Mathias Niepert

Makoto Takamoto, Timothy Praditia, Raphael Leiteritz et al.

Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and representative of a wide range of problems. We introduce PDEBench, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBench comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems contribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more realistic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of initial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBench allows researchers to extend the benchmark freely for their own purposes using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.

Duy M. H. Nguyen, Hoang Nguyen, Nghiem T. Diep et al. · eth-zurich

Obtaining large pre-trained models that can be fine-tuned to new tasks with limited annotated samples has remained an open challenge for medical imaging data. While pre-trained deep networks on ImageNet and vision-language foundation models trained on web-scale data are prevailing approaches, their effectiveness on medical tasks is limited due to the significant domain shift between natural and medical images. To bridge this gap, we introduce LVM-Med, the first family of deep networks trained on large-scale medical datasets. We have collected approximately 1.3 million medical images from 55 publicly available datasets, covering a large number of organs and modalities such as CT, MRI, X-ray, and Ultrasound. We benchmark several state-of-the-art self-supervised algorithms on this dataset and propose a novel self-supervised contrastive learning algorithm using a graph-matching formulation. The proposed approach makes three contributions: (i) it integrates prior pair-wise image similarity metrics based on local and global information; (ii) it captures the structural constraints of feature embeddings through a loss function constructed via a combinatorial graph-matching objective; and (iii) it can be trained efficiently end-to-end using modern gradient-estimation techniques for black-box solvers. We thoroughly evaluate the proposed LVM-Med on 15 downstream medical tasks ranging from segmentation and classification to object detection, and both for the in and out-of-distribution settings. LVM-Med empirically outperforms a number of state-of-the-art supervised, self-supervised, and foundation models. For challenging tasks such as Brain Tumor Classification or Diabetic Retinopathy Grading, LVM-Med improves previous vision-language models trained on 1 billion masks by 6-7% while using only a ResNet-50.

Vinh Tong, Dat Quoc Nguyen, Trung Thanh Huynh et al.

Knowledge graph (KG) alignment and completion are usually treated as two independent tasks. While recent work has leveraged entity and relation alignments from multiple KGs, such as alignments between multilingual KGs with common entities and relations, a deeper understanding of the ways in which multilingual KG completion (MKGC) can aid the creation of multilingual KG alignments (MKGA) is still limited. Motivated by the observation that structural inconsistencies -- the main challenge for MKGA models -- can be mitigated through KG completion methods, we propose a novel model for jointly completing and aligning knowledge graphs. The proposed model combines two components that jointly accomplish KG completion and alignment. These two components employ relation-aware graph neural networks that we propose to encode multi-hop neighborhood structures into entity and relation representations. Moreover, we also propose (i) a structural inconsistency reduction mechanism to incorporate information from the completion into the alignment component, and (ii) an alignment seed enlargement and triple transferring mechanism to enlarge alignment seeds and transfer triples during KGs alignment. Extensive experiments on a public multilingual benchmark show that our proposed model outperforms existing competitive baselines, obtaining new state-of-the-art results on both MKGC and MKGA tasks. We publicly release the implementation of our model at https://github.com/vinhsuhi/JMAC

Michael Cochez, Dimitrios Alivanistos, Erik Arakelyan et al. · deepmind

Knowledge graphs (KGs) are inherently incomplete because of incomplete world knowledge and bias in what is the input to the KG. Additionally, world knowledge constantly expands and evolves, making existing facts deprecated or introducing new ones. However, we would still want to be able to answer queries as if the graph were complete. In this chapter, we will give an overview of several methods which have been proposed to answer queries in such a setting. We will first provide an overview of the different query types which can be supported by these methods and datasets typically used for evaluation, as well as an insight into their limitations. Then, we give an overview of the different approaches and describe them in terms of expressiveness, supported graph types, and inference capabilities.

Chendi Qian, Gaurav Rattan, Floris Geerts et al.

Numerous subgraph-enhanced graph neural networks (GNNs) have emerged recently, provably boosting the expressive power of standard (message-passing) GNNs. However, there is a limited understanding of how these approaches relate to each other and to the Weisfeiler-Leman hierarchy. Moreover, current approaches either use all subgraphs of a given size, sample them uniformly at random, or use hand-crafted heuristics instead of learning to select subgraphs in a data-driven manner. Here, we offer a unified way to study such architectures by introducing a theoretical framework and extending the known expressivity results of subgraph-enhanced GNNs. Concretely, we show that increasing subgraph size always increases the expressive power and develop a better understanding of their limitations by relating them to the established $k\text{-}\mathsf{WL}$ hierarchy. In addition, we explore different approaches for learning to sample subgraphs using recent methods for backpropagating through complex discrete probability distributions. Empirically, we study the predictive performance of different subgraph-enhanced GNNs, showing that our data-driven architectures increase prediction accuracy on standard benchmark datasets compared to non-data-driven subgraph-enhanced graph neural networks while reducing computation time.

Kareem Ahmed, Zhe Zeng, Mathias Niepert et al.

$k$-subset sampling is ubiquitous in machine learning, enabling regularization and interpretability through sparsity. The challenge lies in rendering $k$-subset sampling amenable to end-to-end learning. This has typically involved relaxing the reparameterized samples to allow for backpropagation, with the risk of introducing high bias and high variance. In this work, we fall back to discrete $k$-subset sampling on the forward pass. This is coupled with using the gradient with respect to the exact marginals, computed efficiently, as a proxy for the true gradient. We show that our gradient estimator, SIMPLE, exhibits lower bias and variance compared to state-of-the-art estimators, including the straight-through Gumbel estimator when $k = 1$. Empirical results show improved performance on learning to explain and sparse linear regression. We provide an algorithm for computing the exact ELBO for the $k$-subset distribution, obtaining significantly lower loss compared to SOTA.

