arXiv subjects

Paul Swoboda

Publications and source records attributed to Paul Swoboda.

At least 37 records · Page 2Linked to original sources

arXiv2025

NSA: Neuro-symbolic ARC Challenge

The Abstraction and Reasoning Corpus (ARC) evaluates general reasoning capabilities that are difficult for both machine learning models and combinatorial search methods. We propose a neuro-symbolic approach that combines a transformer for proposal generation with combinatorial search using a domain-specific language. The transformer narrows the search space by proposing promising search directions, which allows the combinatorial search to find the actual solution in short time. We pre-train the trainsformer with synthetically generated data. During test-time we generate additional task-specific training tasks and fine-tune our model. Our results surpass comparable state of the art on the ARC evaluation set by 27% and compare favourably on the ARC train set. We make our code and dataset publicly available at https://github.com/Batorskq/NSA.

cs.AI↗

arXiv2024

DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching

In this work we propose to combine the advantages of learningbased and combinatorial formalisms for 3D shape matching. While learningbased methods lead to state-of-the-art matching performance, they do not ensure geometric consistency, so that obtained matchings are locally non-smooth. On the contrary, axiomatic, optimisation-based methods allow to take geometric consistency into account by explicitly constraining the space of valid matchings. However, existing axiomatic formalisms do not scale to practically relevant problem sizes, and require user input for the initialisation of non-convex optimisation problems. We work towards closing this gap by proposing a novel combinatorial solver that combines a unique set of favourable properties: our approach (i) is initialisation free, (ii) is massively parallelisable and powered by a quasi-Newton method, (iii) provides optimality gaps, and (iv) delivers improved matching quality with decreased runtime and globally optimal results for many instances.

cs.CV↗

arXiv2024

A Mechanistic Analysis of a Transformer Trained on a Symbolic Multi-Step Reasoning Task

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for behavioral studies. However, these studies do not provide insights into the internal mechanisms driving the observed capabilities. To improve our understanding of the internal mechanisms of transformers, we present a comprehensive mechanistic analysis of a transformer trained on a synthetic reasoning task. We identify a set of interpretable mechanisms the model uses to solve the task, and validate our findings using correlational and causal evidence. Our results suggest that it implements a depth-bounded recurrent mechanisms that operates in parallel and stores intermediate results in selected token positions. We anticipate that the motifs we identified in our synthetic setting can provide valuable insights into the broader operating principles of transformers and thus provide a basis for understanding more complex models.

cs.LG↗

arXiv2023

DOGE-Train: Discrete Optimization on GPU with End-to-end Training

We present a fast, scalable, data-driven approach for solving relaxations of 0-1 integer linear programs. We use a combination of graph neural networks (GNN) and the Lagrange decomposition based algorithm FastDOG (Abbas and Swoboda 2022b). We make the latter differentiable for end-to-end training and use GNNs to predict its algorithmic parameters. This allows to retain the algorithm's theoretical properties including dual feasibility and guaranteed non-decrease in the lower bound while improving it via training. We overcome suboptimal fixed points of the basic solver by additional non-parametric GNN update steps maintaining dual feasibility. For training we use an unsupervised loss. We train on smaller problems and test on larger ones showing strong generalization performance with a GNN comprising only around $10k$ parameters. Our solver achieves significantly faster performance and better dual objectives than its non-learned version, achieving close to optimal objective values of LP relaxations of very large structured prediction problems and on selected combinatorial ones. In particular, we achieve better objective values than specialized approximate solvers for specific problem classes while retaining their efficiency. Our solver has better any-time performance over a large time period compared to a commercial solver. Code available at https://github.com/LPMP/BDD

cs.LG↗

arXiv2023

LVM-Med: Learning Large-Scale Self-Supervised Vision Models for Medical Imaging via Second-order Graph Matching

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

cs.CV↗

arXiv2023

Structured Prediction Problem Archive

Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a diverse set of problem classes. We provide archival links to datasets, description of the considered problems and problem formats, and a short summary of problem characteristics including size, number of instances etc. For reference we also give a non-exhaustive selection of algorithms proposed in the literature for their solution. We hope that this central repository will make benchmarking and comparison to established works easier. We welcome submission of interesting new datasets and algorithms for inclusion in our archive.

