FA-99196 / Checkpoint tensor mapping / Open access

Checkpoint mapping: two dimensional shard indices use the tile width as row stride · case 01

two dimensional shard indices use the tile width as row stride.

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

ROOT CAUSE

Flat positions advance by global row width; using tile width aliases cells from different rows.

THE FAILURE

Flat positions advance by global row width; using tile width aliases cells from different rows.

Unsuccessful approach: Adding the global row stride fixes row placement but omits the column tile offset.

Case contract

For a 2D global shape and tile shape, coord is a tile-grid [row,column] coordinate. Return the row-major flat positions occupied by the tile, or [] if dimensions are negative or the whole tile lies outside the global shape.

Why this case matters

A bounded offline model of checkpoint tensor bookkeeping in a training workflow.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(global_shape, tile_shape, coord):
    H,W=global_shape
    th,tw=tile_shape
    tr,tc=coord
    return [(tr*th+r)*tw+tc*tw+c for r in range(th) for c in range(tw)] if min(H,W,th,tw,tr,tc)>=0 and (tr+1)*th<=H and (tc+1)*tw<=W else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior tile', solve(*((4, 6), (2, 2), (1, 1))), [14, 15, 20, 21])
check('top left', solve(*((4, 6), (2, 2), (0, 0))), [0, 1, 6, 7])
check('right edge', solve(*((4, 6), (2, 2), (1, 2))), [16, 17, 22, 23])
check('single cell', solve(*((3, 5), (1, 1), (2, 4))), [14])
check('out of rows', solve(*((3, 5), (2, 2), (1, 0))), [])
check('out of columns', solve(*((3, 5), (2, 2), (0, 2))), [])
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
interior tile	`[6, 7, 8, 9]`	`[14, 15, 20, 21]`	Failed
top left	`[0, 1, 2, 3]`	`[0, 1, 6, 7]`	Failed
right edge	`[8, 9, 10, 11]`	`[16, 17, 22, 23]`	Failed
single cell	`[6]`	`[14]`	Failed
out of rows	`[]`	`[]`	Passed
out of columns	`[]`	`[]`	Passed

SHA-256 / 33cba71d4503f70e8a7a2a7822db42079082103d73f3b55b0182a22b3f5e2bb0

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(global_shape, tile_shape, coord):
    H,W=global_shape
    th,tw=tile_shape
    tr,tc=coord
    return [(tr*th+r)*W+c for r in range(th) for c in range(tw)] if min(H,W,th,tw,tr,tc)>=0 and (tr+1)*th<=H and (tc+1)*tw<=W else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('interior tile', solve(*((4, 6), (2, 2), (1, 1))), [14, 15, 20, 21])
check('top left', solve(*((4, 6), (2, 2), (0, 0))), [0, 1, 6, 7])
check('right edge', solve(*((4, 6), (2, 2), (1, 2))), [16, 17, 22, 23])
check('single cell', solve(*((3, 5), (1, 1), (2, 4))), [14])
check('out of rows', solve(*((3, 5), (2, 2), (1, 0))), [])
check('out of columns', solve(*((3, 5), (2, 2), (0, 2))), [])
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
interior tile	`[12, 13, 18, 19]`	`[14, 15, 20, 21]`	Failed
top left	`[0, 1, 6, 7]`	`[0, 1, 6, 7]`	Passed
right edge	`[12, 13, 18, 19]`	`[16, 17, 22, 23]`	Failed
single cell	`[10]`	`[14]`	Failed
out of rows	`[]`	`[]`	Passed
out of columns	`[]`	`[]`	Passed

SHA-256 / c0f6296b3f9e906d52598b1b5d8b120f598b7562f7946767bab6bb8c79687ec3

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.

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Verification & scope

Inputs are already decoded Python values; this toy contract makes no claim about a framework, file format, or production checkpoint. 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 2026-09-30T16:48:21.243208+00:00.

Case digest / 9e1d0224cebffd0d1efdc2700ae4a9b99e4cfa67787a6a617f067e874fc8c3f9