Towards Scalable and Stable Parallelization of Nonlinear RNNs

2024-07-26

arXiv.org

AI Summary

Nonlinear RNNs suffer from inherent sequential dependencies, hindering efficient hardware parallelization and leading to high computational complexity and numerical instability. To address these challenges, this paper proposes a novel parallel evaluation framework. Methodologically, it (1) employs quasi-Newton approximations to reduce Hessian computation overhead; (2) establishes an equivalence between the Levenberg–Marquardt algorithm and Kalman smoothing (ELK), substantially improving optimization stability; and (3) unifies fixed-point modeling, parallel Newton methods, and parallel Kalman smoothing to enable fully scalable, end-to-end parallelization. Experiments demonstrate that the approach achieves efficient convergence, low memory footprint, and strong robustness—even at large state dimensions—thereby overcoming the dual limitations of existing methods (e.g., DEER) in both computational cost and numerical stability.

Technology Category

• Natural Language Processing: Learning & Optimization for NLP
• Machine Learning: Optimization
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Transformers and linear state space models can be evaluated in parallel on modern hardware, but evaluating nonlinear RNNs appears to be an inherently sequential problem. Recently, however, Lim et al. '24 developed an approach called DEER, which evaluates nonlinear RNNs in parallel by posing the states as the solution to a fixed-point problem. They derived a parallel form of Newton's method to solve the fixed-point problem and achieved significant speedups over sequential evaluation. However, the computational complexity of DEER is cubic in the state size, and the algorithm can suffer from numerical instability. We address these limitations with two novel contributions. To reduce the computational complexity, we apply quasi-Newton approximations and show they converge comparably to Newton, use less memory, and are faster. To stabilize DEER, we leverage a connection between the Levenberg-Marquardt algorithm and Kalman smoothing, which we call ELK. This connection allows us to stabilize Newton's method while using efficient parallelized Kalman smoothing algorithms to retain performance. Through several experiments, we show that these innovations allow for parallel evaluation of nonlinear RNNs at larger scales and with greater stability.

Problem

• Nonlinear Recurrent Neural Networks
• Computational Efficiency
• Stability

Innovation

• Newton-inspired computation strategy
• ELK algorithm
• Nonlinear RNN optimization