# Reward-Informed Sparse Autoencoders and the Solution-Completeness Confound

arXiv: https://arxiv.org/abs/2608.26136 · HTML: https://mlsanity.com/paper/2608.26136/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Steering and interpreting LLM reasoning, one of 13 directions in Mechanistic interpretability.
- Builds on 7 of its 8 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders](https://mlsanity.com/paper/2410.20526/) (2024)
- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)

## Abstract (arXiv)

Sparse autoencoders (SAEs) decompose language-model activations into sparse, interpretable features, and an appealing way to aim them at reasoning is to curate their data with a signal reinforcement learning already produces: the reward. We build such a reward-informed SAE (RI-SAE): we split GRPO trajectories into high-reward ("good") and low-reward ("bad") reasoning continuations, train a standard JumpReLU SAE on their activations, and then ask what the resulting good/bad separation actually measures. On Llama-3.1-8B a sparse subset of the 16,384 features does separate the classes (silhouette 0.79 on the selected features versus 0.005 for the full code), but a control battery shows the separation is largely solution completeness rather than reasoning quality: a TF-IDF text classifier already splits the classes (AUC 0.75--0.83), and three structural cues alone (length, a closed reasoning block, and a boxed answer) reach AUC 0.70 (99% of good versus 69% of bad completions are boxed). A generic SAE that never saw the reward does not separate the classes at all (silhouette 0.01, no discriminative features), so the 0.79 is in-sample fitting of this curated signal rather than structure that a reward-blind dictionary recovers. We therefore present the recipe and its control battery together: reward filtering is a cheap, label-free way to reuse RL signals for interpretability, but most of what it surfaces is completion form. Two discriminative features are still readable (symbolic mathematics; procedural and evaluative language), which we take as illustrative rather than as isolated reasoning.