Jens Sjölund

Ziwei Luo, Fredrik K. Gustafsson, Zheng Zhao et al.

This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean state with fixed Gaussian noise. Then, by simulating the corresponding reverse-time SDE, we are able to restore the origin of the low-quality image without relying on any task-specific prior knowledge. Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing us to compute the ground truth time-dependent score and learn it with a neural network. Moreover, we propose a maximum likelihood objective to learn an optimal reverse trajectory that stabilizes the training and improves the restoration results. The experiments show that our proposed method achieves highly competitive performance in quantitative comparisons on image deraining, deblurring, and denoising, setting a new state-of-the-art on two deraining datasets. Finally, the general applicability of our approach is further demonstrated via qualitative results on image super-resolution, inpainting, and dehazing. Code is available at https://github.com/Algolzw/image-restoration-sde.

Mathilde Papillon, Mustafa Hajij, Helen Jenne et al.

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

Ziwei Luo, Fredrik K. Gustafsson, Zheng Zhao et al.

Vision-language models such as CLIP have shown great impact on diverse downstream tasks for zero-shot or label-free predictions. However, when it comes to low-level vision such as image restoration their performance deteriorates dramatically due to corrupted inputs. In this paper, we present a degradation-aware vision-language model (DA-CLIP) to better transfer pretrained vision-language models to low-level vision tasks as a multi-task framework for image restoration. More specifically, DA-CLIP trains an additional controller that adapts the fixed CLIP image encoder to predict high-quality feature embeddings. By integrating the embedding into an image restoration network via cross-attention, we are able to pilot the model to learn a high-fidelity image reconstruction. The controller itself will also output a degradation feature that matches the real corruptions of the input, yielding a natural classifier for different degradation types. In addition, we construct a mixed degradation dataset with synthetic captions for DA-CLIP training. Our approach advances state-of-the-art performance on both \emph{degradation-specific} and \emph{unified} image restoration tasks, showing a promising direction of prompting image restoration with large-scale pretrained vision-language models. Our code is available at https://github.com/Algolzw/daclip-uir.

Paul Häusner, Aleix Nieto Juscafresa, Jens Sjölund

Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to hyper-parameters. Instead, we replace the hand-engineered algorithm with a graph neural network that is trained to approximate the matrix factorization directly. To apply the output of the neural network as a preconditioner, we propose an output activation function that guarantees that the predicted factorization is invertible. Further, applying a graph neural network architecture allows us to ensure that the output itself is sparse which is desirable from a computational standpoint. We theoretically analyze and empirically evaluate different loss functions to train the learned preconditioners and show their effectiveness in decreasing the number of GMRES iterations and improving the spectral properties on synthetic data. The code is available at https://github.com/paulhausner/neural-incomplete-factorization.

Ziwei Luo, Fredrik K. Gustafsson, Zheng Zhao et al.

This work aims to improve the applicability of diffusion models in realistic image restoration. Specifically, we enhance the diffusion model in several aspects such as network architecture, noise level, denoising steps, training image size, and optimizer/scheduler. We show that tuning these hyperparameters allows us to achieve better performance on both distortion and perceptual scores. We also propose a U-Net based latent diffusion model which performs diffusion in a low-resolution latent space while preserving high-resolution information from the original input for the decoding process. Compared to the previous latent-diffusion model which trains a VAE-GAN to compress the image, our proposed U-Net compression strategy is significantly more stable and can recover highly accurate images without relying on adversarial optimization. Importantly, these modifications allow us to apply diffusion models to various image restoration tasks, including real-world shadow removal, HR non-homogeneous dehazing, stereo super-resolution, and bokeh effect transformation. By simply replacing the datasets and slightly changing the noise network, our model, named Refusion, is able to deal with large-size images (e.g., 6000 x 4000 x 3 in HR dehazing) and produces good results on all the above restoration problems. Our Refusion achieves the best perceptual performance in the NTIRE 2023 Image Shadow Removal Challenge and wins 2nd place overall.

