# Predictive Coding beyond Correlations

arXiv: https://arxiv.org/abs/2306.15479 · HTML: https://mlsanity.com/paper/2306.15479/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 27 Jun 2023.

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Learning the Difference that Makes a Difference with Counterfactually-Augmented Data](https://mlsanity.com/paper/1909.12434/) (2019)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [DoWhy: An End-to-End Library for Causal Inference](https://mlsanity.com/paper/2011.04216/) (2020)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Predictive Coding Approximates Backprop along Arbitrary Computation Graphs](https://mlsanity.com/paper/2006.04182/) (2020)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Discovering Causal Signals in Images](https://mlsanity.com/paper/1605.08179/) (2016)
- [The Neural Coding Framework for Learning Generative Models](https://mlsanity.com/paper/2012.03405/) (2020)
- [Associative Memories via Predictive Coding](https://mlsanity.com/paper/2109.08063/) (2021)
- [Biologically Motivated Algorithms for Propagating Local Target Representations](https://mlsanity.com/paper/1805.11703/) (2018)
- [Learning on Arbitrary Graph Topologies via Predictive Coding](https://mlsanity.com/paper/2201.13180/) (2022)
- [Deep Predictive Coding Network with Local Recurrent Processing for Object Recognition](https://mlsanity.com/paper/1805.07526/) (2018)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [Reverse Differentiation via Predictive Coding](https://mlsanity.com/paper/2103.04689/) (2021)
- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)
- [Predictive Coding beyond Gaussian Distributions](https://mlsanity.com/paper/2211.03481/) (2022)
- [Lifelong Neural Predictive Coding: Learning Cumulatively Online without Forgetting](https://mlsanity.com/paper/1905.10696/) (2019)
- [BayesPCN: A Continually Learnable Predictive Coding Associative Memory](https://mlsanity.com/paper/2205.09930/) (2022)
- [Deep Counterfactual Estimation with Categorical Background Variables](https://mlsanity.com/paper/2210.05811/) (2022)
- [Robust Graph Representation Learning via Predictive Coding](https://mlsanity.com/paper/2212.04656/) (2022)

## Built on by (most cited first, 6 of 6)

- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [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)
- [A Review of Neuroscience-Inspired Machine Learning](https://mlsanity.com/paper/2403.18929/) (2024)
- [Local Loss Optimization in the Infinite Width: Stable Parameterization of Predictive Coding Networks and Target Propagation](https://mlsanity.com/paper/2411.02001/) (2024)
- [A Study of Hidden-State Optimization Order in Predictive Coding Networks](https://mlsanity.com/paper/2609.00686/) (2026)

## Abstract (arXiv)

Recently, there has been extensive research on the capabilities of biologically plausible algorithms. In this work, we show how one of such algorithms, called predictive coding, is able to perform causal inference tasks. First, we show how a simple change in the inference process of predictive coding enables to compute interventions without the need to mutilate or redefine a causal graph. Then, we explore applications in cases where the graph is unknown, and has to be inferred from observational data. Empirically, we show how such findings can be used to improve the performance of predictive coding in image classification tasks, and conclude that such models are able to perform simple end-to-end causal inference tasks.