cs.LG↗

arXiv2023

A Multidimensional Analysis of Social Biases in Vision Transformers

The embedding spaces of image models have been shown to encode a range of social biases such as racism and sexism. Here, we investigate specific factors that contribute to the emergence of these biases in Vision Transformers (ViT). Therefore, we measure the impact of training data, model architecture, and training objectives on social biases in the learned representations of ViTs. Our findings indicate that counterfactual augmentation training using diffusion-based image editing can mitigate biases, but does not eliminate them. Moreover, we find that larger models are less biased than smaller models, and that models trained using discriminative objectives are less biased than those trained using generative objectives. In addition, we observe inconsistencies in the learned social biases. To our surprise, ViTs can exhibit opposite biases when trained on the same data set using different self-supervised objectives. Our findings give insights into the factors that contribute to the emergence of social biases and suggests that we could achieve substantial fairness improvements based on model design choices.

cs.CV↗

arXiv2023

ClusterFuG: Clustering Fully connected Graphs by Multicut

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.

cs.CV↗

arXiv2022

Joint Self-Supervised Image-Volume Representation Learning with Intra-Inter Contrastive Clustering

Collecting large-scale medical datasets with fully annotated samples for training of deep networks is prohibitively expensive, especially for 3D volume data. Recent breakthroughs in self-supervised learning (SSL) offer the ability to overcome the lack of labeled training samples by learning feature representations from unlabeled data. However, most current SSL techniques in the medical field have been designed for either 2D images or 3D volumes. In practice, this restricts the capability to fully leverage unlabeled data from numerous sources, which may include both 2D and 3D data. Additionally, the use of these pre-trained networks is constrained to downstream tasks with compatible data dimensions. In this paper, we propose a novel framework for unsupervised joint learning on 2D and 3D data modalities. Given a set of 2D images or 2D slices extracted from 3D volumes, we construct an SSL task based on a 2D contrastive clustering problem for distinct classes. The 3D volumes are exploited by computing vectored embedding at each slice and then assembling a holistic feature through deformable self-attention mechanisms in Transformer, allowing incorporating long-range dependencies between slices inside 3D volumes. These holistic features are further utilized to define a novel 3D clustering agreement-based SSL task and masking embedding prediction inspired by pre-trained language models. Experiments on downstream tasks, such as 3D brain segmentation, lung nodule detection, 3D heart structures segmentation, and abnormal chest X-ray detection, demonstrate the effectiveness of our joint 2D and 3D SSL approach. We improve plain 2D Deep-ClusterV2 and SwAV by a significant margin and also surpass various modern 2D and 3D SSL approaches.

cs.CV↗

arXiv2022

A Comparative Study of Graph Matching Algorithms in Computer Vision

The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last decades. Since a common standard benchmark has not been developed, their performance claims are often hard to verify as evaluation on differing problem instances and criteria make the results incomparable. To address these shortcomings, we present a comparative study of graph matching algorithms. We create a uniform benchmark where we collect and categorize a large set of existing and publicly available computer vision graph matching problems in a common format. At the same time we collect and categorize the most popular open-source implementations of graph matching algorithms. Their performance is evaluated in a way that is in line with the best practices for comparing optimization algorithms. The study is designed to be reproducible and extensible to serve as a valuable resource in the future. Our study provides three notable insights: 1.) popular problem instances are exactly solvable in substantially less than 1 second and, therefore, are insufficient for future empirical evaluations; 2.) the most popular baseline methods are highly inferior to the best available methods; 3.) despite the NP-hardness of the problem, instances coming from vision applications are often solvable in a few seconds even for graphs with more than 500 vertices.

cs.CV↗

arXiv2022

LMGP: Lifted Multicut Meets Geometry Projections for Multi-Camera Multi-Object Tracking

Multi-Camera Multi-Object Tracking is currently drawing attention in the computer vision field due to its superior performance in real-world applications such as video surveillance in crowded scenes or in wide spaces. In this work, we propose a mathematically elegant multi-camera multiple object tracking approach based on a spatial-temporal lifted multicut formulation. Our model utilizes state-of-the-art tracklets produced by single-camera trackers as proposals. As these tracklets may contain ID-Switch errors, we refine them through a novel pre-clustering obtained from 3D geometry projections. As a result, we derive a better tracking graph without ID switches and more precise affinity costs for the data association phase. Tracklets are then matched to multi-camera trajectories by solving a global lifted multicut formulation that incorporates short and long-range temporal interactions on tracklets located in the same camera as well as inter-camera ones. Experimental results on the WildTrack dataset yield near-perfect performance, outperforming state-of-the-art trackers on Campus while being on par on the PETS-09 dataset.

cs.CV↗

arXiv2022

A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching

We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D shape matching was formulated as an integer linear program over the space of orientation-preserving diffeomorphisms. Until now, the resulting formulation had limited practical applicability due to its complicated constraint structure and its large size. We propose a novel primal heuristic coupled with a Lagrange dual problem that is several orders of magnitudes faster compared to previous solvers. This allows us to handle shapes with substantially more triangles than previously solvable. We demonstrate compelling results on diverse datasets, and, even showcase that we can address the challenging setting of matching two partial shapes without availability of complete shapes. Our code is publicly available at http://github.com/paul0noah/sm-comb .