Maria Bånkestad, Jens Sjölund, Jalil Taghia et al.

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational tractability. Elliptical processes are based on a representation of elliptical distributions as a continuous mixture of Gaussian distributions. We parameterize this mixture distribution as a spline normalizing flow, which we train using variational inference. The proposed form of the variational posterior enables a sparse variational elliptical process applicable to large-scale problems. We highlight advantages compared to Gaussian processes through regression and classification experiments. Elliptical processes can supersede Gaussian processes in several settings, including cases where the likelihood is non-Gaussian or when accurate tail modeling is essential.

Ziwei Luo, Fredrik K. Gustafsson, Zheng Zhao et al.

Diffusion models have achieved remarkable progress in generative modelling, particularly in enhancing image quality to conform to human preferences. Recently, these models have also been applied to low-level computer vision for photo-realistic image restoration (IR) in tasks such as image denoising, deblurring, dehazing, etc. In this review paper, we introduce key constructions in diffusion models and survey contemporary techniques that make use of diffusion models in solving general IR tasks. Furthermore, we point out the main challenges and limitations of existing diffusion-based IR frameworks and provide potential directions for future work.

Zheng Zhao, Ziwei Luo, Jens Sjölund et al.

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their success in these domains, an important open challenge remains: extending these techniques to sample from conditional distributions, as required in, for example, Bayesian inverse problems. In this paper, we present a comprehensive review of existing computational approaches to conditional sampling within generative diffusion models. Specifically, we highlight key methodologies that either utilise the joint distribution, or rely on (pre-trained) marginal distributions with explicit likelihoods, to construct conditional generative samplers.

Jens Sjölund

Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational inference is now the preferred choice for many high-dimensional models and large datasets. This tutorial introduces variational inference from the parametric perspective that dominates these recent developments, in contrast to the mean-field perspective commonly found in other introductory texts.

Shreyas Fadnavis, Jens Sjölund, Anders Eklund et al.

Diffusion MRI (dMRI) is the only non-invasive technique sensitive to tissue micro-architecture, which can, in turn, be used to reconstruct tissue microstructure and white matter pathways. The accuracy of such tasks is hampered by the low signal-to-noise ratio in dMRI. Today, the noise is characterized mainly by visual inspection of residual maps and estimated standard deviation. However, it is hard to estimate the impact of noise on downstream tasks based only on such qualitative assessments. To address this issue, we introduce a novel metric, Noise Uncertainty Quantification (NUQ), for quantitative image quality analysis in the absence of a ground truth reference image. NUQ uses a recent Bayesian formulation of dMRI models to estimate the uncertainty of microstructural measures. Specifically, NUQ uses the maximum mean discrepancy metric to compute a pooled quality score by comparing samples drawn from the posterior distribution of the microstructure measures. We show that NUQ allows a fine-grained analysis of noise, capturing details that are visually imperceptible. We perform qualitative and quantitative comparisons on real datasets, showing that NUQ generates consistent scores across different denoisers and acquisitions. Lastly, by using NUQ on a cohort of schizophrenics and controls, we quantify the substantial impact of denoising on group differences.

Dominik Fay, Sebastian Mair, Jens Sjölund

For scalable machine learning on large data sets, subsampling a representative subset is a common approach for efficient model training. This is often achieved through importance sampling, whereby informative data points are sampled more frequently. In this paper, we examine the privacy properties of importance sampling, focusing on an individualized privacy analysis. We find that, in importance sampling, privacy is well aligned with utility but at odds with sample size. Based on this insight, we propose two approaches for constructing sampling distributions: one that optimizes the privacy-efficiency trade-off; and one based on a utility guarantee in the form of coresets. We evaluate both approaches empirically in terms of privacy, efficiency, and accuracy on the differentially private $k$-means problem. We observe that both approaches yield similar outcomes and consistently outperform uniform sampling across a wide range of data sets. Our code is available on GitHub: https://github.com/smair/personalized-privacy-amplification-via-importance-sampling

