# A Novel Mathematical Framework for Objective Characterization of Ideas

arXiv: https://arxiv.org/abs/2409.07578 · HTML: https://mlsanity.com/paper/2409.07578/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 81 references that are in the map.
- First posted on arXiv 11 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Putting GPT-3's Creativity to the (Alternative Uses) Test](https://mlsanity.com/paper/2206.08932/) (2022)
- [AI-Augmented Brainwriting: Investigating the use of LLMs in group ideation](https://mlsanity.com/paper/2402.14978/) (2024)
- [Deep Learning in a Computational Model for Conceptual Shifts in a Co-Creative Design System](https://mlsanity.com/paper/1906.10188/) (2019)
- [A Novel Idea Generation Tool using a Structured Conversational AI (CAI) System](https://mlsanity.com/paper/2409.05747/) (2024)

## Built on by (most cited first, 1 of 1)

- [MetaMuse: Algorithm Generation via Creative Ideation](https://mlsanity.com/paper/2510.03851/) (2025)

## Abstract (arXiv)

The demand for innovation in product design necessitates a prolific ideation phase. Conversational AI (CAI) systems that use Large Language Models (LLMs) such as GPT (Generative Pre-trained Transformer) have been shown to be fruitful in augmenting human creativity, providing numerous novel and diverse ideas. Despite the success in ideation quantity, the qualitative assessment of these ideas remains challenging and traditionally reliant on expert human evaluation. This method suffers from limitations such as human judgment errors, bias, and oversight. Addressing this gap, our study introduces a comprehensive mathematical framework for automated analysis to objectively evaluate the plethora of ideas generated by CAI systems and/or humans. This framework is particularly advantageous for novice designers who lack experience in selecting promising ideas. By converting the ideas into higher dimensional vectors and quantitatively measuring the diversity between them using tools such as UMAP, DBSCAN and PCA, the proposed method provides a reliable and objective way of selecting the most promising ideas, thereby enhancing the efficiency of the ideation phase.