id string | family int64 | increment int64 | language string | items list | capacity int64 | optimum int64 | optimal_sets list | prompt string |
|---|---|---|---|---|---|---|---|---|
f1-c0-en | 1 | 0 | en | [
{
"id": "A",
"weight": 2,
"value": 24
},
{
"id": "B",
"weight": 8,
"value": 9
},
{
"id": "C",
"weight": 3,
"value": 3
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 5
},
{
"id": "F",
"weight": 9,
... | 18 | 46 | [
[
"A",
"E",
"F"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 18. Maximize total value.
ID | weight | value
A | 2 | 24
B | 8 | 9
C | 3 | 3
D | 9 | 5
E | 5 | 5
F | 9 | 17
Explain your calculation briefly, then give exactly one final line using this format (example o... |
f1-c0-zh | 1 | 0 | zh | [
{
"id": "A",
"weight": 2,
"value": 24
},
{
"id": "B",
"weight": 8,
"value": 9
},
{
"id": "C",
"weight": 3,
"value": 3
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 5
},
{
"id": "F",
"weight": 9,
... | 18 | 46 | [
[
"A",
"E",
"F"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过18。请使总价值最大。
编号 | 重量 | 价值
A | 2 | 24
B | 8 | 9
C | 3 | 3
D | 9 | 5
E | 5 | 5
F | 9 | 17
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
f1-c1-en | 1 | 1 | en | [
{
"id": "A",
"weight": 2,
"value": 24
},
{
"id": "B",
"weight": 8,
"value": 9
},
{
"id": "C",
"weight": 3,
"value": 3
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 5
},
{
"id": "F",
"weight": 9,
... | 19 | 50 | [
[
"A",
"B",
"F"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 19. Maximize total value.
ID | weight | value
A | 2 | 24
B | 8 | 9
C | 3 | 3
D | 9 | 5
E | 5 | 5
F | 9 | 17
Explain your calculation briefly, then give exactly one final line using this format (example o... |
f1-c1-zh | 1 | 1 | zh | [
{
"id": "A",
"weight": 2,
"value": 24
},
{
"id": "B",
"weight": 8,
"value": 9
},
{
"id": "C",
"weight": 3,
"value": 3
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 5
},
{
"id": "F",
"weight": 9,
... | 19 | 50 | [
[
"A",
"B",
"F"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过19。请使总价值最大。
编号 | 重量 | 价值
A | 2 | 24
B | 8 | 9
C | 3 | 3
D | 9 | 5
E | 5 | 5
F | 9 | 17
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
f2-c0-en | 2 | 0 | en | [
{
"id": "A",
"weight": 3,
"value": 7
},
{
"id": "B",
"weight": 4,
"value": 8
},
{
"id": "C",
"weight": 3,
"value": 9
},
{
"id": "D",
"weight": 8,
"value": 16
},
{
"id": "E",
"weight": 3,
"value": 5
},
{
"id": "F",
"weight": 5,
... | 13 | 29 | [
[
"A",
"B",
"C",
"E"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 13. Maximize total value.
ID | weight | value
A | 3 | 7
B | 4 | 8
C | 3 | 9
D | 8 | 16
E | 3 | 5
F | 5 | 9
Explain your calculation briefly, then give exactly one final line using this format (example on... |
f2-c0-zh | 2 | 0 | zh | [
{
"id": "A",
"weight": 3,
"value": 7
},
{
"id": "B",
"weight": 4,
"value": 8
},
{
"id": "C",
"weight": 3,
"value": 9
},
{
"id": "D",
"weight": 8,
"value": 16
},
{
"id": "E",
"weight": 3,
"value": 5
},
{
"id": "F",
"weight": 5,
... | 13 | 29 | [
[
"A",
"B",
"C",
"E"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过13。请使总价值最大。
编号 | 重量 | 价值
A | 3 | 7
B | 4 | 8
C | 3 | 9
D | 8 | 16
E | 3 | 5
F | 5 | 9
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
f2-c1-en | 2 | 1 | en | [
{
"id": "A",
"weight": 3,
"value": 7
},
{
"id": "B",
"weight": 4,
"value": 8
},
{
"id": "C",
"weight": 3,
"value": 9
},
{
"id": "D",
"weight": 8,
"value": 16
},
{
"id": "E",
"weight": 3,
"value": 5
},
{
"id": "F",
"weight": 5,
... | 14 | 32 | [
[
"A",
"C",
"D"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 14. Maximize total value.
