PaperlayerView exact revision on arXiv

Source-linked AI summary

Searching for BSM Experimental Signatures with Large Lagrangian Models

Ibrahim Elsharkawy, Victoria Knapp-Perez, Wahid Bhimji, Aishik Ghosh

arXiv:2609.38309v1hep-phastro-ph.COcs.AIhep-ex

TL;DR

BSM theory proposals abound while discriminating experimental observations remain limited, including for dark matter. hAIthem combines reinforcement-learning searches for viable parameter regions with decision trees and LLM-proposed observables; on a benchmark of 21 Lagrangians, it finds more viable points than differential evolution and explores more distinct regions.

  • Problem

    BSM proposals have grown while positive experimental results remain scarce, and dark matter presents many viable models but limited ways to distinguish them experimentally.

    Source: §I · p. 2

  • Method

    hAIthem trains a Large Lagrangian Model with pretraining and reinforcement learning to find viable regions, then uses decision trees and LLM agents to propose signatures that distinguish them.

    Source: §I · pp. 2–3, §V · p. 22

  • Results

    On a benchmark of 21 Lagrangians, LLaM-medium finds over 5x and LLaM-small over 2x the viable points found by differential evolution.

    Source: §V · p. 22

  • Takeaways & Limitations

    In the considered single-scalar-multiplet dark-matter space, LLM agents propose discriminating, physically reasonable combinations of observables, including previously unexplored combinations of known signatures.

    Source: §V · p. 22

    The proof of concept restricts its dark-matter model-building space to a subset of models.

    Source: §I · p. 2

Abstract

from arXiv · show

The search for physics Beyond the Standard Model (BSM) is generally limited not by the supply of theory descriptions but by the lack of discriminating experimental observations. A case in point is dark matter, where the overwhelming gravitational evidence only goes so far in distinguishing between models within a vast theory space. Exploring the space of testable model signatures may help identify overlooked experimental observables and indicate the utility of future experiments. A challenge is designing a search through model signatures outside what is found in the literature. Our primary contribution is hAIthem, a framework that combines the self-guided exploration of reinforcement learning (RL) with the broad literature-derived knowledge of LLMs. We build an RL agent that learns to find which portions of a theory's high-dimensional parameter space are not excluded under some subset of constraints by playing a Battleship-style "game" against a suite of phenomenology tools. The agent is built as a Large Lagrangian Model (LLaM), an autoregressive transformer that reads a tokenized Lagrangian, is pretrained at scale (here on ~1 billion tokens from ~10,000 Lagrangians), and is fine-tuned in a live environment. The framework then constructs a decision tree that separates RL-found regions using observables computed with established tools, and passes the remaining degenerate regions to a set of LLM agents that compete to produce realistic signatures. In this proof of concept, RL-search outperforms an evolutionary-algorithm baseline, finding more viable regions with greater physical diversity. In a restricted space of single dark scalar multiplet models, we find that hAIthem proposes interesting combinations of previously studied observables, such as the application of a halo-independent kinematic ratio to paleo-detectors.

A. On the Physics Setting and Computational Pipeline

The paper addresses the gap between abundant BSM theories and limited discriminating observations by developing hAIthem to search viable model regions and distinguish their experimental signatures. Its search uses a reinforcement-learning agent over dark-matter parameter spaces and decision trees that combine established observables with LLM-proposed signatures.

I. INTRODUCTION

  • hAIthem divides BSM signature search into finding viable parameter-space regions and distinguishing them with experimental observables.Viability means non-exclusion under the selected constraints, not necessarily viability in nature.Source: §I · p. 2
  • The LLaM searches parameter space as a single-player Battleship game, probing candidate points and receiving deterministic exclusion verdicts from phenomenology tools.Each BSM model is a new board; the agent seeks connected non-excluded regions and treats non-exclusion as binary.Source: §I · p. 2
  • The proposed Large Lagrangian Model is pretrained at scale and fine-tuned with reinforcement learning; hAIthem is its first realization.The paper describes this training paradigm as drawing on AlphaGo-style pretraining and RL, without human-generated training data as in AlphaZero.Source: §I · p. 3, Figure 2 · p. 4
  • A decision tree splits viable regions using binary-outcome observables, then passes leaves still degenerate under computed observables to LLM agents for further proposals.The tree’s leaves group parameter-space regions by their experimental signatures.Source: §I · p. 3

