FA-99486 / Vector retrieval ranking / Open access

Vector retrieval: Weighted distance ignores per-coordinate importance · case 01

Weighted distance ignores per-coordinate importance.

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

ROOT CAUSE

Coordinate weights are discarded or only apply linearly to absolute deltas.

THE FAILURE

Coordinate weights are discarded or only apply linearly to absolute deltas.

Unsuccessful approach: Weighted Manhattan distance remains a different metric from the contract.

Case contract

Rank by sum(weight_i*(candidate_i-query_i)^2), ascending; dimensions match.

Why this case matters

An offline vector retrieval toy model isolates one ranking contract from embedding generation, storage, and serving.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(rows, query, weights):
    return [r[0] for r in sorted(rows,key=lambda r:sum((a-b)**2 for a,b in zip(r[1],query)))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
q=[0,0]
check('important axis',solve([['a',[2,0]],['b',[0,2]]],q,[1,N+2]),['a','b'])
check('reverse weights',solve([['a',[N,0]],['b',[0,2]]],q,[1,N+3]),['a','b'])
check('low weighted axis',solve([['a',[0,N]],['b',[2,0]]],q,[N+4,1]),['a','b'])
check('all equal weights',solve([['z',[0,1]],['a',[1,0]]],q,[1,1]),['a','z'])
check('exact candidate',solve([['x',[0,0]],['y',[1,1]]],q,[N+1,2]),['x','y'])
check('three dimensions',solve([['a',[1,0,0]],['b',[0,0,2]]],[0,0,0],[1,2,N+3]),['a','b'])
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
important axis	`['a', 'b']`	`['a', 'b']`	Passed
reverse weights	`['a', 'b']`	`['a', 'b']`	Passed
low weighted axis	`['a', 'b']`	`['a', 'b']`	Passed
all equal weights	`['z', 'a']`	`['a', 'z']`	Failed
exact candidate	`['x', 'y']`	`['x', 'y']`	Passed
three dimensions	`['a', 'b']`	`['a', 'b']`	Passed

SHA-256 / a6624072d80ce0f8f7c4a9ab897675afec02451fed466f139a44d96e8184e61f

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(rows, query, weights):
    return [r[0] for r in sorted(rows,key=lambda r:sum(w*abs(a-b) for a,b,w in zip(r[1],query,weights)))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
q=[0,0]
check('important axis',solve([['a',[2,0]],['b',[0,2]]],q,[1,N+2]),['a','b'])
check('reverse weights',solve([['a',[N,0]],['b',[0,2]]],q,[1,N+3]),['a','b'])
check('low weighted axis',solve([['a',[0,N]],['b',[2,0]]],q,[N+4,1]),['a','b'])
check('all equal weights',solve([['z',[0,1]],['a',[1,0]]],q,[1,1]),['a','z'])
check('exact candidate',solve([['x',[0,0]],['y',[1,1]]],q,[N+1,2]),['x','y'])
check('three dimensions',solve([['a',[1,0,0]],['b',[0,0,2]]],[0,0,0],[1,2,N+3]),['a','b'])
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
important axis	`['a', 'b']`	`['a', 'b']`	Passed
reverse weights	`['a', 'b']`	`['a', 'b']`	Passed
low weighted axis	`['a', 'b']`	`['a', 'b']`	Passed
all equal weights	`['z', 'a']`	`['a', 'z']`	Failed
exact candidate	`['x', 'y']`	`['x', 'y']`	Passed
three dimensions	`['a', 'b']`	`['a', 'b']`	Passed

SHA-256 / 1184b091f17a6ad9ee3e28efb531a2a883e3f7381b0bbfc8e12af12b8a87145b

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 small exact toy vectors and scores. No production index, ANN recall, embedding quality, or latency claim is implied. 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 2026-09-30T16:48:24.913005+00:00.

Case digest / fced395f411563591d3e21d7f6b6ffcdf57f07f46a348108fed80f9d75635935