# Grounding latent algorithm routing in transformer reasoning

arXiv: https://arxiv.org/abs/2607.24471 · HTML: https://mlsanity.com/paper/2607.24471/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 36 of its 41 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 36)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [State of What Art? A Call for Multi-Prompt LLM Evaluation](https://mlsanity.com/paper/2401.00595/) (2023)
- [Data Distributional Properties Drive Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2205.05055/) (2022)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [General-Purpose In-Context Learning by Meta-Learning Transformers](https://mlsanity.com/paper/2212.04458/) (2022)
- [Uncovering mesa-optimization algorithms in Transformers](https://mlsanity.com/paper/2309.05858/) (2023)
- [What needs to go right for an induction head? A mechanistic study of in-context learning circuits and their formation](https://mlsanity.com/paper/2404.07129/) (2024)
- [Understanding Reasoning in Thinking Language Models via Steering Vectors](https://mlsanity.com/paper/2506.18167/) (2025)
- [Understanding In-Context Learning in Transformers and LLMs by Learning to Learn Discrete Functions](https://mlsanity.com/paper/2310.03016/) (2023)
- [POSIX: A Prompt Sensitivity Index For Large Language Models](https://mlsanity.com/paper/2410.02185/) (2024)
- [How to think step-by-step: A mechanistic understanding of chain-of-thought reasoning](https://mlsanity.com/paper/2402.18312/) (2024)
- [A Mechanistic Analysis of a Transformer Trained on a Symbolic Multi-Step Reasoning Task](https://mlsanity.com/paper/2402.11917/) (2024)
- [Can Language Models Perform Robust Reasoning in Chain-of-thought Prompting with Noisy Rationales?](https://mlsanity.com/paper/2410.23856/) (2024)

## Abstract (arXiv)

A central question in the in-context learning literature is whether transformers can organize episode-level adaptation around different inductive-bias families. We study this question in a controlled setting through latent algorithm routing: route-like behavior in which the solver-family preference changes with the latent data-generating regime while prompt form is held fixed, remains stable under nuisance perturbations, and is selectively influenced by targeted activation interventions without large losses in answer quality. We introduce ROUTEBENCH, a diagnostic benchmark whose regimes differentially favor global shrinkage, sparsity, robustness, and locality, operationalized by ridge-like, lasso-like, Huber-like, and kNN-like family representatives. Across dense decoder-only transformers trained from scratch at 44M-612M parameters, a 306M model closes 80.9 percent of the oracle-routing gap and achieves route F1 of 84.1. The effect remains substantial under natural-language renderings, shuffled supports, lexical paraphrases, and a unified four-way routing setting. Stronger adaptive alternatives, including an input-conditioned soft mixture and an unsupervised Gumbel router, narrow the gap but remain below the 306M and 612M models on route F1 and OOD performance. Probe controls and matched activation-patching controls further show that route-relevant internal directions are decodable and functionally involved in solver-family-consistent output behavior. These results provide controlled evidence that dense transformers trained on ROUTEBENCH can develop route-like internal variables, but they do not establish universal routing in pretrained language models or unrestricted natural-language reasoning.