# Neuro-Symbolic Spatial Reasoning in Segmentation

arXiv: https://arxiv.org/abs/2510.15841 · HTML: https://mlsanity.com/paper/2510.15841/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 53 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 6 of 6)

- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Diffuse, Attend, and Segment: Unsupervised Zero-Shot Segmentation using Stable Diffusion](https://mlsanity.com/paper/2308.12469/) (2023)
- [The All-Seeing Project: Towards Panoptic Visual Recognition and Understanding of the Open World](https://mlsanity.com/paper/2308.01907/) (2023)
- [Diffusion Models for Open-Vocabulary Segmentation](https://mlsanity.com/paper/2306.09316/) (2023)

## Abstract (arXiv)

Open-Vocabulary Semantic Segmentation (OVSS) assigns pixel-level labels from an open set of categories, requiring generalization to unseen and unlabelled objects. Using vision-language models (VLMs) to correlate local image patches with potential unseen object categories suffers from a lack of understanding of spatial relations of objects in a scene. To solve this problem, we introduce neuro-symbolic (NeSy) spatial reasoning in OVSS. In contrast to contemporary VLM correlation-based approaches, we propose Relational Segmentor (RelateSeg) to impose explicit spatial relational constraints by first order logic (FOL) formulated in a neural network architecture. This is the first attempt to explore NeSy spatial reasoning in OVSS. Specifically, RelateSeg automatically extracts spatial relations, e.g., <cat, to-right-of, person>, and encodes them as first-order logic formulas using our proposed pseudo categories. Each pixel learns to predict both a semantic category (e.g., "cat") and a spatial pseudo category (e.g., "right of person") simultaneously, enforcing relational constraints (e.g., a "cat" pixel must lie to the right of a "person"). Finally, these logic constraints are formulated in a deep network architecture by fuzzy logic relaxation, enabling end-to-end learning of spatial-relationally consistent segmentation. RelateSeg achieves state-of-the-art performance in terms of average mIoU across four benchmark datasets and particularly shows clear advantages on images containing multiple categories, with the cost of only introducing a single auxiliary loss function and no additional parameters, validating the effectiveness of NeSy spatial reasoning in OVSS.