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Mathias Niepert

Publications and source records attributed to Mathias Niepert.

At least 37 records · Page 2Linked to original sources
arXiv2026

GraphBench: Next-generation graph learning benchmarking

Machine learning on graphs has made substantial progress across domains such as molecular property prediction and chip design. Yet benchmarking practices remain fragmented, often relying on narrow, task-specific datasets and inconsistent evaluation protocols, hindering reproducibility and broader progress. With the recent popularity of graph foundation models, these weaknesses have become apparent, as existing benchmarks are insufficient for thorough evaluation. To address these challenges, we introduce GraphBench, a comprehensive benchmark suite spanning diverse real-world domains and task settings, including node-level, edge-level, graph-level, and generative tasks. GraphBench provides standardized evaluation protocols, including consistent dataset splits and metrics for assessing out-of-distribution generalization across selected tasks, as well as a unified hyperparameter-tuning framework. We further evaluate GraphBench with recent message-passing neural networks and graph transformer models, establishing principled baselines for future research. See www.graphbench.io for further details.

cs.LG↗
arXiv2026

Logical Guidance for the Exact Composition of Diffusion Models

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 classifier guidance 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.

cs.LG↗
arXiv2026

Adaptive Width Neural Networks

For almost 70 years, researchers have typically selected the width of neural networks' layers either manually or through automated hyperparameter tuning methods such as grid search and, more recently, neural architecture search. 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 method jointly optimizes the width and the parameters of each layer via standard 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. A by product of our width learning approach is the easy truncation of the trained network at virtually zero cost, achieving a smooth trade-off between performance and compute resources. Alternatively, one can dynamically compress the network until performances do not degrade. In light of recent foundation models trained on large datasets, requiring billions of parameters and where hyper-parameter tuning is unfeasible due to huge training costs, our approach introduces a viable alternative for width learning.

cs.LG↗
arXiv2026

GraIP: A Benchmarking Framework For Neural Graph Inverse Problems

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.

cs.LG↗
arXiv2026

Beyond the Training Domain: Robust Generative Transition State Models for Unseen Chemistry

Transition states (TSs) govern the rates and outcomes of chemical reactions, making their accurate prediction a central challenge in computational chemistry. Although recent machine-learning models achieve near chemical accuracy in the prediction of TS structures and the associated reaction barriers for small organic reactions, their ability to generalize beyond the training domain remains largely unexplored. Here, we introduce targeted benchmarks to probe chemical and structural novelty in generative TS prediction. Building on Transition1x, a large-scale dataset of reactions involving small organic molecules, we construct curated extensions incorporating controlled elemental substitutions and diverse transition-metal complexes (TMC). These benchmarks reveal fundamental limitations of generative models in the generalization to previously unseen elements. As a result, they produce unphysical geometries and large energetic errors, even for reactions structurally similar to well-predicted organic systems. To address this challenge, we introduce a self-supervised pretraining strategy based on equilibrium conformers that exposes generative TS models to novel chemical environments prior to targeted fine-tuning. Across the newly proposed benchmarks, self-supervised pretraining substantially improves TS prediction for previously unseen systems, lowering the median RMSD of TS geometries on T1x-TMC reactions from 0.39 to 0.19 $\mathring{A}$ and reducing fine-tuning data requirements by up to 75%, enabling reliable performance even in low-data regimes. Overall, the integration of generative TS models with self-supervised pseudo-reaction pretraining provides an efficient, scalable, and chemically robust framework for elucidating TSs well beyond the small organic molecule domain, establishing a foundation for investigating complex and catalytically relevant reaction landscapes.

physics.chem-ph↗
arXiv2026

LOGLO-FNO: Efficient Learning of Local and Global Features in Fourier Neural Operators

