NSFL: A Post-Training Neuro-Symbolic Fuzzy Logic Framework for Boolean Operators in Neural Embeddings

Standard dense retrievers lack a native calculus for multi-atom logical constraints. We introduce Neuro-Symbolic Fuzzy Logic (NSFL), a framework that adapts formal t-norms and t-conorms to neural embedding spaces without requiring retraining. NSFL operates as a first-order hybrid calculus: it anchors logical operations on isolated zero-order similarity scores while actively steering representations using Neuro-Symbolic Deltas (NS-Delta) -- the first-order marginal differences derived from contextual fusion. This preserves pure atomic meaning while capturing domain reliance, preventing the representation collapse and manifold escape endemic to traditional geometric baselines. For scalable real-time retrieval, Spherical Query Optimization (SQO) leverages Riemannian optimization to project these fuzzy formulas into manifold-stable query vectors. Validated across six distinct encoder configurations and two modalities (including zero-shot and SOTA fine-tuned models), NSFL yields mAP improvements up to +81%. Notably, NSFL provides an additive 20% average and up to 47% boost even when applied to encoders explicitly fine-tuned for logical reasoning. By establishing a training-free, order-aware calculus for high-dimensional spaces, this framework lays the foundation for future dynamic scaling and learned manifold logic.

Few Shots Text to Image Retrieval: New Benchmarking Dataset and Optimization Methods

Pre-trained vision-language models (VLMs) excel in multimodal tasks, commonly encoding images as embedding vectors for storage in databases and retrieval via approximate nearest neighbor search (ANNS). However, these models struggle with compositional queries and out-of-distribution (OOD) image-text pairs. Inspired by human cognition's ability to learn from minimal examples, we address this performance gap through few-shot learning approaches specifically designed for image retrieval. We introduce the Few-Shot Text-to-Image Retrieval (FSIR) task and its accompanying benchmark dataset, FSIR-BD - the first to explicitly target image retrieval by text accompanied by reference examples, focusing on the challenging compositional and OOD queries. The compositional part is divided to urban scenes and nature species, both in specific situations or with distinctive features. FSIR-BD contains 38,353 images and 303 queries, with 82% comprising the test corpus (averaging per query 37 positives, ground truth matches, and significant number of hard negatives) and 18% forming the few-shot reference corpus (FSR) of exemplar positive and hard negative images. Additionally, we propose two novel retrieval optimization methods leveraging single shot or few shot reference examples in the FSR to improve performance. Both methods are compatible with any pre-trained image encoder, making them applicable to existing large-scale environments. Our experiments demonstrate that: (1) FSIR-BD provides a challenging benchmark for image retrieval; and (2) our optimization methods outperform existing baselines as measured by mean Average Precision (mAP). Further research into FSIR optimization methods will help narrow the gap between machine and human-level understanding, particularly for compositional reasoning from limited examples.