Research map / Probabilistic and scientific modeling / Causal discovery
Predictive Coding beyond Correlations
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Shows predictive coding graphs can perform interventional and counterfactual causal inference by zeroing prediction errors of intervened nodes, and learn structure from observational data using acyclicity priors and negative examples.
Problem
Standard predictive coding graphs compute only correlations (conditional queries) and perform poorly on discriminative tasks; the paper asks whether biologically plausible PC can perform interventions, counterfactuals, and structure learning.
Approach
An interventional query on a PC graph is implemented by clamping the intervened node's value and zeroing its prediction error, avoiding graph mutilation; counterfactuals follow via abduction-action-prediction, and structure is learned by a learnable adjacency matrix with L1/L2, acyclicity priors, or negative examples.
Key results
- Interventional queries improved MNIST and FashionMNIST test accuracy of a 2000-neuron fully connected PC graph by almost 2%.
- Counterfactual MSE on the MNIST-based benchmark was 0.0008 ± 0.0002, lower than the original reported 0.001 ± 0.001.
- PC graphs recover the structure of dense ER2 and SF4 graphs with 20 nodes from observational data, with stable SHD and F1 across setups.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an interventional query instead of a conditional query on the input | Fully connected predictive coding classifier · MNIST and FashionMNIST | test accuracy: almost 2% | Helped |
| Use an acyclicity prior during training | Fully connected predictive coding classifier · MNIST and FashionMNIST | test accuracy | Helped |
| Train with negative examples and a Laplace prior | Fully connected predictive coding classifier · MNIST and FashionMNIST | test accuracy | Helped |
| Use an interventional query with a zeroed input error instead of a conditional query (ablation) | Fully connected predictive coding classifier · MNIST and FashionMNIST | test accuracy: almost 2% | Helped |
| Replace the acyclicity prior with negative examples and a Laplace prior (ablation) | Predictive coding graph classifier · MNIST and FashionMNIST | test accuracy | No clear effect |
| Use a predictive coding graph instead of the original work's method | Counterfactual image generation · MNIST counterfactual test | MSE: 0.001 ± 0.001 -> 0.0008 ± 0.0002 | Helped |
| Remove the acyclicity prior without adding negative examples (ablation) | Predictive coding graph structure learning · Classification graph learning | graph degeneracy | Hurt |
| Add negative examples to prevent convergence to a degenerate graph | Predictive coding graph structure learning · Classification graph learning | graph structure | Helped |
Surprising findings
- Without an acyclicity regularizer, structure learning converges to a degenerate graph in which each output node predicts itself and ignores inputs.
Limitations
- Assumes no hidden confounders (causal sufficiency) and hard interventions only.
- Structure learning recovers only up to Markov equivalence class and uses no interventional data.
- Linear classification on MNIST/FashionMNIST is weak; accuracy below 2% test error requires fine-tuning with backpropagation.
Experimental setup
Datasets: MNIST FashionMNIST 2-MNIST (constructed) synthetic linear and non-linear SCM data
Benchmarks: MNIST FashionMNIST synthetic SCM causal queries (fork, collider, confounder, chain, mediator, M-bias, butterfly) synthetic ER/SF graph structure learning
Metrics: test accuracy MAE MMD MeanE StdE MSE SSE SHD F1
Baselines: PC GES NOTEARS ICALiNGAM conditional query PC graph
Builds on: predictive coding graphs NOTEARS Pearl structural causal models
Closest papers by meaning
- Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithm (NeurIPS 2024 · similarity 0.89)
- Understanding and Improving Optimization in Predictive Coding Networks (AAAI 2024 · similarity 0.88)
- A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks (ICLR 2024 · similarity 0.88)
- Understanding Sample Efficiency in Predictive Coding (NeurIPS 2026 · similarity 0.86)
- Only Strict Saddles in the Energy Landscape of Predictive Coding Networks? (NeurIPS 2024 · similarity 0.86)
- Predictive Coding Enhances Meta-RL To Achieve Interpretable Bayes-Optimal Belief Representation Under Partial Observability (NeurIPS 2025 · similarity 0.85)
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