II. SEARCHING PARAMETER SPACE WITH LARGE LAGRANGIAN MODELS

  • Training episodes vary the sampled Lagrangian, active constraints, allowed parameter ranges, and probe budget.The agent proposes continuous parameter points, such as masses and couplings, within each episode’s setup.Source: §II · p. 4
  • The study restricts methodology development to dark-matter models built from electroweak multiplets, with an optional dark U(1)′ sector.Candidates include scalar or fermion fields in singlet, doublet, or triplet representations; the authors describe this as a tractable playground for later expansion.Source: §II · p. 5

A. Considered Experimental Constraints

Viability is evaluated against active experimental constraints, with a scope limited by the tools and cuts used in this proof of concept.

A. Considered Experimental Constraints

  • A point is viable if it survives the active constraints, but the authors do not include every experimental constraint that probes the model space.The computations use micrOMEGAs for cosmological and direct-detection probes and SModelS for simple LHC bounds; thus, viability here does not guarantee viability in nature.Source: A. Considered Experimental Constraints · p. 5
  • The relic-density cut is always active with an episode-dependent allowable error, while each remaining constraint is independently active with probability 1/2.Active constraints are treated as hard exclusions; violating any active cut makes a point non-viable.Source: Table I · p. 6, A. Considered Experimental Constraints · p. 6

B. Automating Lagrangian Generation and Observable Computation

The framework automates the map from model descriptions and parameter points to physical observables and viability scores. The LLaM conditions on the Lagrangian, experimental cuts, and search history, then proposes parameter probes through autoregressive policy heads.

B. Automating Lagrangian Generation and Observable Computation

  • Sym2IntPy and FlavorBuilder turn symmetry and field choices into symbolic Lagrangians, while micrOMEGAs, SModelS, and custom code compute observables and per-point viability and testability scores.The pipeline is designed to scale across compute nodes.Source: B. Automating Lagrangian Generation… · p. 6
  • This proof of concept does not include Sommerfeld enhancements or next-to-leading-order corrections.These omissions qualify the observable computations in the automated pipeline.Source: B. Automating Lagrangian Generation… · pp. 6–7

C. The Large Lagrangian Model

  • The LLaM jointly processes tokens for the fixed Lagrangian, active viability configuration, and dynamic search history, producing a value estimate and four policy-head distributions over parameters.Parameters are sampled autoregressively, one at a time.Source: C. The Large Lagrangian Model · p. 7, Figure 4 · p. 7
  • Each policy head can sample parameters from per-dimension Beta distributions or use a differential-evolution-style path, with the latter mutating a selected base probe using other previously sampled probes.The Beta distribution’s mean-concentration parameterization separates where a head looks from how sharply it looks; its independent per-dimension distributions do not represent parameter correlations.Source: C. The Large Lagrangian Model · p. 8

D. Reinforcement Learning in a Live Environment

The agent is trained with asynchronous PPO in a live search environment, where rewards encourage finding viable, boundary, novel, and testable probes. Offline pretraining on earlier RL episode data warm-starts this live training.

D. Reinforcement Learning in a Live Environment

  • Training uses asynchronous PPO, and the value and policy heads are updated with rewards and value estimates computed each turn rather than from a single episode-level return.Per-turn estimates let the policy adapt across an episode without assigning early actions the consequences of later-turn policies.Source: D. Reinforcement Learning in a Live… · pp. 8, 10
  • The per-probe reward combines bonuses for viability, proximity to a viable/non-viable boundary, novel observable signatures, and testability by the specified experiments.The reward is the weighted sum of these four terms, with weights (3.0, 0.1, 0.5, 0.2), respectively.Source: D. Reinforcement Learning in a Live… · pp. 8–9

E. Offline Pretraining

  • Before live RL fine-tuning, the model is pretrained on roughly 10,000 distinct Lagrangians and over a billion output tokens from earlier RL runs.The dataset includes over 100 million evaluated parameter probes; during pretraining the differential-evolution-style policy path is disabled.Source: D. Reinforcement Learning in a Live… · p. 8, E. Offline Pretraining · p. 10, Table III · p. 10
  • Offline pretraining combines policy learning from viable probes and value regression with auxiliary predictions of episode statistics and probe viability, plus a diversity loss to prevent mode collapse.The dataset need not come from a good policy: even mostly non-viable probes provide ground-truth viability labels.Source: E. Offline Pretraining · pp. 10–11

F. Training the LLaM

LLaM training proceeds from offline pretraining through a warm-up to multi-node RL fine-tuning. The decision-tree method bins predicted signatures, uses information gain to distinguish viable probes, and groups experimentally indistinguishable probes into signature classes and viable regions.