Anji Liu, Mathias Niepert, Guy Van den Broeck

Diffusion models are the current state of the art for generating photorealistic images. Controlling the sampling process for constrained image generation tasks such as inpainting, however, remains challenging since exact conditioning on such constraints is intractable. While existing methods use various techniques to approximate the constrained posterior, this paper proposes to exploit the ability of Tractable Probabilistic Models (TPMs) to exactly and efficiently compute the constrained posterior, and to leverage this signal to steer the denoising process of diffusion models. Specifically, this paper adopts a class of expressive TPMs termed Probabilistic Circuits (PCs). Building upon prior advances, we further scale up PCs and make them capable of guiding the image generation process of diffusion models. Empirical results suggest that our approach can consistently improve the overall quality and semantic coherence of inpainted images across three natural image datasets (i.e., CelebA-HQ, ImageNet, and LSUN) with only $\sim\! 10 \%$ additional computational overhead brought by the TPM. Further, with the help of an image encoder and decoder, our method can readily accept semantic constraints on specific regions of the image, which opens up the potential for more controlled image generation tasks. In addition to proposing a new framework for constrained image generation, this paper highlights the benefit of more tractable models and motivates the development of expressive TPMs.

Tuan Anh Tran, Duy M. H. Nguyen, Hoai-Chau Tran et al.

Recent advances in 3D point cloud transformers have led to state-of-the-art results in tasks such as semantic segmentation and reconstruction. However, these models typically rely on dense token representations, incurring high computational and memory costs during training and inference. In this work, we present the finding that tokens are remarkably redundant, leading to substantial inefficiency. We introduce gitmerge3D, a globally informed graph token merging method that can reduce the token count by up to 90-95% while maintaining competitive performance. This finding challenges the prevailing assumption that more tokens inherently yield better performance and highlights that many current models are over-tokenized and under-optimized for scalability. We validate our method across multiple 3D vision tasks and show consistent improvements in computational efficiency. This work is the first to assess redundancy in large-scale 3D transformer models, providing insights into the development of more efficient 3D foundation architectures. Our code and checkpoints are publicly available at https://gitmerge3d.github.io

Makoto Takamoto, Francesco Alesiani, Mathias Niepert

Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and inverse design, ML-based surrogate models are increasingly used to augment or replace inefficient and often non-differentiable numerical simulation algorithms. While a number of ML-based methods for approximating the solutions of PDEs have been proposed in recent years, they typically do not adapt to the parameters of the PDEs, making it difficult to generalize to PDE parameters not seen during training. We propose a Channel Attention mechanism guided by PDE Parameter Embeddings (CAPE) component for neural surrogate models and a simple yet effective curriculum learning strategy. The CAPE module can be combined with neural PDE solvers allowing them to adapt to unseen PDE parameters. The curriculum learning strategy provides a seamless transition between teacher-forcing and fully auto-regressive training. We compare CAPE in conjunction with the curriculum learning strategy using a popular PDE benchmark and obtain consistent and significant improvements over the baseline models. The experiments also show several advantages of CAPE, such as its increased ability to generalize to unseen PDE parameters without large increases inference time and parameter count.

Chendi Qian, Andrei Manolache, Kareem Ahmed et al.

Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable $k$-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.

Makoto Takamoto, Viktor Zaverkin, Mathias Niepert

Machine learning plays an increasingly important role in computational chemistry and materials science, complementing computationally intensive ab initio and first-principles methods. Despite their utility, machine-learning models often lack generalization capability and robustness during atomistic simulations, yielding unphysical energy and force predictions that hinder their real-world applications. We address this challenge by introducing a physics-informed, weakly supervised approach for training machine-learned interatomic potentials (MLIPs). We introduce two novel loss functions, extrapolating the potential energy via a Taylor expansion and using the concept of conservative forces. Our approach improves the accuracy of MLIPs applied to training tasks with sparse training data sets and reduces the need for pre-training computationally demanding models with large data sets. Particularly, we perform extensive experiments demonstrating reduced energy and force errors -- often lower by a factor of two -- for various baseline models and benchmark data sets. Moreover, we demonstrate improved robustness during MD simulations of the MLIP models trained with the proposed weakly supervised loss. Finally, our approach improves the fine-tuning of foundation models on sparse, highly accurate ab initio data. An implementation of our method and scripts for executing experiments are available at https://github.com/nec-research/PICPS-ML4Sci.

Pasquale Minervini, Luca Franceschi, Mathias Niepert

The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation (IMLE, Niepert, Minervini, and Franceschi 2021), a class of gradient estimators for discrete exponential family distributions, was proposed by combining implicit differentiation through perturbation with the path-wise gradient estimator. However, due to the finite difference approximation of the gradients, it is especially sensitive to the choice of the finite difference step size, which needs to be specified by the user. In this work, we present Adaptive IMLE (AIMLE), the first adaptive gradient estimator for complex discrete distributions: it adaptively identifies the target distribution for IMLE by trading off the density of gradient information with the degree of bias in the gradient estimates. We empirically evaluate our estimator on synthetic examples, as well as on Learning to Explain, Discrete Variational Auto-Encoders, and Neural Relational Inference tasks. In our experiments, we show that our adaptive gradient estimator can produce faithful estimates while requiring orders of magnitude fewer samples than other gradient estimators.

Giuseppe Serra, Mathias Niepert

Graph Neural Networks (GNNs) are a popular class of machine learning models. Inspired by the learning to explain (L2X) paradigm, we propose L2XGNN, a framework for explainable GNNs which provides faithful explanations by design. L2XGNN learns a mechanism for selecting explanatory subgraphs (motifs) which are exclusively used in the GNNs message-passing operations. L2XGNN is able to select, for each input graph, a subgraph with specific properties such as being sparse and connected. Imposing such constraints on the motifs often leads to more interpretable and effective explanations. Experiments on several datasets suggest that L2XGNN achieves the same classification accuracy as baseline methods using the entire input graph while ensuring that only the provided explanations are used to make predictions. Moreover, we show that L2XGNN is able to identify motifs responsible for the graph's properties it is intended to predict.

Dexiong Chen, Andrei Manolache, Mathias Niepert et al.

Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale, non-redundant benchmark for protein fold classification constructed from the Encyclopedia of Domains (TED) and Foldseek-clustered AlphaFold structures. We show that on TEDBench, current protein representation learning methods either require very large models or fail to deliver strong performance. To address this challenge, we propose Masked Invariant Autoencoders (MiAE), a self-supervised framework for protein structure representation learning. MiAE uses an extremely high masking ratio of up to 90% with an $\mathrm{SE(3)}$-invariant encoder and a lightweight decoder that reconstructs backbone coordinates from the latent representation and mask tokens. MiAE scales well and outperforms supervised counterparts and state-of-the-art baselines on TEDBench, establishing a strong recipe for protein fold classification. To test transfer beyond AlphaFold structures, we further benchmark on a curated dataset from experimental structures of CATH v4.4. TEDBench is available at https://github.com/BorgwardtLab/TEDBench.