ID | weight | value
A | 3 | 7
B | 4 | 8
C | 3 | 9
D | 8 | 16
E | 3 | 5
F | 5 | 9
Explain your calculation briefly, then give exactly one final line using this format (example on... |
f2-c1-zh | 2 | 1 | zh | [
{
"id": "A",
"weight": 3,
"value": 7
},
{
"id": "B",
"weight": 4,
"value": 8
},
{
"id": "C",
"weight": 3,
"value": 9
},
{
"id": "D",
"weight": 8,
"value": 16
},
{
"id": "E",
"weight": 3,
"value": 5
},
{
"id": "F",
"weight": 5,
... | 14 | 32 | [
[
"A",
"C",
"D"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过14。请使总价值最大。
编号 | 重量 | 价值
A | 3 | 7
B | 4 | 8
C | 3 | 9
D | 8 | 16
E | 3 | 5
F | 5 | 9
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
f3-c0-en | 3 | 0 | en | [
{
"id": "A",
"weight": 7,
"value": 8
},
{
"id": "B",
"weight": 3,
"value": 9
},
{
"id": "C",
"weight": 8,
"value": 19
},
{
"id": "D",
"weight": 2,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 21
},
{
"id": "F",
"weight": 6,
... | 15 | 45 | [
[
"C",
"D",
"E"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 15. Maximize total value.
ID | weight | value
A | 7 | 8
B | 3 | 9
C | 8 | 19
D | 2 | 5
E | 5 | 21
F | 6 | 6
Explain your calculation briefly, then give exactly one final line using this format (example o... |
f3-c0-zh | 3 | 0 | zh | [
{
"id": "A",
"weight": 7,
"value": 8
},
{
"id": "B",
"weight": 3,
"value": 9
},
{
"id": "C",
"weight": 8,
"value": 19
},
{
"id": "D",
"weight": 2,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 21
},
{
"id": "F",
"weight": 6,
... | 15 | 45 | [
[
"C",
"D",
"E"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过15。请使总价值最大。
编号 | 重量 | 价值
A | 7 | 8
B | 3 | 9
C | 8 | 19
D | 2 | 5
E | 5 | 21
F | 6 | 6
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
f3-c1-en | 3 | 1 | en | [
{
"id": "A",
"weight": 7,
"value": 8
},
{
"id": "B",
"weight": 3,
"value": 9
},
{
"id": "C",
"weight": 8,
"value": 19
},
{
"id": "D",
"weight": 2,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 21
},
{
"id": "F",
"weight": 6,
... | 16 | 49 | [
[
"B",
"C",
"E"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 16. Maximize total value.
ID | weight | value
A | 7 | 8
B | 3 | 9
C | 8 | 19
D | 2 | 5
E | 5 | 21
F | 6 | 6
Explain your calculation briefly, then give exactly one final line using this format (example o... |
f3-c1-zh | 3 | 1 | zh | [
{
"id": "A",
"weight": 7,
"value": 8
},
{
"id": "B",
"weight": 3,
"value": 9
},
{
"id": "C",
"weight": 8,
"value": 19
},
{
"id": "D",
"weight": 2,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 21
},
{
"id": "F",
"weight": 6,
... | 16 | 49 | [
[
"B",
"C",
"E"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过16。请使总价值最大。
编号 | 重量 | 价值
A | 7 | 8
B | 3 | 9
C | 8 | 19
D | 2 | 5
E | 5 | 21
F | 6 | 6
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
f4-c0-en | 4 | 0 | en | [
{
"id": "A",
"weight": 5,
"value": 23
},
{
"id": "B",
"weight": 2,
"value": 9
},
{
"id": "C",
"weight": 2,
"value": 23
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 22
},
{
"id": "F",
"weight": 4,... | 13 | 68 | [
[
"A",
"C",
"E"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 13. Maximize total value.