F. Training the LLaM

  • Training proceeds through offline pretraining, a small warm-up RL run, and multi-node RL fine-tuning; pretraining took about 72 hours for LLaM-small and 60 hours for LLaM-medium.The RL phases ran for 24 hours each for LLaM-small and 48 hours each for LLaM-medium.Source: F. Training the LLaM · p. 11

A. Constructing the Tree

  • The tree is built from viable probes’ predicted observables and expected outcomes, using binned signal strengths relative to projected experimental limits, with bin widths set by expected systematic errors.A simple binary flag per experiment was rejected because it discards much of the information an experiment offers.Source: A. Constructing the Tree · pp. 11–12

III. TURNING DEGENERACIES INTO QUESTIONS WITH DECISION TREES

  • At each node, the method chooses the binary split with the greatest information gain and repeats until each leaf contains a single signature class, ordering observables by their ability to distinguish the viable points.Probes with identical binned observables across all features are experimentally indistinguishable and form a signature class.Source: §III · p. 11, A. Constructing the Tree · p. 12

A. Constructing the Tree

  • DBSCAN clusters probes in parameter space into viable regions, and leaves report both the number of viable probes and the number of regions sharing their signature class.A leaf containing multiple parameter-space regions is degenerate under the experiments considered.Source: A. Constructing the Tree · p. 12

B. LLMs for Splitting Indistinguishable Leaves

In the reported benchmark, LLaM finds more and more diverse viable regions than the baseline, with minimal collapse in search ability as parameter-space dimension grows. LLM agents are then used to propose ordered experimental or novel splits for leaves that remain degenerate.

B. LLMs for Splitting Indistinguishable Leaves

  • For a leaf containing multiple viable regions, LLM agents propose further splits, stopping when degeneracies are resolved, the depth limit of four is reached, or a split is judged practically impossible.Agents can propose published-result splits, literature projections, or novel observables, each with specified evidence or feasibility assessments.Source: B. LLMs for Splitting… · pp. 12–13
  • Agents must first search for a literature split, then consider projections, and propose a novel observable only if no suitable projection is found.A projection judged Next Generation or worse may also prompt a Novel Alternative with the same or better feasibility judgment.Source: B. LLMs for Splitting… · p. 13
  • The full tree is generated five times and an aggregation agent selects the best combination of observables across runs.Agents use web search and arXiv retrieval to verify cited references.Source: B. LLMs for Splitting… · p. 13

IV. RESULTS

  • LLaM finds more and more diverse viable regions than the baseline, with minimal collapse in search ability as parameter-space dimension grows.The framework’s results also include a decision-tree study over the allowed single-scalar-multiplet dark-matter models and scrutiny of LLM-proposed nodes.Source: §IV · p. 13

A. Benchmarking the Large Lagrangian Model

The benchmark compares search policies across representative Lagrangians, turn budgets, and repeated runs, using viable-point discovery and diversity-related measures to assess performance.

A. Benchmarking the Large Lagrangian Model

  • The benchmark tests 21 representative Lagrangians with viability cuts active and the relic-density requirement at its tightest setting, repeating each policy-budget combination three times.Budgets range from 5 to 50 turns, with 128 parameter-point probes per turn.Source: A. Benchmarking the Large Lagrangian… · p. 13
  • Five metrics measure viable-point totals, Lagrangian coverage, parameter-space region diversity, signature-class diversity, and head-to-head wins.The metrics are Nv, Lv, R100, Nσ, and W, respectively.Source: A. Benchmarking the Large Lagrangian… · p. 13
  • Example episodes show the search in the full-dimensional parameter space, with three displayed coordinates chosen where viable points spread most.The figure distinguishes excluded probes, current-turn probes, cumulative viable points, and policy beta-distribution heads.Source: Figure 9 · p. 14

Appendix D 1, and interactive visualizations can be found online.

