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The conclusions provided by deep neural networks (DNNs) must be carefully scrutinized to determine whether they are universal or architecture dependent. The term DAG-DNN refers to a graphical representation of a DNN in which the…
Federated Learning (FL) addresses the need to create models based on proprietary data in such a way that multiple clients retain exclusive control over their data, while all benefit from improved model accuracy due to pooled resources.…
Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…
We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo…
In this work we demonstrate a novel separation between symmetric neural network architectures. Specifically, we consider the Relational Network~\parencite{santoro2017simple} architecture as a natural generalization of the…
Segmentation of anatomical shapes from medical images has taken an important role in the automation of clinical measurements. While typical deep-learning segmentation approaches are performed on discrete voxels, the underlying objects being…
With the increasing imaging and processing capabilities of today's mobile devices, user authentication using iris biometrics has become feasible. However, as the acquisition conditions become more unconstrained and as image quality is…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
Fractional differential equations are powerful mathematical descriptors for intricate physical phenomena in a compact form. However, compared to integer ordinary or partial differential equations, solving fractional differential equations…
While increasingly deep networks are still in general desired for achieving state-of-the-art performance, for many specific inputs a simpler network might already suffice. Existing works exploited this observation by learning to skip…
Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…
A remarkable characteristic of overparameterized deep neural networks (DNNs) is that their accuracy does not degrade when the network's width is increased. Recent evidence suggests that developing compressible representations is key for…
Deep neural networks (DNNs) have recently been applied and used in many advanced and diverse tasks, such as medical diagnosis, automatic driving, etc. Due to the lack of transparency of the deep models, DNNs are often criticized for their…
In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
The expressiveness of deep neural network (DNN) is a perspective to understandthe surprising performance of DNN. The number of linear regions, i.e. pieces thata piece-wise-linear function represented by a DNN, is generally used to…
For complex segmentation tasks, fully automatic systems are inherently limited in their achievable accuracy for extracting relevant objects. Especially in cases where only few data sets need to be processed for a highly accurate result,…
Deep neural networks (DNNs) have demonstrated impressive performance on a wide array of tasks, but they are usually considered opaque since internal structure and learned parameters are not interpretable. In this paper, we re-examine the…