FA-99381 / Embedding vector normalization / Open access

Square-root length pooling divides by squared token count · case 01

Square-root length pooling divides by squared token count.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The token count is squared where its square root is required.

THE FAILURE

The token count is squared where its square root is required.

Unsuccessful approach: A full mean removes length scaling entirely and is wrong for this pooling rule.

Case contract

Return sum(vectors)/sqrt(token_count) coordinatewise; empty input returns empty.

Why this case matters

A small embedding preparation contract can be checked without a model or retrieval system.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(vectors):
    return [sum(v[j] for v in vectors)/len(vectors)**2 for j in range(len(vectors[0]))] if vectors else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two tokens', solve([[N,0],[N,2*N]]), [2*N/2**0.5,2*N/2**0.5])
check('four tokens', solve([[N],[N],[N],[N]]), [2*N])
check('singleton', solve([[N,2*N]]), [N,2*N])
check('empty', solve([]), [])
check('cancellation', solve([[N],[-N]]), [0])
check('three values', solve([[0,N],[0,N],[3*N,0]]), [3*N/3**0.5,2*N/3**0.5])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
two tokens	`[0.5, 0.5]`	`[1.414213562373095, 1.414213562373095]`	Failed
four tokens	`[0.25]`	`[2]`	Failed
singleton	`[1.0, 2.0]`	`[1, 2]`	Passed
empty	`[]`	`[]`	Passed
cancellation	`[0.0]`	`[0]`	Passed
three values	`[0.3333333333333333, 0.2222222222222222]`	`[1.7320508075688774, 1.1547005383792517]`	Failed

SHA-256 / 6a2c2d2359fee9376ea00ddfa0c8759ba58191c80636f37c0de0042e1a413857

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(vectors):
    return [sum(v[j] for v in vectors)/len(vectors) for j in range(len(vectors[0]))] if vectors else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('two tokens', solve([[N,0],[N,2*N]]), [2*N/2**0.5,2*N/2**0.5])
check('four tokens', solve([[N],[N],[N],[N]]), [2*N])
check('singleton', solve([[N,2*N]]), [N,2*N])
check('empty', solve([]), [])
check('cancellation', solve([[N],[-N]]), [0])
check('three values', solve([[0,N],[0,N],[3*N,0]]), [3*N/3**0.5,2*N/3**0.5])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
two tokens	`[1.0, 1.0]`	`[1.414213562373095, 1.414213562373095]`	Failed
four tokens	`[1.0]`	`[2]`	Failed
singleton	`[1.0, 2.0]`	`[1, 2]`	Passed
empty	`[]`	`[]`	Passed
cancellation	`[0.0]`	`[0]`	Passed
three values	`[1.0, 0.6666666666666666]`	`[1.7320508075688774, 1.1547005383792517]`	Failed

SHA-256 / ff9a4150f6489f308e837836e75ec0d6c600b59a5d5405289197f8768064b63b

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

Inputs are finite toy vectors or token rows; this contract makes no claim about model quality or production embedding behavior. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-30T16:48:23.554817+00:00.

Case digest / 80a2a1f33ebce8e51cee4fe798bda05fd9918a08336649118b43760872abfd5f