FA-98486 / Beam search bookkeeping / Open access

Beam search: length penalty favors longer paths under a penalty contract · case 01

length penalty favors longer paths under a penalty contract.

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

ROOT CAUSE

A positive penalty multiplier is applied by increasing, rather than dividing by, length.

THE FAILURE

A positive penalty multiplier is applied by increasing, rather than dividing by, length.

Unsuccessful approach: Dividing by the square root changes the contract for linear length normalization.

Case contract

Return score divided by 1 + alpha*(length-1), for each [score,length]; alpha is nonnegative.

Why this case matters

Beam decoders rely on consistent hypothesis state while expanding and ranking candidates.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(rows, alpha):
    return [s*(1+alpha*(l-1)) for s,l in rows]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('long path penalty',solve([[N,3]],1),[N/3])
check('unit path unchanged',solve([[N,1]],N),[float(N)])
check('zero alpha unchanged',solve([[2*N,4]],0),[float(2*N)])
check('empty rows',solve([],N),[])
check('two lengths',solve([[6,1],[6,3]],1),[6.0,2.0])
check('fractional alpha',solve([[8,3]],.5),[4.0])
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
long path penalty	`[3]`	`[0.3333333333333333]`	Failed
unit path unchanged	`[1]`	`[1.0]`	Passed
zero alpha unchanged	`[2]`	`[2.0]`	Passed
empty rows	`[]`	`[]`	Passed
two lengths	`[6, 18]`	`[6.0, 2.0]`	Failed
fractional alpha	`[16.0]`	`[4.0]`	Failed

SHA-256 / 0660671123822b86ed8070e5004594208602f6cd0ae561f4d2a5b1ab246733e4

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(rows, alpha):
    return [s/(1+alpha*((l-1)**0.5)) for s,l in rows]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('long path penalty',solve([[N,3]],1),[N/3])
check('unit path unchanged',solve([[N,1]],N),[float(N)])
check('zero alpha unchanged',solve([[2*N,4]],0),[float(2*N)])
check('empty rows',solve([],N),[])
check('two lengths',solve([[6,1],[6,3]],1),[6.0,2.0])
check('fractional alpha',solve([[8,3]],.5),[4.0])
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
long path penalty	`[0.4142135623730951]`	`[0.3333333333333333]`	Failed
unit path unchanged	`[1.0]`	`[1.0]`	Passed
zero alpha unchanged	`[2.0]`	`[2.0]`	Passed
empty rows	`[]`	`[]`	Passed
two lengths	`[6.0, 2.4852813742385704]`	`[6.0, 2.0]`	Failed
fractional alpha	`[4.68629150101524]`	`[4.0]`	Failed

SHA-256 / 924364d709ee81074f8595d1cc6eff2ce23f3ebaf979ace9d4e8fccb8133af7d

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

This is a finite toy beam-state contract and makes no claim about neural model quality or production decoding. 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 2026-09-30T16:48:13.672203+00:00.

Case digest / c99addedb7d20556ccf412600a004e875ea1d7b74e6f44cdf15aef71fdb25665