Problem
Research questions and friction points this paper is trying to address.
Lipschitz continuity
certifiable robustness
state-space models
Lipschitz constant estimation
deep neural networks
LipSSM: Structurally Lipschitz-Bounded Cascaded State-Space Model via Metric Transfer between Consecutive SSM Layers
🤖 AI Summary
This study addresses the limitations of conventional layer-wise Lipschitz constraints, which yield overly loose bound estimates and restrict the expressivity and robustness of neural networks. To overcome this, we introduce the LipKernel concept into cascaded state space models (SSMs) for the first time, constructing Lipschitz-continuous deep neural networks with rigorous theoretical guarantees via cross-layer metric propagation. By leveraging a structured Lipschitz bound theorem to facilitate inter-layer information transfer, our approach yields a substantially tighter global Lipschitz bound while effectively modeling long-range dependencies. Consequently, this work transcends conservative constraints without compromising strict robustness assurances, significantly enhancing both model expressivity and empirical performance. The proposed method is theoretically sound and practically effective.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Lipschitz continuity
State-Space Model
Metric Transfer
Certified robustness
Cascaded architecture
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