mlsanityData to 14 Oct 2026

Activation Transport Operators

arXiv 2508.17540 ↗First posted 24 Aug 2025cs.LG cs.AI cs.CLcited by 0

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Abstract (arXiv)

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 10 of its 14 references that are in the map. First posted on arXiv 24 Aug 2025.

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10 of 14 references.

References · 10

  1. 2023Sparse Autoencoders Find Highly Interpretable Features in Language Modelscited by 1,420
  2. 2023Eliciting Latent Predictions from Transformers with the Tuned Lenscited by 623
  3. 2024Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2cited by 394
  4. 2023Localizing Model Behavior with Path Patchingcited by 195
  5. 2024AtP*: An efficient and scalable method for localizing LLM behaviour to componentscited by 111
  6. 2024Information Flow Routes: Automatically Interpreting Language Models at Scalecited by 95
  7. 2024Controlling Language and Diffusion Models by Transporting Activationscited by 68
  8. 2023Quantifying Context Mixing in Transformerscited by 43
  9. 2024Your Transformer is Secretly Linearcited by 23
  10. 2024Residual Stream Analysis with Multi-Layer SAEscited by 19

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  1. 2026Residual Stream Duality in Modern Transformer Architectures
  2. 2026The Residual Stream Is All You Need: On the Redundancy of the KV Cache in Transformer Inference
  3. 2026How Linear Is a Transformer Feed-Forward Block? Per-Block Linear Recoverability Is Learned, Not Architectural
  4. 2026Transformer Field Theory: A Response-Theoretic Approach to Mechanistic Interpretability
  5. 2024GPT-2 Through the Lens of Vector Symbolic Architectures
  6. 2026ReSAE: Residualized Sparse Autoencoders for Multi-Layer Transformer Interventions
  7. 2026The Communication Map of a Transformer
  8. 2026From Correlation to Cause: A Five-Stage Methodology for Feature Analysis in Transformer Language Models