Sebastian Mair, Jens Sjölund

Archetypal analysis is a matrix factorization method with convexity constraints. Due to local minima, a good initialization is essential, but frequently used initialization methods yield either sub-optimal starting points or are prone to get stuck in poor local minima. In this paper, we propose archetypal analysis++ (AA++), a probabilistic initialization strategy for archetypal analysis that sequentially samples points based on their influence on the objective function, similar to $k$-means++. In fact, we argue that $k$-means++ already approximates the proposed initialization method. Furthermore, we suggest to adapt an efficient Monte Carlo approximation of $k$-means++ to AA++. In an extensive empirical evaluation of 15 real-world data sets of varying sizes and dimensionalities and considering two pre-processing strategies, we show that AA++ almost always outperforms all baselines, including the most frequently used ones.

Zheng Zhao, Sebastian Mair, Thomas B. Schön et al.

Recently, partial Bayesian neural networks (pBNNs), which only consider a subset of the parameters to be stochastic, were shown to perform competitively with full Bayesian neural networks. However, pBNNs are often multi-modal in the latent variable space and thus challenging to approximate with parametric models. To address this problem, we propose an efficient sampling-based training strategy, wherein the training of a pBNN is formulated as simulating a Feynman--Kac model. We then describe variations of sequential Monte Carlo samplers that allow us to simultaneously estimate the parameters and the latent posterior distribution of this model at a tractable computational cost. Using various synthetic and real-world datasets we show that our proposed training scheme outperforms the state of the art in terms of predictive performance.

Ruoqi Zhang, Jens Sjölund

Traditional reinforcement learning methods optimize agents without considering safety, potentially resulting in unintended consequences. In this paper, we propose an optimal actor-free policy that optimizes a risk-sensitive criterion based on the conditional value at risk. The risk-sensitive objective function is modeled using an input-convex neural network ensuring convexity with respect to the actions and enabling the identification of globally optimal actions through simple gradient-following methods. Experimental results demonstrate the efficacy of our approach in maintaining effective risk control.

Ruoqi Zhang, Ziwei Luo, Jens Sjölund et al.

This paper presents advanced techniques of training diffusion policies for offline reinforcement learning (RL). At the core is a mean-reverting stochastic differential equation (SDE) that transfers a complex action distribution into a standard Gaussian and then samples actions conditioned on the environment state with a corresponding reverse-time SDE, like a typical diffusion policy. We show that such an SDE has a solution that we can use to calculate the log probability of the policy, yielding an entropy regularizer that improves the exploration of offline datasets. To mitigate the impact of inaccurate value functions from out-of-distribution data points, we further propose to learn the lower confidence bound of Q-ensembles for more robust policy improvement. By combining the entropy-regularized diffusion policy with Q-ensembles in offline RL, our method achieves state-of-the-art performance on most tasks in D4RL benchmarks. Code is available at https://github.com/ruoqizzz/Entropy-Regularized-Diffusion-Policy-with-QEnsemble.

Henri Doerks, Paul Häusner, Daniel Hernández Escobar et al.

Distributed optimization is fundamental in large-scale machine learning and control applications. Among existing methods, the Alternating Direction Method of Multipliers (ADMM) has gained popularity due to its strong convergence guarantees and suitability for decentralized computation. However, ADMM often suffers from slow convergence and sensitivity to hyperparameter choices. In this work, we show that distributed ADMM iterations can be naturally represented within the message-passing framework of graph neural networks (GNNs). Building on this connection, we propose to learn adaptive step sizes and communication weights by a graph neural network that predicts the hyperparameters based on the iterates. By unrolling ADMM for a fixed number of iterations, we train the network parameters end-to-end to minimize the final iterates error for a given problem class, while preserving the algorithm's convergence properties. Numerical experiments demonstrate that our learned variant consistently improves convergence speed and solution quality compared to standard ADMM. The code is available at https://github.com/paulhausner/learning-distributed-admm.

