# Multiway Multislice PHATE: Visualizing Hidden Dynamics of RNNs through Training

arXiv: https://arxiv.org/abs/2406.01969 · HTML: https://mlsanity.com/paper/2406.01969/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 19 of 19)

- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Visualizing and Understanding Neural Models in NLP](https://mlsanity.com/paper/1506.01066/) (2015)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Visualizing and Understanding Recurrent Networks](https://mlsanity.com/paper/1506.02078/) (2015)
- [Recent Advances in Recurrent Neural Networks](https://mlsanity.com/paper/1801.01078/) (2017)
- [RetainVis: Visual Analytics with Interpretable and Interactive Recurrent Neural Networks on Electronic Medical Records](https://mlsanity.com/paper/1805.10724/) (2018)
- [CNN Explainer: Learning Convolutional Neural Networks with Interactive Visualization](https://mlsanity.com/paper/2004.15004/) (2020)
- [Understanding Hidden Memories of Recurrent Neural Networks](https://mlsanity.com/paper/1710.10777/) (2017)
- [Visualizing the PHATE of Neural Networks](https://mlsanity.com/paper/1908.02831/) (2019)
- [Visualizing and Comparing Convolutional Neural Networks](https://mlsanity.com/paper/1412.6631/) (2014)
- [Memory Visualization for Gated Recurrent Neural Networks in Speech Recognition](https://mlsanity.com/paper/1609.08789/) (2016)
- [A Review of Hidden Markov Models and Recurrent Neural Networks for Event Detection and Localization in Biomedical Signals](https://mlsanity.com/paper/2012.06104/) (2020)
- [Clustering and Recognition of Spatiotemporal Features through Interpretable Embedding of Sequence to Sequence Recurrent Neural Networks](https://mlsanity.com/paper/1905.12176/) (2019)
- [Stability of Internal States in Recurrent Neural Networks Trained on Regular Languages](https://mlsanity.com/paper/2006.10828/) (2020)
- [Evaluating Disentanglement in Generative Models Without Knowledge of Latent Factors](https://mlsanity.com/paper/2210.01760/) (2022)

## Built on by (most cited first, 1 of 1)

- [Neighbor Embedding for High-Dimensional Sparse Poisson Data](https://mlsanity.com/paper/2604.16932/) (2026)

## Abstract (arXiv)

Recurrent neural networks (RNNs) are a widely used tool for sequential data analysis; however, they are still often seen as black boxes. Visualizing the internal dynamics of RNNs is a critical step toward understanding their functional principles and developing better architectures and optimization strategies. Prior studies typically emphasize network representations only after training, overlooking how those representations evolve during learning. Here, we present Multiway Multislice PHATE (MM-PHATE), a graph-based embedding method for visualizing the evolution of RNN hidden states across the multiple dimensions spanned by RNNs: time, training epoch, and units. Across controlled synthetic benchmarks and real RNN applications, MM-PHATE preserves hidden-representation community structure among units and reveals training-phase changes in representation geometry. In controlled synthetic systems spanning multiple bifurcation families and smooth state-space warps, MM-PHATE recovers qualitative dynamical progression while distinguishing family-level differences. In task-trained RNNs, the embedding identifies information-processing and compression-related phases during training, and time-resolved geometric and entropy-based summaries align with linear probes, time-step ablations, and label--state mutual information. These results show that MM-PHATE provides an intuitive and comprehensive way to inspect RNN hidden dynamics across training and to better understand how model architecture and learning dynamics relate to performance.