# Encoded but Not Actionable: Auditing the Decode-Generate-Steer Gap in Frozen LLMs for Geometric Constraints

arXiv: https://arxiv.org/abs/2608.17843 · HTML: https://mlsanity.com/paper/2608.17843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 21 of 21)

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- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
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- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [Information-Theoretic Probing for Linguistic Structure](https://mlsanity.com/paper/2004.03061/) (2020)
- [Probing the Probing Paradigm: Does Probing Accuracy Entail Task Relevance?](https://mlsanity.com/paper/2005.00719/) (2020)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [CAD-Llama: Leveraging Large Language Models for Computer-Aided Design Parametric 3D Model Generation](https://mlsanity.com/paper/2505.04481/) (2025)
- [Vitruvion: A Generative Model of Parametric CAD Sketches](https://mlsanity.com/paper/2109.14124/) (2021)
- [Conditional probing: measuring usable information beyond a baseline](https://mlsanity.com/paper/2109.09234/) (2021)
- [No Training Required: Exploring Random Encoders for Sentence Classification](https://mlsanity.com/paper/1901.10444/) (2019)
- [FirePlace: Geometric Refinements of LLM Common Sense Reasoning for 3D Object Placement](https://mlsanity.com/paper/2503.04919/) (2025)
- [CADmium: Fine-Tuning Code Language Models for Text-Driven Sequential CAD Design](https://mlsanity.com/paper/2507.09792/) (2025)
- [Embodied CAD: Solver-Grounded LLM Agents for Parametric B-Rep Assembly Modeling](https://mlsanity.com/paper/2606.31252/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated strong performance on structured reasoning tasks, but what they encode and whether it informs model behavior remain unclear. We investigate this question through geometric reasoning, using parametric CAD constraints as a controlled testbed for separating local pairwise relations from sketch-level constraint status. By probing the hidden states of six frozen decoder-only LLMs, we examine four properties: linear decodability, forced-choice generation, activation-level influence, and behavioral steerability. Pretraining substantially improves the decoding of local geometric relations, and this advantage persists after accounting for positional cues with shuffled-order controls. In contrast, sketch-level DOF status is already highly decodable from randomly initialized representations and improves only modestly with pretraining, indicating that much of its probe performance is available without learned weights. Further analyses show that decodable information is not always actionable. Generation often fails to express this information, and on the two intervention-tested backbones, activation-restoration effects at the patched entity position vanish while decodability persists across depth. Mean-difference steering also does not reliably control outputs. These results show that decodability, generation, activation-level influence, and steerability can diverge in the tested setting. The audit provides a controlled way to distinguish failures to encode geometric structure from failures to express or control encoded information.