Ziwei Luo, Fredrik K. Gustafsson, Jens Sjölund et al.

This work presents a forward-only diffusion (FoD) approach for generative modelling. In contrast to traditional diffusion models that rely on a coupled forward-backward diffusion scheme, FoD directly learns data generation through a single forward diffusion process, yielding a simple yet efficient generative framework. The core of FoD is a state-dependent stochastic differential equation that involves a mean-reverting term in both the drift and diffusion functions. This mean-reversion property guarantees the convergence to clean data, naturally simulating a stochastic interpolation between source and target distributions. More importantly, FoD is analytically tractable and is trained using a simple stochastic flow matching objective, enabling a few-step non-Markov chain sampling during inference. The proposed FoD model, despite its simplicity, achieves state-of-the-art performance on various image restoration tasks. Its general applicability on image-conditioned generation is also demonstrated via qualitative results on image-to-image translation. Our code is available at https://github.com/Algolzw/FoD.

Paul Häusner, Ozan Öktem, Jens Sjölund

The convergence of the conjugate gradient method for solving large-scale and sparse linear equation systems depends on the spectral properties of the system matrix, which can be improved by preconditioning. In this paper, we develop a computationally efficient data-driven approach to accelerate the generation of effective preconditioners. We, therefore, replace the typically hand-engineered preconditioners by the output of graph neural networks. Our method generates an incomplete factorization of the matrix and is, therefore, referred to as neural incomplete factorization (NeuralIF). Optimizing the condition number of the linear system directly is computationally infeasible. Instead, we utilize a stochastic approximation of the Frobenius loss which only requires matrix-vector multiplications for efficient training. At the core of our method is a novel message-passing block, inspired by sparse matrix theory, that aligns with the objective of finding a sparse factorization of the matrix. We evaluate our proposed method on both synthetic problem instances and on problems arising from the discretization of the Poisson equation on varying domains. Our experiments show that by using data-driven preconditioners within the conjugate gradient method we are able to speed up the convergence of the iterative procedure. The code is available at https://github.com/paulhausner/neural-incomplete-factorization.

Sanna Jarl, Maria Bånkestad, Jonathan J. S. Scragg et al.

Bayesian active learning relies on the precise quantification of predictive uncertainty to explore unknown function landscapes. While Gaussian process surrogates are the standard for such tasks, an underappreciated fact is that their posterior variance depends on the observed outputs only through the hyperparameters, rendering exploration largely insensitive to the actual measurements. We propose to inject observation-dependent feedback by warping the input space with a learned, monotone reparameterization. This mechanism allows the design policy to expand or compress regions of the input space in response to observed variability, thereby shaping the behavior of variance-based acquisition functions. We demonstrate that while such warps can be trained via marginal likelihood, a novel self-supervised objective yields substantially better performance. Our approach improves sample efficiency across a range of active learning benchmarks, particularly in regimes where non-stationarity challenges traditional methods.

Ziwei Luo, Fredrik K. Gustafsson, Zheng Zhao et al.

Though diffusion models have been successfully applied to various image restoration (IR) tasks, their performance is sensitive to the choice of training datasets. Typically, diffusion models trained in specific datasets fail to recover images that have out-of-distribution degradations. To address this problem, this work leverages a capable vision-language model and a synthetic degradation pipeline to learn image restoration in the wild (wild IR). More specifically, all low-quality images are simulated with a synthetic degradation pipeline that contains multiple common degradations such as blur, resize, noise, and JPEG compression. Then we introduce robust training for a degradation-aware CLIP model to extract enriched image content features to assist high-quality image restoration. Our base diffusion model is the image restoration SDE (IR-SDE). Built upon it, we further present a posterior sampling strategy for fast noise-free image generation. We evaluate our model on both synthetic and real-world degradation datasets. Moreover, experiments on the unified image restoration task illustrate that the proposed posterior sampling improves image generation quality for various degradations.