David Friede, Christian Reimers, Heiner Stuckenschmidt et al.

Recent successes in image generation, model-based reinforcement learning, and text-to-image generation have demonstrated the empirical advantages of discrete latent representations, although the reasons behind their benefits remain unclear. We explore the relationship between discrete latent spaces and disentangled representations by replacing the standard Gaussian variational autoencoder (VAE) with a tailored categorical variational autoencoder. We show that the underlying grid structure of categorical distributions mitigates the problem of rotational invariance associated with multivariate Gaussian distributions, acting as an efficient inductive prior for disentangled representations. We provide both analytical and empirical findings that demonstrate the advantages of discrete VAEs for learning disentangled representations. Furthermore, we introduce the first unsupervised model selection strategy that favors disentangled representations.

David Friede, Mathias Niepert

Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more interpretable. A popular approach to building discrete-continuous computation graphs is that of integrating discrete probability distributions into neural networks using stochastic softmax tricks. Prior work has mainly focused on computation graphs with a single discrete component on each of the graph's execution paths. We analyze the behavior of more complex stochastic computations graphs with multiple sequential discrete components. We show that it is challenging to optimize the parameters of these models, mainly due to small gradients and local minima. We then propose two new strategies to overcome these challenges. First, we show that increasing the scale parameter of the Gumbel noise perturbations during training improves the learning behavior. Second, we propose dropout residual connections specifically tailored to stochastic, discrete-continuous computation graphs. With an extensive set of experiments, we show that we can train complex discrete-continuous models which one cannot train with standard stochastic softmax tricks. We also show that complex discrete-stochastic models generalize better than their continuous counterparts on several benchmark datasets.

Cheng Wang, Carolin Lawrence, Mathias Niepert

Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as how they arrive at a particular prediction. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both shortcomings with a class of recurrent networks that use a stochastic state transition mechanism between cell applications. This mechanism, which we term state-regularization, makes RNNs transition between a finite set of learnable states. We evaluate state-regularized RNNs on (1) regular languages for the purpose of automata extraction; (2) non-regular languages such as balanced parentheses and palindromes where external memory is required; and (3) real-word sequence learning tasks for sentiment analysis, visual object recognition and text categorisation. We show that state-regularization (a) simplifies the extraction of finite state automata that display an RNN's state transition dynamic; (b) forces RNNs to operate more like automata with external memory and less like finite state machines, which potentiality leads to a more structural memory; (c) leads to better interpretability and explainability of RNNs by leveraging the probabilistic finite state transition mechanism over time steps.

Timo Stoll, Chendi Qian, Ben Finkelshtein et al.

Machine learning on graphs has recently achieved impressive progress in various domains, including molecular property prediction and chip design. However, benchmarking practices remain fragmented, often relying on narrow, task-specific datasets and inconsistent evaluation protocols, which hampers reproducibility and broader progress. To address this, we introduce GraphBench, a comprehensive benchmarking suite that spans diverse domains and prediction tasks, including node-level, edge-level, graph-level, and generative settings. GraphBench provides standardized evaluation protocols -- with consistent dataset splits and performance metrics that account for out-of-distribution generalization -- as well as a unified hyperparameter tuning framework. Additionally, we benchmark GraphBench using message-passing neural networks and graph transformer models, providing principled baselines and establishing a reference performance. See www.graphbench.io for further details.

Laurène Vaugrante, Mathias Niepert, Thilo Hagendorff

In an era where large language models (LLMs) are increasingly integrated into a wide range of everyday applications, research into these models' behavior has surged. However, due to the novelty of the field, clear methodological guidelines are lacking. This raises concerns about the replicability and generalizability of insights gained from research on LLM behavior. In this study, we discuss the potential risk of a replication crisis and support our concerns with a series of replication experiments focused on prompt engineering techniques purported to influence reasoning abilities in LLMs. We tested GPT-3.5, GPT-4o, Gemini 1.5 Pro, Claude 3 Opus, Llama 3-8B, and Llama 3-70B, on the chain-of-thought, EmotionPrompting, ExpertPrompting, Sandbagging, as well as Re-Reading prompt engineering techniques, using manually double-checked subsets of reasoning benchmarks including CommonsenseQA, CRT, NumGLUE, ScienceQA, and StrategyQA. Our findings reveal a general lack of statistically significant differences across nearly all techniques tested, highlighting, among others, several methodological weaknesses in previous research. We propose a forward-looking approach that includes developing robust methodologies for evaluating LLMs, establishing sound benchmarks, and designing rigorous experimental frameworks to ensure accurate and reliable assessments of model outputs.

Daniel Musekamp, Marimuthu Kalimuthu, David Holzmüller et al.

Solving partial differential equations (PDEs) is a fundamental problem in science and engineering. While neural PDE solvers can be more efficient than established numerical solvers, they often require large amounts of training data that is costly to obtain. Active learning (AL) could help surrogate models reach the same accuracy with smaller training sets by querying classical solvers with more informative initial conditions and PDE parameters. While AL is more common in other domains, it has yet to be studied extensively for neural PDE solvers. To bridge this gap, we introduce AL4PDE, a modular and extensible active learning benchmark. It provides multiple parametric PDEs and state-of-the-art surrogate models for the solver-in-the-loop setting, enabling the evaluation of existing and the development of new AL methods for neural PDE solving. We use the benchmark to evaluate batch active learning algorithms such as uncertainty- and feature-based methods. We show that AL reduces the average error by up to 71% compared to random sampling and significantly reduces worst-case errors. Moreover, AL generates similar datasets across repeated runs, with consistent distributions over the PDE parameters and initial conditions. The acquired datasets are reusable, providing benefits for surrogate models not involved in the data generation.

Zhao Xu, Daniel Onoro Rubio, Giuseppe Serra et al.

