Johann Brehmer

Johann Brehmer, Joey Bose, Pim de Haan et al.

Embodied agents operate in a structured world, often solving tasks with spatial, temporal, and permutation symmetries. Most algorithms for planning and model-based reinforcement learning (MBRL) do not take this rich geometric structure into account, leading to sample inefficiency and poor generalization. We introduce the Equivariant Diffuser for Generating Interactions (EDGI), an algorithm for MBRL and planning that is equivariant with respect to the product of the spatial symmetry group SE(3), the discrete-time translation group Z, and the object permutation group Sn. EDGI follows the Diffuser framework (Janner et al., 2022) in treating both learning a world model and planning in it as a conditional generative modeling problem, training a diffusion model on an offline trajectory dataset. We introduce a new SE(3)xZxSn-equivariant diffusion model that supports multiple representations. We integrate this model in a planning loop, where conditioning and classifier guidance let us softly break the symmetry for specific tasks as needed. On object manipulation and navigation tasks, EDGI is substantially more sample efficient and generalizes better across the symmetry group than non-equivariant models.

Risto Vuorio, Pim de Haan, Johann Brehmer et al.

Standard imitation learning can fail when the expert demonstrators have different sensory inputs than the imitating agent. This is because partial observability gives rise to hidden confounders in the causal graph. In previous work, to work around the confounding problem, policies have been trained using query access to the expert's policy or inverse reinforcement learning (IRL). However, both approaches have drawbacks as the expert's policy may not be available and IRL can be unstable in practice. Instead, we propose to train a variational inference model to infer the expert's latent information and use it to train a latent-conditional policy. We prove that using this method, under strong assumptions, the identification of the correct imitation learning policy is theoretically possible from expert demonstrations alone. In practice, we focus on a setting with less strong assumptions where we use exploration data for learning the inference model. We show in theory and practice that this algorithm converges to the correct interventional policy, solves the confounding issue, and can under certain assumptions achieve an asymptotically optimal imitation performance.

Pim de Haan, Taco Cohen, Johann Brehmer

The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer architecture given any geometric (or Clifford) algebra. We study versions of this architecture for Euclidean, projective, and conformal algebras, all of which are suited to represent 3D data, and evaluate them in theory and practice. The simplest Euclidean architecture is computationally cheap, but has a smaller symmetry group and is not as sample-efficient, while the projective model is not sufficiently expressive. Both the conformal algebra and an improved version of the projective algebra define powerful, performant architectures.

Johann Brehmer, Víctor Bresó, Pim de Haan et al.

We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over space-time and is equivariant under Lorentz transformations. The underlying architecture is a versatile and scalable transformer, which is able to break symmetries if needed. We demonstrate the power of L-GATr for amplitude regression and jet classification, and then benchmark it as the first Lorentz-equivariant generative network. For all three LHC tasks, we find significant improvements over previous architectures.

Jonas Spinner, Victor Bresó, Pim de Haan et al.

Extracting scientific understanding from particle-physics experiments requires solving diverse learning problems with high precision and good data efficiency. We propose the Lorentz Geometric Algebra Transformer (L-GATr), a new multi-purpose architecture for high-energy physics. L-GATr represents high-energy data in a geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, the symmetry group of relativistic kinematics. At the same time, the architecture is a Transformer, which makes it versatile and scalable to large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics. We then construct the first Lorentz-equivariant generative model: a continuous normalizing flow based on an L-GATr network, trained with Riemannian flow matching. Across our experiments, L-GATr is on par with or outperforms strong domain-specific baselines.

Johann Brehmer, Sönke Behrends, Pim de Haan et al.

Given large datasets and sufficient compute, is it beneficial to design neural architectures for the structure and symmetries of each problem? Or is it more efficient to learn them from data? We study empirically how equivariant and non-equivariant networks scale with compute and training samples. Focusing on a benchmark problem of rigid-body interactions and on general-purpose transformer architectures, we perform a series of experiments, varying the model size, training steps, and dataset size. We find evidence for three conclusions. First, equivariance improves data efficiency, but training non-equivariant models with data augmentation can close this gap given sufficient epochs. Second, scaling with compute follows a power law, with equivariant models outperforming non-equivariant ones at each tested compute budget. Finally, the optimal allocation of a compute budget onto model size and training duration differs between equivariant and non-equivariant models.

