Related papers: Invariants and Home Spaces in Transition Systems a…

Permutation invariant neural networks are a promising tool for making predictions from sets. However, we show that existing permutation invariant architectures, Deep Sets and Set Transformer, can suffer from vanishing or exploding gradients…

Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we…

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very…

We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully…

Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…

Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness…

In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…

Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space…

The execution of an event in a complex and distributed system where the dependencies vary during the evolution of the system can be represented in many ways, and one of them is to use Context-Dependent Event structures. Event structures are…

The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…

Many applications require robustness, or ideally invariance, of neural networks to certain transformations of input data. Most commonly, this requirement is addressed by training data augmentation, using adversarial training, or defining…

The task of learning to map an input set onto a permuted sequence of its elements is challenging for neural networks. Set-to-sequence problems occur in natural language processing, computer vision and structure prediction, where…

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…

Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…

We investigate bisimulation equivalence on Petri nets under durational semantics. Our motivation was to verify the conjecture that in durational setting, the bisimulation equivalence checking problem becomes more tractable than in ordinary…

Equivariant neural networks incorporate symmetries through group actions, embedding them as an inductive bias to improve performance. Existing methods learn an equivariant action on the latent space, or design architectures that are…

Information flow security properties were defined some years ago (see, e.g., the surveys \cite{FG01,Ry01}) in terms of suitable equivalence checking problems. These definitions were provided by using sequential models of computations (e.g.,…

We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilibrium points, traveling waves, periodic orbits and invariant…

Loop invariants are properties of a program loop that hold both before and after each iteration of the loop. They are often used to verify programs and ensure that algorithms consistently produce correct results during execution.…