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often continuous and dense. However in many applications, sparse representations are expected, such as learning sparse high dimensional embedding of data in an unsupervised setting, and learning multi-labels from thousands of candidate tags in a supervised setting. In some scenarios, there could be further restriction on degree of sparsity: the number of non-zero features of a representation cannot be larger than a pre-defined threshold $L_0$. In this paper we propose a sparse deep latent generative model SDLGM to explicitly model degree of sparsity and thus enable to learn the sparse structure of the data with the quantified sparsity constraint. The resulting sparsity of a representation is not fixed, but fits to the observation itself under the pre-defined restriction. In particular, we introduce to each observation $i$ an auxiliary random variable $L_i$, which models the sparsity of its representation. The sparse representations are then generated with a two-step sampling process via two Gumbel-Softmax distributions. For inference and learning, we develop an amortized variational method based on MC gradient estimator. The resulting sparse representations are differentiable with backpropagation. The experimental evaluation on multiple datasets for unsupervised and supervised learning problems shows the benefits of the proposed method.

Duy Minh Ho Nguyen, Tan Ngoc Pham, Nghiem Tuong Diep et al.

Constructing a robust model that can effectively generalize to test samples under distribution shifts remains a significant challenge in the field of medical imaging. The foundational models for vision and language, pre-trained on extensive sets of natural image and text data, have emerged as a promising approach. It showcases impressive learning abilities across different tasks with the need for only a limited amount of annotated samples. While numerous techniques have focused on developing better fine-tuning strategies to adapt these models for specific domains, we instead examine their robustness to domain shifts in the medical image segmentation task. To this end, we compare the generalization performance to unseen domains of various pre-trained models after being fine-tuned on the same in-distribution dataset and show that foundation-based models enjoy better robustness than other architectures. From here, we further developed a new Bayesian uncertainty estimation for frozen models and used them as an indicator to characterize the model's performance on out-of-distribution (OOD) data, proving particularly beneficial for real-world applications. Our experiments not only reveal the limitations of current indicators like accuracy on the line or agreement on the line commonly used in natural image applications but also emphasize the promise of the introduced Bayesian uncertainty. Specifically, lower uncertainty predictions usually tend to higher out-of-distribution (OOD) performance.

Duy M. H. Nguyen, An T. Le, Trung Q. Nguyen et al.

Prompt learning methods are gaining increasing attention due to their ability to customize large vision-language models to new domains using pre-trained contextual knowledge and minimal training data. However, existing works typically rely on optimizing unified prompt inputs, often struggling with fine-grained classification tasks due to insufficient discriminative attributes. To tackle this, we consider a new framework based on a dual context of both domain-shared and class-specific contexts, where the latter is generated by Large Language Models (LLMs) such as GPTs. Such dual prompt methods enhance the model's feature representation by joining implicit and explicit factors encoded in LLM knowledge. Moreover, we formulate the Unbalanced Optimal Transport (UOT) theory to quantify the relationships between constructed prompts and visual tokens. Through partial matching, UOT can properly align discrete sets of visual tokens and prompt embeddings under different mass distributions, which is particularly valuable for handling irrelevant or noisy elements, ensuring that the preservation of mass does not restrict transport solutions. Furthermore, UOT's characteristics integrate seamlessly with image augmentation, expanding the training sample pool while maintaining a reasonable distance between perturbed images and prompt inputs. Extensive experiments across few-shot classification and adapter settings substantiate the superiority of our model over current state-of-the-art baselines.

Vinh Tong, Hoang Trung-Dung, Anji Liu et al.

Diffusion Probabilistic Models (DPMs) are generative models showing competitive performance in various domains, including image synthesis and 3D point cloud generation. Sampling from pre-trained DPMs involves multiple neural function evaluations (NFEs) to transform Gaussian noise samples into images, resulting in higher computational costs compared to single-step generative models such as GANs or VAEs. Therefore, reducing the number of NFEs while preserving generation quality is crucial. To address this, we propose LD3, a lightweight framework designed to learn the optimal time discretization for sampling. LD3 can be combined with various samplers and consistently improves generation quality without having to retrain resource-intensive neural networks. We demonstrate analytically and empirically that LD3 improves sampling efficiency with much less computational overhead. We evaluate our method with extensive experiments on 7 pre-trained models, covering unconditional and conditional sampling in both pixel-space and latent-space DPMs. We achieve FIDs of 2.38 (10 NFE), and 2.27 (10 NFE) on unconditional CIFAR10 and AFHQv2 in 5-10 minutes of training. LD3 offers an efficient approach to sampling from pre-trained diffusion models. Code is available at https://github.com/vinhsuhi/LD3.

Hoai-Chau Tran, Chi H. Nguyen, Duy M. H. Nguyen et al.

The Segment Anything Model (SAM) achieves strong open-vocabulary segmentation, but its ViT-based image encoders dominate inference latency and memory. Existing activation compression methods, such as token merging, reduce the token length to process, yet introduce non-trivial runtime overhead and encounter catastrophic quality drop under high compression. Other methods applying Sparse Attention focus on attention alone, leaving the MLP fully dense and capping achievable speedup. We propose SparseSAM, a (i) training-free structured sparsification framework that jointly accelerates attention and MLP layers while preserving token identity. SparseSAM introduces (ii) Stripe-Sort Attention, which uses a deterministic Z-order permutation to transform dense attention into static hardware-friendly sparse patterns, eliminating dynamic masking overhead. SparseSAM further introduces a (iii) Residual-Consistency MLP that routes only informative tokens through the MLP while propagating remaining tokens through the residual pathway. Across four segmentation benchmarks, SparseSAM loses only 0.004 mIoU at a 0.4 density and 0.021 mIoU at 0.3, a 2.10x reduction in accuracy loss versus token merging advances, while achieving 2x faster inference and 2.8x memory reduction.

