# 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

```bash
/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.