KOALA++: Efficient Kalman-Based Optimization of Neural Networks with Gradient-Covariance Products

2025-06-04

AI Summary

To address the inefficiency of gradient uncertainty modeling in neural network training—particularly the difficulty of simultaneously achieving structural expressiveness and computational scalability—this paper proposes a scalable Kalman-inspired first-order optimization method. Departing from conventional diagonal covariance assumptions, our approach recursively updates compact gradient covariance products (rather than full covariance matrices), implicitly capturing higher-order correlation structures. By integrating low-rank modeling with a first-order computational paradigm, it avoids matrix inversion and high-dimensional storage overhead. Empirically, on image classification and language modeling benchmarks, our method matches or exceeds the accuracy of state-of-the-art first-order (e.g., Adam) and second-order (e.g., K-FAC) optimizers, while maintaining optimal O(d) time and space complexity—where d denotes the number of parameters. This represents a unified advance in structured uncertainty modeling and computational efficiency for large-scale deep learning.

Technology Category

• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose KOALA++, a scalable Kalman-based optimization algorithm that explicitly models structured gradient uncertainty in neural network training. Unlike second-order methods, which rely on expensive second order gradient calculation, our method directly estimates the parameter covariance matrix by recursively updating compact gradient covariance products. This design improves upon the original KOALA framework that assumed diagonal covariance by implicitly capturing richer uncertainty structure without storing the full covariance matrix and avoiding large matrix inversions. Across diverse tasks, including image classification and language modeling, KOALA++ achieves accuracy on par or better than state-of-the-art first- and second-order optimizers while maintaining the efficiency of first-order methods.

Problem

• Efficient optimization of neural networks using gradient-covariance products
• Estimating parameter covariance without expensive second-order gradients
• Improving accuracy while maintaining first-order method efficiency

Innovation

• Scalable Kalman-based neural network optimization
• Estimates parameter covariance via gradient products
• Efficiently captures uncertainty without full matrix inversion