Autonomous Discovery of Particle Physics Theories from Experimental Data

Abstract

The search for physics beyond the Standard Model is hindered by a combinatorial explosion of possible theories. We introduce \textsc{Albert}, a neuro-symbolic artificial intelligence framework to systematically navigate this vast theory space. By encoding particle physics as a formal language, \textsc{Albert} generates tokenized sequences representing symmetries, particles, and interactions under a rule-based grammar, eliminating the hallucinations common in large language models. The reinforcement learning environment enforces first-principle theoretical constraints, computes observables with radiative corrections, and evaluates statistical likelihood via $χ^2$ analysis against experimental data. As a proof of concept, we train a 25-million-parameter transformer model using only legacy data from the Large Electron-Positron Collider, which contains no direct evidence of the top quark. Remarkably, \textsc{Albert} successfully rediscovered the Standard Model and autonomously inferred necessity and properties of the top quark, predicting its mass at $178.9\pm 5.0~\text{GeV}$, consistent with its modern measurement at the Large Hadron Collider. These results demonstrate the potential of AI-driven theory exploration as a rigorous, hallucination-free, and scalable paradigm for autonomous discovery of new physics.

Figures (5)

• Figure 1: (a) The space of all possible physics theories can be characterized by a set of fundamental axes (e.g. symmetry, unitarity, naturalness, particle content, and experimental agreement) forming a high-dimensional landscape in which the Standard Model occupies a specific location. (b) The symbolic Lagrangian of the Standard Model. (c) Quantum field theories can be encoded into token sequences that contain the information of gauge groups, symmetry breaking patterns, matter field contents, and interaction terms. (d) An example of a tokenized theories.
• Figure 2: At each autoregressive step, the grammar mask assigns $M = -\infty$ to all physically inadmissible tokens prior to softmax normalization, restricting valid completions to singlet, fundamental, and adjoint for the SU(3) representation query. A conventional large language model may hallucinate and assign significant confidence to tokens such as hypercharge(-1/2) at this position. The theory grammar reduces the posterior probability of all such tokens to exactly zero, guaranteeing that every generated sequence constitutes a well-formed Lagrangian term at every decoding step.
• Figure 3: Autonomous theory discovery. A prompt encoding the known gauge structure and particle content is fed into the policy network, which combines a Transformer-based language model with a theory grammar masker to generate a group of $G$ candidate theories as tokenized sequences. Each candidate is evaluated against three hard consistency checks (gauge anomaly cancellation, perturbative unitarity, and absence of detector-accessible exotic particles), with flawed theories discarded and valid theories assigned group-relative advantages. An exploratory bonus computed from pairwise Jaccard similarities between candidates penalizes similar theories and rewards diverse exploration. Surviving theories proceed to a fully automated computation pipeline that derives Feynman rules, computes loop-corrected electroweak observables, and evaluates the $\chi^2$ likelihood against measurements from the LEP experiment, closing the training loop without human intervention.
• Figure 4: Training dynamics of the RL stage.(Left) Sub-rewards for perturbative unitarity (red), absence of detector-accessible exotic particles (blue), and gauge anomaly cancellation (yellow) as a function of training episode. All three sub-rewards converge from large negative values toward zero within approximately $20$ episodes, indicating that the policy has learned to satisfy all consistency constraints simultaneously. (Right) Theory validity success rate (green dashed) and intra-group Jaccard diversity (blue solid) over training. The success rate rises sharply to above $95\%$ within the first $15$ episodes and remains stable thereafter. Diversity initially declines as the policy concentrates on the valid region of theory space. Once the success rate stabilizes at high values, the Jaccard penalty in the training objective forces the policy to simultaneously maintain high validity and high diversity, driving a recovery and stabilization of diversity near $0.4$. Albert achieves broad exploration without sacrificing theoretical consistency.
• Figure 5: Joint posterior distribution of the top quark mass $m_t$ and Higgs boson mass $m_h$ for the SM rediscovered by Albert. Filled contours denote the $1\sigma$, $2\sigma$, and $3\sigma$ credible regions of the joint posterior obtained via Markov Chain Monte Carlo (MCMC) sampling over the free parameters. The red marker with error bars denotes the mean and standard deviation of best-fit parameter pairs $(m_t, m_h)$ obtained from an ensemble of $100$ independent differential evolution optimizations over the discretized parameter space, yielding $m_t = 178.9 \pm 5.0~\text{GeV}$ and $m_h = 146.9 \pm 17.4~\text{GeV}$. The orange marker denotes the current precision measurements from the LHC, $m_t = 172.52 \pm 0.33~\text{GeV}$ and $m_h = 125.20 \pm 0.11~\text{GeV}$pdg2024. Both inferred values are consistent with the LHC measurements at $1\sigma$ and $1.2\sigma$ of Albert's posterior uncertainty, respectively.