Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just a few denoising steps, modern discrete diffusion models still require hundreds or even thousands of denoising steps to perform well. In this paper, we identify a fundamental limitation that prevents discrete diffusion models from achieving strong performance with fewer steps -- they fail to capture dependencies between output variables at each denoising step. To address this issue, we provide a formal explanation and introduce a general approach to supplement the missing dependency information by incorporating another deep generative model, termed the copula model. Our method does not require fine-tuning either the diffusion model or the copula model, yet it enables high-quality sample generation with significantly fewer denoising steps. When we apply this approach to autoregressive copula models, the combined model outperforms both models individually in unconditional and conditional text generation. Specifically, the hybrid model achieves better (un)conditional text generation using 8 to 32 times fewer denoising steps than the diffusion model alone. In addition to presenting an effective discrete diffusion generation algorithm, this paper emphasizes the importance of modeling inter-variable dependencies in discrete diffusion.

Solving partial differential equations (PDEs) is a fundamental problem in engineering and science. 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 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.

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.

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.

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.

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 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.

Machine learning is playing an increasingly important role in computational chemistry and materials science, complementing expensive ab initio and first-principles methods. However, machine-learned interatomic potentials (MLIPs) often struggle with generalization and robustness, leading to unphysical energy and force predictions in atomistic simulations. To address this, we propose a physics-informed, weakly supervised training framework for MLIPs. Our method introduces two novel loss functions: one based on Taylor expansions of the potential energy and another enforcing conservative force constraints. This approach enhances accuracy, particularly in low-data regimes, and reduces the reliance on large, expensive training datasets. Extensive experiments across benchmark datasets show up to 2$\times$ reductions in energy and force errors for multiple baseline models. Additionally, our method improves the stability of molecular dynamics simulations and facilitates effective fine-tuning of ML foundation models on sparse, high-accuracy ab initio data. An implementation of our method and scripts for executing experiments are available at https://github.com/nec-research/PICPS-ML4Sci.

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.

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.

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 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.

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.

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 \textbf{GitMerge3D}, a \textbf{g}lobally \textbf{i}nformed graph \textbf{t}oken \textbf{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 \href{https://gitmerge3d.github.io/}{https://gitmerge3d.github.io}.

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.

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 ~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.

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.

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.

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 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 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.

Message-passing graph neural networks (MPNNs) have emerged as a powerful paradigm for graph-based machine learning. Despite their effectiveness, MPNNs face challenges such as under-reaching and over-squashing, where limited receptive fields and structural bottlenecks hinder information flow in the graph. While graph transformers hold promise in addressing these issues, their scalability is limited due to quadratic complexity regarding the number of nodes, rendering them impractical for larger graphs. Here, we propose implicitly rewired message-passing neural networks (IPR-MPNNs), a novel approach that integrates implicit probabilistic graph rewiring into MPNNs. By introducing a small number of virtual nodes, i.e., adding additional nodes to a given graph and connecting them to existing nodes, in a differentiable, end-to-end manner, IPR-MPNNs enable long-distance message propagation, circumventing quadratic complexity. Theoretically, we demonstrate that IPR-MPNNs surpass the expressiveness of traditional MPNNs. Empirically, we validate our approach by showcasing its ability to mitigate under-reaching and over-squashing effects, achieving state-of-the-art performance across multiple graph datasets. Notably, IPR-MPNNs outperform graph transformers while maintaining significantly faster computational efficiency.

Increasing the throughput of the Transformer architecture, a foundational component used in numerous state-of-the-art models for vision and language tasks (e.g., GPT, LLaVa), is an important problem in machine learning. One recent and effective strategy is to merge token representations within Transformer models, aiming to reduce computational and memory requirements while maintaining accuracy. Prior work has proposed algorithms based on Bipartite Soft Matching (BSM), which divides tokens into distinct sets and merges the top $k$ similar tokens. However, these methods have significant drawbacks, such as sensitivity to token-splitting strategies and damage to informative tokens in later layers. This paper presents a novel paradigm called PiToMe, which prioritizes the preservation of informative tokens using an additional metric termed the \textit{energy score}. This score identifies large clusters of similar tokens as high-energy, indicating potential candidates for merging, while smaller (unique and isolated) clusters are considered as low-energy and preserved. Experimental findings demonstrate that PiToMe saved from 40-60\% FLOPs of the base models while exhibiting superior off-the-shelf performance on image classification (0.5\% average performance drop of ViT-MAEH compared to 2.6\% as baselines), image-text retrieval (0.3\% average performance drop of Clip on Flick30k compared to 4.5\% as others), and analogously in visual questions answering with LLaVa-7B. Furthermore, PiToMe is theoretically shown to preserve intrinsic spectral properties to the original token space under mild conditions.

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.

Abstract 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.

The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation, 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.

