Excited to share that our paper, TopoBench: Benchmarking LLMs on Hard Topological Reasoning, has been accepted at the #ICLR2026 Workshop on Logical Reasoning of Large Language Models. Nils Hoehing will be presenting it at the workshop. Many real-world tasks require maintaining global spatial constraints through a sequence of local updates: for example in circuit layout, route planning, and molecular structure analysis. We introduce TopoBench, a benchmark for topological reasoning across 6 puzzle families and 3 difficulty levels, designed to study how well LLMs handle global spatial constraints such as connectivity, loop closure, symmetry, and visibility. Our main finding is that even frontier reasoning models solve fewer than 25% of hard instances, and two puzzle families are nearly unsolved. So hard topological reasoning still appears to be a real challenge, even for very strong models. To understand why, we annotated 750 chain-of-thought traces and built an error taxonomy. The main breakdowns looked less like a failure of abstract reasoning alone, and more like failures to extract, maintain, and update the right spatial constraints while solving the puzzle. We also tested mitigation strategies, including cell-aligned representations and tool-based structured constraint checking. These help, but they point to the same conclusion: the main bottleneck seems to lie less in reasoning over constraints once available, and more in reliably deriving them from spatial representations in the first place. Paper: arxiv.org/abs/2603.12133 Website: topobench.github.io Happy to hear others’ thoughts and discuss :) Work with @nilshoehing , @JanakKapuriya , @ArjunK018 , Ellen Rushe, Anthony Ventresque, @oconnorn , and @fergal_reid . We also want to thank Intercom Research @intercom for supporting this work. #ICLR2026