DEO: Training-Free Direct Embedding Optimization for Negation-Aware Retrieval

TL;DR

Direct Embedding Optimization (DEO) is proposed, a training-free method for negation-aware text and multimodal retrieval that decomposes queries into positive and negative components and optimizes the query embedding with a contrastive objective.

Abstract

Recent advances in Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) have enabled diverse retrieval methods. However, existing retrieval methods often fail to accurately retrieve results for negation and exclusion queries. To address this limitation, prior approaches rely on embedding adaptation or fine-tuning, which introduce additional computational cost and deployment complexity. We propose Direct Embedding Optimization (DEO), a training-free method for negation-aware text and multimodal retrieval. DEO decomposes queries into positive and negative components and optimizes the query embedding with a contrastive objective. Without additional training data or model updates, DEO outperforms baselines on NegConstraint, with gains of +0.0738 nDCG@10 and +0.1028 MAP@100, while improving Recall@5 by +6\% over OpenAI CLIP in multimodal retrieval. These results demonstrate the practicality of DEO for negation- and exclusion-aware retrieval in real-world settings.

Figures (6)

• Figure 1: Overview of the proposed Direct Embedding Optimization (DEO). (a) Given an input query containing negation, we use an LLM to decompose it into positive and negative sub-queries. (b) The input query embedding is then optimized with a contrastive loss by pulling it closer to positive query embeddings and pushing it farther from negative query embeddings, enabling negation- and exclusion-aware retrieval.
• Figure 2: Retrieval performance with respect to the number of optimization steps on NegConstraint.
• Figure 3: Retrieval performance with respect to the number of optimization steps on COCO-Neg.
• Figure 4: Examples of query decomposition. In NegConstraint (a) and COCO-Neg (b), the LLM decomposes queries into positive sub-queries capturing desired elements and negative sub-queries targeting excluded concepts.
• Figure 5: Trajectory of optimized query embedding $e_u$ in PCA-projected space. The initial embedding (black $\bullet$) moves toward the final state (blue $\bullet$). Positive examples (green $\triangle$) and the ground-truth (yellow $\star$) act as attractors, while negative examples (red $\times$) exert repelling forces. Other corpus embeddings are shown in light gray.