Anuroop Sriram, Logan M. Brabson, Xiaohan Yu et al. · baidu, cmu

Identifying useful sorbent materials for direct air capture (DAC) from humid air remains a challenge. We present the Open DAC 2025 (ODAC25) dataset, a significant expansion and improvement upon ODAC23 (Sriram et al., ACS Central Science, 10 (2024) 923), comprising nearly 60 million DFT single-point calculations for CO$_2$, H$_2$O, N$_2$, and O$_2$ adsorption in 15,000 MOFs. ODAC25 introduces chemical and configurational diversity through functionalized MOFs, high-energy GCMC-derived placements, and synthetically generated frameworks. ODAC25 also significantly improves upon the accuracy of DFT calculations and the treatment of flexible MOFs in ODAC23. Along with the dataset, we release new state-of-the-art machine-learned interatomic potentials trained on ODAC25 and evaluate them on adsorption energy and Henry's law coefficient predictions.

Ekdeep Singh Lubana, Johann Brehmer, Pim de Haan et al.

We explore the viability of casting foundation models as generic reward functions for reinforcement learning. To this end, we propose a simple pipeline that interfaces an off-the-shelf vision model with a large language model. Specifically, given a trajectory of observations, we infer the likelihood of an instruction describing the task that the user wants an agent to perform. We show that this generic likelihood function exhibits the characteristics ideally expected from a reward function: it associates high values with the desired behaviour and lower values for several similar, but incorrect policies. Overall, our work opens the possibility of designing open-ended agents for interactive tasks via foundation models.

Thomas Hehn, Markus Peschl, Tribhuvanesh Orekondy et al.

Modelling the propagation of electromagnetic wireless signals is critical for designing modern communication systems. Wireless ray tracing simulators model signal propagation based on the 3D geometry and other scene parameters, but their accuracy is fundamentally limited by underlying modelling assumptions and correctness of parameters. In this work, we introduce Wi-GATr, a fully-learnable neural simulation surrogate designed to predict the channel observations based on scene primitives (e.g., surface mesh, antenna position and orientation). Recognizing the inherently geometric nature of these primitives, Wi-GATr leverages an equivariant Geometric Algebra Transformer that operates on a tokenizer specifically tailored for wireless simulation. We evaluate our approach on a range of tasks (i.e., signal strength and delay spread prediction, receiver localization, and geometry reconstruction) and find that Wi-GATr is accurate, fast, sample-efficient, and robust to symmetry-induced transformations. Remarkably, we find our results also translate well to the real world: Wi-GATr demonstrates more than 35% lower error than hybrid techniques, and 70% lower error than a calibrated wireless tracer.

Johann Brehmer, Pim de Haan, Sönke Behrends et al.

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric (or Clifford) algebra, which offers an efficient 16-dimensional vector-space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a Transformer, GATr is versatile, efficient, and scalable. We demonstrate GATr in problems from n-body modeling to wall-shear-stress estimation on large arterial meshes to robotic motion planning. GATr consistently outperforms both non-geometric and equivariant baselines in terms of error, data efficiency, and scalability.

Johann Brehmer, Pim de Haan, Phillip Lippe et al.

Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is however identifiable in a weakly supervised setting. This involves a dataset with paired samples before and after random, unknown interventions, but no further labels. We then introduce implicit latent causal models, variational autoencoders that represent causal variables and causal structure without having to optimize an explicit discrete graph structure. On simple image data, including a novel dataset of simulated robotic manipulation, we demonstrate that such models can reliably identify the causal structure and disentangle causal variables.

Yunfan Zhang, Ties van Rozendaal, Johann Brehmer et al.

We propose a method to compress full-resolution video sequences with implicit neural representations. Each frame is represented as a neural network that maps coordinate positions to pixel values. We use a separate implicit network to modulate the coordinate inputs, which enables efficient motion compensation between frames. Together with a small residual network, this allows us to efficiently compress P-frames relative to the previous frame. We further lower the bitrate by storing the network weights with learned integer quantization. Our method, which we call implicit pixel flow (IPF), offers several simplifications over established neural video codecs: it does not require the receiver to have access to a pretrained neural network, does not use expensive interpolation-based warping operations, and does not require a separate training dataset. We demonstrate the feasibility of neural implicit compression on image and video data.

Alexander Lavin, David Krakauer, Hector Zenil et al.