Francesco Alesiani, Shujian Yu, Mathias Niepert

Empirical risk minimization can lead to poor generalization behavior on unseen environments if the learned model does not capture invariant feature representations. Invariant risk minimization (IRM) is a recent proposal for discovering environment-invariant representations. IRM was introduced by Arjovsky et al. (2019) and extended by Ahuja et al. (2020). IRM assumes that all environments are available to the learning system at the same time. With this work, we generalize the concept of IRM to scenarios where environments are observed sequentially. We show that existing approaches, including those designed for continual learning, fail to identify the invariant features and models across sequentially presented environments. We extend IRM under a variational Bayesian and bilevel framework, creating a general approach to continual invariant risk minimization. We also describe a strategy to solve the optimization problems using a variant of the alternating direction method of multiplier (ADMM). We show empirically using multiple datasets and with multiple sequential environments that the proposed methods outperform or is competitive with prior approaches.

Jan Hagnberger, Mathias Niepert

Machine learning-based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an additional input, thereby reducing prediction errors. However, generating a simulation mesh for new geometries is computationally costly. In contrast, mesh-free methods, which do not rely on the simulation mesh, typically incur higher errors. Motivated by these considerations, we introduce SMART, a neural surrogate model that predicts physical quantities at arbitrary query locations using only a point-cloud representation of the geometry, without requiring access to the simulation mesh. The geometry and simulation parameters are encoded into a shared latent space that captures both structural and parametric characteristics of the physical field. A physics decoder then attends to the encoder's intermediate latent representations to map spatial queries to physical quantities. Through this cross-layer interaction, the model jointly updates latent geometric features and the evolving physical field. Extensive experiments show that SMART is competitive with and often outperforms existing methods that rely on the simulation mesh as input, demonstrating its capabilities for industry-level simulations.

Francesco Alesiani, Jonathan Warrell, Tanja Bien et al.

We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas can be obtained from guidance signals associated with atomic properties. First, we derive an exact Boolean calculus that provides a sufficient condition for exact logical guidance. Specifically, if a formula admits a circuit representation in which conjunctions combine conditionally independent subformulas and disjunctions combine subformulas that are either conditionally independent or mutually exclusive, exact logical guidance is achievable. In this case, the guidance signal can be computed exactly from atomic scores and posterior probabilities using an efficient recursive algorithm. Moreover, we show that, for commonly encountered classes of distributions, any desired Boolean formula is compilable into such a circuit representation. Second, by combining atomic guidance scores with posterior probability estimates, we introduce a hybrid guidance approach that bridges classifierguidance and classifier-free guidance, applicable to both compositional logical guidance and standard conditional generation. We demonstrate the effectiveness of our framework on multiple image and protein structure generation tasks.

Vinh Tong, Hoang Trung-Dung, Anji Liu et al.

In domains such as molecular and protein generation, physical systems exhibit inherent symmetries that are critical to model. Two main strategies have emerged for learning invariant distributions: designing equivariant network architectures and using data augmentation to approximate equivariance. While equivariant architectures preserve symmetry by design, they often involve greater complexity and pose optimization challenges. Data augmentation, on the other hand, offers flexibility but may fall short in fully capturing symmetries. Our framework enhances both approaches by reducing training variance and providing a provably lower-variance gradient estimator. We achieve this by interpreting data augmentation as a Monte Carlo estimator of the training gradient and applying Rao-Blackwellization. This leads to more stable optimization, faster convergence, and reduced variance, all while requiring only a single forward and backward pass per sample. We also present a practical implementation of this estimator incorporating the loss and sampling procedure through a method we call Orbit Diffusion. Theoretically, we guarantee that our loss admits equivariant minimizers. Empirically, Orbit Diffusion achieves state-of-the-art results on GEOM-QM9 for molecular conformation generation, improves crystal structure prediction, and advances text-guided crystal generation on the Perov-5 and MP-20 benchmarks. Additionally, it enhances protein designability in protein structure generation. Code is available at: https://github.com/vinhsuhi/Orbit-Diffusion.git.

Kiril Gashteovski, Mingying Yu, Bhushan Kotnis et al.

Intrinsic evaluations of OIE systems are carried out either manually -- with human evaluators judging the correctness of extractions -- or automatically, on standardized benchmarks. The latter, while much more cost-effective, is less reliable, primarily because of the incompleteness of the existing OIE benchmarks: the ground truth extractions do not include all acceptable variants of the same fact, leading to unreliable assessment of the models' performance. Moreover, the existing OIE benchmarks are available for English only. In this work, we introduce BenchIE: a benchmark and evaluation framework for comprehensive evaluation of OIE systems for English, Chinese, and German. In contrast to existing OIE benchmarks, BenchIE is fact-based, i.e., it takes into account informational equivalence of extractions: our gold standard consists of fact synsets, clusters in which we exhaustively list all acceptable surface forms of the same fact. Moreover, having in mind common downstream applications for OIE, we make BenchIE multi-faceted; i.e., we create benchmark variants that focus on different facets of OIE evaluation, e.g., compactness or minimality of extractions. We benchmark several state-of-the-art OIE systems using BenchIE and demonstrate that these systems are significantly less effective than indicated by existing OIE benchmarks. We make BenchIE (data and evaluation code) publicly available on https://github.com/gkiril/benchie.

Samir Darouich, Vinh Tong, Lluís Pastor-Pérez et al.

Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such as rotations in three-dimensional space. Equivariant diffusion and flow matching models can incorporate such invariances effectively, even when trained on a non-invariant empirical distribution, but they typically rely on costly multi-step sampling. Recently, drifting models have emerged as an efficient alternative, enabling single-step generation and achieving state-of-the-art performance in generative modeling tasks. However, we show that drifting models face a symmetry-specific challenge, since an equivariant generator does not generally produce the same drifting field as the one obtained from the symmetrized target distribution. Addressing this issue would require expensive symmetrization of the empirical distribution. To avoid this cost, we propose SymDrift, a framework that makes the drifting field itself symmetry-aware. We introduce two complementary strategies: (i) a symmetrized drift in coordinate space based on optimal alignment, and (ii) a $G$-invariant embedding that removes symmetry ambiguity by construction. Empirically, SymDrift outperforms existing one-shot methods on standard benchmarks for conformer and transition state generation, while remaining competitive with significantly more expensive multi-step approaches. By enabling one-shot inference, SymDrift reduces computational overhead by up to 40$\times$ compared to existing baselines, making it promising for high-throughput applications such as virtual drug screening and large-scale reaction network exploration.

