We present a family of automata networks that solve the k-parity problem when run in parallel. These solutions are constructed by connecting cliques in a non-cyclical fashion. The size of the local neighbourhood is linear in the size of the alphabet, and the convergence time is proven to always be the diameter of the interaction graph. We show that this family of solutions can be slightly altered to obtain an equivalent family of solutions to the k-synchronisation problem, which means that these solutions converge from any initial configuration to the cycle which contains all the uniform configurations over the alphabet, in order.
Recent advances in neuroimaging have enabled studies in functional connectivity (FC) of human brain, alongside investigation of the neuronal basis of cognition. One important FC study is the representation of vision in human brain. The release of publicly available dataset BOLD5000 has made it possible to study the brain dynamics during visual tasks in greater detail. In this paper, a comprehensive analysis of fMRI time series (TS) has been performed to explore different types of visual brain networks (VBN). The novelty of this work lies in (1) constructing VBN with consistently significant direct connectivity using both marginal and partial correlation, which is further analyzed using graph theoretic measures, (2) classification of VBNs as formed by image complexity-specific TS, using graphical features. In image complexity-specific VBN classification, XGBoost yields average accuracy in the range of 86.5% to 91.5% for positively correlated VBN, which is 2% greater than that using negative correlation. This result not only reflects the distinguishing graphical characteristics of each image complexity-specific VBN, but also highlights the importance of studying both positively correlated and negatively correlated VBN to understand the how differently brain functions while viewing different complexities of real-world images.
Placing applications in mobile edge computing servers presents a complex challenge involving many servers, users, and their requests. Existing algorithms take a long time to solve high-dimensional problems with significant uncertainty scenarios. Therefore, an efficient approach is required to maximize the quality of service while considering all technical constraints. One of these approaches is machine learning, which emulates optimal solutions for application placement in edge servers. Machine learning models are expected to learn how to allocate user requests to servers based on the spatial positions of users and servers. In this study, the problem is formulated as a two-stage stochastic programming. A sufficient amount of training records is generated by varying parameters such as user locations, their request rates, and solving the optimization model. Then, based on the distance features of each user from the available servers and their request rates, machine learning models generate decision variables for the first stage of the stochastic optimization model, which is the user-to-server request allocation, and are employed as independent decision agents that reliably mimic the optimization model. Support Vector Machines (SVM) and Multi-layer Perceptron (MLP) are used in this research to achieve practical decisions from the stochastic optimization models. The performance of each model has shown an execution effectiveness of over 80%. This research aims to provide a more efficient approach for tackling high-dimensional problems and scenarios with uncertainties in mobile edge computing by leveraging machine learning models for optimal decision-making in request allocation to edge servers. These results suggest that machine-learning models can significantly improve solution times compared to conventional approaches.
This work presents the cubature scheme for the fitting of spatio-temporal Poisson point processes. The methodology is implemented in the R Core Team (2024) package stopp (D'Angelo and Adelfio, 2023), published on the Comprehensive R Archive Network (CRAN) and available from //CRAN.R-project.org/package=stopp. Since the number of dummy points should be sufficient for an accurate estimate of the likelihood, numerical experiments are currently under development to give guidelines on this aspect.
In this study, we tackle a growing concern around the safety and ethical use of large language models (LLMs). Despite their potential, these models can be tricked into producing harmful or unethical content through various sophisticated methods, including 'jailbreaking' techniques and targeted manipulation. Our work zeroes in on a specific issue: to what extent LLMs can be led astray by asking them to generate responses that are instruction-centric such as a pseudocode, a program or a software snippet as opposed to vanilla text. To investigate this question, we introduce TechHazardQA, a dataset containing complex queries which should be answered in both text and instruction-centric formats (e.g., pseudocodes), aimed at identifying triggers for unethical responses. We query a series of LLMs -- Llama-2-13b, Llama-2-7b, Mistral-V2 and Mistral 8X7B -- and ask them to generate both text and instruction-centric responses. For evaluation we report the harmfulness score metric as well as judgements from GPT-4 and humans. Overall, we observe that asking LLMs to produce instruction-centric responses enhances the unethical response generation by ~2-38% across the models. As an additional objective, we investigate the impact of model editing using the ROME technique, which further increases the propensity for generating undesirable content. In particular, asking edited LLMs to generate instruction-centric responses further increases the unethical response generation by ~3-16% across the different models.
There are now many explainable AI methods for understanding the decisions of a machine learning model. Among these are those based on counterfactual reasoning, which involve simulating features changes and observing the impact on the prediction. This article proposes to view this simulation process as a source of creating a certain amount of knowledge that can be stored to be used, later, in different ways. This process is illustrated in the additive model and, more specifically, in the case of the naive Bayes classifier, whose interesting properties for this purpose are shown.
Markov networks are probabilistic graphical models that employ undirected graphs to depict conditional independence relationships among variables. Our focus lies in constraint-based structure learning, which entails learning the undirected graph from data through the execution of conditional independence tests. We establish theoretical limits concerning two critical aspects of constraint-based learning of Markov networks: the number of tests and the sizes of the conditioning sets. These bounds uncover an exciting interplay between the structural properties of the graph and the amount of tests required to learn a Markov network. The starting point of our work is that the graph parameter maximum pairwise connectivity, $\kappa$, that is, the maximum number of vertex-disjoint paths connecting a pair of vertices in the graph, is responsible for the sizes of independence tests required to learn the graph. On one hand, we show that at least one test with the size of the conditioning set at least $\kappa$ is always necessary. On the other hand, we prove that any graph can be learned by performing tests of size at most $\kappa$. This completely resolves the question of the minimum size of conditioning sets required to learn the graph. When it comes to the number of tests, our upper bound on the sizes of conditioning sets implies that every $n$-vertex graph can be learned by at most $n^{\kappa}$ tests with conditioning sets of sizes at most $\kappa$. We show that for any upper bound $q$ on the sizes of the conditioning sets, there exist graphs with $O(n q)$ vertices that require at least $n^{\Omega(\kappa)}$ tests to learn. This lower bound holds even when the treewidth and the maximum degree of the graph are at most $\kappa+2$. On the positive side, we prove that every graph of bounded treewidth can be learned by a polynomial number of tests with conditioning sets of sizes at most $2\kappa$.
This work introduces the first toolkit around path-norms that fully encompasses general DAG ReLU networks with biases, skip connections and any operation based on the extraction of order statistics: max pooling, GroupSort etc. This toolkit notably allows us to establish generalization bounds for modern neural networks that are not only the most widely applicable path-norm based ones, but also recover or beat the sharpest known bounds of this type. These extended path-norms further enjoy the usual benefits of path-norms: ease of computation, invariance under the symmetries of the network, and improved sharpness on layered fully-connected networks compared to the product of operator norms, another complexity measure most commonly used. The versatility of the toolkit and its ease of implementation allow us to challenge the concrete promises of path-norm-based generalization bounds, by numerically evaluating the sharpest known bounds for ResNets on ImageNet.
In many experimental contexts, whether and how network interactions impact the outcome of interest for both treated and untreated individuals are key concerns. Networks data is often assumed to perfectly represent these possible interactions. This paper considers the problem of estimating treatment effects when measured connections are, instead, a noisy representation of the true spillover pathways. We show that existing methods, using the potential outcomes framework, yield biased estimators in the presence of this mismeasurement. We develop a new method, using a class of mixture models, that can account for missing connections and discuss its estimation via the Expectation-Maximization algorithm. We check our method's performance by simulating experiments on real network data from 43 villages in India. Finally, we use data from a previously published study to show that estimates using our method are more robust to the choice of network measure.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.