# Neural population geometry and optimal coding of tasks with shared latent structure

arXiv: https://arxiv.org/abs/2402.16770 · HTML: https://mlsanity.com/paper/2402.16770/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 97 references that are in the map.
- First posted on arXiv 26 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Markerless tracking of user-defined features with deep learning](https://mlsanity.com/paper/1804.03142/) (2018)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [A mathematical theory of semantic development in deep neural networks](https://mlsanity.com/paper/1810.10531/) (2018)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Learning curves of generic features maps for realistic datasets with a teacher-student model](https://mlsanity.com/paper/2102.08127/) (2021)
- [The Gaussian equivalence of generative models for learning with shallow neural networks](https://mlsanity.com/paper/2006.14709/) (2020)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [Unsupervised deep learning identifies semantic disentanglement in single inferotemporal neurons](https://mlsanity.com/paper/2006.14304/) (2020)
- [Large-scale neural recordings call for new insights to link brain and behavior](https://mlsanity.com/paper/2103.14662/) (2021)
- [Interpreting neural computations by examining intrinsic and embedding dimensionality of neural activity](https://mlsanity.com/paper/2107.04084/) (2021)
- [A Spectral Theory of Neural Prediction and Alignment](https://mlsanity.com/paper/2309.12821/) (2023)
- [Origami in N dimensions: How feed-forward networks manufacture linear separability](https://mlsanity.com/paper/2203.11355/) (2022)
- [Linear Classification of Neural Manifolds with Correlated Variability](https://mlsanity.com/paper/2211.14961/) (2022)
- [Universality of max-margin classifiers](https://mlsanity.com/paper/2310.00176/) (2023)
- [Efficiency of learning vs. processing: Towards a normative theory of multitasking](https://mlsanity.com/paper/2007.03124/) (2020)
- [Semi-orthogonal subspaces for value mediate a tradeoff between binding and generalization](https://mlsanity.com/paper/2309.07766/) (2023)

## Built on by (most cited first, 9 of 9)

- [Emergence of a High-Dimensional Abstraction Phase in Language Transformers](https://mlsanity.com/paper/2405.15471/) (2024)
- [A mathematical theory for understanding when abstract representations emerge in neural networks](https://mlsanity.com/paper/2510.09816/) (2025)
- [Place Cells as Multi-Scale Position Embeddings: Random Walk Transition Kernels for Path Planning](https://mlsanity.com/paper/2505.14806/) (2025)
- [SEMASIA: A Large-Scale Dataset of Semantically Structured Latent Representations](https://mlsanity.com/paper/2605.09485/) (2026)
- [When Does Structure Matter in Continual Learning? Dimensionality Controls When Modularity Shapes Representational Geometry](https://mlsanity.com/paper/2604.27656/) (2026)
- [Dimensionality Controls When Modularity Helps in Continual Learning](https://mlsanity.com/paper/2606.17889/) (2026)
- [Emergent Generalization by Representation Learning in Artificial Neural Networks](https://mlsanity.com/paper/2607.10430/) (2026)
- [Signal-Noise Factorization Isolates Nuisance Variation into Removable Subspaces](https://mlsanity.com/paper/2610.00751/) (2026)
- [Increasing Width Allows Greedy Layer-wise Training to Rival End-to-End Backpropagation in Self-Supervised Learning](https://mlsanity.com/paper/2610.00753/) (2026)

## Abstract (arXiv)

Humans and animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. However, it remains unclear what aspects of neural activity contribute to these computational capabilities. Here, we develop an analytical theory linking the geometry of a neural population's activity to the generalization performance of a linear readout on a set of tasks that depend on a common latent structure. We show that four geometric measures of the activity determine performance across tasks. Using this theory, we find that experimentally observed disentangled representations naturally emerge as an optimal solution to the multi-task learning problem. When data is scarce, these optimal neural codes compress less informative latent variables, and when data is abundant, they expand these variables in the state space. We validate our theory using macaque ventral stream recordings. Our results therefore tie population geometry to multi-task learning.