This thesis explores the theoretical foundations and applications of latent space modeling across three interconnected domains: brain mechanisms, language processing, and decision-making. The central proposition is that latent space representations—abstract encodings that capture underlying structure in complex data—offer a unified computational framework for understanding both biological and artificial intelligence.

The first part of this work investigates spatial cognition in the brain, reconceptualizing hippocampal place cells as collective position embeddings that encode multi-scale transition probabilities through inner products. This novel perspective reveals how the brain might efficiently represent navigational information, with latent vectors approximating symmetric random walk transition kernels. Through mathematical analysis and computational modeling, I demonstrate that hexagonal grid patterns emerge naturally as the optimal solution for maximally distance-preserving embeddings. These models successfully reproduce key neurobiological phenomena, including scale hierarchies along the dorsoventral axis, place field remapping, and preplay-like shortcut discovery.

Building on these neurally-inspired principles, I then develop two innovative frameworks for artificial intelligence. The Latent Thought Language Model (LTM) incorporates explicit latent thought vectors that guide autoregressive token generation, creating a structured design space with additional scaling dimensions beyond traditional language models. This approach demonstrates superior sample and parameter efficiency while exhibiting emergent in-context reasoning capabilities. The Latent Plan Transformer (LPT) extends these concepts to sequential decision-making, employing a latent variable to connect trajectory generation with expected returns, enabling planning as latent space inference without reliance on step-wise rewards.

Across these diverse applications, common computational principles emerge: the importance of multi-scale representations, the efficiency of latent abstractions for capturing complex relationships, and the power of posterior inference for integrating contextual information. This thesis demonstrates that latent space modeling provides a compelling bridge between biological and digital intelligence, offering insights into both how the brain computes and how we might build more capable artificial systems that emulate aspects of human cognition.