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A level graph is the data of a pair $(G,\pi)$ consisting of a finite graph $G$ and an ordered partition $\pi$ on the set of vertices of $G$. To each level graph on $n$ vertices we associate a polytope in $\mathbb R^n$ called its residue polytope. We show that residue polytopes are compatible with each other in the sense that if $\pi'$ is a coarsening of $\pi$, then the polytope associated to $(G,\pi)$ is a face of the one associated to $(G,\pi')$. Moreover, they form all the faces of the residue polytope of $G$, defined as the polytope associated to the level graph with the trivial ordered partition. The results are used in a companion work to describe limits of spaces of Abelian differentials on families of Riemann surfaces approaching a stable Riemann surface on the boundary of the moduli space., Comment: 18 pages, 3 figures

We describe the limits of canonical series along families of curves degenerating to a nodal curve which is general for its topology, in the weak sense that the branches over nodes on each of its components are in general position. We define a fan structure on the space of edge lengths on the dual graph of the limit curve, and construct a projective variety parametrizing the limits, organized in strata associated to the cones of this fan. This extends to all topologies the works by Eisenbud-Harris (Invent. Math. 87: 496-515, 1987) on curves of compact type and Esteves-Medeiros (Invent. Math. 149: 267-338, 2002) on two-component curves., Comment: 80 pages, 10 figures, 3 appendices

An important consequence of human-induced climate change emerges through extreme weather events. The impact of extreme weather events is quantified in some parts of the globe, but it remains underestimated in several countries. In this work we first quantify the extreme temperature and precipitation events in Brazil using data from the Brazilian Institute of Meteorology, which includes 634 meteorological stations that have worked intermittently since 1961. We show that the anomaly in temperature has increased by more than 1{\deg}C in the last 60 years and that extreme events are heterogeneously distributed in the country. In terms of precipitation, our analyses show that it is getting drier in the Northwest region of Brazil while excessive precipitation events are increasing in the South, in agreement with previous works. We then use data from S2iD, an official database that registers disasters in Brazil to estimate their impact in terms of human damage and financial costs in the last ten years. The analysis shows that the drought extreme events are the most expensive, several of them reaching a cost of over a billion USD. Although we are not able to attribute the natural disasters registered in one database to the extreme weather events identified using the meteorological data, we discuss the possible correlations between them. Finally, we present a proposal of using extreme value theory to estimate the probability of having severe extreme events of precipitation in locations where there are already some natural disasters.

Ensuring the reliability and safety of automated decision-making is crucial. It is well-known that data distribution shifts in machine learning can produce unreliable outcomes. This paper proposes a new approach for measuring the reliability of predictions under distribution shifts. We analyze how the outputs of a trained neural network change using clustering to measure distances between outputs and class centroids. We propose this distance as a metric to evaluate the confidence of predictions under distribution shifts. We assign each prediction to a cluster with centroid representing the mean softmax output for all correct predictions of a given class. We then define a safety threshold for a class as the smallest distance from an incorrect prediction to the given class centroid. We evaluate the approach on the MNIST and CIFAR-10 datasets using a Convolutional Neural Network and a Vision Transformer, respectively. The results show that our approach is consistent across these data sets and network models, and indicate that the proposed metric can offer an efficient way of determining when automated predictions are acceptable and when they should be deferred to human operators given a distribution shift., Comment: 9 pages, 10 figures, 3 tables

