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The simple greedy algorithm to find a maximal independent set of a graph can be viewed as a sequential update of a Boolean network, where the update function at each vertex is the conjunction of all the negated variables in its neighbourhood. In general, the convergence of the so-called kernel network is complex. A word (sequence of vertices) fixes the kernel network if applying the updates sequentially according to that word. We prove that determining whether a word fixes the kernel network is coNP-complete. We also consider the so-called permis, which are permutation words that fix the kernel network. We exhibit large classes of graphs that have a permis, but we also construct many graphs without a permis.

We carry on the study of the synthesis problem on data words for fragments of first order logic, and delineate precisely the border between decidability and undecidability.

This paper introduces a novel compatibility attack to detect a steganographic message embedded in the DCT domain of a JPEG image at high-quality factors (close to 100). Because the JPEG compression is not a surjective function, i.e. not every DCT blocks can be mapped from a pixel block, embedding a message in the DCT domain can create incompatible blocks. We propose a method to find such a block, which directly proves that a block has been modified during the embedding. This theoretical method provides many advantages such as being completely independent to Cover Source Mismatch, having good detection power, and perfect reliability since false alarms are impossible as soon as incompatible blocks are found. We show that finding an incompatible block is equivalent to proving the infeasibility of an Integer Linear Programming problem. However, solving such a problem requires considerable computational power and has not been reached for 8x8 blocks. Instead, a timing attack approach is presented to perform steganalysis without potentially any false alarms for large computing power.

This paper proposes a general optimization framework to improve the spectral and energy efficiency (EE) of ultra-reliable low-latency communication (URLLC) simultaneous-transfer-and-receive (STAR) reconfigurable intelligent surface (RIS)-assisted interference-limited systems with finite block length (FBL). This framework can solve a large variety of optimization problems in which the objective and/or constraints are linear functions of the rates and/or EE of users. Additionally, the framework can be applied to any interference-limited system with treating interference as noise as the decoding strategy at receivers. We consider a multi-cell broadcast channel as an example and show how this framework can be specialized to solve the minimum-weighted rate, weighted sum rate, global EE and weighted EE of the system. We make realistic assumptions regarding the (STAR-)RIS by considering three different feasibility sets for the components of either regular RIS or STAR-RIS. Our results show that RIS can substantially increase the spectral and EE of URLLC systems if the reflecting coefficients are properly optimized. Moreover, we consider three different transmission strategies for STAR-RIS as energy splitting (ES), mode switching (MS), and time switching (TS). We show that STAR-RIS can outperform a regular RIS when the regular RIS cannot cover all the users. Furthermore, it is shown that the ES scheme outperforms the MS and TS schemes.

This paper begins with a description of methods for estimating probability density functions for images that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space - not every pattern of pixels is an image. It is common to say that images lie on a lower-dimensional manifold in the high-dimensional space. However, although images may lie on such lower-dimensional manifolds, it is not the case that all points on the manifold have an equal probability of being images. Images are unevenly distributed on the manifold, and our task is to devise ways to model this distribution as a probability distribution. In pursuing this goal, we consider generative models that are popular in AI and computer vision community. For our purposes, generative/probabilistic models should have the properties of 1) sample generation: it should be possible to sample from this distribution according to the modelled density function, and 2) probability computation: given a previously unseen sample from the dataset of interest, one should be able to compute the probability of the sample, at least up to a normalising constant. To this end, we investigate the use of methods such as normalising flow and diffusion models. We then show that such probabilistic descriptions can be used to construct defences against adversarial attacks. In addition to describing the manifold in terms of density, we also consider how semantic interpretations can be used to describe points on the manifold. To this end, we consider an emergent language framework which makes use of variational encoders to produce a disentangled representation of points that reside on a given manifold. Trajectories between points on a manifold can then be described in terms of evolving semantic descriptions.

Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a ceteris paribus nature which supports reasoning about binary input classifiers and their properties. We study a family of classifier models, axiomatize it as two proof systems regarding the cardinality of the language and show completeness of our axiomatics. Moreover, we prove that satisfiability checking problem for our modal language is NEXPTIME-complete in the infinite-variable case, while it becomes polynomial in the finite-variable case. We furthermore identify an interesting NP fragment of our language in the infinite-variable case. We leverage the language to formalize counterfactual conditional as well as a variety of notions of explanation including abductive, contrastive and counterfactual explanations, and biases. Finally, we present two extensions of our language: a dynamic extension by the notion of assignment enabling classifier change and an epistemic extension in which the classifier's uncertainty about the actual input can be represented.

We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define logics whose syntax is determined by the type of linear behaviour, and whose domain of truth values is determined by the type of branching behaviour, and we provide two semantics for them: a step-wise semantics akin to that of standard coalgebraic logics, and a path-based semantics akin to that of standard linear-time logics. The former semantics is useful for model checking, whereas the latter is the more natural semantics, as it measures the extent with which qualitative properties hold along computation paths from a given state. Our main result is the equivalence of the two semantics. We also provide a semantic characterisation of a notion of logical distance induced by these logics. Instances of our logics support reasoning about the possibility, likelihood or minimal cost of exhibiting a given linear-time property.

Maximum weight independent set (MWIS) admits a $\frac1k$-approximation in inductively $k$-independent graphs and a $\frac{1}{2k}$-approximation in $k$-perfectly orientable graphs. These are a a parameterized class of graphs that generalize $k$-degenerate graphs, chordal graphs, and intersection graphs of various geometric shapes such as intervals, pseudo-disks, and several others. We consider a generalization of MWIS to a submodular objective. Given a graph $G=(V,E)$ and a non-negative submodular function $f: 2^V \rightarrow \mathbb{R}_+$, the goal is to approximately solve $\max_{S \in \mathcal{I}_G} f(S)$ where $\mathcal{I}_G$ is the set of independent sets of $G$. We obtain an $\Omega(\frac1k)$-approximation for this problem in the two mentioned graph classes. The first approach is via the multilinear relaxation framework and a simple contention resolution scheme, and this results in a randomized algorithm with approximation ratio at least $\frac{1}{e(k+1)}$. This approach also yields parallel (or low-adaptivity) approximations. Motivated by the goal of designing efficient and deterministic algorithms, we describe two other algorithms for inductively $k$-independent graphs that are inspired by work on streaming algorithms: a preemptive greedy algorithm and a primal-dual algorithm. In addition to being simpler and faster, these algorithms, in the monotone submodular case, yield the first deterministic constant factor approximations for various special cases that have been previously considered such as intersection graphs of intervals, disks and pseudo-disks.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

We consider the problem of zero-shot recognition: learning a visual classifier for a category with zero training examples, just using the word embedding of the category and its relationship to other categories, which visual data are provided. The key to dealing with the unfamiliar or novel category is to transfer knowledge obtained from familiar classes to describe the unfamiliar class. In this paper, we build upon the recently introduced Graph Convolutional Network (GCN) and propose an approach that uses both semantic embeddings and the categorical relationships to predict the classifiers. Given a learned knowledge graph (KG), our approach takes as input semantic embeddings for each node (representing visual category). After a series of graph convolutions, we predict the visual classifier for each category. During training, the visual classifiers for a few categories are given to learn the GCN parameters. At test time, these filters are used to predict the visual classifiers of unseen categories. We show that our approach is robust to noise in the KG. More importantly, our approach provides significant improvement in performance compared to the current state-of-the-art results (from 2 ~ 3% on some metrics to whopping 20% on a few).