# Ensemble perspective for understanding temporal credit assignment

arXiv: https://arxiv.org/abs/2102.03740 · HTML: https://mlsanity.com/paper/2102.03740/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 7 Feb 2021.

## Builds on (most cited first, 14 of 14)

- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [The Recurrent Neural Tangent Kernel](https://mlsanity.com/paper/2006.10246/) (2020)
- [Linking connectivity, dynamics and computations in low-rank recurrent neural networks](https://mlsanity.com/paper/1711.09672/) (2017)
- [Minimal model of permutation symmetry in unsupervised learning](https://mlsanity.com/paper/1904.13052/) (2019)
- [Overcoming the vanishing gradient problem in plain recurrent networks](https://mlsanity.com/paper/1801.06105/) (2018)
- [Statistical physics of unsupervised learning with prior knowledge in neural networks](https://mlsanity.com/paper/1911.02344/) (2019)
- [Learning credit assignment](https://mlsanity.com/paper/2001.03354/) (2020)

## Built on by (most cited first, 2 of 2)

- [Eight challenges in developing theory of intelligence](https://mlsanity.com/paper/2306.11232/) (2023)
- [Meta predictive learning model of languages in neural circuits](https://mlsanity.com/paper/2309.04106/) (2023)

## Abstract (arXiv)

Recurrent neural networks are widely used for modeling spatio-temporal sequences in both nature language processing and neural population dynamics. However, understanding the temporal credit assignment is hard. Here, we propose that each individual connection in the recurrent computation is modeled by a spike and slab distribution, rather than a precise weight value. We then derive the mean-field algorithm to train the network at the ensemble level. The method is then applied to classify handwritten digits when pixels are read in sequence, and to the multisensory integration task that is a fundamental cognitive function of animals. Our model reveals important connections that determine the overall performance of the network. The model also shows how spatio-temporal information is processed through the hyperparameters of the distribution, and moreover reveals distinct types of emergent neural selectivity. To provide a mechanistic analysis of the ensemble learning, we first derive an analytic solution of the learning at the infinitely-large-network limit. We then carry out a low-dimensional projection of both neural and synaptic dynamics, analyze symmetry breaking in the parameter space, and finally demonstrate the role of stochastic plasticity in the recurrent computation. Therefore, our study sheds light on mechanisms of how weight uncertainty impacts the temporal credit assignment in recurrent neural networks from the ensemble perspective.