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LieGroupOptimizer

god_graph::transformer::optimization::lie_group

Struct LieGroupOptimizer 

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pub struct LieGroupOptimizer { /* private fields */ }
Expand description

Lie group optimizer for weight orthogonalization and decomposition

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impl LieGroupOptimizer

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pub fn new(config: LieGroupConfig) -> Self

Create a new Lie group optimizer

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pub fn config(&self) -> &LieGroupConfig

Get the optimizer configuration

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pub fn statistics(&self) -> Ref<'_, HashMap<String, f64>>

Get optimization statistics

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pub fn error_accumulator(&self) -> Ref<'_, ErrorAccumulator>

Get the error accumulator for detailed error analysis

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pub fn error_accumulator_mut(&self) -> RefMut<'_, ErrorAccumulator>

Get a mutable reference to the error accumulator

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pub fn orthogonalize_weights( &self, graph: &mut Graph<OperatorType, WeightTensor>, ) -> GraphResult<()>

Orthogonalize all weights in a graph (two-pass, zero-copy)

This implementation uses a two-pass approach to avoid data cloning:

  1. First pass: collect edge indices only (no data cloning)
  2. Second pass: orthogonalize in-place using IndexMut
§Arguments
  • graph - Graph containing weights to orthogonalize
§Returns

Ok if successful, error if orthogonalization fails

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pub fn orthogonalize_single_weight( &self, graph: &mut Graph<OperatorType, WeightTensor>, edge_idx: EdgeIndex, ) -> GraphResult<f64>

Orthogonalize a single weight in-place (zero-copy)

§Arguments
  • graph - Graph containing the weight to orthogonalize
  • edge_idx - Edge index of the weight to orthogonalize
§Returns

Orthogonalization error (0.0 if skipped)

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pub fn block_decompose( &self, graph: &mut Graph<OperatorType, WeightTensor>, ) -> GraphResult<DecomposedWeights>

Apply block decomposition to weights

Decomposes large weight matrices into blocks of SO(k) matrices.

§Arguments
  • graph - Graph containing weights to decompose
§Returns

Decomposed weights report

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pub fn lie_algebra_regularize( &self, tensor: &DenseTensor, ) -> Result<DenseTensor, TensorError>

Apply Lie algebra regularization

Projects weights onto the Lie algebra and applies regularization.

§Arguments
  • tensor - Weight tensor to regularize
§Returns

Regularized tensor

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pub fn cayley_transform( &self, tensor: &DenseTensor, ) -> Result<DenseTensor, TensorError>

Cayley transform for orthogonalization

The Cayley transform maps skew-symmetric matrices to orthogonal matrices:

cayley(A) = (I - A/2)^(-1) (I + A/2)

§Arguments
  • tensor - Input tensor
§Returns

Orthogonalized tensor

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pub fn is_well_conditioned(&self, tensor: &DenseTensor, threshold: f64) -> bool

Check if a weight matrix is well-conditioned

§Arguments
  • tensor - Weight tensor to check
  • threshold - Condition number threshold
§Returns

True if the matrix is well-conditioned

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