimating one pairwise rotation takes approximately 5 minutes on CPU.The nonlinear residual MLP takes approximately 1 minute on GPU.