FA-98426 / Token sampling filters / Open access

Token sampling: Top-k probability mass is measured before candidate restriction · case 01

Top-k probability mass is measured before candidate restriction.

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

ROOT CAUSE

The nucleus cumulative mass is calculated over the full vocabulary before the top-k restriction.

THE FAILURE

The nucleus cumulative mass is calculated over the full vocabulary before the top-k restriction.

Unsuccessful approach: Using unnormalized exponentials as cumulative mass makes the threshold cease to represent a probability fraction.

Case contract

Select top k by descending score and lexical ties, normalize softmax over this restricted set, and retain its shortest prefix reaching p; p<=0 or k<=0 returns empty.

Why this case matters

A finite, deterministic token-selection contract isolates one decoding operation from model inference and runtime behavior.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(scores, k, p):
    import math
    ranked=sorted(scores,key=lambda t:(-scores[t],t)); m=max(scores.values(),default=0)
    ex={t:math.exp(v-m) for t,v in scores.items()}; z=sum(ex.values()); out=[]; total=0
    for t in ranked:
        total+=ex[t]/z; out.append(t)
        if total>=p:break
    return out[:max(0,k)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('restricted mass',solve({'a':2.0,'b':1.0,'c':0.0},2,.68),['a'])
check('full retained mass',solve({'a':2.0,'b':1.0,'c':0.0},2,.8),['a','b'])
check('one candidate top k',solve({'a':N,'b':0.0},1,.5),['a'])
check('zero k',solve({'a':N},0,.5),[])
check('empty',solve({},2,.5),[])
check('zero target',solve({'a':N,'b':0.0},2,0),[])
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
restricted mass	`['a', 'b']`	`['a']`	Failed
full retained mass	`['a', 'b']`	`['a', 'b']`	Passed
one candidate top k	`['a']`	`['a']`	Passed
zero k	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed
zero target	`['a']`	`[]`	Failed

SHA-256 / ea343be9f1fb68d3a051275845d6fa9eabdb157b845e03dc108c5fc953d7e696

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(scores, k, p):
    import math
    ranked=sorted(scores,key=lambda t:(-scores[t],t))[:max(0,k)]; ex=[math.exp(scores[t]) for t in ranked]; out=[]; total=0
    for t,v in zip(ranked,ex):
        total+=v; out.append(t)
        if total>=p:break
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('restricted mass',solve({'a':2.0,'b':1.0,'c':0.0},2,.68),['a'])
check('full retained mass',solve({'a':2.0,'b':1.0,'c':0.0},2,.8),['a','b'])
check('one candidate top k',solve({'a':N,'b':0.0},1,.5),['a'])
check('zero k',solve({'a':N},0,.5),[])
check('empty',solve({},2,.5),[])
check('zero target',solve({'a':N,'b':0.0},2,0),[])
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
restricted mass	`['a']`	`['a']`	Passed
full retained mass	`['a']`	`['a', 'b']`	Failed
one candidate top k	`['a']`	`['a']`	Passed
zero k	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed
zero target	`['a']`	`[]`	Failed

SHA-256 / 35d644e5786b605522468077b405210052e2ecd36410350ef5ecd99cfc844624

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

These are toy finite-vocabulary contracts with supplied scores, histories, and draws; they do not claim production model quality or compatibility. 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 2026-09-30T16:48:12.803371+00:00.

Case digest / 96cdd7562cf2a434147aee668f1ae5a0ecb2eecb5fd29be899a04364241a85ee