Adrien Corenflos, Zheng Zhao, Simo Särkkä et al.

Given an unconditional diffusion model targeting a joint model $π(x, y)$, using it to perform conditional simulation $π(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the denoising SDE after the fact. In this work, we express \emph{exact} conditional simulation within the \emph{approximate} diffusion model as an inference problem on an augmented space corresponding to a partial SDE bridge. This perspective allows us to implement efficient and principled particle Gibbs and pseudo-marginal samplers marginally targeting the conditional distribution $π(x \mid y)$. Contrary to existing methodology, our methods do not introduce any additional approximation to the unconditional diffusion model aside from the Monte Carlo error. We showcase the benefits and drawbacks of our approach on a series of synthetic and real data examples.

Maria Bånkestad, Jennifer R. Andersson, Sebastian Mair et al.

Reducing a graph while preserving its overall properties is an important problem with many applications. Typically, reduction approaches either remove edges (sparsification) or merge nodes (coarsening) in an unsupervised way with no specific downstream task in mind. In this paper, we present an approach for subsampling graph structures using an Ising model defined on either the nodes or edges and learning the external magnetic field of the Ising model using a graph neural network. Our approach is task-specific as it can learn how to reduce a graph for a specific downstream task in an end-to-end fashion without requiring a differentiable loss function for the task. We showcase the versatility of our approach on four distinct applications: image segmentation, explainability for graph classification, 3D shape sparsification, and sparse approximate matrix inverse determination.

Ruoqi Zhang, Ziwei Luo, Jens Sjölund et al.

Diffusion models have shown impressive performance in capturing complex and multi-modal action distributions for game agents, but their slow inference speed prevents practical deployment in real-time game environments. While consistency models offer a promising approach for one-step generation, they often suffer from training instability and performance degradation when applied to policy learning. In this paper, we present CPQE (Consistency Policy with Q-Ensembles), which combines consistency models with Q-ensembles to address these challenges.CPQE leverages uncertainty estimation through Q-ensembles to provide more reliable value function approximations, resulting in better training stability and improved performance compared to classic double Q-network methods. Our extensive experiments across multiple game scenarios demonstrate that CPQE achieves inference speeds of up to 60 Hz -- a significant improvement over state-of-the-art diffusion policies that operate at only 20 Hz -- while maintaining comparable performance to multi-step diffusion approaches. CPQE consistently outperforms state-of-the-art consistency model approaches, showing both higher rewards and enhanced training stability throughout the learning process. These results indicate that CPQE offers a practical solution for deploying diffusion-based policies in games and other real-time applications where both multi-modal behavior modeling and rapid inference are critical requirements.

Amir Baghi, Jens Sjölund, Joakim Bergdahl et al.

Multi-agent reinforcement learning has shown promise in learning cooperative behaviors in team-based environments. However, such methods often demand extensive training time. For instance, the state-of-the-art method TiZero takes 40 days to train high-quality policies for a football environment. In this paper, we hypothesize that better exploration mechanisms can improve the sample efficiency of multi-agent methods. We propose two different approaches for better exploration in TiZero: a self-supervised intrinsic reward and a random network distillation bonus. Additionally, we introduce architectural modifications to the original algorithm to enhance TiZero's computational efficiency. We evaluate the sample efficiency of these approaches through extensive experiments. Our results show that random network distillation improves training sample efficiency by 18.8% compared to the original TiZero. Furthermore, we evaluate the qualitative behavior of the models produced by both variants against a heuristic AI, with the self-supervised reward encouraging possession and random network distillation leading to a more offensive performance. Our results highlights the applicability of our random network distillation variant in practical settings. Lastly, due to the nature of the proposed method, we acknowledge its use beyond football simulation, especially in environments with strong multi-agent and strategic aspects.

