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name: curvature_memory description: Maintain bounded positive-curvature L-BFGS correction memory for large-scale quasi-Newton optimization.

Curvature Memory

Use this skill when implementing or auditing an L-BFGS optimizer that must store only a small number of recent BFGS correction pairs. Do not use it for dense BFGS updates or constrained optimization logic.

Inputs

• Previous and next iterates x_old, x_new.
• Previous and next gradients g_old, g_new.
• Existing ordered memory of (s, y) pairs.
• Positive integer memory limit m.

Outputs

• A FIFO memory list containing at most m valid pairs.
• Each valid pair satisfies s^T y > tolerance.

Workflow

1. Compute s = x_new - x_old and y = g_new - g_old.
2. Validate matching vector dimensions and memory limit.
3. Reject non-positive or tiny curvature pairs.
4. Append valid pairs and drop oldest entries until the memory length is bounded.
5. Preserve oldest-to-newest order for downstream two-loop recursion.

Validation

Run python tests/test_curvature_memory.py or validate this skill tree with the Paper2Skills module-to-skill validator.

Limitations

This skill manages only correction-pair state. It does not choose step lengths or compute search directions.