The original "Seven Motifs" set forth a roadmap of essential methods for the field of scientific computing, where a motif is an algorithmic method that captures a pattern of computation and data movement. We present the "Nine Motifs of Simulation Intelligence", a roadmap for the development and integration of the essential algorithms necessary for a merger of scientific computing, scientific simulation, and artificial intelligence. We call this merger simulation intelligence (SI), for short. We argue the motifs of simulation intelligence are interconnected and interdependent, much like the components within the layers of an operating system. Using this metaphor, we explore the nature of each layer of the simulation intelligence operating system stack (SI-stack) and the motifs therein: (1) Multi-physics and multi-scale modeling; (2) Surrogate modeling and emulation; (3) Simulation-based inference; (4) Causal modeling and inference; (5) Agent-based modeling; (6) Probabilistic programming; (7) Differentiable programming; (8) Open-ended optimization; (9) Machine programming. We believe coordinated efforts between motifs offers immense opportunity to accelerate scientific discovery, from solving inverse problems in synthetic biology and climate science, to directing nuclear energy experiments and predicting emergent behavior in socioeconomic settings. We elaborate on each layer of the SI-stack, detailing the state-of-art methods, presenting examples to highlight challenges and opportunities, and advocating for specific ways to advance the motifs and the synergies from their combinations. Advancing and integrating these technologies can enable a robust and efficient hypothesis-simulation-analysis type of scientific method, which we introduce with several use-cases for human-machine teaming and automated science.

Ties van Rozendaal, Johann Brehmer, Yunfan Zhang et al.

We introduce a video compression algorithm based on instance-adaptive learning. On each video sequence to be transmitted, we finetune a pretrained compression model. The optimal parameters are transmitted to the receiver along with the latent code. By entropy-coding the parameter updates under a suitable mixture model prior, we ensure that the network parameters can be encoded efficiently. This instance-adaptive compression algorithm is agnostic about the choice of base model and has the potential to improve any neural video codec. On UVG, HEVC, and Xiph datasets, our codec improves the performance of a scale-space flow model by between 21% and 27% BD-rate savings, and that of a state-of-the-art B-frame model by 17 to 20% BD-rate savings. We also demonstrate that instance-adaptive finetuning improves the robustness to domain shift. Finally, our approach reduces the capacity requirements of compression models. We show that it enables a competitive performance even after reducing the network size by 70%.

Johann Brehmer, Sebastian Macaluso, Duccio Pappadopulo et al.

Particle physics experiments often require the reconstruction of decay patterns through a hierarchical clustering of the observed final-state particles. We show that this task can be phrased as a Markov Decision Process and adapt reinforcement learning algorithms to solve it. In particular, we show that Monte-Carlo Tree Search guided by a neural policy can construct high-quality hierarchical clusterings and outperform established greedy and beam search baselines.

Johann Brehmer, Kyle Cranmer

Our predictions for particle physics processes are realized in a chain of complex simulators. They allow us to generate high-fidelity simulated data, but they are not well-suited for inference on the theory parameters with observed data. We explain why the likelihood function of high-dimensional LHC data cannot be explicitly evaluated, why this matters for data analysis, and reframe what the field has traditionally done to circumvent this problem. We then review new simulation-based inference methods that let us directly analyze high-dimensional data by combining machine learning techniques and information from the simulator. Initial studies indicate that these techniques have the potential to substantially improve the precision of LHC measurements. Finally, we discuss probabilistic programming, an emerging paradigm that lets us extend inference to the latent process of the simulator.

Johann Brehmer, Kyle Cranmer

We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs, autoencoders, and energy-based models, they have the potential to represent datasets with a manifold structure more faithfully and provide handles on dimensionality reduction, denoising, and out-of-distribution detection. We argue why such models should not be trained by maximum likelihood alone and present a new training algorithm that separates manifold and density updates. In a range of experiments we demonstrate how M-flows learn the data manifold and allow for better inference than standard flows in the ambient data space.

Kyle Cranmer, Johann Brehmer, Gilles Louppe

Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the rapidly developing field of simulation-based inference and identify the forces giving new momentum to the field. Finally, we describe how the frontier is expanding so that a broad audience can appreciate the profound change these developments may have on science.

Johann Brehmer, Siddharth Mishra-Sharma, Joeri Hermans et al.