The benchmark reports viable-point search performance and diversity, then applies the decision-tree method to single-scalar-multiplet models and examines LLM-generated observable proposals.

Appendix D 1, and interactive visualizations can be found online.

  • LLaM-small finds 5–10 times as many viable regions as DE, while its 29 signature classes exceed DE’s 24; LLaM-medium’s signature count is weaker.The authors report that scaling to LLaM-medium increases viable-point discovery but appears more exploitative, with lower region density and slightly worse Lagrangian coverage.Source: Appendix D · pp. 16–17, Figure 11 · p. 16
  • At B = 25, the RL model finds 1137 ± 202 viable points versus ∼150 for DE; at B = 50, it finds 5747 ± 1302, ∼2.5× ahead.The benchmark covers 21 Lagrangians, and Figure 10 plots viable-point totals against search budget.Source: Figure 10 · p. 15, Table V · p. 16, Appendix D · p. 17
  • As parameter dimension grows, DE’s mean viable-point count falls from ∼40 at d ≤10 to near zero by d ∼35, while the LLaM trend goes the other way.The authors suggest that learned knowledge of relevant parameters may make the policy search an effectively low-dimensional manifold; they also note that greater diversity argues against simple exploitation of found regions.Source: Appendix D · p. 17, Figure 12 · p. 17

B. A Decision Tree over all Single-Scalar-Multiplet Lagrangians

  • The single-multiplet scan covers 11 Lagrangians, combines their viable regions into a tree, and appends LLM-agent nodes to split remaining degeneracies.The scan restricts the search space to one scalar field with one copy; Figure 14 shows the combined tree.Source: B. A Decision Tree over all… · pp. 17–18, Figure 14 · p. 19
  • LLM agents shift from collider-oriented literature splits toward astrophysical novel-observable proposals, many of which concern self-interactions judged impractical.The aggregation agent favors alternatives over the impossible novel-observable proposals.Source: B. A Decision Tree over all… · pp. 18, 20, Table VII · p. 20

1. Interesting Observable Proposals

  • For paleo-detectors, the proposal combines a mass-sensitive recoil-spectrum idea with a more statistically robust moment-matching observable beyond the Emax endpoint.The authors note that measuring Emax may require many detections near galactic escape velocity, motivating the use of paleo-detectors’ long exposure.Source: §1 · pp. 20–21
  • The dark-bremsstrahlung proposal uses Higgs-tagged dimuon + MET events to measure MZ′ independently of ϵ, but feasibility requires a detailed analysis.The authors identify Higgs tagging as the main challenge and describe the VBF channel as a possible route; additional backgrounds may arise.Source: §1 · p. 21, Figure 15 · p. 21

V. CONCLUSION AND OUTLOOK

hAIthem combines a reinforcement-learning Large Lagrangian Model with decision trees and LLM agents to search for viable regions and explore signatures. Its benchmark and single-multiplet scan show promise, while broader scans require more compute and additional tools.

V. CONCLUSION AND OUTLOOK

  • hAIthem uses an autoregressive transformer pretrained on ∼1 billion output tokens to search parameter space with reinforcement learning, then builds LLM-empowered decision trees for underexplored signatures.The pipeline uses established physics tools and is designed to scale to hundreds of compute nodes; additional constraints, tools, and NLO corrections could extend its phenomenology.Source: §V · p. 22
  • On 21 Lagrangians, LLaM-medium found over 5x and LLaM-small over 2x DE’s viable points, and both found 5–10x more distinct disconnected regions per 100 viable points.Both models also matched or exceeded DE on experimental signature classes, according to the reported metrics.Source: §V · p. 22
  • As parameter-space dimension grows, LLaM viable-point counts rise while differential evolution’s collapse; at 640 probes, LLaM-medium found ∼60x DE’s and ∼30x LLaM-small’s viable points.The dimension comparison may reflect an implicitly learned lower-dimensional subspace; the authors present this as a possibility.Source: §V · p. 22
  • Across the considered single-scalar-multiplet models, LLaM-supported decision trees were topologically nontrivial, and LLM agents proposed discriminating, physically reasonable observable combinations.The scan includes per-Lagrangian trees and one tree across the full scan; the agents’ suggestions included previously unexplored combinations of known signatures.Source: §V · p. 22

