> For the complete documentation index, see [llms.txt](https://docs.algenta.ai/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.algenta.ai/machine-learning/ml-feature-hashing.md).

# 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.

**Next:** promote what you trained with [statistical model comparison](/machine-learning/ml-model-comparison.md), or browse the [engine catalog](/engine-runtime/catalog.md).


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