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 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 any 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 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. An implementation of the method and experiments are available at https://anonymous.4open.science/r/CAPE-ML4Sci-145B.

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 networks on ImageNet and vision-language foundation models trained on web-scale data are the 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 through 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.

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.

Kiril Gashteovski, Mingying Yu, Bhushan Kotnis, Carolin Lawrence, Mathias Niepert, Goran Glavaš. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022.

Bhushan Kotnis, Kiril Gashteovski, Daniel Rubio, Ammar Shaker, Vanesa Rodriguez-Tembras, Makoto Takamoto, Mathias Niepert, Carolin Lawrence. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022.

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 $k\mathsf{\text{-}WL}$ 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.

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 repre- sentative 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 con- tribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more real- istic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of ini- tial 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 pur- poses 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.

Representation learning for knowledge graphs (KGs) has focused on the problem of answering simple link prediction queries. In this work we address the more ambitious challenge of predicting the answers of conjunctive queries with multiple missing entities. We propose Bidirectional Query Embedding (BiQE), a method that embeds conjunctive queries with models based on bi-directional attention mechanisms. Contrary to prior work, bidirectional self-attention can capture interactions among all the elements of a query graph. We introduce two new challenging datasets for studying conjunctive query inference and conduct experiments on several benchmark datasets that demonstrate BiQE significantly outperforms state of the art baselines.

Explaining the predictions of neural black-box models is an important problem, especially when such models are used in applications where user trust is crucial. Estimating the influence of training examples on a learned neural model's behavior allows us to identify training examples most responsible for a given prediction and, therefore, to faithfully explain the output of a black-box model. The most generally applicable existing method is based on influence functions, which scale poorly for larger sample sizes and models. We propose gradient rollback, a general approach for influence estimation, applicable to neural models where each parameter update step during gradient descent touches a smaller number of parameters, even if the overall number of parameters is large. Neural matrix factorization models trained with gradient descent are part of this model class. These models are popular and have found a wide range of applications in industry. Especially knowledge graph embedding methods, which belong to this class, are used extensively. We show that gradient rollback is highly efficient at both training and test time. Moreover, we show theoretically that the difference between gradient rollback's influence approximation and the true influence on a model's behavior is smaller than known bounds on the stability of stochastic gradient descent. This establishes that gradient rollback is robustly estimating example influence. We also conduct experiments which show that gradient rollback provides faithful explanations for knowledge base completion and recommender datasets. An implementation and an appendix are available.

Targeted online advertising is a multi-billion dollar business based on the ability of profiling and delivering targeted ads to a wide range of users. Due to the privacy erosion associated with such business, researchers are trying to understand how profiling works and anti-tracking applications are becoming popular among users. Both research and privacy-enhancing apps, however, target ad-networks or over-the-top providers that have unrestricted access to users' online activity. There seems to be little interest in potential profiling activities by "network observers" like ISPs or VPN providers. On the one side, this may be explained by the pervasiveness of TLS that secures connections end-to-end. On the other side, TLS does leak some information, and it is not clear what an eavesdropper can learn about a user, despite her traffic being encrypted.

Graph neural networks have recently received increasing attention. These methods often map nodes into latent spaces and learn vector representations of the nodes for a variety of downstream tasks. To gain trust and to promote collaboration between AIs and humans, it would be better if those representations were interpretable for humans. However, most explainable AIs focus on a supervised learning setting and aim to answer the following question: “Why does the model predict y for an input x?”. For an unsupervised learning setting as node embedding, interpretation can be more complicated since the embedding vectors are usually not understandable for humans. On the other hand, nodes and edges in a graph are often associated with texts in many real-world applications. A question naturally arises: could we integrate the human-understandable textural data into graph learning to facilitate interpretable node embedding? In this paper we present interpretable graph neural networks (iGNN), a model to learn textual explanations for node representations modeling the extra information contained in the associated textual data. To validate the performance of the proposed method, we investigate the learned interpretability of the embedding vectors and use functional interpretability to measure it. Experimental results on multiple text-labeled graphs show the effectiveness of the iGNN model on learning textual explanations of node embedding while performing well in downstream tasks.

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.

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.

Combining discrete probability distributions and combinatorial optimization problems with neural network components has numerous applications but poses several challenges. We propose Implicit Maximum Likelihood Estimation (I-MLE), a framework for end-to-end learning of models combining discrete exponential family distributions and differentiable neural components. I-MLE is widely applicable as it only requires the ability to compute the most probable states and does not rely on smooth relaxations. The framework encompasses several approaches such as perturbation-based implicit differentiation and recent methods to differentiate through black-box combinatorial solvers. We introduce a novel class of noise distributions for approximating marginals via perturb-and-MAP. Moreover, we show that I-MLE simplifies to maximum likelihood estimation when used in some recently studied learning settings that involve combinatorial solvers. Experiments on several datasets suggest that I-MLE is competitive with and often outperforms existing approaches which rely on problem-specific relaxations.

