†DAGGER: Distractor-Aware Graph Generation for Executable Reasoning in Math Problems

Official implementation of "†DAGGER: Distractor-Aware Graph Generation for Executable Reasoning in Math Problems"

Key Results

Model	Weighted Avg. Accuracy	Tokens	Accuracy Drop
Qwen 3-8B (Reasoning)	71.4%	3,128	14.2-19.9 pts
DAGGER-12B (Ours)	69.4%	359	12.0-14.4 pts
Standard CoT (Best)	55.7%	599	up to 40.7 pts

DAGGER achieves comparable accuracy to reasoning models while using 89% fewer tokens.

Installation

Requirements

• Python 3.12+
• CUDA 12.1+ (for GPU training)

Setup

# Clone the repository
git clone https://github.com/dipta007/dagger.git
cd dagger

# Install dependencies using uv (recommended)
uv sync

Dataset: DistractMath-BN

DistractMath-BN is a distractor-augmented benchmark derived from the Bangla subset of MGSM (250 problems) and MSVAMP (1000 problems). It systematically probes reasoning robustness by introducing three classes of cognitive interference.

To illustrate these distractors, consider the following Original Problem:

Original Problem: Julia played tag with 18 children on Monday. On Tuesday she played with 10 children. How many more children did she play with on Monday?

Each problem in the benchmark is augmented with distractors as defined below:

Distractor Type	Definition	Example Augmentation
RED (Related Entity)	Numerical information about the same object type as the target, but associated with different entities or contexts.	"Her younger sister played hide-and-seek with 12 children on Wednesday."
OAD (Orthogonal Attribute)	Supplementary properties (e.g., time, price) measured in dimensions orthogonal to the attribute being queried.	"It took 1 hour to play on Monday... It took 45 minutes to play on Tuesday."
NEED (Null-Effect Event)	Descriptions of events (planned, negated, or hypothetical) that have zero net impact on the final result.	"Julia thought about inviting 5 more children... but she didn't call them later."

Dataset Statistics:

• MGSM (+Distractor): 738 verified problems
• MSVAMP (+Distractor): 2,947 verified problems
• Average distractors per problem: 2.7

Download from HuggingFace:

from datasets import load_dataset
dataset = load_dataset("dipta007/DistractMath-Bn")

Computational Graph Framework

DAGGER reformulates math word problems as directed acyclic graphs (DAGs):

{
  "nodes": [
    {"id": "n1", "op": "const", "val": 122195, "distractor": false, "label": "Mina's pens"},
    {"id": "n2", "op": "const", "val": 25084, "distractor": true, "label": "Raju's pens"},
    {"id": "n3", "op": "const", "val": 45.6, "distractor": false, "label": "Price per pen"},
    {"id": "total", "op": "mul", "args": ["n1", "n3"], "distractor": false, "label": "Total money"},
    {"id": "final_result", "op": "identity", "args": ["total"], "distractor": false}
  ]
}

Supported Operations: add, sub, mul, div, abs, sum, mean, min, max, floor, ceil, round, sqrt, pow, mod, gcd, lcm, const, identity

Usage

Inference

python src/inference.py \
  -c ./checkpoints/sft/my_model \
  -q "আপনার গণিত সমস্যা এখানে"

Or use our pretrained models:

from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained("dipta007/dagger-12B_SFT_GRPO")
tokenizer = AutoTokenizer.from_pretrained("dipta007/dagger-12B_SFT_GRPO")

Training

Supervised Fine-Tuning (SFT)

python src/train/sft/sft.py \
  --model_name "unsloth/gemma-3-12b-it" \
  --dataset_path "./data" \
  --run_name "sft_gemma12b_v1" \
  --lora_rank 64

SFT Hyperparameters:

Parameter	Value
LoRA Rank / Alpha	64 / 128
Global Batch Size	256
Epochs	4
Learning Rate	1e-5 → 1e-6
Max Sequence Length	4096

Group Relative Policy Optimization (GRPO)

python src/train/grpo/grpo.py \
  --model_name "./checkpoints/sft/sft_gemma12b_v1" \
  --dataset_path "./data" \
  --run_name "grpo_gemma12b_v1" \
  --num_generations 8 \
  --beta 0.0

GRPO Reward Function:

R(g, y) = 0.5 * I_fmt + 0.5 * I_exec + I_acc(exec(g), y)

• I_fmt: Valid JSON schema (+0.5)
• I_exec: Successful graph execution (+0.5)
• I_acc: Correct numerical answer (+1.0)

Evaluation

# Evaluate on MGSM
python src/eval/eval.py \
  --model_path ./checkpoints/grpo/grpo_gemma12b_v1 \
  --dataset mgsm \
  --split test

# Evaluate on augmented dataset
python src/eval/eval.py \
  --model_path ./checkpoints/grpo/grpo_gemma12b_v1 \
  --dataset mgsm_augmented \
  --split test

Model Zoo

Model	MGSM	MSVAMP	MGSM (+D)	MSVAMP (+D)	Weighted Avg
dagger-4B_SFT	40.4	65.0	25.1	42.4	44.3
dagger-4B_GRPO (ablation)	29.2	57.1	13.1	29.3	32.5
dagger-4B_SFT_GRPO	54.8	70.3	31.4	42.9	47.3
dagger-12B_SFT	70.0	76.8	56.8	65.4	66.7
dagger-12B_GRPO (ablation)	67.6	75.0	48.4	59.6	61.5
dagger-12B_SFT_GRPO	78.4	78.8	64.0	66.8	69.4

(+D) = with distractors. Rows marked (ablation) are GRPO applied directly to the base model with no SFT initialization; they are released to support the ablation in the paper, not as the recommended checkpoints. _SFT_GRPO is the full pipeline and is what the paper reports as "GRPO".

Project Structure

dagger/
├── data/                       # Training data (train.json, val.json, test.json)
├── src/
│   ├── inference.py           # Main inference script
│   ├── prompt.py              # Prompt templates
│   ├── eval/
│   │   ├── helpers.py         # Graph parsing & execution
│   │   ├── eval.py            # Batch evaluation
│   │   └── mgsm_eval.py       # MGSM benchmark evaluation
│   ├── train/
│   │   ├── sft/
│   │   │   └── sft.py         # Supervised fine-tuning
│   │   └── grpo/
│   │       ├── grpo.py        # GRPO training
│   │       └── grpo_rewards.py # Reward functions
│   └── hf_utils/
│       ├── push_model.py      # Upload models to HuggingFace
│       └── push_data.py       # Upload datasets to HuggingFace
├── evaluation/                 # Benchmark evaluation scripts
└── gpt_evaluation/            # GPT baseline evaluation

Citation

If you find this work useful, please cite our paper:

@inproceedings{nazi2026dagger,
  title={{\dag}DAGGER: Distractor-Aware Graph Generation for Executable Reasoning in Math Problems},
  author={Zabir Al Nazi and Shubhashis Roy Dipta and Sudipta Kar},
  booktitle={Findings of the Association for Computational Linguistics: EMNLP 2026},
  year={2026},
  eprint={2601.06853},
  archivePrefix={arXiv},
  primaryClass={cs.CL},
  url={https://arxiv.org/abs/2601.06853},
}

Acknowledgments

This work builds upon several open-source projects:

• Unsloth for efficient fine-tuning
• TRL for GRPO training
• vLLM for fast inference
• MGSM and MSVAMP for base datasets. MSVAMP is the multilingual extension of SVAMP

Contact

For questions or issues, please open a GitHub issue or contact the authors.