NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equations

TL;DR

NAIS-Net introduces a deep, stable neural network architecture based on non-autonomous differential equations, ensuring stability and improved generalization through adaptive unrolling and skip connections.

Contribution

The paper presents NAIS-Net, a novel deep network architecture derived from non-autonomous dynamical systems with proven stability and practical implementation strategies.

Findings

NAIS-Net achieves stability in deep architectures.

The network reduces the generalization gap compared to ResNets.

Experimental results confirm practical stability and effectiveness.

Abstract

This paper introduces Non-Autonomous Input-Output Stable Network(NAIS-Net), a very deep architecture where each stacked processing block is derived from a time-invariant non-autonomous dynamical system. Non-autonomy is implemented by skip connections from the block input to each of the unrolled processing stages and allows stability to be enforced so that blocks can be unrolled adaptively to a pattern-dependent processing depth. NAIS-Net induces non-trivial, Lipschitz input-output maps, even for an infinite unroll length. We prove that the network is globally asymptotically stable so that for every initial condition there is exactly one input-dependent equilibrium assuming $tanh$ units, and incrementally stable for ReL units. An efficient implementation that enforces the stability under derived conditions for both fully-connected and convolutional layers is also presented. Experimental results show how NAIS-Net exhibits stability in practice, yielding a significant reduction in generalization gap compared to ResNets.