Kenji Doya

Sutashu Tomonaga, Kenji Doya, Noboru Murata

Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multi-stage process of continuous-time modeling and subsequent discretization, which can obscure intuition. We introduce a direct, first-principles framework for constructing discrete-time SSMs that is both flexible and modular. Our approach is based on a novel lag operator, which geometrically derives the discrete-time recurrence by measuring how the system's basis functions "slide" and change from one timestep to the next. The resulting state matrices are computed via a single inner product involving this operator, offering a modular design space for creating novel SSMs by flexibly combining different basis functions and time-warping schemes. To validate our approach, we demonstrate that a specific instance exactly recovers the recurrence of the influential HiPPO model. Numerical simulations confirm our derivation, providing new theoretical tools for designing flexible and robust sequence models.

Theodore Jerome Tinker, Kenji Doya, Jun Tani

Human infants acquire language and action gradually through development, achieving remarkable generalization capabilities from only a minimal number of learning examples. In contrast, recent large language models require exposure to billions of training tokens to achieve such generalization. What mechanisms underlie such efficient developmental learning in humans? This study addresses this question through simulation experiments in which robots learn to perform various actions corresponding to imperative sentences (e.g., \textit{push red cube}) via trials of self-guided exploration. Our approach integrates the active inference framework with reinforcement learning, enabling curiosity-driven developmental learning. The simulations yielded several important findings: i) Generalization is drastically improved as the number of compositional elements increases. ii) Curiosity-driven exploration combined with motor noise substantially outperforms learning without curiosity. iii) Rote pairing of sentences and actions occurs before the emergence of compositional generalization. iv) Simpler, prerequisite-like actions emerge earlier in development, while more complex actions involving these prerequisites develop later. These results shed light into possible mechanisms underlying efficient developmental learning in infants and provide computational parallels to findings in developmental psychology.