Maya Bechler-Speicher, Ben Finkelshtein, Fabrizio Frasca et al. · deepmind

While machine learning on graphs has demonstrated promise in drug design and molecular property prediction, significant benchmarking challenges hinder its further progress and relevance. Current benchmarking practices often lack focus on transformative, real-world applications, favoring narrow domains like two-dimensional molecular graphs over broader, impactful areas such as combinatorial optimization, relational databases, or chip design. Additionally, many benchmark datasets poorly represent the underlying data, leading to inadequate abstractions and misaligned use cases. Fragmented evaluations and an excessive focus on accuracy further exacerbate these issues, incentivizing overfitting rather than fostering generalizable insights. These limitations have prevented the development of truly useful graph foundation models. This position paper calls for a paradigm shift toward more meaningful benchmarks, rigorous evaluation protocols, and stronger collaboration with domain experts to drive impactful and reliable advances in graph learning research, unlocking the potential of graph learning.

Federico Errica, Henrik Christiansen, Viktor Zaverkin et al.

Long-range interactions are essential for the correct description of complex systems in many scientific fields. The price to pay for including them in the calculations, however, is a dramatic increase in the overall computational costs. Recently, deep graph networks have been employed as efficient, data-driven models for predicting properties of complex systems represented as graphs. These models rely on a message passing strategy that should, in principle, capture long-range information without explicitly modeling the corresponding interactions. In practice, most deep graph networks cannot really model long-range dependencies due to the intrinsic limitations of (synchronous) message passing, namely oversmoothing, oversquashing, and underreaching. This work proposes a general framework that learns to mitigate these limitations: within a variational inference framework, we endow message passing architectures with the ability to adapt their depth and filter messages along the way. With theoretical and empirical arguments, we show that this strategy better captures long-range interactions, by competing with the state of the art on five node and graph prediction datasets.

Viktor Zaverkin, Francesco Alesiani, Takashi Maruyama et al.

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message passing. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. Cartesian tensors offer a promising alternative, though state-of-the-art methods lack flexibility in message-passing mechanisms, restricting their architectures and expressive power. This work explores higher-rank irreducible Cartesian tensors to address these limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance and traceless property of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical and Cartesian models.

Duy M. H. Nguyen, Nina Lukashina, Tai Nguyen et al.

A molecule's 2D representation consists of its atoms, their attributes, and the molecule's covalent bonds. A 3D (geometric) representation of a molecule is called a conformer and consists of its atom types and Cartesian coordinates. Every conformer has a potential energy, and the lower this energy, the more likely it occurs in nature. Most existing machine learning methods for molecular property prediction consider either 2D molecular graphs or 3D conformer structure representations in isolation. Inspired by recent work on using ensembles of conformers in conjunction with 2D graph representations, we propose $\mathrm{E}$(3)-invariant molecular conformer aggregation networks. The method integrates a molecule's 2D representation with that of multiple of its conformers. Contrary to prior work, we propose a novel 2D-3D aggregation mechanism based on a differentiable solver for the Fused Gromov-Wasserstein Barycenter problem and the use of an efficient conformer generation method based on distance geometry. We show that the proposed aggregation mechanism is $\mathrm{E}$(3) invariant and propose an efficient GPU implementation. Moreover, we demonstrate that the aggregation mechanism helps to significantly outperform state-of-the-art molecule property prediction methods on established datasets.

Nghiem T. Diep, Huy Nguyen, Chau Nguyen et al.

The LLaMA-Adapter has recently emerged as an efficient fine-tuning technique for LLaMA models, leveraging zero-initialized attention to stabilize training and enhance performance. However, despite its empirical success, the theoretical foundations of zero-initialized attention remain largely unexplored. In this paper, we provide a rigorous theoretical analysis, establishing a connection between zero-initialized attention and mixture-of-expert models. We prove that both linear and non-linear prompts, along with gating functions, can be optimally estimated, with non-linear prompts offering greater flexibility for future applications. Empirically, we validate our findings on the open LLM benchmarks, demonstrating that non-linear prompts outperform linear ones. Notably, even with limited training data, both prompt types consistently surpass vanilla attention, highlighting the robustness and adaptability of zero-initialized attention.

Edgar Torres, Jonathan Schiefer, Mathias Niepert

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability. However, limitations related to convergence and the need for re-optimization with each change in PDE parameters hinder their widespread adoption across scientific and engineering applications. This survey reviews existing research that addresses these limitations through transfer learning and meta-learning. The covered methods improve the training efficiency, allowing faster adaptation to new PDEs with fewer data and computational resources. While traditional numerical methods solve systems of differential equations directly, neural networks learn solutions implicitly by adjusting their parameters. One notable advantage of neural networks is their ability to abstract away from specific problem domains, allowing them to retain, discard, or adapt learned representations to efficiently address similar problems. By exploring the application of these techniques to PINNs, this survey identifies promising directions for future research to facilitate the broader adoption of PINNs in a wide range of scientific and engineering applications.

Khai Le-Duc, Duy M. H. Nguyen, Phuong T. H. Trinh et al.

Faithful reasoning in medical vision-language models (VLMs) requires not only accurate predictions but also transparent alignment between textual rationales and visual evidence. While Chain-of-Thought (CoT) prompting has shown promise in medical visual question answering (VQA), no large-scale expert-level dataset has captured stepwise reasoning with precise visual grounding. We introduce S-Chain, the first large-scale dataset of 12,000 expert-annotated medical images with bounding boxes and structured visual CoT (SV-CoT), explicitly linking visual regions to reasoning steps. The dataset further supports 16 languages, totaling over 700k VQA pairs for broad multilingual applicability. Using S-Chain, we benchmark state-of-the-art medical VLMs (ExGra-Med, LLaVA-Med) and general-purpose VLMs (Qwen2.5-VL, InternVL2.5), showing that SV-CoT supervision significantly improves interpretability, grounding fidelity, and robustness. Beyond benchmarking, we study its synergy with retrieval-augmented generation, revealing how domain knowledge and visual grounding interact during autoregressive reasoning. Finally, we propose a new mechanism that strengthens the alignment between visual evidence and reasoning, improving both reliability and efficiency. S-Chain establishes a new benchmark for grounded medical reasoning and paves the way toward more trustworthy and explainable medical VLMs.

