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Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…
There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…
Deep neural networks tend to make overconfident predictions and often require additional detectors for misclassifications, particularly for safety-critical applications. Existing detection methods usually only focus on adversarial attacks…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
Transformer models bring propelling advances in various NLP tasks, thus inducing lots of interpretability research on the learned representations of the models. However, we raise a fundamental question regarding the reliability of the…
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…
Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
The execution of different cases of a process is often restricted by inter-case dependencies through e.g., queueing or shared resources. Various high-level Petri net formalisms have been proposed that are able to model and analyze…
A compositional Petri net-based semantics is given to a simple language allowing pointer manipulation and parallelism. The model is then applied to give a notion of validity to the judgements made by concurrent separation logic that…
For every finite Petri net, we construct a commutative polynomial in two variables and with coefficients from the semiring of natural numbers. We also present an inverse construction and show that multiplication of polynomials…
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
A wide variety of models for concurrent programs has been proposed during the past decades, each one focusing on various aspects of computations: trace equivalence, causality between events, conflicts and schedules due to resource accesses,…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
We give a novel descriptive-complexity theoretic characterization of L and NL computable queries over finite structures using traversal invariance. We summarize this as (N)L = FO + (breadth-first) traversal-invariance.