# Introducing Verification Task of Set Consistency with Set-Consistency Energy Networks

arXiv: https://arxiv.org/abs/2503.10695 · HTML: https://mlsanity.com/paper/2503.10695/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [SummaC: Re-Visiting NLI-based Models for Inconsistency Detection in Summarization](https://mlsanity.com/paper/2111.09525/) (2021)
- [Asking and Answering Questions to Evaluate the Factual Consistency of Summaries](https://mlsanity.com/paper/2004.04228/) (2020)
- [QAFactEval: Improved QA-Based Factual Consistency Evaluation for Summarization](https://mlsanity.com/paper/2112.08542/) (2021)
- [Logic-Guided Data Augmentation and Regularization for Consistent Question Answering](https://mlsanity.com/paper/2004.10157/) (2020)
- [WIQA: A dataset for "What if..." reasoning over procedural text](https://mlsanity.com/paper/1909.04739/) (2019)
- [Structured Prediction Energy Networks](https://mlsanity.com/paper/1511.06350/) (2015)
- [Sunny and Dark Outside?! Improving Answer Consistency in VQA through Entailed Question Generation](https://mlsanity.com/paper/1909.04696/) (2019)
- [Improving Joint Training of Inference Networks and Structured Prediction Energy Networks](https://mlsanity.com/paper/1911.02891/) (2019)

## Built on by (most cited first, 2 of 2)

- [On Finding Inconsistencies in Documents](https://mlsanity.com/paper/2512.18601/) (2025)
- [Retrieving a Set, Not Independent Passages: Set-Level Compatibility Learning for Efficient Set Exploration](https://mlsanity.com/paper/2607.05712/) (2026)

## Abstract (arXiv)

Examining logical inconsistencies among multiple statements (such as collections of sentences or question-answer pairs) is a crucial challenge in machine learning, particularly for ensuring the safety and reliability of models. Traditional methods that rely on pairwise comparisons often fail to capture inconsistencies that only emerge when more than two statements are evaluated collectively. To address this gap, we introduce the task of set-consistency verification, an extension of natural language inference (NLI) that assesses the logical coherence of entire sets rather than isolated pairs. Building on this task, we present the Set-Consistency Energy Network (SC-Energy), a novel model that employs a contrastive loss framework to learn the compatibility among a collection of statements. Our approach not only efficiently verifies inconsistencies and pinpoints the specific statements responsible for logical contradictions, but also significantly outperforms existing methods including prompting-based LLM models. Furthermore, we release two new datasets: Set-LConVQA and Set-SNLI for set-consistency verification task.