Besov-Weighted Gaussian Persistence Regularizer MVP

Contents

• experiment.py: depthwise Gaussian scale-space, Difference-of-Gaussians, Besov aggregation, math checks, and a fixed-seed toy classification experiment.
• results.json: output from the completed run.

Reproduce

/home/maxwelhelp/main/bin/python3 experiment.py

The script uses CUDA when available and falls back to CPU if a CUDA execution error occurs. The observed run fell back to CPU after a CUDA convolution backend error.

Implementation

For a feature tensor (B,C,H,W), the regularizer computes four replicate-padded, depthwise Gaussian smoothings at sigma = 1, 2, 4, 8, forms three adjacent DoG responses, computes spatial RMS values, and aggregates

mean_{B,C} sqrt(sum_j ((2**(j*s))*RMS(D_j))**2).

The toy model applies this to the second convolutional feature map and adds 0.01 * regularizer to cross-entropy. The baseline uses the same model, optimizer, data, seed, and weight decay, with the regularizer disabled.

Observations

• The finite telescoping identity had maximum absolute residual 1.19e-7.
• Baseline and regularized models both reached validation accuracy 1.0 at all logged checkpoints on this very easy synthetic task.
• Thus this run provides no validation-accuracy win for the idea; the regularizer adds positive loss and computation without improving the measured metric.
• The formula's stated indexing deserves care: with D_j = U(sigma_0 r^j)-U(sigma_0 r^(j+1)), increasing positive s multiplies larger j (larger/coarser smoothing scales) more strongly. It does not intrinsically weight fine scales unless the scale index is reversed or the weight is changed.

The toy task is not a CIFAR-10 or BSD denoising benchmark, and no artifact, PSNR, broad hyperparameter sweep, or FLOP-matched timing study was performed.