# Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE

arXiv: https://arxiv.org/abs/2011.04798 · HTML: https://mlsanity.com/paper/2011.04798/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 30 of 48)

- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
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- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
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- [Indeterminacy in Generative Models: Characterization and Strong Identifiability](https://mlsanity.com/paper/2206.00801/) (2022)
- [Isometric Representation Learning for Disentangled Latent Space of Diffusion Models](https://mlsanity.com/paper/2407.11451/) (2024)
- [Drop, Swap, and Generate: A Self-Supervised Approach for Generating Neural Activity](https://mlsanity.com/paper/2111.02338/) (2021)
- [Inferring stochastic low-rank recurrent neural networks from neural data](https://mlsanity.com/paper/2406.16749/) (2024)
- [Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics](https://mlsanity.com/paper/2212.07892/) (2022)
- [NeuroBind: Towards Unified Multimodal Representations for Neural Signals](https://mlsanity.com/paper/2407.14020/) (2024)
- [Interpretable statistical representations of neural population dynamics and geometry](https://mlsanity.com/paper/2304.03376/) (2023)
- [Latent Diffusion for Neural Spiking Data](https://mlsanity.com/paper/2407.08751/) (2024)
- [Neuroformer: Multimodal and Multitask Generative Pretraining for Brain Data](https://mlsanity.com/paper/2311.00136/) (2023)
- [Building population models for large-scale neural recordings: opportunities and pitfalls](https://mlsanity.com/paper/2102.01807/) (2021)
- [Multi-modal Gaussian Process Variational Autoencoders for Neural and Behavioral Data](https://mlsanity.com/paper/2310.03111/) (2023)
- [Exploring Behavior-Relevant and Disentangled Neural Dynamics with Generative Diffusion Models](https://mlsanity.com/paper/2410.09614/) (2024)
- [Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research](https://mlsanity.com/paper/2504.13101/) (2025)
- [BRAID: Input-Driven Nonlinear Dynamical Modeling of Neural-Behavioral Data](https://mlsanity.com/paper/2509.18627/) (2025)
- [Extraction and Recovery of Spatio-Temporal Structure in Latent Dynamics Alignment with Diffusion Models](https://mlsanity.com/paper/2306.06138/) (2023)
- [POCO: Scalable Neural Forecasting through Population Conditioning](https://mlsanity.com/paper/2506.14957/) (2025)
- [BACE: Behavior-Adaptive Connectivity Estimation for Interpretable Graphs of Neural Dynamics](https://mlsanity.com/paper/2510.20831/) (2025)
- [Neural Latent Aligner: Cross-trial Alignment for Learning Representations of Complex, Naturalistic Neural Data](https://mlsanity.com/paper/2308.06443/) (2023)
- [Temporal Conditioning Spiking Latent Variable Models of the Neural Response to Natural Visual Scenes](https://mlsanity.com/paper/2306.12045/) (2023)
- [Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectives](https://mlsanity.com/paper/2309.00380/) (2023)
- [BLEND: Behavior-guided Neural Population Dynamics Modeling via Privileged Knowledge Distillation](https://mlsanity.com/paper/2410.13872/) (2024)
- [Generative Modeling of Neural Dynamics via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2412.12112/) (2024)
- [Covariate-informed Representation Learning to Prevent Posterior Collapse of iVAE](https://mlsanity.com/paper/2202.04206/) (2022)

## Abstract (arXiv)

The ability to record activities from hundreds of neurons simultaneously in the brain has placed an increasing demand for developing appropriate statistical techniques to analyze such data. Recently, deep generative models have been proposed to fit neural population responses. While these methods are flexible and expressive, the downside is that they can be difficult to interpret and identify. To address this problem, we propose a method that integrates key ingredients from latent models and traditional neural encoding models. Our method, pi-VAE, is inspired by recent progress on identifiable variational auto-encoder, which we adapt to make appropriate for neuroscience applications. Specifically, we propose to construct latent variable models of neural activity while simultaneously modeling the relation between the latent and task variables (non-neural variables, e.g. sensory, motor, and other externally observable states). The incorporation of task variables results in models that are not only more constrained, but also show qualitative improvements in interpretability and identifiability. We validate pi-VAE using synthetic data, and apply it to analyze neurophysiological datasets from rat hippocampus and macaque motor cortex. We demonstrate that pi-VAE not only fits the data better, but also provides unexpected novel insights into the structure of the neural codes.