# Accelerated Predictive Coding Networks via Direct Kolen-Pollack Feedback Alignment

arXiv: https://arxiv.org/abs/2602.15571 · HTML: https://mlsanity.com/paper/2602.15571/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 61 references that are in the map.
- First posted on arXiv 17 Feb 2026.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [Predictive Coding: a Theoretical and Experimental Review](https://mlsanity.com/paper/2107.12979/) (2021)
- [The History Began from AlexNet: A Comprehensive Survey on Deep Learning Approaches](https://mlsanity.com/paper/1803.01164/) (2018)
- [Random feedback weights support learning in deep neural networks](https://mlsanity.com/paper/1411.0247/) (2014)
- [Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?](https://mlsanity.com/paper/2202.09467/) (2022)
- [Deep supervised learning using local errors](https://mlsanity.com/paper/1711.06756/) (2017)
- [Energy-based learning algorithms for analog computing: a comparative study](https://mlsanity.com/paper/2312.15103/) (2023)
- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [Benchmarking Predictive Coding Networks -- Made Simple](https://mlsanity.com/paper/2407.01163/) (2024)
- [Direct Feedback Alignment with Sparse Connections for Local Learning](https://mlsanity.com/paper/1903.02083/) (2019)
- [Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learning](https://mlsanity.com/paper/2206.02629/) (2022)
- [A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks](https://mlsanity.com/paper/2212.00720/) (2022)
- [Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligence](https://mlsanity.com/paper/2106.01288/) (2021)
- [A Theoretical Framework for Inference and Learning in Predictive Coding Networks](https://mlsanity.com/paper/2207.12316/) (2022)
- [Predictive Coding beyond Gaussian Distributions](https://mlsanity.com/paper/2211.03481/) (2022)
- [Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignment](https://mlsanity.com/paper/2312.09257/) (2023)
- [Backpropagation through space, time, and the brain](https://mlsanity.com/paper/2403.16933/) (2024)
- [Efficient Convolutional Neural Network Training with Direct Feedback Alignment](https://mlsanity.com/paper/1901.01986/) (2019)
- [Predictive Coding as a Neuromorphic Alternative to Backpropagation: A Critical Evaluation](https://mlsanity.com/paper/2304.02658/) (2023)

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

- [Error Highways: Scaling Predictive Coding to Very Deep Networks](https://mlsanity.com/paper/2606.22744/) (2026)
- [Single State Update Predictive Coding training for Time Series Forecasting and Anomaly Detection](https://mlsanity.com/paper/2608.24697/) (2026)

## Abstract (arXiv)

Predictive coding (PC) is a biologically inspired algorithm for training neural networks that relies only on local updates, allowing parallel learning across layers. However, practical implementations face two key limitations: error signals must still propagate from the output to early layers through multiple inference-phase steps, and feedback decays exponentially during this process, leading to vanishing updates in early layers. We propose direct Kolen-Pollack predictive coding (DKP-PC), which simultaneously addresses both feedback delay and exponential decay, yielding a more efficient and scalable variant of PC while preserving update locality. Leveraging direct feedback alignment and direct Kolen-Pollack algorithms, DKP-PC introduces learnable feedback connections from the output layer to all hidden layers, establishing a direct pathway for error transmission. This yields an algorithm that reduces the theoretical error propagation time complexity from O(L), with L being the network depth, to O(1), removing depth-dependent delay in error signals. Moreover, empirical results demonstrate that DKP-PC achieves performance at least comparable to, and often exceeding, that of standard PC, while offering improved latency and computational performance, supporting its potential for custom hardware-efficient implementations.