A. Outlook

  • Broader scans could help assess future experiments’ ability to distinguish diverse dark-matter and BSM models, but would require substantial compute and potentially intelligent Lagrangian sampling.Extending to larger Lagrangian classes requires more computable probes and software beyond micrOMEGAs and SModelS; the authors also note the need for cross-disciplinary coordination.Source: A. Outlook · p. 22

CODE AVAILABILITY, DATASET, AND INTERACTIVE VISUALIZATIONS

1. Experimental Bounds

  • For mass-dependent experimental bounds, the pipeline interpolates literature curves in log-log space and compares predicted observables with the interpolated limits.For IceCube’s summed solar muon flux, it uses the least-constraining b̄b bound, a choice that can under-constrain but not over-constrain a model.Source: §1 · pp. 27–28

2. Invisible Higgs Branching Ratio

The pipeline rejects parameter points using invisible-Higgs and LHC constraints. It computes approximate dark-matter production cross sections for SModelS across the production channels allowed by the model’s quantum numbers.

2. Invisible Higgs Branching Ratio

  • For mDM ≥ mh/2 the invisible decay is closed; otherwise the invisible width sums dark-matter channels, and points with BR(h → inv) > 0.11 are rejected.Source: §2 · p. 28

3. SModelS Large Hadron Collider Bounds

  • For points surviving other bounds, SModelS compares predicted final-state topology cross sections with ATLAS and CMS limits; a point is LHC-excluded when its maximum ratio rmax exceeds 1.The pipeline exports approximate production cross sections and dark-matter decay branching ratios in an SLHA file for SModelS.Source: §3 · p. 29

a. Computing Approximate Cross Sections for SModelS

4. EWSB, Mass Mixing, and Dark-U(1) Kinetic Mixing

The pipeline diagonalizes dark-sector mass matrices to obtain physical masses and mixing matrices needed for observable calculations. For dark U(1)′ models, kinetic mixing creates a photon coupling, with a narrow approximation failure near the Z pole.

4. EWSB, Mass Mixing, and Dark-U(1) Kinetic Mixing

  • For components sharing post-EWSB conserved quantum numbers, the pipeline groups fields into mixing blocks and numerically diagonalizes them to obtain physical masses and mixing matrices for micrOMEGAs.Source: §4 · p. 31

a. Kinetic Mixing

  • In dark U(1)′ models, kinetic normalization, a Weinberg rotation, and Z–Z′ mass diagonalization yield a mostly dark eigenstate coupled to the SM photon, the portal for dilepton and direct-detection signals.The approximation fails near MZ′ ≈ mZ; its non-validity window is at most a few GeV wide, and fewer than 0.1% of viable points fell near it.Source: a. Kinetic Mixing · p. 31

5. Limiting the Copy Coupling Combinatorics

The pipeline constrains copied-field couplings to keep model complexity manageable, generates Lagrangians, and evaluates proposed parameter points against experimental constraints. Its inputs encode model, search, and experiment information, while history tokens summarize previous probes.

5. Limiting the Copy Coupling Combinatorics

  • Without restrictions, renormalizable couplings grow as ∼n^4 with field count and can exceed the d = 128 training cap; a discrete symmetry keeps copy masses independent but shares their couplings.Copies are interchangeable except for their masses, including shared self-couplings, cross-couplings, and couplings to fields outside the copy set.Source: §5 · p. 31

a. From Symmetries to Lagrangian

  • Sym2IntPy generates invariant operators from symmetries and field content, then FlavorBuilder expands them in gauge and flavor indices to produce the explicit Lagrangian.Source: a. From Symmetries to Lagrangian · p. 32

b. From Lagrangian to Observable

  • Generated models are compiled for micrOMEGAs, which computes relic abundance, direct-detection cross sections, annihilation spectra, indirect fluxes, and invisible-Higgs branching ratios; surviving electroweak-charged points also face SModelS limits.Viability and testability scores are returned for each proposed point; the work does not impose a vacuum-stability requirement, so a local minimum need not be global.Source: §6 · p. 31, b. From Lagrangian to Observable · p. 32

7. Allowed Quantum Numbers, Parameter Ranges, and Representative Examples

  • The agent proposes points in [0, 1]^d that map to physical parameters; each episode samples parameter subranges with minimum width 0.2 of the full logarithmic range.Tables X and XI present representative models and allowed single-multiplet quantum numbers; the scan restricts triplets to Y = 0, while real scalars and Majorana fermions cannot carry hypercharge or dark U(1)′ charge.Source: §7 · pp. 32–33, Table X · p. 33, Table XI · p. 33

