A key challenge in artificial intelligence and neuroscience is understanding how neural systems learn representations that capture the underlying dynamics of the world. Most world models represent the transition function with unstructured neural networks, limiting interpretability, sample efficiency, and generalization to unseen states or action compositions. We address these issues with a generalizable world model grounded in Vector Symbolic Architecture (VSA) principles as geometric priors. Our approach utilizes learnable Fourier Holographic Reduced Representation (FHRR) encoders to map states and actions into a high dimensional complex vector space with learned group structure and models transitions with element-wise complex multiplication. We formalize the framework's group theoretic foundation and show how training such structured representations to be approximately invariant enables strong multi-step composition directly in latent space and generalization performances over various experiments. On a discrete grid world environment, our model achieves 87.5% zero shot accuracy to unseen state-action pairs, obtains 53.6% higher accuracy on 20-timestep horizon rollouts, and demonstrates 4x higher robustness to noise relative to an MLP baseline. These results highlight how training to have latent group structure yields generalizable, data-efficient, and interpretable world models, providing a principled pathway toward structured models for real-world planning and reasoning.
Figures & tables
Figure 1: Overview of the FHRR-based world modeling framework. a) Visualization of the partially held-out GridWorld Environment. b) Difference between MLP-based and FHRR-based dynamics modeling. Direct predictions of s^t+1 by MLPs cannot easily generalize to OOD samples, while FHRR can.
Figure 2: a) Shaded red represents out of the training distribution. Cleanup during FHRR Inference can ameliorate error accumulation due to distribution shift between train and test. b) Cleanup mechanism equations via similarity search in FHRR.
Task
FHRR (Ours)
MLP-Small
MLP-Medium
MLP-Large
1-step Accuracy
96.3%
80.0%
80.0%
80.25%
1-step Accuracy (Zero-Shot)
87.5%
0.0%
0.0%
1.25%
Cosine Similarity
83.0
79.5
79.9
80.6
Cosine Similarity (Zero-Shot)
80.5
0.9
0.15
3.1
Rollout (5 steps)
74.6%
39.8%
38.0%
40.8%
Rollout (20 steps)
34.6%
2.0%
4.0%
6.2%
Table 3
Figure 3: Latent Rollout Accuracy of FHRR and MLP-M over varying zero-shot ratios
Figure 4: t-SNE visualization of state embeddings for VSA (FHRR) vs MLP-M labeled per row
State-of-the-art model-based reinforcement learning methods learn neural world models that allow policy improvement by planning in a latent space, without assumptions on the structure of the underlying environment. While expressive, these models are generally task-dependent: they learn uninterpretable latent representations that are tied to the training task and thus hard to generalize to new tasks. In this work, we present a novel world model formulation where the reward prediction only depends on a subset of structured, symbolic components of the whole latent state. Decoupling observation reconstruction and reward prediction allows us to learn world models that can adapt zero-shot, i.e. without further environment interactions, to new reward functions defined over the same symbolic state space. We discuss the main advantages and challenges of learning these neurosymbolic world models and demonstrate the strong generalisation properties of our approach over purely neural methods.
Isidoro Tamassia, Lennert De Smet, Giuseppe Marra
KU Leuven, Department of Computer Science, Belgium
World models aim to learn compact representations of an environment from observations, enabling agents to predict future states and plan their behaviour. However, most existing approaches learn black-box representations, with limited ability to incorporate prior knowledge about the world. We introduce Concept-Grounded World Models (CGWMs), a neurosymbolic world model design that instead learns interpretable concept representations. We learn these concepts from observations using explicit and complete knowledge, expressed in temporal logic, that specifies the valid world states and the temporal relations governing their dynamics. Furthermore, we directly use this knowledge by formulating planning as differentiable reasoning, optimising the agent's actions by gradient ascent to satisfy a goal. We experimentally compare CGWM with a purely neural baseline and a neurosymbolic baseline on two game environments. We find that CGWMs ground concepts much more accurately, even over long horizons, resulting in significantly more robust planning both in and out of distribution.
A world model matters to an agent only through the state it constructs. That state must preserve some information, discard other information, and support some future function: prediction, control, planning, memory, grounding, or counterfactual reasoning. This paper treats world-model research as latent state design under sufficiency constraints. We propose a functional taxonomy that groups methods by what their latent state is for, rather than by architecture or application domain: predictive embedding, recurrent belief state, object/causal structure, latent action interface, grounded planning interface, and memory substrate. These roles expose distinctions that architecture-based groupings hide, including the gap between predictive sufficiency and control sufficiency, and the gap between passive video prediction and counterfactual action modeling. The taxonomy supports an evaluation framework that judges a model by the sufficiency constraint its latent state was built to satisfy. We compare methods along seven axes: representation, prediction, planning, controllability, causal/counterfactual support, memory, and uncertainty. We use the resulting matrix as a diagnostic for what a latent state preserves, discards, and enables. The conclusion that follows is that an actionable world model is the one whose state construction matches the task, not the one that preserves the most information.