ID | weight | value
A | 5 | 23
B | 2 | 9
C | 2 | 23
D | 9 | 5
E | 5 | 22
F | 4 | 4
Explain your calculation briefly, then give exactly one final line using this format (example ... |
f4-c0-zh | 4 | 0 | zh | [
{
"id": "A",
"weight": 5,
"value": 23
},
{
"id": "B",
"weight": 2,
"value": 9
},
{
"id": "C",
"weight": 2,
"value": 23
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 22
},
{
"id": "F",
"weight": 4,... | 13 | 68 | [
[
"A",
"C",
"E"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过13。请使总价值最大。
编号 | 重量 | 价值
A | 5 | 23
B | 2 | 9
C | 2 | 23
D | 9 | 5
E | 5 | 22
F | 4 | 4
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
f4-c1-en | 4 | 1 | en | [
{
"id": "A",
"weight": 5,
"value": 23
},
{
"id": "B",
"weight": 2,
"value": 9
},
{
"id": "C",
"weight": 2,
"value": 23
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 22
},
{
"id": "F",
"weight": 4,... | 14 | 77 | [
[
"A",
"B",
"C",
"E"
]
] | Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most 14. Maximize total value.
ID | weight | value
A | 5 | 23
B | 2 | 9
C | 2 | 23
D | 9 | 5
E | 5 | 22
F | 4 | 4
Explain your calculation briefly, then give exactly one final line using this format (example ... |
f4-c1-zh | 4 | 1 | zh | [
{
"id": "A",
"weight": 5,
"value": 23
},
{
"id": "B",
"weight": 2,
"value": 9
},
{
"id": "C",
"weight": 2,
"value": 23
},
{
"id": "D",
"weight": 9,
"value": 5
},
{
"id": "E",
"weight": 5,
"value": 22
},
{
"id": "F",
"weight": 4,... | 14 | 77 | [
[
"A",
"B",
"C",
"E"
]
] | 从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过14。请使总价值最大。
编号 | 重量 | 价值
A | 5 | 23
B | 2 | 9
C | 2 | 23
D | 9 | 5
E | 5 | 22
F | 4 | 4
简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。 |
Capacity-boundary optimization with Spark-X2.5-1.7B
This project contains an original evaluation for HER Hack-Astron #6. The report is in DISCUSSION.md. Creating or publishing these artifacts is not an award or payment.
The experiment checks whether increasing a six-item 0/1 knapsack's capacity by one causes the model to find the new optimum. Four seeded item families produce eight mathematical instances, each in English and Chinese. Every prompt runs once with thinking off and once on: 32 greedy generations, 1536 new tokens each, no tools, original BF16 weights. See the design frozen before evaluation in PROTOCOL.md.
The dataset license applies to the original problem corpus. The reproduction scripts are MIT-licensed, as described in LICENSE. problems.jsonl is a line-oriented export of the exact16 prompts in corpus.json for the Hub viewer; it is not a new or separate split.
Files
study.py,corpus.json: deterministic original problem generation, exact enumeration oracle, independent dynamic-programming check and final-answer scorer.test_study.py: checks for oracle agreement, valid answers, wrong answers, malformed answers, truncation and ambiguous output.download_model.py,model-artifacts.json: pinned public download and SHA-256 inventory. Model weights are not part of the submission package.run_study.py: local CUDA execution, rendered prompts, full visible output and token IDs. Existing measured runs are never overwritten.analyze_study.py: requires every planned run exactly once, recomputes scores and verifies source/corpus hashes before making tables.- After execution:
environment.json,smoke.json,runs.jsonl,summary.json,RESULTS.md,RESPONSES.md. Separate interpretation belongs inDISCUSSION.md.
