Training-free guidance that stops generated trajectories from hugging the constraint boundary
AspireAI community · arXiv
Steering diffusion and flow-matching models to satisfy strict constraints, such as preserving identity in image editing or avoiding obstacles in robotics, usually relies on min-norm controllers that only account for immediate constraint satisfaction, so trajectories end up hovering near the boundary and the model loses room to optimise toward its target. AegisFlow recasts guided generation as a safety-critical optimal control problem with global scope, folding a time-varying barrier function into the global cost functional so constraints hold along the entire generative path, and derives a tractable approximation of the Hamilton-Jacobi-Bellman equation to compute the global optimal control. The authors report outperforming state-of-the-art methods on text-guided image manipulation and robotic planning with a better trade-off between target alignment and constraint satisfaction. Code is public.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.