The paper introduces AlgoTrace, a framework that traces and steers algorithmic operations in large language models’ latent space during multi‑step reasoning. By clustering latent activations on tasks such as TSP, 3SAT, AIME, and Graph Navigation, the authors identify reusable primitive vectors that can be injected to elicit specific algorithmic behaviors, composed algebraically, and transferred across models and tasks. Fine‑tuning further improves the composition of these primitives, suggesting that LLM reasoning can be viewed as a walk through algorithmic primitives governed by compositional geometry.
By Samuel Lippl, Thomas McGee, Kimberly Lopez, Ziwen Pan, Pierce Zhang, Salma Ziadi, Oliver Eberle, Ida Momennejad
arXiv:2605. 16385v3 Announce Type: replace-cross Abstract: Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial diagrams and complex reasoning.
By Ruoran Xu, Haoyu Cheng, Bin Dong, Qiufeng Wang
arXiv:2603. 04852v2 Announce Type: replace Abstract: Multi-step theorem prediction is a central challenge in geometry problem solving.
By Junbo Zhao, Ting Zhang, Can Li, Wei He, Jingdong Wang, Hua Huang
arXiv:2606. 04381v1 Announce Type: cross Abstract: Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space.
By Chen Chu, Bita Azarijoo, Li Xiong, Khurram Shafique, Cyrus Shahabi
arXiv:2606. 27967v1 Announce Type: new Abstract: Real-world knowledge graphs are often incomplete, lacking many valid facts.
By Yike Liu, Peijia Xie, Chao He, Huiling Zhu
arXiv:2607. 13454v1 Announce Type: cross Abstract: Although multimodal large language models (MLLMs) have achieved remarkable progress, understanding 3D spatial relationships from 2D images remains a critical challenge.
By Hao Li, Han Fang, Zixin Pan, Xin Wei, Hongbo Sun, Jinglin Xu, Zhiyu Lin, Ye Yuan, Zhongjiang He, Yu Yu, Hao Sun
arXiv:2606. 15656v1 Announce Type: new Abstract: Modern artificial intelligence remains fundamentally divided between the continuous, probabilistic spaces of Foundation Models and the discrete, deterministic structures of Knowledge Graphs.
By Sahil Rajesh Dhayalkar
Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators.
arXiv:2606. 11946v1 Announce Type: cross Abstract: The conventional approach to deep learning over relational databases applies neural models, such as Graph Neural Networks (GNNs), to a graph representation of the database.
By Arie Soeteman, Balder ten Cate, Maurice Funk, Benny Kimelfeld, Carsten Lutz, Moritz Sch\"onherr
The paper introduces TTL‑SR, a geometry‑aware Test‑Time Learning framework designed to improve quantitative spatial reasoning in visual‑language models. By augmenting queries with geometrically coupled auxiliary prompts, filtering unreliable predictions, and updating models with a geometry‑aware multi‑objective loss on unlabeled test data, TTL‑SR adapts models to new domains without additional 3D supervision. Experiments show substantial accuracy gains on the Q‑Spatial‑ScanNet dataset for two state‑of‑the‑art VLMs.
By Gege Zhang, Shuaicheng Niu, Gang Dai, Lei Sun, Shuangping Huang
Although multimodal large language models (MLLMs) have achieved remarkable progress, understanding 3D spatial relationships from 2D images remains a critical challenge. Existing methods primarily rely on symbolic text tokens, which inherently lack the fidelity to represent continuous geometric information.
GeoLatent introduces a geometry‑guided latent structuring approach for 3D reasoning from 2D images, separating position, direction, and global geometry under geometric supervision. It combines Common–Residual Geometry Alignment (CR‑GEO) with routed optimization to prevent latent collapse and to direct visual answer learning through the latents while maintaining full attention. The method achieves state‑of‑the‑art performance on SPAR‑Bench and SPBench, improving geometry effective rank and overall accuracy.
By Yakun Zhu, Yi Bin, Yujuan Ding, Zheng Wang, Pengpeng Zeng, Duo Peng, Jingkuan Song, Heng Tao Shen