finite lark
Hi, I wanted to share an interesting concept from a algorithm paper from Johannes Kepler University on matrix multiplication that might have applications to chess engines.
https://arxiv.org/pdf/2505.05896
In matrix multiplication research, they introduced "flip graphs", a way to represent solution spaces where:
- Nodes = different computation schemes
- Edges = local transformations (flips) between equivalent representations
- Goal = find optimal solutions by exploiting symmetry and navigating through equivalent states
What if we view chess positions through a similar lens?
- Nodes = board positions
- Edges = symmetry transformations (horizontal/vertical flips, rotations, color swaps)
- Goal = "CANONICAL" representation to reduce search redundancy
Potential Benefits:
- TT: Instead of storing symmetric variants separately, map them all to one canonical form.
- Move Ordering: If position P1 and mirror(P1) are symmetric, good moves in P1 should inform move ordering in mirror(P1), better alpha-beta cutoffs
- NNUE: Enforce symmetry invariance during training, faster convergence, better generalization, effective training data.
Has anyone explored symmetry exploitation at this level before? Would be interested to hear thoughts on feasibility and whether this direction is worth prototyping.
The original concept comes from exploiting local structure rather than brute force, similar to how flip graphs achieved breakthroughs in matrix multiplication complexity.
Thoughts?
slate shuttle