# Hybrid Predictive Coding: Inferring, Fast and Slow

arXiv: https://arxiv.org/abs/2204.02169 · HTML: https://mlsanity.com/paper/2204.02169/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 152 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning](https://mlsanity.com/paper/1605.08104/) (2016)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Generative replay with feedback connections as a general strategy for continual learning](https://mlsanity.com/paper/1809.10635/) (2018)
- [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)
- [Semi-Amortized Variational Autoencoders](https://mlsanity.com/paper/1802.02550/) (2018)
- [Predictive Coding: a Theoretical and Experimental Review](https://mlsanity.com/paper/2107.12979/) (2021)
- [The free energy principle for action and perception: A mathematical review](https://mlsanity.com/paper/1705.09156/) (2017)
- [Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?](https://mlsanity.com/paper/2202.09467/) (2022)
- [On the Relationship Between Active Inference and Control as Inference](https://mlsanity.com/paper/2006.12964/) (2020)
- [Combining Generative and Discriminative Models for Hybrid Inference](https://mlsanity.com/paper/1906.02547/) (2019)
- [Tutorial: Deriving the Standard Variational Autoencoder (VAE) Loss Function](https://mlsanity.com/paper/1907.08956/) (2019)
- [Hybrid Discriminative-Generative Training via Contrastive Learning](https://mlsanity.com/paper/2007.09070/) (2020)
- [Neural Networks with Recurrent Generative Feedback](https://mlsanity.com/paper/2007.09200/) (2020)
- [Recurrent computations for visual pattern completion](https://mlsanity.com/paper/1706.02240/) (2017)
- [Going in circles is the way forward: the role of recurrence in visual inference](https://mlsanity.com/paper/2003.12128/) (2020)
- [Iterative Amortized Policy Optimization](https://mlsanity.com/paper/2010.10670/) (2020)
- [Relaxing the Constraints on Predictive Coding Models](https://mlsanity.com/paper/2010.01047/) (2020)
- [Control as Hybrid Inference](https://mlsanity.com/paper/2007.05838/) (2020)
- [Feedforward Initialization for Fast Inference of Deep Generative Networks is biologically plausible](https://mlsanity.com/paper/1606.01651/) (2016)

## Built on by (most cited first, 26 of 26)

- [Zamba: A Compact 7B SSM Hybrid Model](https://mlsanity.com/paper/2405.16712/) (2024)
- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [A Theoretical Framework for Inference and Learning in Predictive Coding Networks](https://mlsanity.com/paper/2207.12316/) (2022)
- [BayesPCN: A Continually Learnable Predictive Coding Associative Memory](https://mlsanity.com/paper/2205.09930/) (2022)
- [Only Strict Saddles in the Energy Landscape of Predictive Coding Networks?](https://mlsanity.com/paper/2408.11979/) (2024)
- [Predictive Coding Networks and Inference Learning: Tutorial and Survey](https://mlsanity.com/paper/2407.04117/) (2024)
- [Preventing Deterioration of Classification Accuracy in Predictive Coding Networks](https://mlsanity.com/paper/2208.07114/) (2022)
- [Active Sensing with Predictive Coding and Uncertainty Minimization](https://mlsanity.com/paper/2307.00668/) (2023)
- [ePC: Fast and Deep Predictive Coding in Digital Simulation](https://mlsanity.com/paper/2505.20137/) (2025)
- [Bidirectional predictive coding](https://mlsanity.com/paper/2505.23415/) (2025)
- [On the Relationship Between Variational Inference and Auto-Associative Memory](https://mlsanity.com/paper/2210.08013/) (2022)
- [Learning Policies for Continuous Control via Transition Models](https://mlsanity.com/paper/2209.08033/) (2022)
- [Curvature-Sensitive Predictive Coding with Approximate Laplace Monte Carlo](https://mlsanity.com/paper/2303.04976/) (2023)
- [Possible Principles for Aligned Structure Learning Agents](https://mlsanity.com/paper/2410.00258/) (2024)
- [Faster Predictive Coding Networks via Better Initialization](https://mlsanity.com/paper/2601.20895/) (2026)
- [Brain-like Flexible Visual Inference by Harnessing Feedback-Feedforward Alignment](https://mlsanity.com/paper/2310.20599/) (2023)
- [Introduction to Predictive Coding Networks for Machine Learning](https://mlsanity.com/paper/2506.06332/) (2025)
- [Deep Predictive Coding with Bi-directional Propagation for Classification and Reconstruction](https://mlsanity.com/paper/2305.18472/) (2023)
- [Closed-form predictive coding via hierarchical Gaussian filters](https://mlsanity.com/paper/2605.20293/) (2026)
- [When in Doubt, Think Slow: Iterative Reasoning with Latent Imagination](https://mlsanity.com/paper/2402.15283/) (2024)
- [Sensory robustness through top-down feedback and neural stochasticity in recurrent vision models](https://mlsanity.com/paper/2508.07115/) (2025)
- [RECAP: Local Hebbian Prototype Learning as a Self-Organizing Readout for Reservoir Dynamics](https://mlsanity.com/paper/2603.06639/) (2026)
- [Robust Auto-associative Memory via Convolutional Restricted Hopfield Networks](https://mlsanity.com/paper/2606.20666/) (2026)
- [Accelerating Hierarchical Sparse Predictive Coding with Hybrid Amortized Inference](https://mlsanity.com/paper/2606.27802/) (2026)
- [A Study of Hidden-State Optimization Order in Predictive Coding Networks](https://mlsanity.com/paper/2609.00686/) (2026)
- [DeltaNet-PC: Test-Time Memory Without Backpropagation Through Time](https://mlsanity.com/paper/2610.15185/) (2026)

## Abstract (arXiv)

Predictive coding is an influential model of cortical neural activity. It proposes that perceptual beliefs are furnished by sequentially minimising "prediction errors" - the differences between predicted and observed data. Implicit in this proposal is the idea that perception requires multiple cycles of neural activity. This is at odds with evidence that several aspects of visual perception - including complex forms of object recognition - arise from an initial "feedforward sweep" that occurs on fast timescales which preclude substantial recurrent activity. Here, we propose that the feedforward sweep can be understood as performing amortized inference and recurrent processing can be understood as performing iterative inference. We propose a hybrid predictive coding network that combines both iterative and amortized inference in a principled manner by describing both in terms of a dual optimization of a single objective function. We show that the resulting scheme can be implemented in a biologically plausible neural architecture that approximates Bayesian inference utilising local Hebbian update rules. We demonstrate that our hybrid predictive coding model combines the benefits of both amortized and iterative inference -- obtaining rapid and computationally cheap perceptual inference for familiar data while maintaining the context-sensitivity, precision, and sample efficiency of iterative inference schemes. Moreover, we show how our model is inherently sensitive to its uncertainty and adaptively balances iterative and amortized inference to obtain accurate beliefs using minimum computational expense. Hybrid predictive coding offers a new perspective on the functional relevance of the feedforward and recurrent activity observed during visual perception and offers novel insights into distinct aspects of visual phenomenology.