Technical Summary: Activation Steering of Video Generation Models via Reduced-Order Linear Optimal Control

Problem Statement

Text-to-video (T2V) models trained on large-scale web data often inherit undesired concepts, including nudity, graphic violence, copyrighted material, and depictions of public figures. These safety risks necessitate interventions that constrain outputs without sacrificing visual quality or prompt fidelity. Existing mitigation strategies face significant limitations:

• Finetuning requires extensive training resources.
• Model editing (weight modification) can degrade output quality and induce unpredictable behavior.
• Prompt filtering is vulnerable to jailbreaks and indirect prompts.
• Existing activation steering methods are typically non-anticipative, applying fixed or myopic interventions that fail to account for how perturbations propagate through the model. This often leads to over-steering, content degradation, or sensitivity to adversarial prompts.

Furthermore, applying optimal control directly to the high-dimensional activation spaces of T2V models (which can exceed 80 million dimensions) is computationally intractable, requiring petabytes of memory for full-space Jacobian matrices.

Methodology: LA-LQR

The authors propose Latent Activation Linear-Quadratic Regulator (LA-LQR), a reduced-order optimal control framework designed for minimally invasive T2V steering. The method formalizes T2V inference as a dynamical system and computes closed-loop feedback interventions.

1. Formalizing T2V as a Dynamical System

The T2V generation process (based on Diffusion Transformers, or DiTs) is recast as a finite-horizon dynamical system where internal activations serve as states. The system evolves over diffusion timesteps $t \in [T]$ and transformer layers $l \in [L]$. The state transition is governed by the model's weights and architecture, with steering signals acting as control inputs ($u_s$) applied to video-token activations or text-embeddings.

2. Reduced-Order Latent Space Construction

To make control feasible, LA-LQR projects high-dimensional raw activations ($x \in \mathbb{R}^{D_{act}}$) onto a low-dimensional, task-relevant latent subspace ($z \in \mathbb{R}^{D_{lat}}$), where $D_{lat} \ll D_{act}$.

• Contrastive Basis: The subspace is derived from contrastive prompt pairs ($D^+$ containing the target feature, $D^-$ without it).
• Randomized SVD: The authors use streaming randomized Singular Value Decomposition (SVD) on the difference vectors of these prompt pairs to identify dominant feature directions without materializing massive Jacobian matrices.
• Projection: Activations are projected onto this basis ($P_s$), and local linear dynamics are estimated in this latent space using Jacobian-vector products (JVP).

3. Latent Linear Feature Setpoints (LLFS)

Within the latent space, the method defines a Latent Linear Feature Setpoint (LLFS) representing the desired feature strength.

• A feature direction $v^z_s$ is computed by averaging projected contrastive vectors.
• A target strength $\beta^*_s$ is set via a hyperparameter $\lambda$.
• The tracking error $\alpha_s$ is calculated as the difference between the target strength and the current projected feature strength.

4. Optimal Control via LQR

LA-LQR solves a Linear-Quadratic Regulator (LQR) problem in the latent space to determine the optimal control signal $u^*_s$.

• Objective: Minimize a cost function that penalizes deviations from the desired feature setpoint while simultaneously penalizing unnecessary perturbations (control effort).
• Closed-Loop Feedback: Unlike open-loop methods, LA-LQR computes a feedback gain $K_s$ via Riccati recursions. The intervention is $u^*_s = \bar{u}_s - K_s \delta z_s$, where $\delta z_s$ is the deviation from the nominal trajectory.
• Adaptivity: The controller adapts online to the realized latent activation at each timestep and layer, anticipating natural activation evolution and intervening only when necessary to reach the setpoint.

5. Theoretical Guarantees

The paper provides theoretical bounds relating the latent setpoint tracking to raw activation-space feature control. It demonstrates that if the projection retains the dominant feature energy (quantified by $\rho_s$) and the projected dynamics are locally linear, the raw-space feature tracking error is bounded by the latent tracking error, projection loss, and linearization residuals.

Key Contributions

1. Formalization: The authors formalize T2V generation as a finite-horizon dynamical system and propose a linear optimal control framework for inference-time steering, deriving minimally invasive online feedback interventions.
2. Tractability: They introduce a reduced-order latent space construction using contrastive vectors, making optimal control feasible for T2V models by avoiding full activation-space Jacobians.
3. Theoretical Justification: The paper quantifies feature information loss during projection and validates the local linearity of the latent space, providing bounds on the performance of the reduced-order controller.
4. Empirical Validation: Extensive evaluation on concept steering and video safety benchmarks demonstrates that LA-LQR reduces unsafe generations while preserving prompt fidelity and visual quality, outperforming existing T2V steering and safety baselines.

Results

The method was evaluated on two state-of-the-art T2V models: Wan2.1-T2V-14B and HunyuanVideo-1.5, using benchmarks T2VSafetyBench and SafeSora.

• Safety Performance: LA-LQR achieved the lowest violation rates across categories (e.g., Pornography, Gore, Public Figures, Copyright) compared to baselines like SAFREE [10], weight unlearning [9], and LLM-assisted steering [69]. For instance, on Wan2.1, the average violation rate dropped from ~36.9% (baseline) to 14.6% with LA-LQR.
• Quality Preservation: The method maintained high Subject Consistency scores (VBench), often matching or exceeding baselines (e.g., 0.971 vs 0.964 average for Wan2.1), indicating that safety interventions did not degrade visual coherence.
• Concept Steering: Qualitative results showed effective steering of concepts (e.g., changing "red" to prominent in a scene) with increasing control strength, demonstrating precise feature modulation.
• Comparison: Unlike baselines that either fail on jailbroken prompts (filtering) or introduce severe artifacts when tuned aggressively (weight editing), LA-LQR successfully balanced safety and quality through minimal-norm perturbations.

Significance and Claims

The paper claims that LA-LQR represents a significant step forward in mechanistic interpretability and safety alignment for generative video models. By treating inference as a control problem and utilizing reduced-order optimal control, the method achieves:

• Reliability: It provides a training-free, inference-time solution that is robust against adversarial prompts where input-level filtering fails.
• Precision: It enables minimally invasive interventions, avoiding the "over-steering" and visual degradation common in previous activation steering approaches.
• Scalability: It solves the computational intractability of controlling high-dimensional video activations by leveraging low-dimensional latent dynamics derived from contrastive learning.

The authors position LA-LQR as a promising direction for reliable, training-free alignment of T2V models, suggesting that control-theoretic activation steering can effectively constrain harmful outputs while preserving the utility and quality of generative models. They explicitly note that the method should be paired with prompt filtering or output moderation, as it assumes white-box access and does not guarantee safety against all possible adversarial inputs.