The subtle and unique imprint of dark matter substructure on extended arcs in strong lensing systems contains a wealth of information about the properties and distribution of dark matter on small scales and, consequently, about the underlying particle physics. However, teasing out this effect poses a significant challenge since the likelihood function for realistic simulations of population-level parameters is intractable. We apply recently-developed simulation-based inference techniques to the problem of substructure inference in galaxy-galaxy strong lenses. By leveraging additional information extracted from the simulator, neural networks are efficiently trained to estimate likelihood ratios associated with population-level parameters characterizing substructure. Through proof-of-principle application to simulated data, we show that these methods can provide an efficient and principled way to simultaneously analyze an ensemble of strong lenses, and can be used to mine the large sample of lensing images deliverable by near-future surveys for signatures of dark matter substructure.

Johann Brehmer, Felix Kling, Irina Espejo et al.

Precision measurements at the LHC often require analyzing high-dimensional event data for subtle kinematic signatures, which is challenging for established analysis methods. Recently, a powerful family of multivariate inference techniques that leverage both matrix element information and machine learning has been developed. This approach neither requires the reduction of high-dimensional data to summary statistics nor any simplifications to the underlying physics or detector response. In this paper we introduce MadMiner, a Python module that streamlines the steps involved in this procedure. Wrapping around MadGraph5_aMC and Pythia 8, it supports almost any physics process and model. To aid phenomenological studies, the tool also wraps around Delphes 3, though it is extendable to a full Geant4-based detector simulation. We demonstrate the use of MadMiner in an example analysis of dimension-six operators in ttH production, finding that the new techniques substantially increase the sensitivity to new physics.

Johann Brehmer, Kyle Cranmer, Irina Espejo et al.

One major challenge for the legacy measurements at the LHC is that the likelihood function is not tractable when the collected data is high-dimensional and the detector response has to be modeled. We review how different analysis strategies solve this issue, including the traditional histogram approach used in most particle physics analyses, the Matrix Element Method, Optimal Observables, and modern techniques based on neural density estimation. We then discuss powerful new inference methods that use a combination of matrix element information and machine learning to accurately estimate the likelihood function. The MadMiner package automates all necessary data-processing steps. In first studies we find that these new techniques have the potential to substantially improve the sensitivity of the LHC legacy measurements.

Markus Stoye, Johann Brehmer, Gilles Louppe et al.

We extend recent work (Brehmer, et. al., 2018) that use neural networks as surrogate models for likelihood-free inference. As in the previous work, we exploit the fact that the joint likelihood ratio and joint score, conditioned on both observed and latent variables, can often be extracted from an implicit generative model or simulator to augment the training data for these surrogate models. We show how this augmented training data can be used to provide a new cross-entropy estimator, which provides improved sample efficiency compared to previous loss functions exploiting this augmented training data.

Johann Brehmer, Gilles Louppe, Juan Pavez et al.

Simulators often provide the best description of real-world phenomena. However, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based inference techniques that go beyond the traditional Approximate Bayesian Computation approach, which struggles in a high-dimensional setting, and extend methods that use surrogate models based on neural networks. We show that additional information, such as the joint likelihood ratio and the joint score, can often be extracted from simulators and used to augment the training data for these surrogate models. Finally, we demonstrate that these new techniques are more sample efficient and provide higher-fidelity inference than traditional methods.

Johann Brehmer, Kyle Cranmer, Gilles Louppe et al.

We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator. This augmented data can be used to train neural networks that precisely estimate the likelihood ratio. The new methods scale well to many observables and high-dimensional parameter spaces, do not require any approximations of the parton shower and detector response, and can be evaluated in microseconds. Using weak-boson-fusion Higgs production as an example process, we compare the performance of several techniques. The best results are found for likelihood ratio estimators trained with extra information about the score, the gradient of the log likelihood function with respect to the theory parameters. The score also provides sufficient statistics that contain all the information needed for inference in the neighborhood of the Standard Model. These methods enable us to put significantly stronger bounds on effective dimension-six operators than the traditional approach based on histograms. They also outperform generic machine learning methods that do not make use of the particle physics structure, demonstrating their potential to substantially improve the new physics reach of the LHC legacy results.

Johann Brehmer, Kyle Cranmer, Gilles Louppe et al.

We present powerful new analysis techniques to constrain effective field theories at the LHC. By leveraging the structure of particle physics processes, we extract extra information from Monte-Carlo simulations, which can be used to train neural network models that estimate the likelihood ratio. These methods scale well to processes with many observables and theory parameters, do not require any approximations of the parton shower or detector response, and can be evaluated in microseconds. We show that they allow us to put significantly stronger bounds on dimension-six operators than existing methods, demonstrating their potential to improve the precision of the LHC legacy constraints.