KAN-Dreamer: Benchmarking Kolmogorov-Arnold Networks as Function Approximators in World Models

DreamerV3 is a state-of-the-art online model-based reinforcement learning (MBRL) algorithm known for remarkable sample efficiency. Concurrently, Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to Multi-Layer Perceptrons (MLPs), offering superior parameter efficiency and interpretability. To mitigate KANs' computational overhead, variants like FastKAN leverage Radial Basis Functions (RBFs) to accelerate inference. In this work, we investigate integrating KAN architectures into the DreamerV3 framework. We introduce KAN-Dreamer, replacing specific MLP and convolutional components of DreamerV3 with KAN and FastKAN layers. To ensure efficiency within the JAX-based World Model, we implement a tailored, fully vectorized version with simplified grid management. We structure our investigation into three subsystems: Visual Perception, Latent Prediction, and Behavior Learning. Empirical evaluations on the DeepMind Control Suite (walker_walk) analyze sample efficiency, training time, and asymptotic performance. Experimental results demonstrate that utilizing our adapted FastKAN as a drop-in replacement for the Reward and Continue predictors yields performance on par with the original MLP-based architecture, maintaining parity in both sample efficiency and training speed. This report serves as a preliminary study for future developments in KAN-based world models.

Argument-based Belief in Topological Structures

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.