8. Future Experiments

  • Twelve projected experiments serve as testability targets, reusing observables already computed for viability rather than requiring additional computation.Source: §8 · p. 33, Table XIII · p. 34

1. Input Tokens

  • Input tokens encode the Lagrangian’s fields and symmetries, active experimental cuts, parameter ranges, turn budget, and episode-level search and region summaries.The range, budget, current-turn, probes-used, and relic-width inputs vary across training episodes.Source: §1 · p. 34
  • Sixty-four learned queries summarize prior probe signatures with a learned recency bias, giving the agent a history-based map of where viable territory has been found.Each probe also records its proposing policy head and turn position; the query outputs become history tokens.Source: Figure 20 · p. 33, §1 · pp. 34–35
  • A sliding hard ν window moves each head from broad exploration toward sharp exploitation, while autoregressive chain tokens generate parameter values one at a time and a value token supplies PPO’s per-turn estimate.The figure describes staggered windows across heads; context tokens are encoded independently of the sampled actions.Source: Figure 21 · p. 35, §1 · p. 35

2. Concentration Schedule.

The schedule forces the policy from broad exploration toward sharp exploitation, while other subsections specify the differential-evolution objective, model hyperparameter tables, and observable binning.

2. Concentration Schedule.

  • The concentration window moves from [2] [8] at turn 0 to [100, 500] at the final turn, forcing broad exploration before sharp exploitation.The network chooses the means and each head’s concentration within the scheduled window; four heads divide labor from broad scouting to fine resolution, with 32 probes sampled per head each turn.Source: §2 · p. 36

3. Differential Evolution

  • The differential-evolution objective combines relic-density deviation and summed experimental-bound excess, adding −103 only for viable probes.The viability term is intended to make viability dominate the objective; σ = 0.5.Source: §3 · p. 36

4. Model and Training Hyperparameters

  • LLaM-small and LLaM-medium have size-specific hyperparameters in Table XIV and shared hyperparameters in Table XV.The supplied table captions identify where these parameter sets are reported but do not give their values.Source: Table XIV · p. 36, §4 · p. 36, Table XV · p. 37

1. Deterministic Observable Bin Widths

  • Observable bin widths reflect expected systematic error: high-error observables use larger bins, while less error-prone observables use tighter bins.The decision-tree inputs use μ_e = log10(O_pred/O_lim), discretized into fixed-width bins with overflow bins; indirect-detection signatures are binned per annihilation channel, while HL-LHC signatures are binary by final state.Source: §1 · p. 37, Table XVI · p. 37

2. Choosing Splits That Maximize Information Gain

The paper selects decision-tree measurements by information gain, groups viable parameter points into regions, and reports a 21-Lagrangian benchmark alongside scan trees for models with viable points.

2. Choosing Splits That Maximize Information Gain

  • Information gain selects the measurement split that most reduces mixing among the viable points’ signature classes.Entropy is largest when many classes are mixed and zero when only one class remains; class fractions define the entropy calculation.Source: §2 · p. 37

3. Defining Regions

  • Regions are DBSCAN clusters in log θ with at least five points, represented by d-dimensional bounding boxes and combined when one range is strictly contained in another.The DBSCAN neighborhood radius is ϵ = 0.8 p^(d/3), where d is the parameter-space dimension.Source: §3 · p. 38

1. The Benchmark

  • The benchmark comprises 21 Lagrangian classes ordered by parameter-space dimension, with per-Lagrangian results reported across budgets; captions specify B = 5, 10, and 25, with means and errors over three repeats.Source: §1 · p. 38, Table XVII · p. 38, Table XIX · p. 39

2. Scan Trees

  • Decision trees are shown for one-multiplet models with nonzero viable points, with LLM-agent trees included when available; three displayed trees do not meet the condition for applying the agent.The trees ask whether signals are seen at DarkSide and LZ; the figure captions identify examples including a complex scalar singlet with dark U(1)′.Source: §2 · p. 44, Figure 24 · p. 44, Figure 27 · p. 47

Related papers

Loading 2609.38309v1…