# Sparse Readout Prism: Explaining Logit-Lens Scores in Features Instead of Tokens

arXiv: https://arxiv.org/abs/2609.01936 · HTML: https://mlsanity.com/paper/2609.01936/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 80 references that are in the map.
- First posted on arXiv 1 Sep 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [LegalBench: A Collaboratively Built Benchmark for Measuring Legal Reasoning in Large Language Models](https://mlsanity.com/paper/2308.11462/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Breaking the Softmax Bottleneck: A High-Rank RNN Language Model](https://mlsanity.com/paper/1711.03953/) (2017)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [Ministral 3](https://mlsanity.com/paper/2601.08584/) (2026)
- [Sparse Autoencoders Trained on the Same Data Learn Different Features](https://mlsanity.com/paper/2501.16615/) (2025)
- [Tying Word Vectors and Word Classifiers: A Loss Framework for Language Modeling](https://mlsanity.com/paper/1611.01462/) (2016)
- [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [Do Multilingual LLMs Think In English?](https://mlsanity.com/paper/2502.15603/) (2025)
- [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (2025)
- [LLM Unlearning via Neural Activation Redirection](https://mlsanity.com/paper/2502.07218/) (2025)
- [Overcoming Sparsity Artifacts in Crosscoders to Interpret Chat-Tuning](https://mlsanity.com/paper/2504.02922/) (2025)
- [Interpretability in Parameter Space: Minimizing Mechanistic Description Length with Attribution-based Parameter Decomposition](https://mlsanity.com/paper/2501.14926/) (2025)
- [Disentangling Dense Embeddings with Sparse Autoencoders](https://mlsanity.com/paper/2408.00657/) (2024)

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

- [From Latent Space to Jacobian Space: Measuring, Evading, and Training Against Safety-Content Accessibility](https://mlsanity.com/paper/2610.04316/) (2026)

## Abstract (arXiv)

A language model's prediction of its next token develops across layers, and lens methods track this process by decoding intermediate hidden states into tokens. But a lens reading reflects both the hidden state and the readout (the unembedding matrix) used to decode it. Many lenses are fit on a corpus, and we show that two lenses differing only in their fitting corpus can report different tokens for the same hidden states. We call this dependence corpus conditionality. To examine readout structure independently of the fitting corpus, we introduce Sparse Readout Prism (SRP), which decomposes the readout using only its weights and expresses any token logit or logit difference as a sum of contributions from sparse readout features. This reveals readout features as a new unit of analysis for lens readings, exposing structure that token identities can obscure and enabling comparisons across tokens, contexts, layers, and lenses. Replacing the original readout with SRP's sparse approximation reconstructs 8.9-17.3 percentage points more of the tested logit differences than the strongest of six baselines built on geometric relations among readout rows. Ablating features shifts logit differences in proportion to their SRP contributions. Although token readings vary with the fitting corpus, the dominant readout feature remains stable. Because SRP uses no corpus in its construction, it provides a control independent of the fitting corpus for lens analyses.