# A Calibrated Test of Internal Action Maps: State Signals Without Global Affine Closure

arXiv: https://arxiv.org/abs/2608.13626 · HTML: https://mlsanity.com/paper/2608.13626/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 16 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [Evaluating the World Model Implicit in a Generative Model](https://mlsanity.com/paper/2406.03689/) (2024)
- [Simulating Action Dynamics with Neural Process Networks](https://mlsanity.com/paper/1711.05313/) (2017)
- [Language Models use Lookbacks to Track Beliefs](https://mlsanity.com/paper/2505.14685/) (2025)
- [(How) Do Language Models Track State?](https://mlsanity.com/paper/2503.02854/) (2025)
- [How Do Language Models Compose Functions?](https://mlsanity.com/paper/2510.01685/) (2025)
- [AlgoTrace: Algorithmic Primitives and Compositional Geometry of Reasoning in Language Models](https://mlsanity.com/paper/2510.15987/) (2025)
- [A Held-Out Transition-Pair Falsifier for Long-Horizon Non-Abelian State Tracking](https://mlsanity.com/paper/2606.07254/) (2026)
- [Representational Homomorphism Predicts and Improves Compositional Generalization In Transformer Language Model](https://mlsanity.com/paper/2601.18858/) (2026)

## Abstract (arXiv)

A hidden state signal can be decodable or causally usable without supporting a reusable action map. We test whether action maps fitted without a source reach its natural post-action activation and compose. We organize the tests as an evidence lattice and validate the geometric branch on a known affine S_5 carrier: all held-source folds pass one-step, composition, inverse, decoding, and commutativity gates. Structured curvature and held-domain conjugacy raise error monotonically, but only 23/30 strongest cells flip a closure gate, bounding rather than universalizing calibration. In post-trained Qwen/Qwen3-4B, frozen final-token h28 affine maps have mean held-entity error .519, versus .398 for within-test-domain cross-fit. Seven randomized entity splits and map geometry do not support a purely entity-specific account. Earlier h4/h16 layers fit one-step transitions better, but h4 conflict-state decoding is weak and lexical controls remain unresolved. Three matched intervention datasets regenerated from one frozen checkpoint show causal effects only at h28/h36. Outcome-aware refitting improves h28 one-step error to .474 (.469 with weighting), yet no refit passes composition. Learned finite worlds likewise preserve relative algebraic signals or shared charts without held-source affine closure. Within the tested carriers, state availability, causal use, local geometry, and reusable closure are separable. The result is limited to one pretrained model, sampled final-token layers, two finite worlds, and the tested affine or diagnostic function classes.