LION.optimizers.EquivariantSolver

Classes

EquivariantSolver(model, optimizer, loss_fn)	Equivariant imaging (Chen, Tachella and Davies, 2021): trains from measurements alone.
RotationGroup([cardinality])	The rotations of an image by the multiples of 360 / cardinality degrees, as a sequence of functions (random.choice picks one).

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class LION.optimizers.EquivariantSolver.EquivariantSolver(model, optimizer, loss_fn, operator_params=None, solver_params=None, model_regularization=None, scheduler=None, scheduler_step='epoch', verbose=1, device=None, seed=0, deterministic=False)

Bases: LIONsolver

Equivariant imaging (Chen, Tachella and Davies, 2021): trains from measurements alone. The loss is data consistency, loss_fn(A(f(y)), y), plus equivariance_strength times the equivariance of the whole reconstruction to a random transformation T of the group: loss_fn(f(A(T f(y))), T f(y)). For CT, f reconstructs (FDK, then the model, for image-domain models).

Every solver takes (model, optimizer, loss_fn, operator_params, solver_params, model_regularization, scheduler, scheduler_step, verbose, device, seed, deterministic), in that order (ARSolver has no loss_fn).

operator_params: the parameters of the operator (for CT, the geometry); the model’s, if it has them.

solver_params: the solver’s settings, from default_parameters().

model_regularization: None, or a term added to the training loss of every mini-batch, model_regularization(model, step): a penalty on the model’s weights (step unused) or on what it does with the mini-batch (e.g. LION.losses.jacobian_penalty). step has input (what the model was given), output, target (what the output is compared with; None for solvers without one) and forward (the model as the solver calls it, e.g. with the noise level). Recorded as loss_fn is.

scheduler: a torch learning-rate scheduler made on optimizer (e.g. torch.optim.lr_scheduler.StepLR(optimizer, 30)), or None. It steps after every epoch (scheduler_step="epoch", torch’s convention) or every mini-batch ("batch", e.g. for OneCycleLR). ReduceLROnPlateau steps with the validation value of the epochs that validate, or with the training loss when there is no validation. Its state is saved in checkpoints, and the training record has it and the learning rate of every epoch.

seed: the training seed. When training starts, torch (CPU and CUDA), numpy and Python’s random are seeded with it, so the same solver, model and data give the same training, and checkpoints keep the random state, so a resumed run continues the same way. The randomness within a run (shuffling, noise a solver adds) still changes every batch and epoch. Two runs with the same seed give the same model: use different seeds for an ensemble. None: unseeded.

deterministic: use only deterministic algorithms (torch’s use_deterministic_algorithms, deterministic cuDNN), so that on a GPU two runs with the same seed give exactly the same model, and a resumed run the uninterrupted one. Slower; a few operations then raise (torch names them). It applies to the whole program from here on. Off, GPU runs with the same seed differ slightly (e.g. ~1e-3 in the weights after a few epochs). On a GPU it needs CUBLAS_WORKSPACE_CONFIG=:4096:8 before cuBLAS starts: it is set here if it isn’t (exporting it before the script is surer).

verbose: how much progress is shown. 0: nothing; 1 (default): one progress bar for training (every mini-batch of every epoch, with the epoch, the loss, the last validation value and the time left) and one for testing; 2: also the validation bars and messages (each epoch’s losses, checkpoints, the seed). True is 1, False 0.

static rotation_group(cardinality)

The rotations by multiples of 360 / cardinality degrees.

static default_parameters()

transformation_group: the transformations (the 360 rotations by whole degrees); equivariance_strength: the weight of the equivariance term (100).

mini_batch_step(y, target_batch)

The loss: data consistency plus the weighted equivariance term (see the class; target_batch isn’t used: self-supervised).

static cite(cite_format='bib')

Where EquivariantSolver comes from: its citation, BibTeX (“bib”) or “MLA”.

class LION.optimizers.EquivariantSolver.RotationGroup(cardinality=360)

Bases: object

The rotations of an image by the multiples of 360 / cardinality degrees, as a sequence of functions (random.choice picks one). Kept as its cardinality, so solver parameters holding it can be saved.