ePC: a Predictive Coding algorithm that scales

Official codebase for "ePC: Fast and Deep Predictive Coding for Digital Hardware" [arXiv]

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👉 What ePC can do for you

On digital hardware, traditional state-based Predictive Coding (sPC) suffers from extreme signal decay.
This is why it doesn't work well for deep networks (5+ layers).

Error-based PC fixes that:

State-based PC	Error-based PC
🚫 Struggles with depth (4-5 layers max)	✅ Scales to any depth you want
🐌 Slow convergence (thousands of iterations)	⚡ 100-1000x faster convergence
📉 Poor performance on deep networks	🎯 Matches backprop performance
📃 Energy minimization, local weight updates	📋 Verified 100% still PC
🧠 Meant for neuromorphic hardware	🖥️ Designed for GPUs

Bottom line: If you're working with Predictive Coding on digital hardware, ePC is what you need. Using sPC will lead to incorrect conclusions!

⚡ Quickstart

1. Install dependencies via Conda

   # Clone and setup (2 minutes)
   git clone https://github.com/cgoemaere/error_based_PC
   cd error_based_PC/
   conda create --name ePC_test_env --file requirements.txt -c conda-forge -c pytorch
   conda activate ePC_test_env
   
   # Sanity check
   python3 -c "from pc_e import PCE; print('Installation successful!')"

2. Play around with the interactive notebook
   Launch PredictiveCodingPlayground.ipynb in Jupyter for hands-on experimentation with sPC and ePC.

📂 Repository structure

> main branch              # Code for MNIST & FashionMNIST
├── sweep.py               # Launches experiment sweeps (reproduce paper results)
├── requirements.txt       # All dependencies (see below)
├── PredictiveCodingPlayground.ipynb  # Notebook for interactive exploration
├── datamodules/           # PyTorch Lightning datamodules (datasets, augmentations)
├── get_arch.py            # Model architectures
├── pc_e.py                # Core PC formulation
└── get_variants.py        # All loss/optimization variants (sPC, ePC, BP)

> cifar branch             # Same as above, for CIFAR-10/100 (with VGG/ResNet)
├── configs_results/       # YAML files with final training configurations
├── configs_sweeps/        # YAML files with hyperparameter sweep settings
├── {arch}_{algo}.py       # Dedicated file per architecture / algorithm (instead of sweep.py)
└── ...

📊 Reproducing our results

Important

For historical reasons, the codebase uses SO for sPC and EO for ePC (from earlier names "State Optimization" and "Error Optimization"). These names were preserved to maintain code stability.

• Reproduce MNIST/FashionMNIST experiments

   # Run a sweep (prepend with 'nohup' to run in background)
   python3 sweep.py

  The sweep works with a config file to select your desired setup:

   sweep_configuration = {
      "method": "grid",
      "metric": {"goal": "maximize", "name": "val_acc"},
      "parameters": {
          "dataset": {"value": "FashionMNIST"},  # or "MNIST"
          "algorithm": {"value": "EO"},          # "SO", "EO", or "BP"
          "USE_DEEP_MLP": {"values": [True]},    # 20 layers vs 4
          "e_lr": {"values": [0.1, 0.3]},        # state/error learning rate
          "iters": {"values": [64, 256]},        # nr of optimization steps
          ...
      },
   }

  (see Appendix E for all hyperparameter settings used in our experiments)

• Reproduce MNIST figures See mnist_poc folder:

  • Fig. 1: fig1.ipynb
  • Fig. B.1: fig1_float64_binomial.ipynb
  • Fig. 5: analysis_deep_linear.ipynb
  • Fig. C.1: analysis_deep_linear.ipynb
  • Fig. D.1: analysis_deep_MLP.ipynb

• Reproduce CIFAR-10/100 experiments

  git checkout cifar
  python3 vgg_pce.py  # or resnet_bp.py or ...

All experiment configs, logging, and results generation go directly to wandb.

📚 Citation

If our work helps your research, please cite:

@article{goemaere2025ePC,
	title = {ePC: Fast and Deep Predictive Coding for Digital Hardware},
	author = {C\'edric Goemaere and Gaspard Oliviers and Rafal Bogacz and Thomas Demeester},
	year = {2025},
	journal = {arXiv preprint arXiv: 2505.20137}
}