Models and their options

SPDnet, RResNet and GBWBNRResNet take 28 to 37 constructor arguments, because they expose every option of the layers they contain. Most can be left at their default. This page groups them by role; the Models page lists them one by one.

Which model

SPDnet

The SPDNet of Huang & Van Gool (AAAI 2017): [BiMap → ReEig → (BatchNorm)] × L → LogEig → Vec → Linear, with L = len(hidden_layers_size). The default choice.

RResNet

A Riemannian residual network (Katsman et al., NeurIPS 2023) with several stages: [BiMap → (ReEig) → (BatchNorm) → ResidualBlock × k] × L. The residual blocks move each matrix along a learned tangent vector (Riemannian residual networks). No ReEig by default.

GBWBNRResNet

The single-stage residual network of the GBWBN paper (Wang et al., 2025): BiMap → GBWBN → ResidualBlock → LogEig. Kept to reproduce that paper; RResNet covers the same architecture with more options.

Arguments by role

Shared by the three models unless noted.

Role	Arguments	What to know
Sizes	input_dim, hidden_layers_size (hidden_dim for GBWBNRResNet), output_dim, n_residual_blocks (RResNet)	hidden_layers_size=[84, 63] means two BiMaps \(n \to 84 \to 63\).
Non-linearity	reeig_eps, reeig (RResNet)	Eigenvalues below reeig_eps are clamped: set it to the scale of the data (Layers and parametrizations).
BiMap weights	bimap_parametrized, bimap_parametrization_mode, bimap_parametrization_options, bimap_n_steps_ref_update	Stiefel constraint, static or dynamic (Layers and parametrizations).
Batch normalization: which	batchnorm, batchnorm_type, batchnorm_mean_type, batchnorm_mean_options	batchnorm_type="mean_only" centres; "mean_var_scalar" also rescales (and is GBWBN with "bures_wasserstein"). Default mean: GAH for SPDnet, affine-invariant for RResNet, Bures–Wasserstein for GBWBNRResNet (Batch normalization).
Batch normalization: statistics	batchnorm_momentum, batchnorm_norm_strategy, batchnorm_minibatch_mode, batchnorm_minibatch_momentum, batchnorm_minibatch_maxstep	Running statistics and smoothing of the batch mean.
Batch normalization: bias	batchnorm_parametrization, batchnorm_parametrization_mode, batchnorm_n_steps_ref_update	How the SPD bias stays SPD.
GBWBN	batchnorm_bw_options	{"bw_theta": 0.5, "bw_batch_stats_grad": True} by default (Batch normalization).
Residual blocks (RResNet, GBWBNRResNet)	spectrum_type, spectrum_hidden_dim, spectrum_n_layers, spectrum_kernel_size, stiefel_parametrization_mode, stiefel_n_steps_ref_update, residual_metric	The spectral vector field and the exponential map (Riemannian residual networks).
Head	use_logeig, vec_type, softmax	vec_type="vech" halves the size of the linear layer.
Numerics	use_autograd, dtype, device, generator	use_autograd takes a bool or a dict per layer type ("bimap", "reeig", "logeig", "batchnorm", "vec", "residual") (Numerical and optimization techniques).

After building the optimizer

If any part uses a dynamic parametrization (*_parametrization_mode="dynamic"), register the optimizer once:

optimizer = torch.optim.SGD(model.parameters(), lr=0.05, momentum=0.9, nesterov=True)
model.register_optimizer_hook(optimizer)

Configurations of the published experiments

These configurations reproduce published results with this library (see the spdnet-benchmark-demo repository for the training loop).

SPDNet batch normalization paper, HyperLeaf (204×204 hyperspectral covariances, 4 cultivars); SGD with Nesterov momentum, 5 warm-up epochs, learning rate halved on plateau, early stopping:

SPDnet(
    input_dim=204,
    hidden_layers_size=[184, 158],
    output_dim=4,
    reeig_eps=0.01,
    batchnorm=True,
    batchnorm_mean_type="arithmetic",  # batch 48, lr 0.05
)

Same paper, HDM05 (93×93 skeleton covariances scaled by 190, 117 classes):

SPDnet(
    input_dim=93,
    hidden_layers_size=[84, 63],
    output_dim=117,
    reeig_eps=0.8,
    batchnorm=True,
    batchnorm_mean_type="geometric_arithmetic_harmonic",  # batch 16, lr 0.25
)

GBWBN paper, HDM05 (raw matrices; Adam with AMSGrad, lr 2.5e-3, batch 30, 200 epochs):

GBWBNRResNet(  # GBWBN (momentum 0.1) is on by default
    input_dim=93,
    hidden_dim=30,
    output_dim=117,
    batchnorm_bw_options={"bw_theta": 0.5},
)