cs.CV↗

arXiv2022

FastDOG: Fast Discrete Optimization on GPU

We present a massively parallel Lagrange decomposition method for solving 0--1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique for decoding primal solutions. For representing subproblems we follow Lange et al. (2021) and use binary decision diagrams (BDDs). Our primal and dual algorithms require little synchronization between subproblems and optimization over BDDs needs only elementary operations without complicated control flow. This allows us to exploit the parallelism offered by GPUs for all components of our method. We present experimental results on combinatorial problems from MAP inference for Markov Random Fields, quadratic assignment and cell tracking for developmental biology. Our highly parallel GPU implementation improves upon the running times of the algorithms from Lange et al. (2021) by up to an order of magnitude. In particular, we come close to or outperform some state-of-the-art specialized heuristics while being problem agnostic. Our implementation is available at https://github.com/LPMP/BDD.

math.OC↗

arXiv2022

RAMA: A Rapid Multicut Algorithm on GPU

We propose a highly parallel primal-dual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps executed recursively: (1) Finding conflicted cycles that correspond to violated inequalities of the underlying multicut relaxation, (2) Performing message passing between the edges and cycles to optimize the Lagrange relaxation coming from the found violated cycles producing reduced costs and (3) Contracting edges with high reduced costs through matrix-matrix multiplications. Our algorithm produces primal solutions and lower bounds that estimate the distance to optimum. We implement our algorithm on GPUs and show resulting one to two orders-of-magnitudes improvements in execution speed without sacrificing solution quality compared to traditional sequential algorithms that run on CPUs. We can solve very large scale benchmark problems with up to $\mathcal{O}(10^8)$ variables in a few seconds with small primal-dual gaps. Our code is available at https://github.com/pawelswoboda/RAMA.

cs.DC↗

arXiv2021

Efficient Message Passing for 0-1 ILPs with Binary Decision Diagrams

We present a message passing method for 0-1 integer linear programs. Our algorithm is based on a decomposition of the original problem into subproblems that are represented as binary decision diagrams. The resulting Lagrangean dual is solved iteratively by a series of efficient block coordinate ascent steps. Our method has linear iteration complexity in the size of the decomposition and can be effectively parallelized. The characteristics of our approach are desirable towards solving ever larger problems arising in structured prediction. We present experimental results on combinatorial problems from MAP inference for Markov Random Fields, quadratic assignment, discrete tomography and cell tracking for developmental biology and show promising performance.

math.OC↗

arXiv2021

Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach

We propose a fully differentiable architecture for simultaneous semantic and instance segmentation (a.k.a. panoptic segmentation) consisting of a convolutional neural network and an asymmetric multiway cut problem solver. The latter solves a combinatorial optimization problem that elegantly incorporates semantic and boundary predictions to produce a panoptic labeling. Our formulation allows to directly maximize a smooth surrogate of the panoptic quality metric by backpropagating the gradient through the optimization problem. Experimental evaluation shows improvement by backpropagating through the optimization problem w.r.t. comparable approaches on Cityscapes and COCO datasets. Overall, our approach shows the utility of using combinatorial optimization in tandem with deep learning in a challenging large scale real-world problem and showcases benefits and insights into training such an architecture.

cs.CV↗

arXiv2021

Making Higher Order MOT Scalable: An Efficient Approximate Solver for Lifted Disjoint Paths

We present an efficient approximate message passing solver for the lifted disjoint paths problem (LDP), a natural but NP-hard model for multiple object tracking (MOT). Our tracker scales to very large instances that come from long and crowded MOT sequences. Our approximate solver enables us to process the MOT15/16/17 benchmarks without sacrificing solution quality and allows for solving MOT20, which has been out of reach up to now for LDP solvers due to its size and complexity. On all these four standard MOT benchmarks we achieve performance comparable or better than current state-of-the-art methods including a tracker based on an optimal LDP solver.

cs.CV↗

arXiv2020

Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers

Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of heavily optimized combinatorial solvers together with some improvements in architecture design, we advance state-of-the-art on deep graph matching benchmarks for keypoint correspondence. In addition, we highlight the conceptual advantages of incorporating solvers into deep learning architectures, such as the possibility of post-processing with a strong multi-graph matching solver or the indifference to changes in the training setting. Finally, we propose two new challenging experimental setups. The code is available at https://github.com/martius-lab/blackbox-deep-graph-matching

cs.LG↗