Randomness Is All You Need: Semantic Traversal of Problem-Solution Spaces with Large Language Models

TL;DR

This paper tackles the challenge of ideation within enterprise knowledge by semantically traversing problem and solution spaces using dual LoRA-finetuned LLM mappings between the spaces $\wp$ (problems) and $\mathcal{S}$ (solutions). It introduces a tree-like, depth-first exploration framework that combines selection of known related statements with sampling of novel ones, controlled by LLM temperature to balance proximity and creativity. The authors validate the approach on a dataset of 313 problem–solution pairs and demonstrate feasibility with a Slack-based innovation assistant, showing that higher temperatures increase lexical novelty while preserving semantic relevance. The work contributes a practical, privacy-aware method for semantically guided ideation and problem refinement with potential for integration into enterprise workflows and knowledge bases.

Abstract

We present a novel approach to exploring innovation problem and solution domains using LLM fine-tuning with a custom idea database. By semantically traversing the bi-directional problem and solution tree at different temperature levels we achieve high diversity in solution edit distance while still remaining close to the original problem statement semantically. In addition to finding a variety of solutions to a given problem, this method can also be used to refine and clarify the original problem statement. As further validation of the approach, we implemented a proof-of-concept Slack bot to serve as an innovation assistant.

Figures (10)

• Figure 1: The pair of LLM-based mappings between the spaces of problem statements and solution statements.
• Figure 2: Exploring the Problem Statement space by finding related known problem statements and generating a new problem statement using the two LLM + LoRA mappings of Fig. reffig:llmprobsoln.
• Figure 3: The effect of the temperature parameter on the histogram of the output (single) token of the Pythia-Chat-Base-7B LLM (see Sec. \ref{['sec:pythia-chat-base-7b']}) for the next word in the completion prompt "I like to _" from $100$ different trials. The two most frequently occurring outcomes, "enjoy" and "eat" are labeled for the $0.2$ temperature plot but the labels are omitted in subsequent plots for brevity, using instead the red bar for "enjoy" and blue for "eat".
• Figure 4: Illustrating a wide depth-first exploration of the Problem Statement space by iteratively applying the two LLM + LoRA mappings of Fig. \ref{['fig:llmprobsoln']} to the newest generated problem statement, or alternatively, by searching for known problem statements related to one of the known problem statements discovered in the previous iteration.
• Figure 5: 3-level depth-first traversal of problem-solution tree