# MIDGARD: Self-Consistency Using Minimum Description Length for Structured Commonsense Reasoning

arXiv: https://arxiv.org/abs/2405.05189 · HTML: https://mlsanity.com/paper/2405.05189/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 8 May 2024.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 19 of 19)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Large Language Models Are Not Robust Multiple Choice Selectors](https://mlsanity.com/paper/2309.03882/) (2023)
- [Is ChatGPT a Good NLG Evaluator? A Preliminary Study](https://mlsanity.com/paper/2303.04048/) (2023)
- [GPTScore: Evaluate as You Desire](https://mlsanity.com/paper/2302.04166/) (2023)
- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [PiVe: Prompting with Iterative Verification Improving Graph-based Generative Capability of LLMs](https://mlsanity.com/paper/2305.12392/) (2023)

## Built on by (most cited first, 3 of 3)

- [Embedding Trajectory for Out-of-Distribution Detection in Mathematical Reasoning](https://mlsanity.com/paper/2405.14039/) (2024)
- [Accurate and Consistent Graph Model Generation from Text with Large Language Models](https://mlsanity.com/paper/2508.00255/) (2025)
- [FedCoT: Communication-Efficient Federated Reasoning Enhancement for Large Language Models](https://mlsanity.com/paper/2508.10020/) (2025)

## Abstract (arXiv)

We study the task of conducting structured reasoning as generating a reasoning graph from natural language input using large language models (LLMs). Previous approaches have explored various prompting schemes, yet they suffer from error propagation due to the autoregressive nature and single-pass-based decoding, which lack error correction capability. Additionally, relying solely on a single sample may result in the omission of true nodes and edges. To counter this, we draw inspiration from self-consistency (SC), which involves sampling a diverse set of reasoning chains and taking the majority vote as the final answer. To tackle the substantial challenge of applying SC on generated graphs, we propose MIDGARD (MInimum Description length Guided Aggregation of Reasoning in Directed acyclic graph) that leverages Minimum Description Length (MDL)-based formulation to identify consistent properties among the different graph samples generated by an LLM. This formulation helps reject properties that appear in only a few samples, which are likely to be erroneous, while enabling the inclusion of missing elements without compromising precision. Our method demonstrates superior performance than comparisons across various structured reasoning tasks, including argument structure extraction, explanation graph generation, inferring dependency relations among actions for everyday tasks, and semantic graph generation from natural texts.