Sebastian Lehner

Fabian Paischer, Thomas Adler, Vihang Patil et al.

In a partially observable Markov decision process (POMDP), an agent typically uses a representation of the past to approximate the underlying MDP. We propose to utilize a frozen Pretrained Language Transformer (PLT) for history representation and compression to improve sample efficiency. To avoid training of the Transformer, we introduce FrozenHopfield, which automatically associates observations with pretrained token embeddings. To form these associations, a modern Hopfield network stores these token embeddings, which are retrieved by queries that are obtained by a random but fixed projection of observations. Our new method, HELM, enables actor-critic network architectures that contain a pretrained language Transformer for history representation as a memory module. Since a representation of the past need not be learned, HELM is much more sample efficient than competitors. On Minigrid and Procgen environments HELM achieves new state-of-the-art results. Our code is available at https://github.com/ml-jku/helm.

Laura Lewis, Hsin-Yuan Huang, Viet T. Tran et al.

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an $n$-qubit gapped local Hamiltonian after learning from only $\mathcal{O}(\log(n))$ data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $\mathcal{O}(n^c)$ data for a large constant $c$. Furthermore, the training and prediction time of the proposed ML model scale as $\mathcal{O}(n \log n)$ in the number of qubits $n$. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

Sebastian Sanokowski, Wilhelm Berghammer, Sepp Hochreiter et al.

Several recent unsupervised learning methods use probabilistic approaches to solve combinatorial optimization (CO) problems based on the assumption of statistically independent solution variables. We demonstrate that this assumption imposes performance limitations in particular on difficult problem instances. Our results corroborate that an autoregressive approach which captures statistical dependencies among solution variables yields superior performance on many popular CO problems. We introduce subgraph tokenization in which the configuration of a set of solution variables is represented by a single token. This tokenization technique alleviates the drawback of the long sequential sampling procedure which is inherent to autoregressive methods without sacrificing expressivity. Importantly, we theoretically motivate an annealed entropy regularization and show empirically that it is essential for efficient and stable learning.

Martin Gauch, Maximilian Beck, Thomas Adler et al.

We introduce SubGD, a novel few-shot learning method which is based on the recent finding that stochastic gradient descent updates tend to live in a low-dimensional parameter subspace. In experimental and theoretical analyses, we show that models confined to a suitable predefined subspace generalize well for few-shot learning. A suitable subspace fulfills three criteria across the given tasks: it (a) allows to reduce the training error by gradient flow, (b) leads to models that generalize well, and (c) can be identified by stochastic gradient descent. SubGD identifies these subspaces from an eigendecomposition of the auto-correlation matrix of update directions across different tasks. Demonstrably, we can identify low-dimensional suitable subspaces for few-shot learning of dynamical systems, which have varying properties described by one or few parameters of the analytical system description. Such systems are ubiquitous among real-world applications in science and engineering. We experimentally corroborate the advantages of SubGD on three distinct dynamical systems problem settings, significantly outperforming popular few-shot learning methods both in terms of sample efficiency and performance.

Philip M. Winter, Christoph Burger, Sebastian Lehner et al.

Fast and accurate treatment of collisions in the context of modern N-body planet formation simulations remains a challenging task due to inherently complex collision processes. We aim to tackle this problem with machine learning (ML), in particular via residual neural networks. Our model is motivated by the underlying physical processes of the data-generating process and allows for flexible prediction of post-collision states. We demonstrate that our model outperforms commonly used collision handling methods such as perfect inelastic merging and feed-forward neural networks in both prediction accuracy and out-of-distribution generalization. Our model outperforms the current state of the art in 20/24 experiments. We provide a dataset that consists of 10164 Smooth Particle Hydrodynamics (SPH) simulations of pairwise planetary collisions. The dataset is specifically suited for ML research to improve computational aspects for collision treatment and for studying planetary collisions in general. We formulate the ML task as a multi-task regression problem, allowing simple, yet efficient training of ML models for collision treatment in an end-to-end manner. Our models can be easily integrated into existing N-body frameworks and can be used within our chosen parameter space of initial conditions, i.e. where similar-sized collisions during late-stage terrestrial planet formation typically occur.

Sebastian Sanokowski, Wilhelm Berghammer, Martin Ennemoser et al.

Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has demonstrated the potential of diffusion models in this domain. However, existing methods face limitations in memory scaling and thus the number of attainable diffusion steps since they require backpropagation through the entire generative process. To overcome these limitations we introduce two novel training methods for discrete diffusion samplers, one grounded in the policy gradient theorem and the other one leveraging Self-Normalized Neural Importance Sampling (SN-NIS). These methods yield memory-efficient training and achieve state-of-the-art results in unsupervised combinatorial optimization. Numerous scientific applications additionally require the ability of unbiased sampling. We introduce adaptations of SN-NIS and Neural Markov Chain Monte Carlo that enable for the first time the application of discrete diffusion models to this problem. We validate our methods on Ising model benchmarks and find that they outperform popular autoregressive approaches. Our work opens new avenues for applying diffusion models to a wide range of scientific applications in discrete domains that were hitherto restricted to exact likelihood models.

Sebastian Sanokowski, Lukas Gruber, Christoph Bartmann et al.

Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.

Carlos Ruiz-Gonzalez, Sören Arlt, Sebastian Lehner et al.

Physics simulators are essential in science and engineering, enabling the analysis, control, and design of complex systems. In experimental sciences, they are increasingly used to automate experimental design, often via combinatorial search and optimization. However, as the setups grow more complex, the computational cost of traditional, CPU-based simulators becomes a major limitation. Here, we show how neural surrogate models can significantly reduce reliance on such slow simulators while preserving accuracy. Taking the design of interferometric gravitational wave detectors as a representative example, we train a neural network to surrogate the gravitational wave physics simulator Finesse, which was developed by the LIGO community. Despite that small changes in physical parameters can change the output by orders of magnitudes, the model rapidly predicts the quality and feasibility of candidate designs, allowing an efficient exploration of large design spaces. Our algorithm loops between training the surrogate, inverse designing new experiments, and verifying their properties with the slow simulator for further training. Assisted by auto-differentiation and GPU parallelism, our method proposes high-quality experiments much faster than direct optimization. Solutions that our algorithm finds within hours outperform designs that take five days for the optimizer to reach. Though shown in the context of gravitational wave detectors, our framework is broadly applicable to other domains where simulator bottlenecks hinder optimization and discovery.

Maximilian Beck, Kajetan Schweighofer, Sebastian Böck et al.

Scaling laws play a central role in the success of Large Language Models (LLMs), enabling the prediction of model performance relative to compute budgets prior to training. While Transformers have been the dominant architecture, recent alternatives such as xLSTM offer linear complexity with respect to context length while remaining competitive in the billion-parameter regime. We conduct a comparative investigation on the scaling behavior of Transformers and xLSTM along the following lines, providing insights to guide future model design and deployment. First, we study the scaling behavior for xLSTM in compute-optimal and over-training regimes using both IsoFLOP and parametric fit approaches on a wide range of model sizes (80M-7B) and number of training tokens (2B-2T). Second, we examine the dependence of optimal model sizes on context length, a pivotal aspect that was largely ignored in previous work. Finally, we analyze inference-time scaling characteristics. Our findings reveal that in typical LLM training and inference scenarios, xLSTM scales favorably compared to Transformers. Importantly, xLSTM's advantage widens as training and inference contexts grow.

Sebastian Sanokowski, Sepp Hochreiter, Sebastian Lehner

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based approaches rely primarily on generative models that yield exact sample likelihoods. This work introduces a method that lifts this restriction and opens the possibility to employ highly expressive latent variable models like diffusion models. Our approach is conceptually based on a loss that upper bounds the reverse Kullback-Leibler divergence and evades the requirement of exact sample likelihoods. We experimentally validate our approach in data-free Combinatorial Optimization and demonstrate that our method achieves a new state-of-the-art on a wide range of benchmark problems.

Andreas Mayr, Sebastian Lehner, Arno Mayrhofer et al.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

Andreas Mayr, Sebastian Lehner, Arno Mayrhofer et al.

Recently, the application of machine learning models has gained momentum in natural sciences and engineering, which is a natural fit due to the abundance of data in these fields. However, the modeling of physical processes from simulation data without first principle solutions remains difficult. Here, we present a Graph Neural Networks approach towards accurate modeling of complex 3D granular flow simulation processes created by the discrete element method LIGGGHTS and concentrate on simulations of physical systems found in real world applications like rotating drums and hoppers. We discuss how to implement Graph Neural Networks that deal with 3D objects, boundary conditions, particle - particle, and particle - boundary interactions such that an accurate modeling of relevant physical quantities is made possible. Finally, we compare the machine learning based trajectories to LIGGGHTS trajectories in terms of particle flows and mixing entropies.