Operators from Scratch

Standalone script: operators.py

This example implements the bind, release, and bundle operators in pure Python using only the low-level offset API, then verifies correctness against the library’s built-in implementations.

The script does not call hv.bind(), hv.release(), or hv.bundle() for computation — it reimplements them to show how they work at the offset level.

Bind

Per-segment offset addition modulo segment size:

for seg in range(cardinality):
    result[seg] = (core_a.offset(seg) + core_b.offset(seg)) % segment_size

Properties:

• Result is nearly orthogonal to both inputs (overlap ≈ 1)
• Commutative: bind(a, b) == bind(b, a)
• Associative: bind(a, b, c) == bind(bind(a, b), c)

Release (Unbind)

Per-segment offset subtraction modulo segment size:

for seg in range(cardinality):
    result[seg] = (core_c.offset(seg) - core_k.offset(seg)) % segment_size

Properties:

• release(bind(a, b), b) = a (exact recovery)
• Multi-release: release(release(bind(a, b, c), c), b) = a

Bundle

PRNG-based random selection among inputs. For each segment, a seeded PRNG picks which input vector contributes its offset. The selection probability is proportional to each input’s weight.

# Compute cumulative anchors from weights (weights sum to 1.0).
# For equal weights [0.33, 0.33, 0.33]: anchors ≈ [21845, 43690, 65535]
# For weighted [0.6, 0.2, 0.2]:        anchors ≈ [39321, 52428, 65535]
cumulative = 0.0
anchors = []
for w in weights:
    cumulative += w
    anchors.append(int(cumulative * 65535))

for seg in range(0, cardinality, 4):
    r = so.uint64()                          # one PRNG call → 4 × 16-bit values
    for j in range(4):
        dial = (r >> (48 - 16 * j)) & 0xFFFF # extract 16-bit random value
        chosen = first input whose anchor >= dial
        result[seg + j] = cores[chosen].offset(seg + j)

Properties:

• Result is similar to all inputs (overlap ≈ weight × cardinality)
• Not reversible — information is lost

Note: The library supports two bundling strategies: classic (shown above) and fisher_yates (default). To verify exact match with the pure Python implementation, set:

KONGMING_LEARNER_SAMPLING=classic python operators.py

Running

pip install kongming-rs-hv

# Classic sampling — all operators match exactly
KONGMING_LEARNER_SAMPLING=classic python operators.py