Ella J. Schmidtobreick, Daniel Arnström, Paul Häusner et al.

Quadratic programming (QP) solvers are widely used in real-time control and optimization, but their computational cost often limits applicability in time-critical settings. We propose a learning-to-optimize approach using graph neural networks (GNNs) to predict active sets in the dual active-set solver DAQP. The method exploits the structural properties of QPs by representing them as bipartite graphs and learning to identify the optimal active set for efficiently warm-starting the solver. Across varying problem sizes, the GNN consistently reduces the number of solver iterations compared to cold-starting, while performance is comparable to a multilayer perceptron (MLP) baseline. Furthermore, a GNN trained on varying problem sizes generalizes effectively to unseen dimensions, demonstrating flexibility and scalability. These results highlight the potential of structure-aware learning to accelerate optimization in real-time applications such as model predictive control.

Adhithyan Kalaivanan, Zheng Zhao, Jens Sjölund et al.

Guiding pretrained flow-based generative models for conditional generation or to produce samples with desired target properties enables solving diverse tasks without retraining on paired data. We present ESS-Flow, a gradient-free method that leverages the typically Gaussian prior of the source distribution in flow-based models to perform Bayesian inference directly in the source space using Elliptical Slice Sampling. ESS-Flow only requires forward passes through the generative model and observation process, no gradient or Jacobian computations, and is applicable even when gradients are unreliable or unavailable, such as with simulation-based observations or quantization in the generation or observation process. We demonstrate its effectiveness on designing materials with desired target properties and predicting protein structures from sparse inter-residue distance measurements.

Laura van Weesep, Samuel Genheden, Ola Engkvist et al.

Large-language models (LLMs) and agentic systems present exciting opportunities to accelerate drug discovery. In this study, we examine the modularity of LLM-based agentic systems for drug discovery, i.e., whether parts of the system such as the LLM and type of agent are interchangeable, a topic that has received limited attention in drug discovery. We compare the performance of different LLMs and the effectiveness of tool-calling agents versus code-generating agents. Our case study, comparing performance in orchestrating tools for chemistry and drug discovery using an LLM-as-a-judge score, shows that Claude-3.5-Sonnet, Claude-3.7-Sonnet and GPT-4o outperform alternative language models such as Llama-3.1-8B, Llama-3.1-70B, GPT-3.5-Turbo, and Nova-Micro. Although we confirm that code-generating agents outperform the tool-calling ones on average, we show that this is highly question- and model-dependent. Furthermore, the impact of replacing system prompts is dependent on the question and model, underscoring that even in this particular domain one cannot just replace components of the system without re-engineering. Our study highlights the necessity of further research into the modularity of agentic systems to enable the development of reliable and modular solutions for real-world problems.

Niklas Gunnarsson, Jens Sjölund, Peter Kimstrand et al.

Image monitoring and guidance during medical examinations can aid both diagnosis and treatment. However, the sampling frequency is often too low, which creates a need to estimate the missing images. We present a probabilistic motion model for sequential medical images, with the ability to both estimate motion between acquired images and forecast the motion ahead of time. The core is a low-dimensional temporal process based on a linear Gaussian state-space model with analytically tractable solutions for forecasting, simulation, and imputation of missing samples. The results, from two experiments on publicly available cardiac datasets, show reliable motion estimates and an improved forecasting performance using patient-specific adaptation by online learning.