Data sparsity and data imbalance are practical and challenging issues in cross-domain recommender systems (RSs). This paper addresses those problems by leveraging the concepts which derive from representation learning, adversarial learning, and transfer learning (particularly, domain adaptation). Although various transfer learning methods have shown promising performance in this context, our proposed novel method RecSys-DAN focuses on alleviating the cross-domain and within-domain data sparsity and data imbalance and learns transferable latent representations for users, items, and their interactions. Different from the existing approaches, the proposed method transfers the latent representations from a source domain to a target domain in an adversarial way. The mapping functions in the target domain are learned by playing a min-max game with an adversarial loss, aiming to generate domain indistinguishable representations for a discriminator. Four neural architectural instances of ResSys-DAN are proposed and explored. Empirical results on real-world Amazon data show that, even without using labeled data (i.e., ratings) in the target domain, RecSys-DAN achieves competitive performance as compared to the state-of-the-art supervised methods. More importantly, RecSys-DAN is highly flexible to both unimodal and multimodal scenarios, and thus it is more robust to the cold-start recommendation which is difficult for the previous methods.

Kosuke Akimoto, Takuya Hiraoka, Kunihiko Sadamasa, Mathias Niepert. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.

Carolin Lawrence, Bhushan Kotnis, Mathias Niepert. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.

We present Mmkg, a collection of three knowledge graphs that contain both numerical features and (links to) images for all entities as well as entity alignments between pairs of KGs. Therefore, multi-relational link prediction and entity matching communities can benefit from this resource. We believe this data set has the potential to facilitate the development of novel multi-modal learning approaches for knowledge graphs. We validate the utility of Mmkg in the $$\mathtt {sameAs}$$ link prediction task with an extensive set of experiments. These experiments show that the task at hand benefits from learning of multiple feature types.

Graph neural networks (GNNs) are a popular class of machine learning models that have been successfully applied to a range of problems. Their major advantage lies in their ability to explicitly incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Recurrent neural networks are a widely used class of neural architectures with two shortcomings. First, it is difficult to understand what exactly they learn. 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) nonregular languages such as balanced parentheses, palindromes, and the copy task where external memory is required; and (3) real-word sequence learning tasks for sentiment analysis, visual object recognition, and language modeling. We show that state-regularization simplifies the extraction of finite state automata from the RNN’s state transition dynamics; forces RNNs to operate more like automata with external memory and less like finite state machines; and makes RNNs more interpretable.

Many real-world domains can be expressed as graphs and, more generally, as multi-relational knowledge graphs. Though reasoning and learning with knowledge graphs has traditionally been addressed by symbolic approaches such as Statistical relational learning, recent methods in (deep) representation learning have shown promising results for specialised tasks such as knowledge base completion. These approaches, also known as distributional, abandon the traditional symbolic paradigm by replacing symbols with vectors in Euclidean space. With few exceptions, symbolic and distributional approaches are explored in different communities and little is known about their respective strengths and weaknesses. In this work, we compare distributional and symbolic relational learning approaches on various standard relational classification and knowledge base completion tasks. Furthermore, we analyse the properties of the datasets and relate them to the performance of the methods in the comparison. The results reveal possible indicators that could help in choosing one approach over the other for particular knowledge graphs.

Research on link prediction in knowledge graphs has mainly focused on static multirelational data.In this work we consider temporal knowledge graphs where relations between entities may only hold for a time interval or a specific point in time.In line with previous work on static knowledge graphs, we propose to address this problem by learning latent entity and relation type representations.To incorporate temporal information, we utilize recurrent neural networks to learn timeaware representations of relation types which can be used in conjunction with existing latent factorization methods.The proposed approach is shown to be robust to common challenges in real-world KGs: the sparsity and heterogeneity of temporal expressions.Experiments show the benefits of our approach on four temporal KGs.The data sets are available under a permissive BSD-3 license 1 .

Multimodal learning has shown promising performance in content-based recommendation due to the auxiliary user and item information of multiple modalities such as text and images.However, the problem of incomplete and missing modality is rarely explored and most existing methods fail in learning a recommendation model with missing or corrupted modalities.In this paper, we propose LRMM, a novel framework that mitigates not only the problem of missing modalities but also more generally the cold-start problem of recommender systems.We propose modality dropout (m-drop) and a multimodal sequential autoencoder (m-auto) to learn multimodal representations for complementing and imputing missing modalities.Extensive experiments on real-world Amazon data show that LRMM achieves state-of-the-art performance on rating prediction tasks.More importantly, LRMM is more robust to previous methods in alleviating data-sparsity and the cold-start problem.

