New BiLipREN model makes nonlinear dynamics robustly invertible for control and generation
A recurrent neural network that guarantees both forward prediction and input reconstruction with stability
A new paper on arXiv introduces BiLipREN (bi-Lipschitz recurrent equilibrium network), a neural network architecture designed for robustly invertible nonlinear dynamics. The researchers — Yurui Zhang, Ruigang Wang, and Ian R. Manchester — define robust invertibility as the existence of a causal inverse system where both forward and inverse models are contracting and have bounded incremental input-output gains (bi-Lipschitz). This means the system can reliably predict future states from inputs and reconstruct inputs from outputs, even under signal perturbations or initial-state mismatch.
BiLipREN is constructed via series composition of static orthogonal layers and dynamic layers with strong input-output monotonicity. It also supports nonlinear minimum-phase/all-pass factorization through dynamic orthogonal layers. The team demonstrates its utility in three key applications: data-driven internal model control (robust control), dynamic surrogate loss learning (trajectory optimization), and signal-space normalizing flows (generative modeling of complex trajectories). This work bridges control theory and generative AI, offering a principled way to build invertible dynamical models with guaranteed stability.
- Defines robust invertibility as bi-Lipschitz condition on forward and inverse dynamics, ensuring stability under noise.
- BiLipREN uses static orthogonal layers + monotonic dynamic layers to guarantee invertibility by design.
- Demonstrates applications in robust control, trajectory optimization, and generative trajectory modeling via normalizing flows.
Why It Matters
Enables AI systems to both predict and reconstruct trajectories with stability guarantees, unlocking safer control and generative models.