# Discrete World Models via Regularization Source: [Discrete World Models via Regularization]() Collection index: [llms.txt]() Data updated: 2026-03-04T05:00:19.274Z Authors: Davide Bizzaro, Luciano Serafini Published: 2026-03-02T11:17:38.000Z ## Abstract World models aim to capture the states and dynamics of an environment in a compact latent space. Moreover, using Boolean state representations is particularly useful for search heuristics and symbolic reasoning and planning. Existing approaches keep latents informative via decoder-based reconstruction, or instead via contrastive or reward signals. In this work, we introduce Discrete World Models via Regularization (DWMR): a reconstruction-free and contrastive-free method for unsupervised Boolean world-model learning. In particular, we introduce a novel world-modeling loss that couples latent prediction with specialized regularizers. Such regularizers maximize the entropy and independence of the representation bits through variance, correlation, and coskewness penalties, while simultaneously enforcing a locality prior for sparse action changes. To enable effective optimization, we also introduce a novel training scheme improving robustness to discrete roll-outs. Experiments on two benchmarks with underlying combinatorial structure show that DWMR learns more accurate representations and transitions than reconstruction-based alternatives. Finally, DWMR can also be paired with an auxiliary reconstruction decoder, and this combination yields additional gains. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Encoder Board Reconstruction on MNIST 8-puzzle Clean](): Encoder Board Reconstruction; MNIST 8-puzzle Clean; F1 Score: 96. - [Encoder Board Reconstruction on MNIST 8-puzzle (Noisy)](): Encoder Board Reconstruction; MNIST 8-puzzle (Noisy); F1 Score: 98. - [Encoder Board Reconstruction on IceSlider Clean](): Encoder Board Reconstruction; IceSlider Clean; F1 Score: 99. - [Encoder Board Reconstruction on IceSlider Noisy](): Encoder Board Reconstruction; IceSlider Noisy; F1-Score: 86. - [Imagination Board Reconstruction on MNIST 8-puzzle Clean](): Imagination Board Reconstruction; MNIST 8-puzzle Clean; F1 Score: 91. - [Imagination Board Reconstruction on MNIST 8-puzzle Noisy](): Imagination Board Reconstruction; MNIST 8-puzzle (Noisy); F1 Score: 90. - [Imagination Board Reconstruction on IceSlider Clean](): Imagination Board Reconstruction; IceSlider Clean; F1 Score: 95. - [Imagination Board Reconstruction on IceSlider Noisy](): Imagination Board Reconstruction; IceSlider Noisy; F1 Score: 88. ## Original sources and implementation [Original paper]() [PDF]()