This study introduces the Misclassification Likelihood Matrix (MLM) as a novel tool for quantifying the reliability of neural network predictions under distribution shifts. The MLM is obtained by leveraging softmax outputs and clustering techniques to measure the distances between the predictions of a trained neural network and class centroids. By analyzing these distances, the MLM provides a comprehensive view of the model's misclassification tendencies, enabling decision-makers to identify the most common and critical sources of errors. The MLM allows for the prioritization of model improvements and the establishment of decision thresholds based on acceptable risk levels. The approach is evaluated on the MNIST dataset using a Convolutional Neural Network (CNN) and a perturbed version of the dataset to simulate distribution shifts. The results demonstrate the effectiveness of the MLM in assessing the reliability of predictions and highlight its potential in enhancing the interpretability and risk mitigation capabilities of neural networks. The implications of this work extend beyond image classification, with ongoing applications in autonomous systems, such as self-driving cars, to improve the safety and reliability of decision-making in complex, real-world environments., Comment: 9 pages, 7 figures, 1 table

We posit that data can only be safe to use up to a certain threshold of the data distribution shift, after which control must be relinquished by the autonomous system and operation halted or handed to a human operator. With the use of a computer vision toy example we demonstrate that network predictive accuracy is impacted by data distribution shifts and propose distance metrics between training and testing data to define safe operation limits within said shifts. We conclude that beyond an empirically obtained threshold of the data distribution shift, it is unreasonable to expect network predictive accuracy not to degrade, Comment: 13 pages, 10 figures, 4 tables

Myocardial Infarction is a main cause of mortality globally, and accurate risk prediction is crucial for improving patient outcomes. Machine Learning techniques have shown promise in identifying high-risk patients and predicting outcomes. However, patient data often contain vast amounts of information and missing values, posing challenges for feature selection and imputation methods. In this article, we investigate the impact of the data preprocessing task and compare three ensembles boosted tree methods to predict the risk of mortality in patients with myocardial infarction. Further, we use the Tree Shapley Additive Explanations method to identify relationships among all the features for the performed predictions, leveraging the entirety of the available data in the analysis. Notably, our approach achieved a superior performance when compared to other existing machine learning approaches, with an F1-score of 91,2% and an accuracy of 91,8% for LightGBM without data preprocessing., Comment: This article has been accepted at the 2023 International Conference on Computational Science and Computational Intelligence (CSCI 23)

Multivariate time series have many applications, from healthcare and meteorology to life science. Although deep learning models have shown excellent predictive performance for time series, they have been criticised for being "black-boxes" or non-interpretable. This paper proposes a novel modular neural network model for multivariate time series prediction that is interpretable by construction. A recurrent neural network learns the temporal dependencies in the data while an attention-based feature selection component selects the most relevant features and suppresses redundant features used in the learning of the temporal dependencies. A modular deep network is trained from the selected features independently to show the users how features influence outcomes, making the model interpretable. Experimental results show that this approach can outperform state-of-the-art interpretable Neural Additive Models (NAM) and variations thereof in both regression and classification of time series tasks, achieving a predictive performance that is comparable to the top non-interpretable methods for time series, LSTM and XGBoost.

Machine learning offers great potential for automated prediction of post-stroke symptoms and their response to rehabilitation. Major challenges for this endeavour include the very high dimensionality of neuroimaging data, the relatively small size of the datasets available for learning, and how to effectively combine neuroimaging and tabular data (e.g. demographic information and clinical characteristics). This paper evaluates several solutions based on two strategies. The first is to use 2D images that summarise MRI scans. The second is to select key features that improve classification accuracy. Additionally, we introduce the novel approach of training a convolutional neural network (CNN) on images that combine regions-of-interest extracted from MRIs, with symbolic representations of tabular data. We evaluate a series of CNN architectures (both 2D and a 3D) that are trained on different representations of MRI and tabular data, to predict whether a composite measure of post-stroke spoken picture description ability is in the aphasic or non-aphasic range. MRI and tabular data were acquired from 758 English speaking stroke survivors who participated in the PLORAS study. The classification accuracy for a baseline logistic regression was 0.678 for lesion size alone, rising to 0.757 and 0.813 when initial symptom severity and recovery time were successively added. The highest classification accuracy 0.854 was observed when 8 regions-of-interest was extracted from each MRI scan and combined with lesion size, initial severity and recovery time in a 2D Residual Neural Network.Our findings demonstrate how imaging and tabular data can be combined for high post-stroke classification accuracy, even when the dataset is small in machine learning terms. We conclude by proposing how the current models could be improved to achieve even higher levels of accuracy using images from hospital scanners.

