# When and How Long? The Readout-Mediator Angle in Temporal Reasoning

arXiv: https://arxiv.org/abs/2605.29126 · HTML: https://mlsanity.com/paper/2605.29126/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)
- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

## Builds on (most cited first, 9 of 9)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Language Models Use Trigonometry to Do Addition](https://mlsanity.com/paper/2502.00873/) (2025)
- [The Origins of Representation Manifolds in Large Language Models](https://mlsanity.com/paper/2505.18235/) (2025)
- [When Models Manipulate Manifolds: The Geometry of a Counting Task](https://mlsanity.com/paper/2601.04480/) (2026)
- [Dimensional Collapse in Transformer Attention Outputs: A Challenge for Sparse Dictionary Learning](https://mlsanity.com/paper/2508.16929/) (2025)
- [Seed-Induced Uniqueness in Transformer Models: Subspace Alignment Governs Subliminal Transfer](https://mlsanity.com/paper/2511.01023/) (2025)

## Built on by (most cited first, 1 of 1)

- [Decodable In-Context State and Model Output Across Training](https://mlsanity.com/paper/2609.31401/) (2026)

## Abstract (arXiv)

A linear probe can decode a representation almost perfectly and yet be completely irrelevant to how the model uses it. On calendar-date duration reasoning in language models, a sin/cos probe recovers day-of-year from a layer's activations, yet ablating its direction has no effect on the model's answers -- while ablating a four-dimensional subspace found by Distributed Alignment Search (DAS) at the same layer collapses performance entirely. We measure the angle between these two subspaces -- the readout-mediator angle -- and find it indistinguishable from the angle between two random subspaces (the Haar-uniform null), meaning the probe has learned a direction orthogonal to the model's actual computation. Reverse-engineering the circuit reveals why: attention heads route month-grained context through learned QK offsets at ±30 and ±61 days, and MLPs then convert when (absolute date) into how long (duration) -- all downstream of the causal subspace the probe never touches. Sparse-autoencoder decomposition confirms the split: probe-aligned and DAS-aligned features encode semantically disjoint concepts with negligible causal overlap. The dissociation replicates across four scales (1.5-9,B) and two model families, with preliminary evidence on two further domains (spatial displacement, symbolic arithmetic), suggesting that readout-mediator orthogonality is a general failure mode of probe-based interpretability. This directly undermines proposals to deploy probes as runtime safety monitors: the probe can report high confidence on a direction the model has silently abandoned.