# Beyond Linear Activation Steering: Invertible Latent Transformations for Controlling LLM Behavior

arXiv: https://arxiv.org/abs/2606.08454 · HTML: https://mlsanity.com/paper/2606.08454/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Activation steering methods, one of 13 directions in Mechanistic interpretability.
- Builds on 27 of its 31 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Placed in

- Mechanistic interpretability / [Activation steering methods](https://mlsanity.com/mechinterp/activation-steering-methods/)

## Builds on (most cited first, 27 of 27)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [ARGS: Alignment as Reward-Guided Search](https://mlsanity.com/paper/2402.01694/) (2024)
- [Adaptive Activation Steering: A Tuning-Free LLM Truthfulness Improvement Method for Diverse Hallucinations Categories](https://mlsanity.com/paper/2406.00034/) (2024)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [Controlling Language and Diffusion Models by Transporting Activations](https://mlsanity.com/paper/2410.23054/) (2024)
- [Aligning Large Language Models with Representation Editing: A Control Perspective](https://mlsanity.com/paper/2406.05954/) (2024)
- [A Unified Understanding and Evaluation of Steering Methods](https://mlsanity.com/paper/2502.02716/) (2025)
- [Householder Pseudo-Rotation: A Novel Approach to Activation Editing in LLMs with Direction-Magnitude Perspective](https://mlsanity.com/paper/2409.10053/) (2024)
- [ODESteer: A Unified ODE-Based Steering Framework for LLM Alignment](https://mlsanity.com/paper/2602.17560/) (2026)
- [Analyzing Finetuning Representation Shift for Multimodal LLMs Steering](https://mlsanity.com/paper/2501.03012/) (2025)
- [Investigating and Mitigating Object Hallucinations in Pretrained Vision-Language (CLIP) Models](https://mlsanity.com/paper/2410.03176/) (2024)
- [ShareChat: A Dataset of Chatbot Conversations in the Wild](https://mlsanity.com/paper/2512.17843/) (2025)
- [TruthFlow: Truthful LLM Generation via Representation Flow Correction](https://mlsanity.com/paper/2502.04556/) (2025)
- [Adapters Mixup: Mixing Parameter-Efficient Adapters to Enhance the Adversarial Robustness of Fine-tuned Pre-trained Text Classifiers](https://mlsanity.com/paper/2401.10111/) (2024)
- [Generalizability of Mixture of Domain-Specific Adapters from the Lens of Signed Weight Directions and its Application to Effective Model Pruning](https://mlsanity.com/paper/2402.10639/) (2024)
- [Unraveling Interwoven Roles of Large Language Models in Authorship Privacy: Obfuscation, Mimicking, and Verification](https://mlsanity.com/paper/2505.14195/) (2025)

## Built on by (most cited first, 3 of 3)

- [ST2U: Stateful Test-Time Unlearning via Restricted Knowledge Boundary Control](https://mlsanity.com/paper/2608.23034/) (2026)
- [Does Steering Break Your Model? A Multi-Dimensional Evaluation Suite for LLM Steering Methods](https://mlsanity.com/paper/2610.07722/) (2026)
- [MetaSteer: Context-Conditioned, nonlinear Steering via Attention-Projection Adaptation](https://mlsanity.com/paper/2609.38718/) (2026)

## Abstract (arXiv)

Activation steering provides a lightweight inference-time mechanism for controlling large language models (LLMs) by modifying their internal activation vectors toward desired behaviors. Most existing methods compute a fixed steering direction in the original activation space, typically from pairs of contrastive examples using mean differences, linear probes, or arbitrary separability criteria. While effective to a certain extent, these methods treat behavioral control as a global, linear, additive offset: the same direction is applied across inputs, and behaviors are linearly separable. This can be restrictive when behavioral features vary nonlinearly across the activation space or lie on curved and anisotropic manifolds, where the optimal intervention may be input-dependent. To address this limitation, we propose INNSteer, a nonlinear activation steering framework based on invertible latent transformations. Rather than searching for a better steering vector in the original representation space, INNSteer learns a lightweight invertible neural network φ that maps an LLM's activations into a latent space where behavioral classes are more amenable to linear control. At inference time, activations are mapped through φ, steered in the latent space, and mapped back through the exact inverse transformation φ-1. This makes a simple latent-space translation become a nonlinear, input-dependent intervention in the original activation space. Across experiment settings on multiple LLM families, scales, behavioral traits, and safety benchmarks, INNSteer consistently improves model control over linear, transport-based, and nonlinear steering baselines while largely preserving generation fluency.