Position Paper: LLMs Have a Hard Ceiling on Spatial and Positional Reasoning

The paper's central claim is direct: LLMs cannot reliably perform reasoning tasks that require non-local jumps through a sequence. The title is a deliberate reference to spatial movement — the kind of step-skipping logic that humans handle with mental models but that autoregressive token prediction does not naturally support.

The argument is architectural, not empirical. Next-token prediction optimizes for local coherence. Tasks that require holding a position in a structure, jumping to a non-adjacent element, or reversing traversal direction expose a gap that more parameters and longer context windows do not close. Scaling does not fix a structural mismatch.

For engineers building on top of LLMs, the implication is concrete. Workflows that treat an LLM as a general reasoning engine — particularly for grid traversal, spatial layout interpretation, index manipulation, or any task with a non-linear reference structure — are likely hitting this ceiling without knowing it. Failures tend to look like hallucination when the actual cause is the model's inability to jump positions in a structured space.

The position also pushes back on benchmark framing. Many standard evaluations test sequential reasoning, where LLMs perform well. The failure mode surfaces in tasks deliberately designed to require positional non-locality — benchmarks that current standard suites underrepresent.

Practical mitigation exists: externalize the positional state. Tools, retrieval layers, and scaffolding that track position explicitly and hand it back to the model reduce the demand on the LLM itself. The model handles language; the scaffolding handles the index. This is not a workaround — it is the correct architectural division.

The paper is a position submission, not an empirical study with novel benchmarks. Its value is in naming the limitation cleanly and directing attention toward the structural cause rather than treating spatial reasoning failures as fixable through prompting or fine-tuning alone.

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