Implement cross-modal binding benchmark (ARC-like tasks)

[Tristan-Stoltz-ERC]

Summary

The psych-bench suite includes ARC-style reasoning tasks but cross-modal binding (visual + semantic + temporal) needs dedicated benchmarks to stress-test HDC's binding capabilities.

Background

HDC binding via XOR creates associative structures, but cross-modal binding — where information from different sensory modalities must be unified — is a harder problem that tests the limits of hyperdimensional representation.

Benchmark tasks to design

• Shape + color association — bind visual feature HVs, test retrieval accuracy
• Temporal sequence + spatial location — bind ordered events to positions using bind_temporal
• Auditory + visual synchrony — cross-modal binding with temporal alignment
• Abstract rule extraction — ARC-style grid transformations requiring multi-feature binding
• Relational reasoning — "A is to B as C is to ?" using compositional binding

Current state

• Binding domain psych-bench score: recently improved from -0.83 to ~0 after switching to BinaryHV + cyclic permutation (bind_temporal)
• bind_temporal uses ρ(self) ⊕ other for non-commutative temporal encoding
• 16,384D hypervectors provide high capacity for multi-modal binding

Key files

• symthaea-core/src/hdc/binary_hv.rs — bind(), bind_temporal(), bundle()
• symthaea-core/src/hdc/unified_hv.rs — unified HV interface
• benches/ and tests/ — existing benchmark patterns