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Although statistical inference in stochastic differential equations (SDEs) driven by Wiener process has received significant attention in the literature, inference in those driven by fractional Brownian motion seem to have seen much less…
Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to…
This paper introduces a network architecture to solve the structure-from-motion (SfM) problem via feature-metric bundle adjustment (BA), which explicitly enforces multi-view geometry constraints in the form of feature-metric error. The…
The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive…
Purpose: To systematically investigate the influence of various data consistency layers, (semi-)supervised learning and ensembling strategies, defined in a $\Sigma$-net, for accelerated parallel MR image reconstruction using deep learning.…
Semantic segmentation is applied extensively in autonomous driving and intelligent transportation with methods that highly demand spatial and semantic information. Here, an STDC-MA network is proposed to meet these demands. First, the…
Attention mechanisms underpin the computational power of Transformer models, which have achieved remarkable success across diverse domains. Yet understanding and extending the principles underlying self-attention remains a key challenge for…
Cancer detection and prognosis relies heavily on medical imaging, particularly CT and PET scans. Deep Neural Networks (DNNs) have shown promise in tumor segmentation by fusing information from these modalities. However, a critical…
Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of…
The emergence of spontaneous symmetry breaking among a few heads of multi-head attention (MHA) across transformer blocks in classification tasks was recently demonstrated through the quantification of single-nodal performance (SNP). This…
In this article we propose feature graph architectures (FGA), which are deep learning systems employing a structured initialisation and training method based on a feature graph which facilitates improved generalisation performance compared…
Hyperspectral Imaging (HSI) is known for its advantages over traditional RGB imaging in remote sensing, agriculture, and medicine. Recently, it has gained attention for enhancing Advanced Driving Assistance Systems (ADAS) perception.…
With the introduction of Transformers, different attention-based models have been proposed for image segmentation with promising results. Although self-attention allows capturing of long-range dependencies, it suffers from a quadratic…
Stochasticity plays a key role in many biological systems, necessitating the calibration of stochastic mathematical models to interpret associated data. For model parameters to be estimated reliably, it is typically the case that they must…
In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prove…
Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization…
Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for…
The self-attention mechanism (SAM) is widely used in various fields of artificial intelligence and has successfully boosted the performance of different models. However, current explanations of this mechanism are mainly based on intuitions…
The emerging graph Transformers have achieved impressive performance for graph representation learning over graph neural networks (GNNs). In this work, we regard the self-attention mechanism, the core module of graph Transformers, as a…
Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…