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Learning in Deep Factor Graphs with Gaussian Belief Propagation
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Proposes GBP Learning, which treats activations and parameters of deep convolutional factor graphs as Gaussian random variables and trains/predicts via Gaussian belief propagation, with continual learning by Bayesian filtering over parameters.
Problem
Training deep networks with backpropagation suffers from backward locking and is hard to distribute, and incremental/continual learning requires principled fusion of old and new information.
Approach
Model all quantities (inputs, outputs, parameters, activations) as random variables in a Gaussian factor graph with inter-layer consistency factors, treat training and prediction as BP inference with different observed nodes, and use BP-estimated parameter posteriors as priors for the next task for continual learning.
Key results
- On MNIST, GBP Learning reaches 98.16±0.03% test accuracy with a single epoch, matching a CNN with a 6000-example replay buffer and outperforming the prior GBP MLP method by 0.8%.
- On CIFAR10, GBP Learning achieves 53.1±0.3% test accuracy versus 41.3±0.1% for the prior GBP method (11.8% gain).
- On video denoising, learnable factor graphs outperform a pairwise smoothing baseline in PSNR, with the five-layer model performing best; asynchronous layerwise training yields 98.11% vs 98.16% synchronous on MNIST.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use convolutional GBP Learning instead of the dense [cite] method | image classification · MNIST | accuracy (%): 97.40±0.04 -> 98.16±0.03 | Helped |
| use convolutional GBP Learning instead of the dense [cite] method | image classification · FashionMNIST | accuracy (%): 88.2±0.1 -> 88.2±0.1 | No clear effect |
| use convolutional GBP Learning instead of the dense [cite] method | image classification · CIFAR10 | accuracy (%): 41.3±0.1 -> 53.1±0.3 | Helped |
| use random layer-wise asynchronous updates instead of synchronous forward/backward sweeps (ablation) | GBP Learning · MNIST | accuracy (%): 98.16±0.03% -> 98.11±0.04% | No clear effect |
| add learnable parameters instead of using a hand-designed pairwise smoother | video denoising · DAVIS bear video | PSNR | Helped |
| add continual parameter learning instead of learning parameters per frame (ablation) | GBP Learning video denoising · DAVIS bear video | PSNR | Helped |
| add four additional layers (five layers rather than one) (ablation) | GBP Learning video denoising · DAVIS bear video | PSNR | Helped |
| use five-layer continual learning rather than single-layer per-frame learning (ablation) | GBP Learning video denoising · DAVIS bear video, frame 5 | PSNR: 32.6 -> 34.3 | Helped |
Surprising findings
- Asynchronous layer-wise random update schedules give nearly the same MNIST accuracy as synchronous sweeps (98.11% vs 98.16%).
- The single-layer continual model sometimes learns to reconstruct noise, requiring prior interpolation regularisation.
Limitations
- Full-dataset GBP training is much slower (~3 hours on RTX3090) than backprop CNNs on CPU.
- Only scalar variable nodes are used, limiting capture of correlations; GBP convergence is not guaranteed with loops or non-linear factors.
- Tested only on small datasets and models (MNIST, CIFAR10, short video), not scaled to large models.
Experimental setup
Datasets: MNIST FashionMNIST CIFAR10 DAVIS (bear video)
Benchmarks: MNIST FashionMNIST CIFAR10 DAVIS bear video denoising
Metrics: test accuracy PSNR
Baselines: Linear classifier (Adam) CNN + replay buffer (Adam) Pairwise smoothing Prior BP-trained MLP factor graph method
Builds on: belief propagation predictive coding Gaussian belief propagation
Closest papers by meaning
- Belief Propagation Converges to Gaussian Distributions in Sparsely-Connected Factor Graphs (ICML 2026 · similarity 0.89)
- Factor Graph Neural Networks (NeurIPS 2020 · similarity 0.87)
- Scalable Deep Gaussian Markov Random Fields for General Graphs (ICML 2022 · similarity 0.87)
- Stochastic Deep Gaussian Processes over Graphs (NeurIPS 2020 · similarity 0.85)
- Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems (NeurIPS 2023 · similarity 0.85)
- Knowledge Distillation of Uncertainty using Deep Latent Factor Model (NeurIPS 2025 · similarity 0.84)
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