# Learning First-Order Symbolic Representations for Planning from the Structure of the State Space

arXiv: https://arxiv.org/abs/1909.05546 · HTML: https://mlsanity.com/paper/1909.05546/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 30 of 38)

- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Leveraging Pre-trained Large Language Models to Construct and Utilize World Models for Model-based Task Planning](https://mlsanity.com/paper/2305.14909/) (2023)
- [Predicate Invention for Bilevel Planning](https://mlsanity.com/paper/2203.09634/) (2022)
- [Learning General Optimal Policies with Graph Neural Networks: Expressive Power, Transparency, and Limits](https://mlsanity.com/paper/2109.10129/) (2021)
- [Symbols as a Lingua Franca for Bridging Human-AI Chasm for Explainable and Advisable AI Systems](https://mlsanity.com/paper/2109.09904/) (2021)
- [Learning adaptive planning representations with natural language guidance](https://mlsanity.com/paper/2312.08566/) (2023)
- [Learning First-Order Representations for Planning from Black-Box States: New Results](https://mlsanity.com/paper/2105.10830/) (2021)
- [Classical Planning in Deep Latent Space](https://mlsanity.com/paper/2107.00110/) (2021)
- [Learning Generalized Policies Without Supervision Using GNNs](https://mlsanity.com/paper/2205.06002/) (2022)
- [Learning Efficient Abstract Planning Models that Choose What to Predict](https://mlsanity.com/paper/2208.07737/) (2022)
- [From Pixels to Predicates: Learning Symbolic World Models via Pretrained Vision-Language Models](https://mlsanity.com/paper/2501.00296/) (2024)
- [Discovering User-Interpretable Capabilities of Black-Box Planning Agents](https://mlsanity.com/paper/2107.13668/) (2021)
- [Expressing and Exploiting the Common Subgoal Structure of Classical Planning Domains Using Sketches: Extended Version](https://mlsanity.com/paper/2105.04250/) (2021)
- [Online Learning of Reusable Abstract Models for Object Goal Navigation](https://mlsanity.com/paper/2203.02583/) (2022)
- [Learning Lifted STRIPS Models from Action Traces Alone: A Simple, General, and Scalable Solution](https://mlsanity.com/paper/2411.14995/) (2024)
- [PDSketch: Integrated Planning Domain Programming and Learning](https://mlsanity.com/paper/2303.05501/) (2023)
- [Learning Logic Specifications for Soft Policy Guidance in POMCP](https://mlsanity.com/paper/2303.09172/) (2023)
- [Target Languages (vs. Inductive Biases) for Learning to Act and Plan](https://mlsanity.com/paper/2109.07195/) (2021)
- [Neuro-Symbolic Imitation Learning: Discovering Symbolic Abstractions for Skill Learning](https://mlsanity.com/paper/2503.21406/) (2025)
- [Learning Planning Abstractions from Language](https://mlsanity.com/paper/2405.03864/) (2024)
- [Learning General Policies with Policy Gradient Methods](https://mlsanity.com/paper/2512.19366/) (2025)
- [Learning Lifted Action Models from Unsupervised Visual Traces](https://mlsanity.com/paper/2604.19043/) (2026)
- [Learning First-Order Symbolic Planning Representations That Are Grounded](https://mlsanity.com/paper/2204.11902/) (2022)
- [Learning Lifted Action Models From Traces of Incomplete Actions and States](https://mlsanity.com/paper/2508.21449/) (2025)
- [Few-Shot Neuro-Symbolic Imitation Learning for Long-Horizon Planning and Acting](https://mlsanity.com/paper/2508.21501/) (2025)
- [From Next Token Prediction to (STRIPS) World Models](https://mlsanity.com/paper/2509.13389/) (2025)
- [Learning Visual Planning Models from Partially Observed Images](https://mlsanity.com/paper/2211.15666/) (2022)
- [Planning for Learning Object Properties](https://mlsanity.com/paper/2301.06054/) (2023)
- [Influence of the Geometry of the world model on Curiosity Based Exploration](https://mlsanity.com/paper/2304.00188/) (2023)
- [Action Model Learning with Guarantees](https://mlsanity.com/paper/2404.09631/) (2024)

## Abstract (arXiv)

One of the main obstacles for developing flexible AI systems is the split between data-based learners and model-based solvers. Solvers such as classical planners are very flexible and can deal with a variety of problem instances and goals but require first-order symbolic models. Data-based learners, on the other hand, are robust but do not produce such representations. In this work we address this split by showing how the first-order symbolic representations that are used by planners can be learned from non-symbolic inputs that encode the structure of the state space. The representation learning problem is formulated as the problem of inferring planning instances over a common but unknown first-order domain that account for the structure of the observed state space. This means to infer a complete first-order representation (i.e. general action schemas, relational symbols, and objects) that explains the observed state space structures. The inference problem is cast as a two-level combinatorial search where the outer level searches for values of a small set of hyperparameters and the inner level, solved via SAT, searches for a first-order symbolic model. The framework is shown to produce general and correct first-order representations for standard problems like Gripper, Blocksworld, and Hanoi from input graphs that encode the flat state-space structure of a single instance.