Word2Li/CoTranslator-Nemotron-SFT-Math-v4-Pairs

CoTranslator Nemotron Math CoT Translation Pairs

This dataset contains paired reverse and verified forward chain-of-thought (CoT) trajectories for training the translator introduced in CoTranslator: Reverse to Forward Chain-of-Thought Translator for Reasoning Distillation.

CoTranslator learns to translate answer-conditioned reverse trajectories toward the distribution of question-only, answer-verified forward trajectories. The trained translator then converts reverse trajectories into supervision for downstream reasoning students.

Overview of CoTranslator. The translator learns from paired reverse and verified forward trajectories, then translates reverse trajectories at scale to construct student training data.

Data construction

Following the manuscript, the mathematical problems and verified forward targets come from the cot portion of nvidia/Nemotron-SFT-Math-v4. The forward targets were generated by DeepSeek-V4-Pro and retained after final-answer verification. Reverse source trajectories are generated by the same teacher with the reference answer available and semantic suppression prompting.

For each paired example, the translator's user input is the reverse trajectory and its assistant target is the matched verified forward trajectory. The system instruction specifies trajectory refinement. The released files store the paired trajectories in chat format, with source_uuid linking each pair to its source record.

Configurations

Both configurations have a train split. The full file and subset are available in this single repository.

Configuration	Rows	File size (decimal GB)	Translator checkpoint
full (default)	266,288	12.679	Word2Li/CoTranslator-4B-Full, step 4921
subset_1_8	33,286	1.583	Word2Li/CoTranslator-4B, step 616

Counts are measured from the released JSONL files, before model-specific tokenization and packing. Every subset record is present in full, with identical serialized record content apart from line endings. Use the configurations as alternative training sets: subset_1_8 overlaps full.

Record format

Each line is a JSON object with two fields:

Field	Meaning
source_uuid	Identifier of the corresponding source example.
messages	Three messages, ordered system, user, assistant; each has string fields role and content.

The following schematic example illustrates the layout; the ellipses stand for complete trajectories in the actual records.

{
  "source_uuid": "<source UUID from the upstream dataset>",
  "messages": [
    {
      "role": "system",
      "content": "You are a reasoning trajectory refiner. Given a teacher-generated solution trajectory, produce a more natural reasoning trajectory. Preserve the mathematical conclusion and answer format."
    },
    {
      "role": "user",
      "content": "<think>Reverse reasoning trajectory...</think>\nTeacher final response..."
    },
    {
      "role": "assistant",
      "content": "<think>Verified forward reasoning trajectory...</think>\nVerified final response..."
    }
  ]
}

The user and assistant contents retain reasoning and final-answer text, including <think> blocks where present. Training predicts the assistant trajectory from the preceding system and user messages.

Loading

from datasets import load_dataset

repo_id = "Word2Li/CoTranslator-Nemotron-SFT-Math-v4-Pairs"
full = load_dataset(repo_id, "full", split="train", streaming=True)
subset = load_dataset(repo_id, "subset_1_8", split="train", streaming=True)

example = next(iter(subset))
translation_input = example["messages"][:2]
forward_target = example["messages"][2]["content"]

Streaming reads examples without first materializing the complete dataset locally. Omit streaming=True to build a local dataset.

License and attribution

The upstream dataset card specifies CC BY 4.0 for AoPS-derived samples and CC BY-SA 4.0 for Math StackExchange-derived samples. This release retains the upstream identifiers in source_uuid, supporting lookup of the original source and its attribution and license metadata.

The paired files add answer-conditioned reverse trajectories and organize the sources and verified forward targets as translator training conversations. Please preserve the applicable source-specific attribution and license information when redistributing data.