# Bidirectional predictive coding

arXiv: https://arxiv.org/abs/2505.23415 · HTML: https://mlsanity.com/paper/2505.23415/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 69 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning](https://mlsanity.com/paper/1605.08104/) (2016)
- [Iterative Amortized Inference](https://mlsanity.com/paper/1807.09356/) (2018)
- [Predictive Coding Approximates Backprop along Arbitrary Computation Graphs](https://mlsanity.com/paper/2006.04182/) (2020)
- [Associative Memories via Predictive Coding](https://mlsanity.com/paper/2109.08063/) (2021)
- [Learning on Arbitrary Graph Topologies via Predictive Coding](https://mlsanity.com/paper/2201.13180/) (2022)
- [Benchmarking Predictive Coding Networks -- Made Simple](https://mlsanity.com/paper/2407.01163/) (2024)
- [Hybrid Predictive Coding: Inferring, Fast and Slow](https://mlsanity.com/paper/2204.02169/) (2022)
- [Dendritic predictive coding: A theory of cortical computation with spiking neurons](https://mlsanity.com/paper/2205.05303/) (2022)
- [Sample as You Infer: Predictive Coding With Langevin Dynamics](https://mlsanity.com/paper/2311.13664/) (2023)
- [The implications of perception as probabilistic inference for correlated neural variability during behavior](https://mlsanity.com/paper/1409.0257/) (2014)
- [How does the primate brain combine generative and discriminative computations in vision?](https://mlsanity.com/paper/2401.06005/) (2024)
- [Correlative Information Maximization: A Biologically Plausible Approach to Supervised Deep Neural Networks without Weight Symmetry](https://mlsanity.com/paper/2306.04810/) (2023)
- [Deep Predictive Coding with Bi-directional Propagation for Classification and Reconstruction](https://mlsanity.com/paper/2305.18472/) (2023)

## Built on by (most cited first, 5 of 5)

- [Why the Brain Consolidates: Predictive Forgetting for Optimal Generalisation](https://mlsanity.com/paper/2603.04688/) (2026)
- [Closed-form predictive coding via hierarchical Gaussian filters](https://mlsanity.com/paper/2605.20293/) (2026)
- [Learning Compositional Latent Structure with Vector Networks](https://mlsanity.com/paper/2605.28007/) (2026)
- [RECAP: Local Hebbian Prototype Learning as a Self-Organizing Readout for Reservoir Dynamics](https://mlsanity.com/paper/2603.06639/) (2026)
- [Learning in Deep Networks under Dale's Constraint](https://mlsanity.com/paper/2608.06963/) (2026)

## Abstract (arXiv)

Predictive coding (PC) is an influential computational model of visual learning and inference in the brain. Classical PC was proposed as a top-down generative model, where the brain actively predicts upcoming visual inputs, and inference minimises the prediction errors. Recent studies have also shown that PC can be formulated as a discriminative model, where sensory inputs predict neural activities in a feedforward manner. However, experimental evidence suggests that the brain employs both generative and discriminative inference, while unidirectional PC models show degraded performance in tasks requiring bidirectional processing. In this work, we propose bidirectional PC (bPC), a PC model that incorporates both generative and discriminative inference while maintaining a biologically plausible circuit implementation. We show that bPC matches or outperforms unidirectional models in their specialised generative or discriminative tasks, by developing an energy landscape that simultaneously suits both tasks. We also demonstrate bPC's superior performance in two biologically relevant tasks including multimodal learning and inference with missing information, suggesting that bPC resembles biological visual inference more closely.