# Target Propagation via Regularized Inversion

arXiv: https://arxiv.org/abs/2112.01453 · HTML: https://mlsanity.com/paper/2112.01453/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 72 references that are in the map.
- First posted on arXiv 2 Dec 2021.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group](https://mlsanity.com/paper/1901.08428/) (2019)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [Orthogonal Recurrent Neural Networks with Scaled Cayley Transform](https://mlsanity.com/paper/1707.09520/) (2017)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Training Neural Networks Without Gradients: A Scalable ADMM Approach](https://mlsanity.com/paper/1605.02026/) (2016)
- [A Theoretical Framework for Target Propagation](https://mlsanity.com/paper/2006.14331/) (2020)
- [Understanding Synthetic Gradients and Decoupled Neural Interfaces](https://mlsanity.com/paper/1703.00522/) (2017)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Learning to solve the credit assignment problem](https://mlsanity.com/paper/1906.00889/) (2019)
- [Direct Feedback Alignment with Sparse Connections for Local Learning](https://mlsanity.com/paper/1903.02083/) (2019)
- [Two Routes to Scalable Credit Assignment without Weight Symmetry](https://mlsanity.com/paper/2003.01513/) (2020)
- [GAIT-prop: A biologically plausible learning rule derived from backpropagation of error](https://mlsanity.com/paper/2006.06438/) (2020)
- [Deriving Differential Target Propagation from Iterating Approximate Inverses](https://mlsanity.com/paper/2007.15139/) (2020)
- [LocoProp: Enhancing BackProp via Local Loss Optimization](https://mlsanity.com/paper/2106.06199/) (2021)
- [Proximal Backpropagation](https://mlsanity.com/paper/1706.04638/) (2017)
- [Training Language Models Using Target-Propagation](https://mlsanity.com/paper/1702.04770/) (2017)
- [Iterative Linearized Control: Stable Algorithms and Complexity Guarantees](https://mlsanity.com/paper/1908.07615/) (2019)
- [Deep Learning in Target Space](https://mlsanity.com/paper/2006.01578/) (2020)
- [Differentiable Programming `a la Moreau](https://mlsanity.com/paper/2012.15458/) (2020)

## Built on by (most cited first, 3 of 3)

- [Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignment](https://mlsanity.com/paper/2312.09257/) (2023)
- [Zenkai -- Framework For Exploring Beyond Backpropagation](https://mlsanity.com/paper/2311.09663/) (2023)
- [Dopamine-driven synaptic credit assignment in neural networks](https://mlsanity.com/paper/2510.22178/) (2025)

## Abstract (arXiv)

Target Propagation (TP) algorithms compute targets instead of gradients along neural networks and propagate them backward in a way that is similar yet different than gradient back-propagation (BP). The idea was first presented as a perturbative alternative to back-propagation that may achieve greater accuracy in gradient evaluation when training multi-layer neural networks (LeCun et al., 1989). However, TP has remained more of a template algorithm with many variations than a well-identified algorithm. Revisiting insights of LeCun et al., (1989) and more recently of Lee et al. (2015), we present a simple version of target propagation based on regularized inversion of network layers, easily implementable in a differentiable programming framework. We compare its computational complexity to the one of BP and delineate the regimes in which TP can be attractive compared to BP. We show how our TP can be used to train recurrent neural networks with long sequences on various sequence modeling problems. The experimental results underscore the importance of regularization in TP in practice.