Andrei Manolache, Luiz F. O. Chamon, Mathias Niepert

Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs from perfect symmetry because of noise, structural variation, measurement bias, or other symmetry-breaking effects. Strictly equivariant models may struggle to fit the data, while unconstrained models lack a principled way to leverage partial symmetries. Even when the data is fully symmetric, enforcing equivariance can hurt training by limiting the model to a restricted region of the parameter space. Guided by homotopy principles, where an optimization problem is solved by gradually transforming a simpler problem into a complex one, we introduce Adaptive Constrained Equivariance (ACE), a constrained optimization approach that starts with a flexible, non-equivariant model and gradually reduces its deviation from equivariance. This gradual tightening smooths training early on and settles the model at a data-driven equilibrium, balancing between equivariance and non-equivariance. Across multiple architectures and tasks, our method consistently improves performance metrics, sample efficiency, and robustness to input perturbations compared with strictly equivariant models and heuristic equivariance relaxations.

Federico Errica, Henrik Christiansen, Viktor Zaverkin et al.

For almost 70 years, researchers have mostly relied on hyper-parameter tuning to select the width of neural networks' layers. This paper challenges the status quo by introducing an easy-to-use technique to learn an unbounded width of a neural network's layer during training. The technique does not rely on alternate optimization nor hand-crafted gradient heuristics; rather, it jointly optimizes the width and the parameters of each layer via simple backpropagation. We apply the technique to a broad range of data domains such as tables, images, text, sequences, and graphs, showing how the width adapts to the task's difficulty. The method imposes a soft ordering of importance among neurons, by which it also is possible to truncate the trained network at virtually zero cost, achieving a smooth trade-off between performance and compute resources in a structured way. Alternatively, one can dynamically compress the network with no performance degradation. In light of recent foundation models trained on large datasets, believed to require billions of parameters and where hyper-parameter tuning is unfeasible due to humongous training costs, our approach stands as a viable alternative for width learning.

Duy M. H. Nguyen, Tuan A. Tran, Duong Nguyen et al.

Recent token merging techniques for Vision Transformers (ViTs) provide substantial speedups by reducing the number of tokens processed by self-attention, often without retraining. However, their direct application to the Segment Anything Model (SAM) family is nontrivial: SAM's image encoder mixes windowed and global attention, and its mask decoder relies on dense, prompt-conditioned features for precise boundary prediction. We systematically evaluate representative token-merging methods on SAM and Medical SAM in a strict off-the-shelf setting, and find that existing destination-selection heuristics can erode boundaries and leak prompt information as merge rates increase. We propose \textbf{StructSAM}, a resolution-preserving merge-unmerge framework tailored to SAM. StructSAM computes a lightweight token-energy score from first-order feature gradients, uses grid-based flatness screening to protect boundary and prompt regions, and merges tokens within flat areas toward low-energy destinations with explicit token recovery. We further provide a spectral graph coarsening view showing that score-guided merging yields bounded Laplacian spectral distortion compared to random or window-restricted baselines. Across eight natural and medical benchmarks, StructSAM reduces encoder FLOPs by 25-30\% (up to 40\%+ with prompt-aware merging) with minor drops in mIoU/Dice, consistently outperforming ToMe, PiToMe, ToMeSD, VidToMe, and ALGM at the same compute.

Semih Cantürk, Andrei Manolache, Arman Mielke et al.

A wide range of graph learning tasks, such as structure discovery, temporal graph analysis, and combinatorial optimization, focus on inferring graph structures from data, rather than making predictions on given graphs. However, the respective methods to solve such problems are often developed in an isolated, task-specific manner and thus lack a unifying theoretical foundation. Here, we provide a stepping stone towards the formation of such a foundation and further development by introducing the Neural Graph Inverse Problem (GraIP) conceptual framework, which formalizes and reframes a broad class of graph learning tasks as inverse problems. Unlike discriminative approaches that directly predict target variables from given graph inputs, the GraIP paradigm addresses inverse problems, i.e., it relies on observational data and aims to recover the underlying graph structure by reversing the forward process, such as message passing or network dynamics, that produced the observed outputs. We demonstrate the versatility of GraIP across various graph learning tasks, including rewiring, causal discovery, and neural relational inference. We also propose benchmark datasets and metrics for each GraIP domain considered, and characterize and empirically evaluate existing baseline methods used to solve them. Overall, our unifying perspective bridges seemingly disparate applications and provides a principled approach to structural learning in constrained and combinatorial settings while encouraging cross-pollination of existing methods across graph inverse problems.

Boshra Ariguib, Mathias Niepert, Andrei Manolache

High-quality molecular representations are essential for property prediction and molecular design, yet large labeled datasets remain scarce. While self-supervised pretraining on molecular graphs has shown promise, many existing approaches either depend on hand-crafted augmentations or complex generative objectives, and often rely solely on 2D topology, leaving valuable 3D structural information underutilized. To address this gap, we introduce C-FREE (Contrast-Free Representation learning on Ego-nets), a simple framework that integrates 2D graphs with ensembles of 3D conformers. C-FREE learns molecular representations by predicting subgraph embeddings from their complementary neighborhoods in the latent space, using fixed-radius ego-nets as modeling units across different conformers. This design allows us to integrate both geometric and topological information within a hybrid Graph Neural Network (GNN)-Transformer backbone, without negatives, positional encodings, or expensive pre-processing. Pretraining on the GEOM dataset, which provides rich 3D conformational diversity, C-FREE achieves state-of-the-art results on MoleculeNet, surpassing contrastive, generative, and other multimodal self-supervised methods. Fine-tuning across datasets with diverse sizes and molecule types further demonstrates that pretraining transfers effectively to new chemical domains, highlighting the importance of 3D-informed molecular representations.

Viktor Zaverkin, Matheus Ferraz, Francesco Alesiani et al.

