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Differential Equation Framework for Smarter CNNs

Research · Applied deep learning

Applied a physics-based diffusion equation, the kind normally used to model heat and fluid flow, as a smoothing layer inside a ResNet-18 image classifier trained on CIFAR-10. The diffusion conductance is built as a learnable sub-network rather than a fixed formula, so the model adapts its own smoothing behavior based on what it sees.

90.8%Accuracy, diffusion layer
90.0%Baseline accuracy

What the comparison showed

  1. 01

    A learnable smoothing layer. Instead of hardcoding the diffusion conductance, it's a sub-network that learns how much to smooth based on the input, rather than applying the same fixed formula everywhere.

  2. 02

    A controlled comparison. Tested baseline vs. diffusion-layer vs. two optimization techniques, cosine annealing and stochastic weight averaging, to isolate what was actually driving any gains.

  3. 03

    An honest trade-off. The diffusion layer produced a modest accuracy gain, 90.8% against a 90.0% baseline, but confidence calibration got slightly worse. That trade-off is reported as-is rather than left out.

Python CNN PDE ResNet-18 CIFAR-10

A note on the code: the repository isn't public yet, it's part of an ongoing publication process.

Visit diffusify.in GitHub · Private