# Interpretable statistical representations of neural population dynamics and geometry

arXiv: https://arxiv.org/abs/2304.03376 · HTML: https://mlsanity.com/paper/2304.03376/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 84 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [Directional Graph Networks](https://mlsanity.com/paper/2010.02863/) (2020)
- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Universality and individuality in neural dynamics across large populations of recurrent networks](https://mlsanity.com/paper/1907.08549/) (2019)
- [Attractor and integrator networks in the brain](https://mlsanity.com/paper/2112.03978/) (2021)
- [Linking connectivity, dynamics and computations in low-rank recurrent neural networks](https://mlsanity.com/paper/1711.09672/) (2017)
- [Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE](https://mlsanity.com/paper/2011.04798/) (2020)
- [Data-driven discovery of intrinsic dynamics](https://mlsanity.com/paper/2108.05928/) (2021)
- [Neural tuning and representational geometry](https://mlsanity.com/paper/2104.09743/) (2021)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [Steerable Partial Differential Operators for Equivariant Neural Networks](https://mlsanity.com/paper/2106.10163/) (2021)
- [Parallel Transport Unfolding: A Connection-based Manifold Learning Approach](https://mlsanity.com/paper/1806.09039/) (2018)
- [Comparing high-dimensional neural recordings by aligning their low-dimensional latent representations](https://mlsanity.com/paper/2205.08413/) (2022)
- [Connecting the dots in ethology: applying network theory to understand neural and animal collectives](https://mlsanity.com/paper/2112.02361/) (2021)

## Built on by (most cited first, 12 of 12)

- [Carr'e du champ flow matching: better quality-generalisation tradeoff in generative models](https://mlsanity.com/paper/2510.05930/) (2025)
- [Implicit Gaussian process representation of vector fields over arbitrary latent manifolds](https://mlsanity.com/paper/2309.16746/) (2023)
- [InputDSA: Demixing then Comparing Recurrent and Externally Driven Dynamics](https://mlsanity.com/paper/2510.25943/) (2025)
- [DFORM: Diffeomorphic vector field alignment for assessing dynamics across learned models](https://mlsanity.com/paper/2402.09735/) (2024)
- [Information-Theoretic Measures on Lattices for High-Order Interactions](https://mlsanity.com/paper/2408.07533/) (2024)
- [Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds](https://mlsanity.com/paper/2603.28764/) (2026)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [Disentangling Shared and Private Neural Dynamics with SPIRE: A Latent Modeling Framework for Deep Brain Stimulation](https://mlsanity.com/paper/2510.25023/) (2025)
- [Diffusion Processes on Implicit Manifolds](https://mlsanity.com/paper/2604.07213/) (2026)
- [What is Intelligence? A Cycle Closure Perspective](https://mlsanity.com/paper/2404.05484/) (2024)
- [A Universal Space of Brain Dynamics for Unveiling Cognitive Transitions and Individual Differences](https://mlsanity.com/paper/2605.02936/) (2026)
- [Machine Learning Methods for Studying Latent Neural Activity Dynamics](https://mlsanity.com/paper/2606.10530/) (2026)

## Abstract (arXiv)

The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a representation learning method, MARBLE, that decomposes on-manifold dynamics into local flow fields and maps them into a common latent space using unsupervised geometric deep learning. In simulated non-linear dynamical systems, recurrent neural networks, and experimental single-neuron recordings from primates and rodents, we discover emergent low-dimensional latent representations that parametrise high-dimensional neural dynamics during gain modulation, decision-making, and changes in the internal state. These representations are consistent across neural networks and animals, enabling the robust comparison of cognitive computations. Extensive benchmarking demonstrates state-of-the-art within- and across-animal decoding accuracy of MARBLE compared with current representation learning approaches, with minimal user input. Our results suggest that manifold structure provides a powerful inductive bias to develop powerful decoding algorithms and assimilate data across experiments.