arXiv research

INNs can approximate diverse functions despite layer restrictions.

This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.

CF-INNs can approximate any invertible function, resolving a long-standing problem.

INNs improve acceptance rates in electron spectra analysis.

INNs produce interval-valued uncertainty scores for DNNs.

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of param…

INN method refines clean labeled data from noisy labels.

The Information Bottleneck (IB) objective uses information theory to formulate a task-performance versus robustness trade-off. It has been successfully applied in the standard discriminative classification setting. We pose the question whether the IB can also be used to train generative likelihood models such as normal…

An automorphism $α$ of a group $G$ is normal if it fixes every normal subgroup of $G$ setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group $G$, $Inn(G)$ has finite index in the subgroup $Aut_n(G)$ of normal au…

Let $A_1,...,A_k$ be a system of free factors of $F_n$. The group of relative automorphisms $Aut(F_n;A_1,...,A_k)$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The group of relative outer automorphisms is defined as $Out(F_n;A_1,...,A_k) = Aut(F_n…

Let $\mathcal{A} = {A_1, ..., A_k}$ be a system of free factors of $F_n$. The group of relative automorphisms $\mathrm{Aut}(F_n; \mathcal{A})$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The group of relative outer automorphisms is defined as $\m…

Multispectral optical imaging is becoming a key tool in the operating room. Recent research has shown that machine learning algorithms can be used to convert pixel-wise reflectance measurements to tissue parameters, such as oxygenation. However, the accuracy of these algorithms can only be guaranteed if the spectra acq…

ISR creates analytical relationships from data via invertible maps.

Stochastic gradient descent (SGD) has been the dominant optimization method for training deep neural networks due to its many desirable properties. One of the more remarkable and least understood quality of SGD is that it generalizes relatively well on unseen data even when the neural network has millions of parameters…

Study bi-Lipschitz equivalence of mixed polynomials under specific conditions.

Intraductal papillary mucinous neoplasm (IPMN) is a precursor to pancreatic ductal adenocarcinoma. While over half of patients are diagnosed with pancreatic cancer at a distant stage, patients who are diagnosed early enjoy a much higher 5-year survival rate of $34\%$ compared to $3\%$ in the former; hence, early diagno…

Study of profinite quandles with constructions and characterizations.

In this paper we study different questions concerning automorphisms of quandles. For a conjugation quandle $Q={\rm Conj}(G)$ of a group $G$ we determine several subgroups of ${\rm Aut}(Q)$ and find necessary and sufficient conditions when these subgroups coincide with the whole group ${\rm Aut}(Q)$. In particular, we p…

Study confirms non-injective monodromy for even genus 4 translation surfaces.

AutoPQ automates quantile forecasting for smart grids, reducing workload and environmental impact.

Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction fairly may degrade the performance. For example, the interactions of a useless featur…

Logical neural networks solve mazes by filling dead ends, but not all methods generalize well.

New MIP methods improve training of integer-valued neural networks.