Modeling high-frequency information is a critical challenge in scientific machine learning. For instance, fully turbulent flow simulations of the 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 nets depends on the accurate reconstruction of moderate to high frequencies. However, it has been well known that neural nets exhibit spectral or frequency bias towards learning low-frequency components. Meanwhile, Fourier Neural Operators (FNOs) have emerged as a popular class of data-driven models for surrogate modeling and solving PDEs. Although impressive results were achieved on several PDE benchmark problems, FNOs perform poorly in learning non-dominant frequencies characterized by local features. This limitation stems from spectral bias inherent in neural nets 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 convolution (ii) a high-frequency propagation module. Moreover, we propose a novel frequency-sensitive loss based on radially binned spectral errors. This introduction of a parallel branch for local convolution reduces the trainable parameters by up to 50% while achieving the accuracy of FNO that relies solely on global convolution. Moreover, our findings demonstrate that the proposed model improves stability over longer rollouts. Experiments on six challenging PDEs in fluid mechanics, wave propagation, and biological pattern formation, and the qualitative and spectral analysis of predictions, show the effectiveness of our method over SOTA neural operator families of baselines.

cs.LG↗
arXiv2025

Learning (Approximately) Equivariant Networks via Constrained Optimization

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.

cs.LG↗
arXiv2025

ExGra-Med: Extended Context Graph Alignment for Medical Vision-Language Models

State-of-the-art medical multi-modal LLMs (med-MLLMs), such as LLaVA-Med and BioMedGPT, primarily depend on scaling model size and data volume, with training driven largely by autoregressive objectives. However, we reveal that this approach can lead to weak vision-language alignment, making these models overly dependent on costly instruction-following data. To address this, we introduce ExGra-Med, a novel multi-graph alignment framework that jointly aligns images, instruction responses, and extended captions in the latent space, advancing semantic grounding and cross-modal coherence. To scale to large LLMs (e.g., LLaMA-7B), we develop an efficient end-to-end training scheme using black-box gradient estimation, enabling fast and scalable optimization. Empirically, ExGra-Med matches LLaVA-Med's performance using just 10% of the pre-training data, achieving a 20.13% gain on VQA-RAD and approaching full-data performance. It also outperforms strong baselines like BioMedGPT and RadFM on visual chatbot and zero-shot classification tasks, demonstrating its promise for efficient, high-quality vision-language integration in medical AI.

cs.LG↗
arXiv2025

How Many Tokens Do 3D Point Cloud Transformer Architectures Really Need?

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

cs.CV↗
arXiv2025

S-Chain: Structured Visual Chain-of-Thought For Medicine

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.

cs.LG↗
arXiv2025

CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs

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.

cs.LG↗
arXiv2025

Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion

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.

cs.LG↗
arXiv2025

Performance of universal machine-learned potentials with explicit long-range interactions in biomolecular simulations

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.

physics.chem-ph↗
arXiv2025

Adaptive Transition State Refinement with Learned Equilibrium Flows

Identifying transition states (TSs), the high-energy configurations that molecules pass through during chemical reactions, is essential for understanding and designing chemical processes. However, accurately and efficiently identifying these states remains one of the most challenging problems in computational chemistry. In this work, we introduce a new generative AI approach that improves the quality of initial guesses for TS structures. Our method can be combined with a variety of existing techniques, including both machine learning models and fast, approximate quantum methods, to refine their predictions and bring them closer to chemically accurate results. Applied to TS guesses from a state-of-the-art machine learning model, our approach reduces the median structural error to just 0.088 $\unicode{x212B}$ and lowers the median absolute error in reaction barrier heights to 0.79 kcal mol$^{-1}$. When starting from a widely used tight-binding approximation, it increases the success rate of locating valid TSs by 41\% and speeds up high-level quantum optimization by a factor of three. By making TS searches more accurate, robust, and efficient, this method could accelerate reaction mechanism discovery and support the development of new materials, catalysts, and pharmaceuticals.

physics.chem-ph↗
arXiv2025

Tractable Transformers for Flexible Conditional Generation

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.

cs.CL↗
arXiv2025

On Zero-Initialized Attention: Optimal Prompt and Gating Factor Estimation

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.

cs.LG↗
arXiv2025

Preference-Based Gradient Estimation for ML-Guided Approximate Combinatorial Optimization

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.

cs.LG↗
arXiv2025

Learning to Discretize Denoising Diffusion ODEs

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.

cs.LG↗