  Machines that can replicate human intelligence with type 2 reasoning
capabilities should be able to reason at multiple levels of spatio-temporal
abstractions and scales using internal world models. Devising formalisms to
develop such internal world models, which accurately reflect the causal
hierarchies inherent in the dynamics of the real world, is a critical research
challenge in the domains of artificial intelligence and machine learning. This
thesis identifies several limitations with the prevalent use of state space
models (SSMs) as internal world models and propose two new probabilistic
formalisms namely Hidden-Parameter SSMs and Multi-Time Scale SSMs to address
these drawbacks. The structure of graphical models in both formalisms
facilitates scalable exact probabilistic inference using belief propagation, as
well as end-to-end learning via backpropagation through time. This approach
permits the development of scalable, adaptive hierarchical world models capable
of representing nonstationary dynamics across multiple temporal abstractions
and scales. Moreover, these probabilistic formalisms integrate the concept of
uncertainty in world states, thus improving the system's capacity to emulate
the stochastic nature of the real world and quantify the confidence in its
predictions. The thesis also discuss how these formalisms are in line with
related neuroscience literature on Bayesian brain hypothesis and predicitive
processing. Our experiments on various real and simulated robots demonstrate
that our formalisms can match and in many cases exceed the performance of
contemporary transformer variants in making long-range future predictions. We
conclude the thesis by reflecting on the limitations of our current models and
suggesting directions for future research.
