Topological Steering

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.

Activation-based control steers large language models (LLMs) by intervening on their internal representations during inference, and has emerged as an effective paradigm for controlling behaviors such as persona and style. However, existing methods often rely on fixed steering directions or task-specific intervention modules, making them difficult to adapt to fine-grained concepts and compositional constraints. We propose UniSteer, a text-guided activation flow matching model that learns a conditional distribution over residual-stream activations from natural-language conditions. Instead of fitting a separate intervention for each target behavior, UniSteer learns a universal conditional velocity field in activation space. At inference time, UniSteer performs flow inversion by partially transporting a source activation toward a latent state and regenerating it under a target textual condition before injecting it back into the frozen LLM. The same conditional model supports activation-space classification by selecting the textual label with the lowest reconstruction energy. Experiments on three target LLMs show that UniSteer provides a unified interface across behavioral control, truthfulness steering, fine-grained concept steering, multi-constraint instruction following, and activation-space classification.

Controlling the behavior of large language models (LLMs) remains a critical challenge for AI alignment. Existing steering methods, such as Contrastive Activation Addition (CAA), typically rely on fixed single-layer interventions derived from aggregate activation differences. These methods impose a single intervention across semantically diverse inputs and often fail to sustain consistent behavioral changes across layers, limiting the effectiveness of the steering. In this work, we introduce CircuitSteer, a novel framework that leverages Sparse Autoencoders (SAEs) to identify and manipulate coherent semantic circuits distributed across multiple layers. By constructing a feature flow circuit based on feature co-activation and the geometric alignment of decoder directions, we isolate the specific multi-layer subcircuits responsible for a target behavior. We then synthesize dense steering vectors from these sparse features and apply multi-point interventions to guide the model's internal semantic trajectory. We evaluate CircuitSteer using contrastive examples across a diverse set of tasks, including toxicity, emotion-intensity, sycophancy, and refusal, spanning two model families. Across all models and datasets, CircuitSteer is the only method to consistently produce fluency-preserving interventions; competing methods either sacrifice text quality or lack coverage, failing entirely on complex behaviors like sycophancy and refusal. These results demonstrate that multi-layer circuit steering, enabled by enforcing geometric alignment among selected features, yields strictly more robust and effective behavioral control than static single-point interventions. Code is available at https://github.com/mehrshad-sdtn/CircuitSteer.