用卡尔曼滤波替代反向传播，实现无需梯度的模型训练
From Gradients to Riccati Geometry: Kalman World Models for Single-Pass Learning
- 用卡尔曼滤波更新参数，以创新信号代替梯度进行学习
- 在序列建模任务中表现媲美传统方法，且更鲁棒、支持持续适应
- 适用于大语言模型，为神经网络提供基于控制理论的新训练范式
反向传播主导现代机器学习，但并非优化动态系统的唯一合理方法。我们提出卡尔曼世界模型（KWM），一类通过递归贝叶斯滤波而非反向自动微分训练的可学习状态空间模型。参数学习被卡尔曼增益调整取代，训练变为在线滤波，误差信号转化为创新项。我们进一步将该框架拓展至基于Transformer的大语言模型（LLM），其中内部激活被视为由创新项修正的潜在动态状态。这带来一种基于控制理论的无梯度训练与适应范式。我们推导了稳定性条件，分析了计算复杂度，并在序列建模任务上提供了实证结果，展示了与现有方法相当的性能，同时具备更强的鲁棒性与持续适应能力。
原文摘要 · Abstract (English)
Backpropagation dominates modern machine learning, yet it is not the only principled method for optimizing dynamical systems. We propose Kalman World Models (KWM), a class of learned state-space models trained via recursive Bayesian filtering rather than reverse-mode automatic differentiation. Instead of gradient descent updates, we replace parameter learning with Kalman-style gain adaptation. Training becomes online filtering; error signals become innovations. We further extend this framework to transformer-based large language models (LLMs), where internal activations are treated as latent dynamical states corrected via innovation terms. This yields a gradient-free training and adaptation paradigm grounded in control theory. We derive stability conditions, analyze computational complexity, and provide empirical results on sequence modeling tasks demonstrating competitive performance with improved robustness and continual adaptation properties.
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