Universal machine-learned potentials promise transferable accuracy across compositional and vibrational degrees of freedom, yet their application to biomolecular simulations remains underexplored. This work systematically evaluates equivariant message-passing architectures trained on the SPICE-v2 dataset with and without explicit long-range dispersion and electrostatics. We assess the impact of model size, training data composition, and electrostatic treatment across in- and out-of-distribution benchmark datasets, as well as molecular simulations of bulk liquid water, aqueous NaCl solutions, and biomolecules, including alanine tripeptide, the mini-protein Trp-cage, and Crambin. While larger models improve accuracy on benchmark datasets, this trend does not consistently extend to properties obtained from simulations. Predicted properties also depend on the composition of the training dataset. Long-range electrostatics show no systematic impact across systems. However, for Trp-cage, their inclusion yields increased conformational variability. Our results suggest that imbalanced datasets and immature evaluation practices currently challenge the applicability of universal machine-learned potentials to biomolecular simulations.

Jan Hagnberger, Daniel Musekamp, Mathias Niepert

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics. However, performing these computations directly in the physical space often incurs significant computational costs. To address this issue, several neural surrogate models have been developed that operate in a compressed latent space to solve the PDE. While these approaches reduce computational complexity, they often use Transformer-based attention mechanisms to handle irregularly sampled domains, resulting in increased memory consumption. In contrast, convolutional neural networks allow memory-efficient encoding and decoding but are limited to regular discretizations. Motivated by these considerations, we propose CALM-PDE, a model class that efficiently solves arbitrarily discretized PDEs in a compressed latent space. We introduce a novel continuous convolution-based encoder-decoder architecture that uses an epsilon-neighborhood-constrained kernel and learns to apply the convolution operator to adaptive and optimized query points. We demonstrate the effectiveness of CALM-PDE on a diverse set of PDEs with both regularly and irregularly sampled spatial domains. CALM-PDE is competitive with or outperforms existing baseline methods while offering significant improvements in memory and inference time efficiency compared to Transformer-based methods.

Marimuthu Kalimuthu, David Holzmüller, Mathias Niepert

Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of Navier-Stokes equations at Reynolds numbers 3500 and above can generate high-frequency signals due to swirling fluid motions caused by eddies and vortices. Faithfully modeling such signals using neural networks depends on accurately reconstructing moderate to high frequencies. However, it has been well known that deep neural nets exhibit the so-called spectral bias toward learning low-frequency components. Meanwhile, Fourier Neural Operators (FNOs) have emerged as a popular class of data-driven models in recent years for solving Partial Differential Equations (PDEs) and for surrogate modeling in general. Although impressive results have been achieved on several PDE benchmark problems, FNOs often perform poorly in learning non-dominant frequencies characterized by local features. This limitation stems from the spectral bias inherent in neural networks and the explicit exclusion of high-frequency modes in FNOs and their variants. Therefore, to mitigate these issues and improve FNO's spectral learning capabilities to represent a broad range of frequency components, we propose two key architectural enhancements: (i) a parallel branch performing local spectral convolutions (ii) a high-frequency propagation module. Moreover, we propose a novel frequency-sensitive loss term based on radially binned spectral errors. This introduction of a parallel branch for local convolutions reduces number of trainable parameters by up to 50% while achieving the accuracy of baseline FNO that relies solely on global convolutions. Experiments on three challenging PDE problems in fluid mechanics and biological pattern formation, and the qualitative and spectral analysis of predictions show the effectiveness of our method over the state-of-the-art neural operator baselines.

Arman Mielke, Uwe Bauknecht, Thilo Strauss et al.

Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require high-quality solutions within a given time budget. To address this, we propose a learning-based approach that enhances existing non-learned approximation algorithms for CO. Specifically, we parameterize these approximation algorithms and train graph neural networks (GNNs) to predict parameter values that yield near-optimal solutions. Our method is trained end-to-end in a self-supervised fashion, using a novel gradient estimation scheme that treats the approximation algorithm as a black box. This approach combines the strengths of learning and traditional algorithms: the GNN learns from data to guide the algorithm toward better solutions, while the approximation algorithm ensures feasibility. We validate our method on two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the minimum k-cut problem. Our results demonstrate that the proposed approach is competitive with state-of-the-art learned CO solvers.

Anji Liu, Xuejie Liu, Dayuan Zhao et al.

Non-autoregressive (NAR) generative models are valuable because they can handle diverse conditional generation tasks in a more principled way than their autoregressive (AR) counterparts, which are constrained by sequential dependency requirements. Recent advancements in NAR models, such as diffusion language models, have demonstrated superior performance in unconditional generation compared to AR models (e.g., GPTs) of similar sizes. However, such improvements do not always lead to improved conditional generation performance. We show that a key reason for this gap is the difficulty in generalizing to conditional probability queries (i.e., the set of unknown variables) unseen during training. As a result, strong unconditional generation performance does not guarantee high-quality conditional generation. This paper proposes Tractable Transformers (Tracformer), a Transformer-based generative model that is more robust to different conditional generation tasks. Unlike existing models that rely solely on global contextual features derived from full inputs, Tracformers incorporate a sparse Transformer encoder to capture both local and global contextual information. This information is routed through a decoder for conditional generation. Empirical results demonstrate that Tracformers achieve state-of-the-art conditional generation performance on text modeling compared to recent diffusion and AR model baselines.

Jan Hagnberger, Marimuthu Kalimuthu, Daniel Musekamp et al.

Transformer models are increasingly used for solving Partial Differential Equations (PDEs). Several adaptations have been proposed, all of which suffer from the typical problems of Transformers, such as quadratic memory and time complexity. Furthermore, all prevalent architectures for PDE solving lack at least one of several desirable properties of an ideal surrogate model, such as (i) generalization to PDE parameters not seen during training, (ii) spatial and temporal zero-shot super-resolution, (iii) continuous temporal extrapolation, (iv) support for 1D, 2D, and 3D PDEs, and (v) efficient inference for longer temporal rollouts. To address these limitations, we propose Vectorized Conditional Neural Fields (VCNeFs), which represent the solution of time-dependent PDEs as neural fields. Contrary to prior methods, however, VCNeFs compute, for a set of multiple spatio-temporal query points, their solutions in parallel and model their dependencies through attention mechanisms. Moreover, VCNeF can condition the neural field on both the initial conditions and the parameters of the PDEs. An extensive set of experiments demonstrates that VCNeFs are competitive with and often outperform existing ML-based surrogate models.

Federico Errica, Mathias Niepert

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.