Reproduction
Commands below use PowerShell in a fresh copy of this directory, with Python 3.12 available. Use a CUDA 12.8-compatible NVIDIA driver and sufficient BF16-capable GPU memory. CUDA unavailability stops execution; the script never buys or switches to a hosted service.
python -m venv .venv
& .\.venv\Scripts\python.exe -m pip install 'torch==2.9.1' --index-url https://download.pytorch.org/whl/cu128 --disable-pip-version-check --progress-bar off
& .\.venv\Scripts\python.exe -m pip install 'transformers==4.57.1' --disable-pip-version-check --progress-bar off
& .\.venv\Scripts\python.exe -m pip install 'accelerate==1.12.0' --disable-pip-version-check --progress-bar off
& .\.venv\Scripts\python.exe -X utf8 study.py
& .\.venv\Scripts\python.exe -X utf8 -m unittest -v test_study
& .\.venv\Scripts\python.exe -X utf8 -u download_model.py
& .\.venv\Scripts\python.exe -X utf8 -u run_study.py --smoke-only
& .\.venv\Scripts\python.exe -X utf8 -u run_study.py
& .\.venv\Scripts\python.exe -X utf8 analyze_study.py
The actual local execution used the bundled Python 3.12 interpreter to create the venv; its user-specific absolute path is intentionally omitted. requirements-lock.txt, when present, records the installed package versions. CUDA-wheel installation uses the official PyTorch index first. The public, non-gated model is downloaded directly from Hugging Face HTTPS at revision 448e61eb392c00f2c403185c5b56d5e0665bfaab; no access token is used. The two upstream custom Python model/configuration modules were reviewed before local execution. trust_remote_code=True loads these pinned, hashed local files, with offline mode enabled for inference.
The first smoke-only startup failed with a native Python/ntdll event and no model output. A separate staged diagnostic then imported Torch/Transformers successfully in 90.1 seconds and confirmed CUDA/BF16 availability. Before any measured generation, the runner was changed to one OMP/MKL/CPU thread and direct placement on cuda:0 through Accelerate, reducing the need for CPU-resident model weights. This does not establish the cause of the original crash. See EXECUTION_NOTES.md.
A second setup attempt loaded the model but inherited sampling defaults with top_k=-1, which Transformers rejected before producing an answer. The runner explicitly passes use_model_defaults=False and do_sample=False, validates greedy mode, and records the resolved configuration. Both changes preceded all measured generations and preserve the frozen experimental design. The initial status line in PROTOCOL.md describes the time that protocol was frozen; it is not the current publication status.
The separate smoke-only setup check and the warmup at the start of the measured run both use 2+3; neither is a study observation. To reproduce with the supplied recorded results present, use a new directory without runs.jsonl and environment.json, keeping the published originals intact. Do not overwrite measured logs to select better outputs.
This is a selected, tiny descriptive study, not a benchmark-wide accuracy estimate. The same token limit is operationally comparable but constrains the modes differently: thinking consumes part of its budget before the final answer. Seeded fresh numeric problems do not prove an absence of training-data contamination. GPU timing excludes setup, loading, warmup and analysis; peak allocated PyTorch memory is not total device memory.
Resumption provenance
Two tool-session interruptions left18 and then19 completed records. Both prefixes and their byte-for-byte backups are retained. The first continuation used resume_study.py; the second uses resume_study_02.py in an independent hidden local process, with the same model and generation code. Each continuation checks its effective configuration against the original environment and appends only missing cases. RESUME-01.json and RESUME-02.json disclose the boundaries. No completed answer was replaced. Interrupted attempts at the next cases had no persisted output; timing totals cannot include their unknown durations. analyze_study.py verifies both prefixes and resumption hashes before producing results.
For a fresh full reproduction, use the original run_study.py command above in a separate copy containing only scripts, protocol and corpus, without the recorded outputs or RESUME-*.json. This avoids the interruptions entirely. The analyzer performs additional prefix and environment checks whenever resumption evidence exists and records those segments. Preserve the published originals intact; do not manufacture a resumption record for a fresh run.
Attribution and licenses
Development, execution, scoring, review and writing use Codex. There is no claim of independent human review or of an AI persona being a human contributor. The original generated problem corpus is dedicated under CC0-1.0. Original scripts are MIT-licensed; upstream Spark-X2.5 artifacts retain their Apache-2.0 license. Model weights, credentials and local account/cache paths must not enter a public submission archive.
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