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Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model
Atılım Güneş Baydin, Lukas Heinrich, Wahid Bhimji, Lei Shao, Saeid Naderiparizi, Andreas Munk, Jialin Liu, Bradley Gram-Hansen, Gilles Louppe, Lawrence Meadows, Philip Torr, Victor Lee, Prabhat, Kyle Cranmer, Frank Wood
TL;DR
Complex simulators often have intractable likelihoods, limiting traditional inference, while existing probabilistic programming languages are not designed to support simulator code bases directly. This paper connects such simulators to general-purpose inference engines through a cross-platform execution protocol and demonstrates inference on tau-lepton decay. The framework supports interpretable posterior inference tied to simulator processes, though its execution protocol currently precludes gradient-based inference engines.
Problem
Complex simulators define non-differentiable generative models with intractable likelihoods, and existing probabilistic programming languages are not designed to support their code bases directly.
Source: §1 · p. 1, §4.1 · p. 4Method
A cross-platform probabilistic execution protocol connects existing simulator code to general-purpose inference engines, which control simulator random draws for posterior inference.
Source: §1 · p. 1, §4.2 · p. 6Results
The framework controls SHERPA with minimal modifications to infer tau-lepton decay details from an LHC-like detector observation and compare posteriors to ground truth.
Source: §1 · p. 2Takeaways & Limitations
Bayesian inference through simulator code can expose the model processes and uncertainty associated with predictions, supporting interpretable results.
Source: §6 · p. 9The execution protocol currently precludes gradient-based inference engines; incorporating differentiability is left for future work.
Source: §4.1 · p. 4
Abstract
from arXiv · showhide
We present a novel probabilistic programming framework that couples directly to existing large-scale simulators through a cross-platform probabilistic execution protocol, which allows general-purpose inference engines to record and control random number draws within simulators in a language-agnostic way. The execution of existing simulators as probabilistic programs enables highly interpretable posterior inference in the structured model defined by the simulator code base. We demonstrate the technique in particle physics, on a scientifically accurate simulation of the tau lepton decay, which is a key ingredient in establishing the properties of the Higgs boson. Inference efficiency is achieved via inference compilation where a deep recurrent neural network is trained to parameterize proposal distributions and control the stochastic simulator in a sequential importance sampling scheme, at a fraction of the computational cost of a Markov chain Monte Carlo baseline.
1 Introduction
Complex simulators can define causal generative models whose non-differentiability and intractable likelihoods limit traditional inference. This work puts existing simulators under general-purpose inference-engine control and demonstrates the approach on tau-lepton decay.
1 Introduction
- Complex simulators often have non-differentiable models and intractable likelihoods, making many traditional statistical inference algorithms inapplicable and motivating likelihood-free methods.Such simulators are built from low-level mechanistic components and serve as causal generative models across scientific fields.Source: §1 · p. 1
- Likelihood-free inference either trains a surrogate likelihood for conventional inference or uses the original simulator directly, as in approximate Bayesian computation.Variational inference is not directly applicable when the data-generating likelihood is unknown.Source: §1 · p. 1
- The cross-platform protocol lets general-purpose inference engines control existing simulator code, supporting probabilistic execution without replacing the simulator with an approximating model.The framework provides C++ and Python bindings and can support other languages with a lightweight front end.Source: §1 · pp. 1–2, Figure 1 · p. 2
- The framework controls SHERPA to infer tau-lepton decay details from an LHC-like detector observation, with minimal simulator modifications, and compares posteriors to ground truth.The authors report controlling a code base of nearly one million lines of code.Source: §1 · p. 2
2 Particle Physics and Probabilistic Inference
Particle physics seeks to infer particle properties from complex collision events and detector data, but the complexity has limited likelihood-free inference for individual events. The paper focuses on tau-lepton decay, a process relevant to establishing Higgs-boson properties.
2 Particle Physics and Probabilistic Inference
- The complexity of particle physics and its detectors has so far prevented likelihood-free inference for individual collision events, despite sophisticated simulators of physical processes and detector interactions.Examples include SHERPA, Geant4, Pythia8, Herwig++, and MadGraph5.Source: §2 · p. 2
- Particle-physics simulators encode scientifically accurate generative models in general-purpose, Turing-complete languages, motivating infrastructure that supports probabilistic inference over their code.The paper frames this as a setting for universal probabilistic programming rather than methods limited to finite probabilistic graphical models.Source: §2 · p. 3
- Tau-lepton decay inside an LHC-like detector is the paper's use case and is relevant to establishing Higgs-boson properties through Higgs decay to tau particles.The decay channels have prior probabilities called branching ratios.Source: §2 · p. 3
3 Related Work
Related work covers universal probabilistic programming and particle-physics analysis, contrasting general inference over simulator-defined latent variables with reconstruction, surrogates, and deep-learning approaches.
