Feature hashing (the hashing trick)

Seeded FNV-1a feature hashing for fixed-width vectorization of unbounded feature names.

feature_hashing maps arbitrary feature names/tokens into a fixed number of buckets in pure Mojo with zero Python imports — replacing sklearn.feature_extraction.FeatureHasher (and the hashing side of sklearn's HashingVectorizer). Hashing is seeded 64-bit FNV-1a with a hash-derived sign, so colliding features cancel in expectation instead of biasing a bucket upward (Weinberger et al. 2009 hashing trick).

The module

Module	What it does
feature_hashing	seeded 64-bit FNV-1a hashing trick — bucket + sign per feature name, dense row assembly, and a birthday-bound collision-rate estimate, fully deterministic and pure Mojo

Functions

Function	What it does
hash_feature(name, n_buckets, seed)	Bucket index in [0, n_buckets) for a feature name. n_buckets <= 0 returns 0 (degenerate config).
hash_sign(name, seed)	+1 / −1 hashing-trick sign, taken from bit 63 of the same seeded hash — one hash evaluation determines (bucket, sign).
hash_features_row(names, values, n_buckets, seed)	Dense length-n_buckets row: row[bucket] += sign * value per pair. Pass value 1.0 for bare categorical/token presence.
collision_rate_estimate(n_features, n_buckets)	Birthday-bound estimate of P(any bucket collision): 1 − exp(−n(n−1)/2m); pigeonhole cases return 1.0.

Determinism and seeding

• Fully deterministic: the same (name, n_buckets, seed) always yields the same bucket and sign — the tests assert repeated calls are identical (e.g. "sym=SPY" at seed 42, m = 1000 is always bucket 281, sign −1).
• Different seeds re-partition the feature space; use one fixed seed per trained model. Seed 0 folds eight zero bytes, so results still differ from unseeded textbook FNV-1a but remain fully deterministic; negative seeds map to their magnitude.
• Edge behavior never traps: n_buckets <= 0 gives bucket 0 / an empty row; mismatched names/values lengths process min(len(names), len(values)); empty names hash like any other string.

Verification

Expected buckets and signs in the tests were hand-computed with an independent reference implementation of seeded 64-bit FNV-1a:

• Reference hashes pinned exactly: h64("price", seed 42) = 15582674013810968360 → bucket 360 at m = 1000 ("volume" → 49, "side=buy" → 17), and a 2³² modulus pins the low 32 bits ("price" → 2078918440).
• Reference signs: "price" → −1, "volume" → +1 at seed 42; row output is asserted consistent with the hash_feature + hash_sign composition.
• Exact cancellation: at seed 7, m = 4, "volume" (sign −1) and "side=buy" (sign +1) share bucket 0, and equal values cancel to exactly 0 — the property that makes the trick unbiased.
• collision_rate_estimate matches the birthday formula to 1e-12: (23, 365) → 0.5000017521827107 and (100, 1000) → 0.9929165910709479, with pigeonhole cases (n_features > n_buckets) returning exactly 1.0.

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