This volume contains the Technical Communications presented at the 39th International Conference on Logic Programming (ICLP 2023), held at Imperial College London, UK from July 9 to July 15, 2023. Technical Communications included here concern the Main Track, the Doctoral Consortium, the Application and Systems/Demo track, the Recently Published Research Track, the Birds-of-a-Feather track, the Thematic Tracks on Logic Programming and Machine Learning, and Logic Programming and Explainability, Ethics, and Trustworthiness.

Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a property of non-classical reasoning typically seen in commonsense reasoning, whereby a reasoning system is allowed (differently from classical logic) to jump to conclusions which may be retracted later, when new information becomes available. Neural-symbolic systems such as Logic Tensor Networks (LTN) have been shown to be effective at enabling deep neural networks to achieve reasoning capabilities. In this paper, we show that by combining a neural-symbolic system with methods from continual learning, LTN can obtain a higher level of accuracy when addressing non-monotonic reasoning tasks. Continual learning is added to LTNs by adopting a curriculum of learning from knowledge and data with recall. We call this process Continual Reasoning, a new methodology for the application of neural-symbolic systems to reasoning tasks. Continual Reasoning is applied to a prototypical non-monotonic reasoning problem as well as other reasoning examples. Experimentation is conducted to compare and analyze the effects that different curriculum choices may have on overall learning and reasoning results. Results indicate significant improvement on the prototypical non-monotonic reasoning problem and a promising outlook for the proposed approach on statistical relational learning examples., Comment: 13 pages, 2 figures, to be published in NeSy 2023: 17th International Workshop on Neural-Symbolic Learning and Reasoning

The field of neuro-symbolic AI aims to benefit from the combination of neural networks and symbolic systems. A cornerstone of the field is the translation or encoding of symbolic knowledge into neural networks. Although many neuro-symbolic methods and approaches have been proposed, and with a large increase in recent years, no common definition of encoding exists that can enable a precise, theoretical comparison of neuro-symbolic methods. This paper addresses this problem by introducing a semantic framework for neuro-symbolic AI. We start by providing a formal definition of semantic encoding, specifying the components and conditions under which a knowledge-base can be encoded correctly by a neural network. We then show that many neuro-symbolic approaches are accounted for by this definition. We provide a number of examples and correspondence proofs applying the proposed framework to the neural encoding of various forms of knowledge representation. Many, at first sight disparate, neuro-symbolic methods, are shown to fall within the proposed formalization. This is expected to provide guidance to future neuro-symbolic encodings by placing them in the broader context of semantic encodings of entire families of existing neuro-symbolic systems. The paper hopes to help initiate a discussion around the provision of a theory for neuro-symbolic AI and a semantics for deep learning.

Encoder-decoder architectures are prominent building blocks of state-of-the-art solutions for tasks across multiple fields where deep learning (DL) or foundation models play a key role. Although there is a growing community working on the provision of interpretation for DL models as well as considerable work in the neuro-symbolic community seeking to integrate symbolic representations and DL, many open questions remain around the need for better tools for visualization of the inner workings of DL architectures. In particular, encoder-decoder models offer an exciting opportunity for visualization and editing by humans of the knowledge implicitly represented in model weights. In this work, we explore ways to create an abstraction for segments of the network as a two-way graph-based representation. Changes to this graph structure should be reflected directly in the underlying tensor representations. Such two-way graph representation enables new neuro-symbolic systems by leveraging the pattern recognition capabilities of the encoder-decoder along with symbolic reasoning carried out on the graphs. The approach is expected to produce new ways of interacting with DL models but also to improve performance as a result of the combination of learning and reasoning capabilities.