# Capacity and Trainability in Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1611.09913 · HTML: https://mlsanity.com/paper/1611.09913/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2016.

## Built on by (most cited first, 28 of 28)

- [General-Purpose In-Context Learning by Meta-Learning Transformers](https://mlsanity.com/paper/2212.04458/) (2022)
- [Gradients are Not All You Need](https://mlsanity.com/paper/2111.05803/) (2021)
- [How much do language models memorize?](https://mlsanity.com/paper/2505.24832/) (2025)
- [Criteria for Classifying Forecasting Methods](https://mlsanity.com/paper/2212.03523/) (2022)
- [Is it enough to optimize CNN architectures on ImageNet?](https://mlsanity.com/paper/2103.09108/) (2021)
- [How Does a Deep Learning Model Architecture Impact Its Privacy? A Comprehensive Study of Privacy Attacks on CNNs and Transformers](https://mlsanity.com/paper/2210.11049/) (2022)
- [Entanglement-induced provable and robust quantum learning advantages](https://mlsanity.com/paper/2410.03094/) (2024)
- [ONE-NAS: An Online NeuroEvolution based Neural Architecture Search for Time Series Forecasting](https://mlsanity.com/paper/2202.13471/) (2022)
- [Multi-layer Perceptron Trainability Explained via Variability](https://mlsanity.com/paper/2105.08911/) (2021)
- [Understanding How Encoder-Decoder Architectures Attend](https://mlsanity.com/paper/2110.15253/) (2021)
- [DeepGraviLens: a Multi-Modal Architecture for Classifying Gravitational Lensing Data](https://mlsanity.com/paper/2205.00701/) (2022)
- [Training neural networks using Metropolis Monte Carlo and an adaptive variant](https://mlsanity.com/paper/2205.07408/) (2022)
- [Memory-Augmented Graph Neural Networks: A Brain-Inspired Review](https://mlsanity.com/paper/2209.10818/) (2022)
- [Online Evolutionary Neural Architecture Search for Multivariate Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2302.10347/) (2023)
- [Trainability, Expressivity and Interpretability in Gated Neural ODEs](https://mlsanity.com/paper/2307.06398/) (2023)
- [Adaptive First- and Second-Order Algorithms for Large-Scale Machine Learning](https://mlsanity.com/paper/2111.14761/) (2021)
- [TeKo: Text-Rich Graph Neural Networks with External Knowledge](https://mlsanity.com/paper/2206.07253/) (2022)
- [Task-Optimized Convolutional Recurrent Networks Align with Tactile Processing in the Rodent Brain](https://mlsanity.com/paper/2505.18361/) (2025)
- [Hybrid Quantum-Classical Recurrent Neural Networks](https://mlsanity.com/paper/2510.25557/) (2025)
- [Intelligent Acoustic Module for Autonomous Vehicles using Fast Gated Recurrent approach](https://mlsanity.com/paper/2112.03174/) (2021)
- [Fast Saturating Gate for Learning Long Time Scales with Recurrent Neural Networks](https://mlsanity.com/paper/2210.01348/) (2022)
- [Adaptive-saturated RNN: Remember more with less instability](https://mlsanity.com/paper/2304.11790/) (2023)
- [The minimal computational substrate of fluid intelligence](https://mlsanity.com/paper/2308.07039/) (2023)
- [Measuring and Controlling Solution Degeneracy across Task-Trained Recurrent Neural Networks](https://mlsanity.com/paper/2410.03972/) (2024)
- [The impact of allocation strategies in subset learning on the expressive power of neural networks](https://mlsanity.com/paper/2502.06300/) (2025)
- [Comparison of neural network training strategies for the simulation of dynamical systems](https://mlsanity.com/paper/2512.03851/) (2025)
- [Forecast Accuracy Is Not Trading Profit: Evolving Small Recurrent Networks for Stock Return Prediction](https://mlsanity.com/paper/2610.07825/) (2026)
- [Compression Through Time: An Interplay of Separability, Stationarity and Capacity](https://mlsanity.com/paper/2610.16660/) (2026)

## Abstract (arXiv)

Two potential bottlenecks on the expressiveness of recurrent neural networks (RNNs) are their ability to store information about the task in their parameters, and to store information about the input history in their units. We show experimentally that all common RNN architectures achieve nearly the same per-task and per-unit capacity bounds with careful training, for a variety of tasks and stacking depths. They can store an amount of task information which is linear in the number of parameters, and is approximately 5 bits per parameter. They can additionally store approximately one real number from their input history per hidden unit. We further find that for several tasks it is the per-task parameter capacity bound that determines performance. These results suggest that many previous results comparing RNN architectures are driven primarily by differences in training effectiveness, rather than differences in capacity. Supporting this observation, we compare training difficulty for several architectures, and show that vanilla RNNs are far more difficult to train, yet have slightly higher capacity. Finally, we propose two novel RNN architectures, one of which is easier to train than the LSTM or GRU for deeply stacked architectures.