Interaction Networks for Learning about Objects, Relations and Physics (1612.00222v1)

Abstract: Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact, supporting dynamical predictions, as well as inferences about the abstract properties of the system. Our model takes graphs as input, performs object- and relation-centric reasoning in a way that is analogous to a simulation, and is implemented using deep neural networks. We evaluate its ability to reason about several challenging physical domains: n-body problems, rigid-body collision, and non-rigid dynamics. Our results show it can be trained to accurately simulate the physical trajectories of dozens of objects over thousands of time steps, estimate abstract quantities such as energy, and generalize automatically to systems with different numbers and configurations of objects and relations. Our interaction network implementation is the first general-purpose, learnable physics engine, and a powerful general framework for reasoning about object and relations in a wide variety of complex real-world domains.

• The paper introduces Interaction Networks that explicitly separate relational and object reasoning to simulate physical systems.
• It uses a graph representation with MLP-based functions to predict dynamics accurately, achieving low errors (e.g., MSE = 0.25 on n-body simulation).
• The model's scalability and combinatorial generalization enable accurate simulation across diverse scenarios, paving the way for advanced physics and planning applications.

Interaction Networks for Learning about Objects, Relations and Physics

The paper "Interaction Networks for Learning about Objects, Relations and Physics" by Peter W. Battaglia et al., presents the Interaction Network (IN), a model designed for reasoning about objects, their interactions, and physical dynamics. This paper resides at the intersection of structured models, simulation, and deep learning, aiming to simulate complex physical systems and infer their abstract properties.

Model Architecture and Methodology

The Interaction Network explicitly separates the reasoning about relations from reasoning about objects. It processes inputs represented as graphs with nodes (objects) and edges (relations) using distinct model components. The model consists of two main functions: the relational model $\phi_R$ and the object model $\phi_O$. The relational model processes the effects of interactions between objects, while the object model predicts the objects' states by incorporating both the interactions and the objects' own states.

Key Components of the IN Architecture:

1. Marshalling Function (m): Rearranges the objects and relations into interaction terms.
2. Relational Model ($\phi_R$): Uses Multi-Layer Perceptrons (MLPs) to predict interaction effects.
3. Aggregation Function (a): Collects all interaction effects relevant to each object and combines them.
4. Object Model ($\phi_O$): Uses MLPs to predict new object states based on the aggregated effects and the objects' states.

Experimental Evaluation

The paper evaluates the IN's performance across three challenging domains: n-body problems, rigid-body collision (bouncing balls), and non-rigid dynamics (spring-based strings). Key objectives were to predict future states and estimate abstract properties like potential energy.

Domains and Key Results:

• N-Body Problems: The IN demonstrated the ability to predict the dynamics of systems with varying numbers of gravitational bodies with low Mean Squared Error (MSE). Training on systems with 6 bodies and generalizing well to systems with 3 and 12 bodies highlighted the IN's scalability.
• Bouncing Balls: The IN effectively simulated collisions among multiple balls and walls within a box. Despite the sparsity of collision events, the model achieved significant accuracy in velocity prediction.
• Spring-Based Strings: The IN accurately simulated the complex behaviors of strings composed of masses connected by springs interacting with rigid objects, showcasing its ability to handle multiple types of relations and external effects.

Numerical Results

The model consistently outperformed baseline methods in terms of prediction accuracy:

• For n-body dynamics, the MSE for the IN was 0.25, significantly lower than that of the constant velocity (82) and baseline MLP (79).
• In the bouncing balls experiment, the IN produced an MSE of 0.0020 compared to 0.074 for the constant velocity and 0.072 for the baseline MLP.
• For the spring-based strings, the IN achieved an MSE of 0.0011, far surpassing the constant velocity (0.018) and baseline MLP (0.016).

Implications and Future Work

This research establishes the IN as a flexible, efficient model for physical reasoning. Its capabilities extend beyond physical simulations, potentially applying to areas like scene understanding and hierarchical planning.

Practical Implications:

• Simulation and Prediction: The IN can simulate physical systems over thousands of steps accurately, enabling applications in real-time physics engines.
• Learning Abstract Properties: Extending the IN to estimate abstract properties presents an opportunity for automated scientific discovery and analysis in physical systems.

Theoretical Implications:

• Combinatorial Generalization: By decomposing a system into objects and relations, the IN supports generalization to novel configurations, addressing a crucial challenge in AI.
• Scalability: Future work can focus on improving the handling of large systems with numerous interactions by selectively processing interactions of significant effect.

Prospective Developments:

• Model-Predictive Control: Leveraging the IN's differentiation capabilities for planning and control tasks.
• Recurrent Extensions: Enhancing long-term predictions by incorporating recurrent neural network components.
• Probabilistic Models: Adapting the interaction network into a probabilistic generative model for robust inference.

In summary, the Interaction Network offers a robust framework for learning and reasoning about complex physical systems, marking a significant advancement in the integration of structured models, simulation, and deep learning. Future research will likely explore its applications to even broader domains and further enhance its computational efficiency and scalability.