Sebastian Mair, Anqi Fu, Jens Sjölund

Radiation treatment planning involves optimization over a large number of voxels, many of which carry limited information about the clinical problem. We propose an approach to reduce the large optimization problem by only using a representative subset of informative voxels. This way, we drastically improve planning efficiency while maintaining the plan quality. Within an initial probing step, we pre-solve an easier optimization problem involving a simplified objective from which we derive an importance score per voxel. This importance score is then turned into a sampling distribution, which allows us to subsample a small set of informative voxels using importance sampling. By solving a - now reduced - version of the original optimization problem using this subset, we effectively reduce the problem's size and computational demands while accounting for regions where satisfactory dose deliveries are challenging. In contrast to other stochastic (sub-)sampling methods, our technique only requires a single probing and sampling step to define a reduced optimization problem. This problem can be efficiently solved using established solvers without the need of modifying or adapting them. Empirical experiments on open benchmark data highlight substantially reduced optimization times, up to 50 times faster than the original ones, for intensity-modulated radiation therapy (IMRT), all while upholding plan quality comparable to traditional methods. Our novel approach has the potential to significantly accelerate radiation treatment planning by addressing its inherent computational challenges. We reduce the treatment planning time by reducing the size of the optimization problem rather than modifying and improving the optimization method. Our efforts are thus complementary to many previous developments.

Jens Sjölund, Maria Bånkestad

We describe a graph-based neural acceleration technique for nonnegative matrix factorization that builds upon a connection between matrices and bipartite graphs that is well-known in certain fields, e.g., sparse linear algebra, but has not yet been exploited to design graph neural networks for matrix computations. We first consider low-rank factorization more broadly and propose a graph representation of the problem suited for graph neural networks. Then, we focus on the task of nonnegative matrix factorization and propose a graph neural network that interleaves bipartite self-attention layers with updates based on the alternating direction method of multipliers. Our empirical evaluation on synthetic and two real-world datasets shows that we attain substantial acceleration, even though we only train in an unsupervised fashion on smaller synthetic instances.

Alessa Hering, Lasse Hansen, Tony C. W. Mok et al.

Image registration is a fundamental medical image analysis task, and a wide variety of approaches have been proposed. However, only a few studies have comprehensively compared medical image registration approaches on a wide range of clinically relevant tasks. This limits the development of registration methods, the adoption of research advances into practice, and a fair benchmark across competing approaches. The Learn2Reg challenge addresses these limitations by providing a multi-task medical image registration data set for comprehensive characterisation of deformable registration algorithms. A continuous evaluation will be possible at https://learn2reg.grand-challenge.org. Learn2Reg covers a wide range of anatomies (brain, abdomen, and thorax), modalities (ultrasound, CT, MR), availability of annotations, as well as intra- and inter-patient registration evaluation. We established an easily accessible framework for training and validation of 3D registration methods, which enabled the compilation of results of over 65 individual method submissions from more than 20 unique teams. We used a complementary set of metrics, including robustness, accuracy, plausibility, and runtime, enabling unique insight into the current state-of-the-art of medical image registration. This paper describes datasets, tasks, evaluation methods and results of the challenge, as well as results of further analysis of transferability to new datasets, the importance of label supervision, and resulting bias. While no single approach worked best across all tasks, many methodological aspects could be identified that push the performance of medical image registration to new state-of-the-art performance. Furthermore, we demystified the common belief that conventional registration methods have to be much slower than deep-learning-based methods.

Niklas Gunnarsson, Peter Kimstrand, Jens Sjölund et al.

Spatiotemporal imaging has applications in e.g. cardiac diagnostics, surgical guidance, and radiotherapy monitoring, In this paper, we explain the temporal motion by identifying the underlying dynamics, only based on the sequential images. Our dynamical model maps the inputs of observed high-dimensional sequential images to a low-dimensional latent space wherein a linear relationship between a hidden state process and the lower-dimensional representation of the inputs holds. For this, we use a conditional variational auto-encoder (CVAE) to nonlinearly map the higher-dimensional image to a lower-dimensional space, wherein we model the dynamics with a linear Gaussian state-space model (LG-SSM). The model, a modified version of the Kalman variational auto-encoder, is end-to-end trainable, and the weights, both in the CVAE and LG-SSM, are simultaneously updated by maximizing the evidence lower bound of the marginal likelihood. In contrast to the original model, we explain the motion with a spatial transformation from one image to another. This results in sharper reconstructions and the possibility of transferring auxiliary information, such as segmentation, through the image sequence. Our experiments, on cardiac ultrasound time series, show that the dynamic model outperforms traditional image registration in execution time, to a similar performance. Further, our model offers the possibility to impute and extrapolate for missing samples.

