Generating particle physics Lagrangians with transformers (2501.09729v1)

Abstract: In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model -- proven to be effective in natural language tasks -- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model $\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)$ gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: \url{https://huggingface.co/spaces/JoseEliel/generate-lagrangians}.

• The paper demonstrates that transformer models can generate Lagrangians with over 90% accuracy, adhering to Standard Model symmetries.
• It employs a customized tokenization scheme and AutoEFT to train on systems with up to six matter fields, ensuring robust generalization.
• The study highlights the potential for automating symbolic mathematics in theoretical physics, paving the way for research beyond conventional models.

Analyzing the Application of Transformers in Generating Particle Physics Lagrangians

The paper investigates the innovative use of transformer models in the symbolic domain of theoretical particle physics, specifically to generate Lagrangians from specified particles. Traditionally used in NLP, transformers have demonstrated remarkable capability in linguistic tasks owing to their self-attention mechanisms and ability to capture contextual dependencies in sequences. This study extends their use to the generation of Lagrangians, a fundamental concept in Quantum Field Theory (QFT), which encapsulates the dynamics and interactions of particles.

Key Findings

The authors report promising results, achieving over 90% accuracy in generating Lagrangians that respect the Standard Model (SM) symmetries, specifically $SU(3)_C \times SU(2)_L \times U(1)_Y$. The study demonstrates the ability of transformers to recognize and apply group theoretical concepts such as representations and conjugations. This is a critical step toward automating complex symbolic algebra crucial to theoretical physics.

Methodology

Transformers were specifically trained to predict Lagrangians for systems containing up to six matter fields, demonstrating significant generalization capabilities even for sequences not explicitly covered during training. The training data were generated using AutoEFT, which allows for constructing Lagrangian terms automatically in compliance with the stated symmetries. These terms are then tokenized into sequences that transformers can process, leveraging a customized tokenization scheme aligning with the mathematical constructs involved.

Implications

1. Theoretical Implications: This research indicates that machine learning models can discern structural patterns and symbolic relationships fundamental to physics. It highlights the potential to apply deep learning models beyond conventional data tasks, extending their proficiency to abstract, rule-driven environments like theoretical physics.
2. Practical Implications: The implications for physics research are substantial. Automating Lagrangian generation could accelerate model-testing against observable data, refining conjectures about particle interactions and advancing beyond the SM theories. This offers a tool for physicists to explore new models without labor-intensive derivations.
3. Future Directions: The capability to generate theoretically consistent Lagrangians creates a foundation for exploring more expansive field models, including those with additional global or discrete symmetries not fully explored in this study. Additionally, the successful application in generating symbolic mathematics suggests potential for other domains within physics that rely heavily on algebraic representations.

Generalizability and Limitations

While the model shows significant promise, there is room for enhancement concerning more complex interactions, particularly trilinear terms beyond the training range. Expanding model training to include richer datasets capturing extended field interactions and diverse symmetry schemes will be indispensable for addressing broader theoretical questions, especially models like Supersymmetry (SUSY) and Grand Unified Theories (GUTs).

Conclusion

The research pioneers in using transformers for symbolic tasks, stepping into domains traditionally thought to require explicit, human-mediated derivation. It underscores the potential of machine learning to augment theoretical physics by providing a method to systematically explore various Lagrangian configurations efficiently, enriching the predictive power and explorative capacity of modern theoretical frameworks. This progress anticipates a future where hybrid AI-augmented research methodologies become mainstream in theoretical physics, providing robust tools for physicists to explore the depths of quantum theories and the pursuit of new physics beyond established paradigms.