# A Universal Space of Brain Dynamics for Unveiling Cognitive Transitions and Individual Differences

arXiv: https://arxiv.org/abs/2605.02936 · HTML: https://mlsanity.com/paper/2605.02936/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 138 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
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- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Graph Neural Networks in Network Neuroscience](https://mlsanity.com/paper/2106.03535/) (2021)
- [Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI](https://mlsanity.com/paper/1902.07186/) (2019)
- [Assessing and tuning brain decoders: cross-validation, caveats, and guidelines](https://mlsanity.com/paper/1606.05201/) (2016)
- [Toward universal steering and monitoring of AI models](https://mlsanity.com/paper/2502.03708/) (2025)
- [The Dynamics of Functional Brain Networks: Integrated Network States during Cognitive Function](https://mlsanity.com/paper/1511.02976/) (2015)
- [Interpretable statistical representations of neural population dynamics and geometry](https://mlsanity.com/paper/2304.03376/) (2023)
- [Mapping effective connectivity by virtually perturbing a surrogate brain](https://mlsanity.com/paper/2301.00148/) (2022)
- [Enhanced brain structure-function tethering in transmodal cortex revealed by high-frequency eigenmodes](https://mlsanity.com/paper/2207.03569/) (2022)

## Abstract (arXiv)

Representing dynamical systems through data-driven universal spaces has proven effective; however, achieving this universality for human brain activity remains a significant challenge, further aggravated by diverse cognitive states and individual subjects. Recognizing that spatial properties reflect physical wiring while temporal properties reflect brain function, we develop Universal Brain Dynamics (UBD) to construct a universal space tailored to brain activity and quantify corresponding dynamics using a model-derived Jacobian matrix. Crucially, we validate UBD's universality by accurately predicting functional magnetic resonance imaging (fMRI) signals (Pearson's r > 0.9) across eight states and 963 subjects in the Human Connectome Project (HCP). Through evaluating resting-state fMRI represented within UBD, we gain insight into how infra-slow fluctuation (ISF) underpins brain activity. Furthermore, we reveal a new perspective on structure-function coupling (SFC) by analyzing the temporal sequence of brain dynamics. Extending UBD to task-evoked states, we derive brain dynamics across various cognitive conditions, elucidating the neural mechanisms driving cognitive transitions at a finer granularity. For individual differences, we compare brain dynamics across subjects to identify the neural underpinnings of these variations. Our findings suggest that synergistically integrating spatial and temporal properties of brain activity establishes a universal space for its unfolding, enabling the precise numerical analysis of underlying neural mechanisms across varying conditions.