We propose EP, Embedding Propagation, an unsupervised learning framework for graph-structured data. EP learns vector representations of graphs by passing two types of messages between neighboring nodes. Forward messages consist of label representations such as representations of words and other attributes associated with the nodes. Backward messages consist of gradients that result from aggregating the label representations and applying a reconstruction loss. Node representations are finally computed from the representation of their labels. With significantly fewer parameters and hyperparameters, an instance of EP is competitive with and often outperforms state of the art unsupervised and semi-supervised learning methods on a range of benchmark data sets.

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.

We present discriminative Gaifman models, a novel family of relational machine learning models. Gaifman models learn feature representations bottom up from representations of locally connected and bounded-size regions of knowledge bases (KBs). Considering local and bounded-size neighborhoods of knowledge bases renders logical inference and learning tractable, mitigates the problem of overfitting, and facilitates weight sharing. Gaifman models sample neighborhoods of knowledge bases so as to make the learned relational models more robust to missing objects and relations which is a common situation in open-world KBs. We present the core ideas of Gaifman models and apply them to large-scale relational learning problems. We also discuss the ways in which Gaifman models relate to some existing relational machine learning approaches.

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.

Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical property that renders probabilistic inference tractable is less well-understood. We develop a theory of finite exchangeability and its relation to tractable probabilistic inference. The theory is complementary to that of independence and conditional independence. We show that tractable inference in probabilistic models with high treewidth and millions of variables can be explained with the notion of finite (partial) exchangeability. We also show that existing lifted inference algorithms implicitly utilize a combination of conditional independence and partial exchangeability.

A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are partially exchangeable sequences, a generalization of exchangeable sequences. We prove that a family of tractable EVMs is optimal under zero-one loss for a large class of functions, including parity and threshold functions, and strictly subsumes existing tractable independence-based model families. Extensive experiments show that EVMs outperform state of the art classifiers such as SVMs and probabilistic models which are solely based on independence assumptions.

The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to outperform standard estimators by several orders of magnitude. The developed theory and algorithms apply to a broad class of probabilistic models including statistical relational models considered not susceptible to lifted probabilistic inference.

RockIt is a maximum a-posteriori (MAP) query engine for statistical relational models. MAP inference in graphical models is an optimization problem which can be compiled to integer linear programs (ILPs).We describe several advances in translating MAP queries to ILP instances and present the novel meta-algorithm cutting plane aggregation (CPA). CPA exploits local context-specific symmetries and bundles up sets of linear constraints. The resulting counting constraints lead to more compact ILPs and make the symmetry of the ground model more explicit to state-of-the-art ILP solvers. Moreover, RockIt parallelizes most parts of the MAP inference pipeline taking advantage of ubiquitous shared-memory multi-core architectures. We report on extensive experiments with Markov logic network (MLN) benchmarks showing that RockIt outperforms the state-of-the-art systems Alchemy, Markov TheBeast, and Tuffy both in terms of efficiency and quality of results.

A majority of the approaches to activity recognition in sensor environments are either based on manually constructed rules for recognizing activities or lack the ability to incorporate complex temporal dependencies. Furthermore, in many cases, the rather unrealistic assumption is made that the subject carries out only one activity at a time. In this paper, we describe the use of Markov logic as a declarative framework for recognizing interleaved and concurrent activities incorporating both input from pervasive light-weight sensor technology and common-sense background knowledge. In particular, we assess its ability to learn statistical-temporal models from training data and to combine these models with background knowledge to improve the overall recognition accuracy. To this end, we propose two Markov logic formulations for inferring the foreground activity as well as each activities' start and end times. We evaluate the approach on an established dataset. where it outperforms state-of-the-art algorithms for activity recognition.

Ontology matching is the problem of determining correspondences between concepts, properties, and individuals of different heterogeneous ontologies. With this paper we present a novel probabilistic-logical framework for ontology matching based on Markov logic. We define the syntax and semantics and provide a formalization of the ontology matching problem within the framework. The approach has several advantages over existing methods such as ease of experimentation, incoherence mitigation during the alignment process, and the incorporation of a-priori confidence values. We show empirically that the approach is efficient and more accurate than existing matchers on an established ontology alignment benchmark dataset.

The logical and algorithmic properties of stable conditional independence (CI) as an alternative structural representation of conditional independence information are investigated. We utilize recent results concerning a complete axiomatization of stable conditional independence relative to discrete probability measures to derive perfect model properties of stable conditional independence structures. We show that stable CI can be interpreted as a generalization of Markov networks and establish a connection between sets of stable CI statements and propositional formulas in conjunctive normal form. Consequently, we derive that the implication problem for stable CI is coNP-complete. Finally, we show that Boolean satisfiability (SAT) solvers can be employed to efficiently decide the implication problem and to compute concise, non-redundant representations of stable CI, even for instances involving hundreds of random variables.