勾配からリッカチ幾何へ：単一パス学習のためのカルマンワールドモデル
From Gradients to Riccati Geometry: Kalman World Models for Single-Pass Learning
誤差逆伝播に代わり、カルマンフィルタリングに基づく再帰的ベイズ推定で状態空間モデルを学習する手法を提案。勾配を使わずにオンライン学習が可能で、LLMにも応用できる。
著者: Andrew Kiruluta
分類: cs.LG, cs.CL
原文アブストラクト
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.