# Statistical inference on representational geometries

arXiv: https://arxiv.org/abs/2112.09200 · HTML: https://mlsanity.com/paper/2112.09200/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2021.

## Built on by (most cited first, 13 of 13)

- [Duality of Bures and Shape Distances with Implications for Comparing Neural Representations](https://mlsanity.com/paper/2311.11436/) (2023)
- [The Topology and Geometry of Neural Representations](https://mlsanity.com/paper/2309.11028/) (2023)
- [Testing the limits of natural language models for predicting human language judgments](https://mlsanity.com/paper/2204.03592/) (2022)
- [Distinguishing representational geometries with controversial stimuli: Bayesian experimental design and its application to face dissimilarity judgments](https://mlsanity.com/paper/2211.15053/) (2022)
- [Estimating Shape Distances on Neural Representations with Limited Samples](https://mlsanity.com/paper/2310.05742/) (2023)
- [Vision CNNs trained to estimate spatial latents learned similar ventral-stream-aligned representations](https://mlsanity.com/paper/2412.09115/) (2024)
- [Spectral Analysis of Representational Similarity with Limited Neurons](https://mlsanity.com/paper/2502.19648/) (2025)
- [Shared representations in brains and models reveal a two-route cortical organization during scene perception](https://mlsanity.com/paper/2507.13941/) (2025)
- [Bayesian Comparisons Between Representations](https://mlsanity.com/paper/2411.08739/) (2024)
- [Extremely coarse learning objectives induce human-aligned representations in AI vision models](https://mlsanity.com/paper/2605.05556/) (2026)
- [Perceived face similarity reflects inverse-generative and naturalistic discriminative objectives](https://mlsanity.com/paper/2605.12619/) (2026)
- [Similarity-based representation factorization for revealing interpretable dimensions in representational data](https://mlsanity.com/paper/2605.26921/) (2026)
- [AffineTok: Semantic Affine Consistency for Diffusion-Friendly Visual Tokenizer](https://mlsanity.com/paper/2608.23864/) (2026)

## Abstract (arXiv)

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big models with our new big data. Here, we introduce new inference methods enabling researchers to evaluate and compare models based on the accuracy of their predictions of representational geometries: A good model should accurately predict the distances among the neural population representations (e.g. of a set of stimuli). Our inference methods combine novel 2-factor extensions of crossvalidation (to prevent overfitting to either subjects or conditions from inflating our estimates of model accuracy) and bootstrapping (to enable inferential model comparison with simultaneous generalization to both new subjects and new conditions). We validate the inference methods on data where the ground-truth model is known, by simulating data with deep neural networks and by resampling of calcium imaging and functional MRI data. Results demonstrate that the methods are valid and conclusions generalize correctly. These data analysis methods are available in an open-source Python toolbox (rsatoolbox.readthedocs.io).