3.1 Probabilistic Programming
- Probabilistic programming languages express sampling and conditioning in general-purpose programs, which define joint distributions and can be run with general-purpose inference engines.Inference compilation combines importance sampling with deep-learning proposals trained on program-generated data to enable amortized inference.Source: §3.1 · p. 3
3.2 Data Analysis in Particle Physics
- Particle-physics reconstruction typically returns candidate particles, types, and momentum point estimates; Bayesian inference over an individual event's latent structure is rare and has required drastic simulator simplification.Machine-learning surrogates have also been used to learn implicit simulator densities for likelihood-free inference.Source: §3.2 · p. 3
- Particle-physics workflows run simulators forward to generate large datasets, reduce them to a few domain-informed variables, and train classifiers or regressors on the resulting data.The generated datasets can exceed the size of actual collision datasets.Source: §3.2 · p. 3
- Deep-learning methods increasingly process high-dimensional, low-level data, but do not estimate the posterior over the full latent state or provide the framework's level of interpretability.The framework ties inference results directly to the latent process encoded by the simulator.Source: §3.2 · p. 4
4 Probabilistic Inference in Large-Scale Simulators
The framework makes existing stochastic simulators usable as probabilistic programs, so general-purpose inference engines can condition on observations and infer latent variables in the simulator’s structured model. It combines inference compilation with a cross-platform execution protocol and adapts both to SHERPA’s random draws and rejection-sampling loops.
4.1 Designing a PPL for Existing Large-Scale Simulators
- The framework captures random-number calls and adds conditioning so existing stochastic simulators can support Bayesian inference with interpretable posteriors tied to their code.The paper implements MCMC and importance-sampling engines, with inference compilation as its main efficient inference method.Source: §4.1 · p. 4, §4 · p. 4
- The protocol rules out gradient-based inference engines in the current setup, so the implemented engine families are MCMC and importance sampling.The authors plan to extend the protocol to incorporate differentiability.Source: §4.1 · p. 4
- Inference compilation trains a recurrent neural network to propose latent values conditioned on observations, and selected addresses can remain proposed from the prior.Training draws simulator-generated (x, y) pairs to optimize the proposal; the network can learn only a subset of sample addresses.Source: §4.1 · p. 5
- Prior inflation generates more training examples of rare outcomes, while inference retains the original prior so importance weights and the empirical posterior remain correct under that model.The need arises because simulator prior probabilities can vary widely, including decay probabilities differing by about 10^4.Source: §4.1 · pp. 5–6
4.2 A Cross-Platform Probabilistic Execution Protocol
- The execution protocol specifies cross-language sample and observe messages, allowing simulators and inference engines to run in different languages, processes, or machines.The protocol also supports runtime control of probabilistic models, not merely message serialization.Source: §4.2 · p. 6
4.3 Controlling SHERPA’s Simulation of Fundamental Particle Physics
- SHERPA is coupled through system-wide RNG rerouting; a problem-specific categorical address enables prior inflation to balance decay-channel examples during training.The experiments otherwise work with SHERPA’s low-level uniform random draws.Source: §4.3 · pp. 6–7
- Unbounded rejection-sampling traces slow IC training, so the reported approach excludes replace addresses from IC proposals and leaves them to the prior.Those addresses are treated as regular raw addresses in MCMC.Source: §4.3 · p. 7
5 Experiments
The tau-decay experiments infer simulator latent states from calorimeter observations, with inference compilation (IC) producing posteriors that agree with the Markov chain Monte Carlo (RMH) baseline much faster. A prior-inflation scheme also recovers posterior mass for a difficult, low-prior-probability decay channel.
5 Experiments
- The experiment simulates tau decays and calorimeter observations using a joint-density model for decay-product momenta and a fast, approximate stochastic detector.The detector simulation uses 20×35×35 voxels; electrons and π0 deposit most energy in earlier layers, while charged hadrons deposit deeper with larger fluctuations.Source: §5 · pp. 7–8
- RMH sampling required about 10^6 iterations for convergence and approximately 10^5 iterations per effectively independent sample in the example case.The reported RMH baseline used 7.7M traces and took 115 compute hours on one CPU node.Source: §5 · p. 8
- Less than 30 minutes per case, IC posteriors show good agreement with RMH baselines; the RMH example took 115 compute hours.IC uses a trained neural-network proposal, and training is incurred only once for a given simulator setup, enabling repeated inference.Source: §5 · p. 8
- IC recovers the small posterior probability mass of low-prior Channel 22 events through prior inflation and subsequent importance weighting.The Channel 22 calorimeter depositions resemble Channel 2, making this a difficult case for inference.Source: §5 · p. 8
6 Conclusions
The paper presents a first step toward bringing existing scientific simulators into a universal probabilistic programming framework. It argues that this enables interpretable model-based machine learning and identifies real-detector collision data as an ultimate particle-physics aim.
6 Conclusions
- The work presents a first step toward incorporating scientific simulators as causal generative models in a universal probabilistic programming framework.Scaling inference to large simulators remains difficult and involves challenges including simulator interfaces, long-tailed priors, addressing schemes, network architectures, and distributed training and inference.Source: §6 · p. 9
- Using simulator code as a structured generative model supports interpretable predictions by exposing the model locations and processes associated with them and their uncertainty.The stated ultimate particle-physics aim is inference on real-detector collision data through a full LHC physics analysis and posterior.Source: §6 · p. 9
- The proposed interface is intended to support applied work spanning machine learning and science and engineering.For particle physics, the authors describe discovery of new physics via simulations containing processes beyond the current Standard Model as an ultimate aim.Source: §6 · p. 9