added backward sampling in a layer-wise manner

[gengala]

as per title. related to #403.

use it as follows:

import torch
import matplotlib.pyplot as plt

from cirkit.backend.torch.queries import SamplingQuery

circuit = torch.load("circuit.pt", weights_only=False)

torch.manual_seed(131)
sq_backward = SamplingQuery(circuit, backward=True)
td_samples, _ = sq_backward(num_samples=16)

images = td_samples.cpu().reshape(16, 28, 28).numpy()
fig, axes = plt.subplots(4, 4, figsize=(8, 8))
for i, ax in enumerate(axes.flat):
    ax.imshow(images[i], cmap="gray", vmin=0, vmax=255)
    ax.axis("off")
fig.suptitle("Top-down sampling (backward=True)")
plt.show()

what I got from the MNIST circuit in the notebook:

[codecov]

Codecov Report

❌ Patch coverage is 21.81818% with 86 lines in your changes missing coverage. Please review.
✅ Project coverage is 67.86%. Comparing base (eb99f6f) to head (ed07fe2).
⚠️ Report is 24 commits behind head on main.

Files with missing lines	Patch %	Lines
cirkit/backend/torch/queries.py	13.79%	49 Missing and 1 partial ⚠️
cirkit/backend/torch/layers/inner.py	34.48%	19 Missing ⚠️
cirkit/backend/torch/layers/input.py	15.38%	11 Missing ⚠️
cirkit/backend/torch/layers/optimized.py	25.00%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #412      +/-   ##
==========================================
- Coverage   68.71%   67.86%   -0.86%     
==========================================
  Files          58       58              
  Lines        6007     6114     +107     
  Branches      773      790      +17     
==========================================
+ Hits         4128     4149      +21     
- Misses       1590     1675      +85     
- Partials      289      290       +1     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[dylanponsford]

If we want to allow for heterogeneous inputs (as is the case in TabPC, where we have both categoricals and Gaussians), setting the dtype explicitly as int here causes errors later when we try to write floats into the samples tensor. Equally, if it is set to be float then we will have to cast the integer samples from the TorchCategoricalLayer before writing them.

[chbricout]

On this note, would be nice if you or I could push the code for gaussian layers

[chbricout]

nice to have it, and definitely it should not be lost, but I think that this logic should be in my custom layers (when I make the PR to add them).
Otherwise, it's the only place in these layers where we mention parameter sharing / fold of the parameter being different from the layers fold

[chbricout]

In general, this looks quite good to me. Two point that I raised (1) remove reference to parameter sharing, (2) implement the logic for gaussian layers (I already have it and I believe Dylan has it also).

One thing that does strike me is the absence of tests, I think it should be quite easy to manually create a circuit to follow an objective distribution and compare the distribution of the samples to the objective distribution.