Dominik Fay, Jens Sjölund, Tobias J. Oechtering

When it comes to preserving privacy in medical machine learning, two important considerations are (1) keeping data local to the institution and (2) avoiding inference of sensitive information from the trained model. These are often addressed using federated learning and differential privacy, respectively. However, the commonly used Federated Averaging algorithm requires a high degree of synchronization between participating institutions. For this reason, we turn our attention to Private Aggregation of Teacher Ensembles (PATE), where all local models can be trained independently without inter-institutional communication. The purpose of this paper is thus to explore how PATE -- originally designed for classification -- can best be adapted for semantic segmentation. To this end, we build low-dimensional representations of segmentation masks which the student can obtain through low-sensitivity queries to the private aggregator. On the Brain Tumor Segmentation (BraTS 2019) dataset, an Autoencoder-based PATE variant achieves a higher Dice coefficient for the same privacy guarantee than prior work based on noisy Federated Averaging.

Niklas Gunnarsson, Jens Sjölund, Thomas B. Schön

Our anatomy is in constant motion. With modern MR imaging it is possible to record this motion in real-time during an ongoing radiation therapy session. In this paper we present an image registration method that exploits the sequential nature of 2D MR images to estimate the corresponding displacement field. The method employs several discriminative correlation filters that independently track specific points. Together with a sparse-to-dense interpolation scheme we can then estimate of the displacement field. The discriminative correlation filters are trained online, and our method is modality agnostic. For the interpolation scheme we use a neural network with normalized convolutions that is trained using synthetic diffeomorphic displacement fields. The method is evaluated on a segmented cardiac dataset and when compared to two conventional methods we observe an improved performance. This improvement is especially pronounced when it comes to the detection of larger motions of small objects.

Maria Bånkestad, Jens Sjölund, Jalil Taghia et al.

We present the elliptical processes -- a family of non-parametric probabilistic models that subsumes the Gaussian process and the Student-t process. This generalization includes a range of new fat-tailed behaviors yet retains computational tractability. We base the elliptical processes on a representation of elliptical distributions as a continuous mixture of Gaussian distributions and derive closed-form expressions for the marginal and conditional distributions. We perform numerical experiments on robust regression using an elliptical process defined by a piecewise constant mixing distribution, and show advantages compared with a Gaussian process. The elliptical processes may become a replacement for Gaussian processes in several settings, including when the likelihood is not Gaussian or when accurate tail modeling is critical.

Kenneth Lau, Jonas Adler, Jens Sjölund

Over the last few years machine learning has demonstrated groundbreaking results in many areas of medical image analysis, including segmentation. A key assumption, however, is that the train- and test distributions match. We study a realistic scenario where this assumption is clearly violated, namely segmentation with missing input modalities. We describe two neural network approaches that can handle a variable number of input modalities. The first is modality dropout: a simple but surprisingly effective modification of the training. The second is the unified representation network: a network architecture that maps a variable number of input modalities into a unified representation that can be used for downstream tasks such as segmentation. We demonstrate that modality dropout makes a standard segmentation network reasonably robust to missing modalities, but that the same network works even better if trained on the unified representation.

Jens Sjölund, Anders Eklund, Evren Özarslan et al.

We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an alternative reconstruction method guaranteeing a nonnegative EAP that integrates to unity. The reconstruction is validated on data simulated from two Gaussians at various crossing angles. Moreover, we demonstrate on non-uniformly sampled in vivo data that the method is far superior to linear interpolation, and allows a drastic undersampling of the data with only a minor loss of accuracy. We envision the method as a potential replacement for standard diffusion spectrum imaging, in particular when acquistion time is limited.