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

TL;DR

This work addresses the vulnerability of Bangla math word problem solving to semantically coherent but computationally irrelevant distractors. It reframes problem solving as executable computational-graph generation, introducing †DAGGER to explicitly model distractor nodes and dependencies, achieving robustness with far lower token usage than traditional chain-of-thought approaches. The DistractMath-BN benchmark, comprising $3{,}685$ distractor-augmented problems, enables controlled evaluation across seven model classes, with GRPO fine-tuning (SFT→GRPO) yielding comparable accuracy to reasoning models while using $89 ext{ percent}$ fewer tokens. The results demonstrate that structured intermediate representations improve both robustness and inference efficiency in noisy, low-resource settings, and extend across languages, offering practical implications for scalable educational tools in underrepresented languages.

Abstract

Chain-of-Thought (CoT) prompting is widely adopted for mathematical problem solving, including in low-resource languages, yet its behavior under irrelevant context remains underexplored. To systematically study this challenge, we introduce DISTRACTMATH-BN, a Bangla benchmark that augments MGSM and MSVAMP with semantically coherent but computationally irrelevant information. Evaluating seven models ranging from 3B to 12B parameters, we observe substantial performance degradation under distractors: standard models drop by up to 41 points, while reasoning-specialized models decline by 14 to 20 points despite consuming five times more tokens. We propose †DAGGER, which reformulates mathematical problem solving as executable computational graph generation with explicit modeling of distractor nodes. Fine-tuning Gemma-3 models using supervised fine-tuning followed by Group Relative Policy Optimization achieves comparable weighted accuracy on augmented benchmarks while using 89 percent fewer tokens than reasoning models. Importantly, this robustness emerges without explicit training on distractor-augmented examples. Our results suggest that enforcing structured intermediate representations improves robustness and inference efficiency in mathematical reasoning compared to free-form approaches, particularly in noisy, low-resource settings.

Figures (4)

• Figure 1: Identification of relevant information using computational graph to solve a Bangla MWP.
• Figure 2: Accuracy vs. Efficiency. We compare our method ($\bigstar$) against CoT baselines and reasoning models. Dashed arrows in (a) and (b) show performance drops due to distractors. Marker size indicates model parameter count. Overall, our method approaches reasoning model accuracy with significantly lower computational cost.
• Figure 3: Error rates across distractor types for different model categories.
• Figure 4: Output token usage as a function of computational complexity ($|V_{\text{op}}|$).