Model longer dependencies with robust lipschitz state space networks
LipSSM: Structurally Lipschitz-Bounded Cascaded State-Space Model via Metric Transfer between Consecutive SSM Layers
Machine Learning
Summary
Ensuring a neural network is robust often involves controlling a property called the Lipschitz constant, but doing this one layer at a time can make the network overly simple and less effective. The authors extend a new idea that shares this control information across network layers to a special kind of model called a cascaded state-space model, which helps capture long-term patterns. Their approach, called LipSSM, provides stronger guarantees about robustness while preserving the ability to learn complex sequences. They support their method with mathematical reasoning and practical tests.
What this means in practice
- •For signal processing engineers: Build sequence models that maintain robustness guarantees while capturing long-term data patterns more effectively.
- •For control systems developers: Design control algorithms with strong theoretical robustness using cascaded state-space models bounded by tighter Lipschitz constants.
Authors
Natsuki Yoshino, Ren Uchida, Kazuki Matsumoto, Kohei Yatabe
Abstract
Lipschitz continuity is a fundamental principle in the design of certifiably robust deep neural networks (DNNs), wherein adjusting the Lipschitz constant, which quantifies network robustness, is of central theoretical importance. A standard approach to enforcing Lipschitz continuity requires each layer of a DNN to be Lipschitz continuous, thereby guaranteeing overall Lipschitz continuity. However, this layer-wise approach typically imposes overly conservative restrictions by producing a loose estimate of the overall Lipschitz constant, which limits the expressive capacity of the DNN and degrades empirical performance at a prescribed level of robustness. To overcome this loose estimation, the recently proposed LipKernel transfers information across layers to yield a much tighter overall Lipschitz bound than conventional layer-wise construction. In this paper, we extend this concept to cascaded state-space models (SSMs) to construct Lipschitz-continuous DNNs capable of modeling longer-term dependencies. The proposed architecture, named LipSSM, is theoretically justified and empirically evaluated.