Results

This page records small, reproducible checks for the public package paths. The numbers below are small-scale validation results, not benchmark claims. They answer a narrower question: does the package load the dataset, build the SILVA tensors, solve the equilibrium system, backpropagate through the layer, and report residuals?

The public experiment runner writes one JSON file per run:

silva-experiment \
  --config wdbc_tabular_silva \
  --output-dir outputs

For a supervised classification validation run, the reported accuracy is

\[ \operatorname{acc} = \frac{1}{n}\sum_{i=1}^{n} \mathbf{1}\{\arg\max_c \hat y_{ic}=y_i\}, \]

where \(\hat y_{ic}\) is the class logit produced after the final equilibrium solve. The loss is the cross entropy

\[ \mathcal{L} = -\frac{1}{n}\sum_{i=1}^{n} \log \frac{\exp(\hat y_{i,y_i})} {\sum_{c=1}^{C}\exp(\hat y_{ic})}. \]

The residual entries come from the fixed-point solves inside the model. For a SILVA layer with equilibrium state \(z^\star\),

\[ r = \left\lVert z^\star - f_\theta(z^\star,x)\right\rVert_2. \]

A decreasing training loss and finite residuals show that the public path is connected end to end: data adapter, model construction, solver, objective, gradient, and optimizer.

Tabular Graph Smokes

These runs use UCI datasets downloaded through the package registry. When a classification config uses a small subset, the subset is stratified so the validation subset does not accidentally select only one class.

Config	Dataset	Samples	Features	Classes	Loss trace	Accuracy	Solver residuals
`wdbc_tabular_silva.json`	WDBC	250	30	2	0.723, 0.515, 0.311, 0.235, 0.193, 0.156	0.964	2.442, 0.894
`wine_tabular_silva.json`	Wine	178	13	3	1.253, 0.973, 0.872, 0.751, 0.675, 0.588	0.882	4.994, 3.451

The compact tabular suite covers a broader set of loaders and graph adapters:

Dataset	Samples	Features	Classes	Final loss	Accuracy
Iris	150	4	3	0.691	0.667
Wine	178	13	3	0.704	0.916
WDBC	250	30	2	0.218	0.944
Seeds	210	7	3	0.815	0.729
Glass	214	9	6	1.422	0.407
Banknote Authentication	300	4	2	0.440	0.803
Yeast	300	8	10	2.145	0.213

Run the same suite with:

silva-experiment \
  --config tabular_dataset_suite \
  --output-dir outputs

CIFAR And TorchVision Smokes

The vision adapter supports MNIST, FashionMNIST, KMNIST, EMNIST, CIFAR10, CIFAR100, and SVHN when the optional vision extra is installed:

python -m pip install -e ".[vision]"
silva-download-datasets --torchvision --list

For CIFAR10, the raw tensor has shape

\[ x \in \mathbb{R}^{B\times 3\times 32\times 32}. \]

The vector validation run flattens each image,

\[ u_i = \operatorname{vec}(x_i) \in \mathbb{R}^{3072}, \]

then applies a SILVA vector classifier. The cortex validation run keeps the image structure, first computes a convolutional retinal embedding, and then solves linked equilibrium points:

\[ z_\ell^\star = f_{\theta,\ell} \left( z_\ell^\star,\, s_\ell,\, \alpha_{\ell-1} z_{\ell-1}^\star \right). \]

The public CIFAR checks are:

silva-experiment \
  --config cifar10_vector_smoke \
  --output-dir outputs

silva-experiment \
  --config cifar10_cortex_smoke \
  --output-dir outputs

Measured CIFAR10 CPU validation results from the public configs:

Config	Preset	Samples	Image shape	Output shape	State shape	Loss	Accuracy	Solver residuals
`cifar10_vector_smoke.json`	vector	24	\(3\times32\times32\)	\(24\times10\)	\(24\times16\)	2.306	0.167	3.826
`cifar10_cortex_smoke.json`	cortex	24	\(3\times32\times32\)	\(24\times10\)	\(24\times12\)	2.359	0.125	8.855, 5.962

These rows verify the public image pipeline: TorchVision dataset construction, image tensor batching, vector or cortex model construction, equilibrium solves, cross-entropy loss, backward pass, optimizer step, and metric serialization.

The full TorchVision suite is opt-in because it downloads several datasets:

silva-experiment \
  --config torchvision_dataset_suite \
  --output-dir outputs

The suite config includes MNIST, FashionMNIST, KMNIST, EMNIST, CIFAR10, CIFAR100, and SVHN. Unit tests cover the runner route with local in-memory datasets; real full-suite execution is best done on a machine where the image archives can be cached once under data/.

Point Architecture Smokes

The point architecture catalog runs each built-in field inside a SILVACortexLayer for two damped Picard steps. The deterministic tiny batches use vector, token, or bar-image states according to the architecture's tensor contract. Each row includes a backward pass and one optimizer update.

Architecture	Parameters	Loss	Initial residual	Final residual	Gradient norm
`mlp`	368	0.7489	2.670	2.003	4.669e-4
`residual_mlp`	456	0.6127	2.676	1.963	1.476e-2
`residual_cnn`	312	0.7001	21.42	16.32	6.279e-3
`unet`	1,758	0.6958	21.19	15.86	1.061e-3
`dense_cnn`	369	0.6990	21.18	15.86	5.823e-3
`transformer`	532	0.7195	4.740	3.723	6.807e-2
`inverted_residual`	172	0.6934	21.03	16.01	2.309e-4
`fourier_operator`	596	0.7073	21.08	15.84	3.258e-3
`mlp_mixer`	474	0.7014	4.760	3.683	1.020e-2
`convnext_v2`	300	0.7568	21.44	16.16	1.039e-2

All ten fields preserve the input-state shape, produce finite outputs, receive nonzero parameter gradients, and reduce the residual after the second damped step. Parameter counts describe the compact validation configurations, not canonical model sizes or an accuracy ranking.

Reproduce the table with:

python examples/point_architecture_catalog.py

The Point Architecture Catalog notebook adds a 300 DPI residual-ratio plot and examples of composition within one point and across linked points.

Interpreting These Numbers

Validation metrics are useful for implementation fidelity, but they are intentionally small. They verify tensor shapes, solver integration, gradients, and dataset preprocessing. Full experiment reproduction should be reported separately with the exact configs, seeds, splits, training budgets, hardware, and saved artifacts used for the article-scale runs.

Where to Go Next

Question	Page
Which compact metrics are collected by case?	Benchmark Cards
What evidence is needed for a paper-level claim?	Reconstructing Paper Experiments
How should metrics and citations be reported?	Citation-Aware Reporting
How can I reproduce these outputs?	Run Everything