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Convolutional Differentiable Logic Gate Networks
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Extends differentiable logic gate networks with convolutional logic-gate-tree kernels, logical OR pooling, and residual initializations, yielding LogicTreeNet models that reach 86.29% on CIFAR-10 with 61M gates.
Problem
Differentiable logic gate networks are fast for inference but used random, fixed connections that cannot capture spatial structure, limiting accuracy on images (about 62% on CIFAR-10) and depth to around 6 layers.
Approach
Convolve inputs with learnable complete binary trees of logic gates (shared across kernel placements), replace pooling with logical OR via max t-conorm, and initialize each gate near the feedforward gate 'A' so deep logic networks train without vanishing gradients.
Key results
- LogicTreeNet-G reaches 86.29% test accuracy on CIFAR-10 with 61.0M logic gates, matching XNOR-Net (NIN) at 1,780M gates (29x fewer).
- On MNIST, LogicTreeNet-M reaches 99.23% accuracy with 566K gates, improving over the BNN literature.
- LogicTreeNet-B reaches 80.17% on CIFAR-10 with 24 ns per-image FPGA inference, versus 45.6 us for FINN CNV at the same accuracy.
- Removing residual initialization drops CIFAR-10 accuracy by almost 9% (to 76.18%), and removing OR pooling drops it by 3.5%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use convolutional tree depths 1,1,1,1 instead of the full depths (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 84.99% -> 80.98% | Hurt |
| use convolutional tree depths 1,1,2,2 instead of the full depths (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 84.99% -> 82.68% | Hurt |
| use convolutional tree depths 2,2,2,2 instead of the full depths (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 84.99% -> 83.32% | Hurt |
| use convolutional tree depths 2,2,3,3 instead of the full depths (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 84.99% -> 84.13% | Hurt |
| add OR pooling (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 81.45% -> 84.99% | Helped |
| add residual initialization instead of Gaussian initialization (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 76.18% -> 84.99% | Helped |
| add weight decay (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 83.94% -> 84.99% | Helped |
| use 2 input channels per tree instead of 8 (ablation) | LogicTreeNet-L · CIFAR-10 | accuracy: 83.53% -> 84.99% | Helped |
| set residual-initialization parameter z3 to 1.5 rather than a value at least 2 (ablation) | MNIST model · MNIST | accuracy: 13% | Hurt |
Surprising findings
- OR pooling causes pre-pooling activations to decrease during training so post-pooling activations converge to the no-pooling level, without explicit regularization.
- Using 2 input channels per tree outperforms 8 input channels (84.99% vs 83.53% for L-size vs ablation), attributed to enforcing within-channel comparisons.
Limitations
- Gains are reported for discretized logic gate networks; differentiable training accuracy differs during early training.
- Small models show notable variance from fixed random connectivity (S-size MNIST 98.21% plus or minus 0.31%).
- Training remains computationally expensive; the paper limits hardware development to model B due to labor cost.
Experimental setup
Datasets: CIFAR-10 MNIST
Benchmarks: CIFAR-10 MNIST
Metrics: test accuracy number of logic gates FPGA inference time per image throughput (FPS)
Baselines: DiffLogic Net Conv. TTNet FINN CNV LUTNet XNOR-Net BinaryNet FBNA CNV RebNet Hirtzlin et al. DWN FracBNN LowBitNN
Builds on: differentiable logic gate networks probabilistic logic relaxation AdamW
Closest papers by meaning
- Mind the Gap: Removing the Discretization Gap in Differentiable Logic Gate Networks (NeurIPS 2025 · similarity 0.90)
- LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints (ICLR 2024 · similarity 0.85)
- BOLD: Boolean Logic Deep Learning (NeurIPS 2024 · similarity 0.84)
- Towards Cheaper Inference in Deep Networks with Lower Bit-Width Accumulators (ICLR 2024 · similarity 0.83)
- An Efficient Matrix Multiplication Algorithm for Accelerating Inference in Binary and Ternary Neural Networks (ICML 2025 · similarity 0.83)
- Layer Compression of Deep Networks with Straight Flows (AAAI 2024 · similarity 0.83)
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