Machine learning has become a common approach to predicting the outcomes of soccer matches, and the body of literature in this domain has grown substantially in the past decade and a half. This chapter discusses available datasets, the types of models and features, and ways of evaluating model performance in this application domain. The aim of this chapter is to give a broad overview of the current state and potential future developments in machine learning for soccer match results prediction, as a resource for those interested in conducting future studies in the area. Our main findings are that while gradient-boosted tree models such as CatBoost, applied to soccer-specific ratings such as pi-ratings, are currently the best-performing models on datasets containing only goals as the match features, there needs to be a more thorough comparison of the performance of deep learning models and Random Forest on a range of datasets with different types of features. Furthermore, new rating systems using both player- and team-level information and incorporating additional information from, e.g., spatiotemporal tracking and event data, could be investigated further. Finally, the interpretability of match result prediction models needs to be enhanced for them to be more useful for team management.

Signed graphs are an emergent way of representing data in a variety of contexts were conflicting interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability geometry for signed graphs, proving that metrics in this space, such as the communicability distance and angles, are Euclidean and spherical. We then apply these metrics to solve several problems in data analysis of signed graphs in a unified way. They include the partitioning of signed graphs, dimensionality reduction, finding hierarchies of alliances in signed networks as well as the quantification of the degree of polarization between the existing factions in systems represented by this type of graphs.

The increasing utilization of emerging technologies in the Food & Agriculture (FA) sector has heightened the need for security to minimize cyber risks. Considering this aspect, this manuscript reviews disclosed and documented cybersecurity incidents in the FA sector. For this purpose, thirty cybersecurity incidents were identified, which took place between July 2011 and April 2023. The details of these incidents are reported from multiple sources such as: the private industry and flash notifications generated by the Federal Bureau of Investigation (FBI), internal reports from the affected organizations, and available media sources. Considering the available information, a brief description of the security threat, ransom amount, and impact on the organization are discussed for each incident. This review reports an increased frequency of cybersecurity threats to the FA sector. To minimize these cyber risks, popular cybersecurity frameworks and recent agriculture-specific cybersecurity solutions are also discussed. Further, the need for AI assurance in the FA sector is explained, and the Farmer-Centered AI (FCAI) framework is proposed. The main aim of the FCAI framework is to support farmers in decision-making for agricultural production, by incorporating AI assurance. Lastly, the effects of the reported cyber incidents on other critical infrastructures, food security, and the economy are noted, along with specifying the open issues for future development.

This paper describes how to analyze the influence of Earth system variables on the errors when providing temperature forecasts. The initial framework to get the data has been based on previous research work, which resulted in a very interesting discovery. However, the aforementioned study only worked on individual correlations of the variables with respect to the error. This research work is going to re-use the main ideas but introduce three main novelties: (1) applying a data science approach by a few representative locations; (2) taking advantage of the rankings created by Spearman correlation but enriching them with other metrics looking for a more robust ranking of the variables; (3) evaluation of the methodology by learning random forest models for regression with the distinct experimental variations. The main contribution is the framework that shows how to convert correlations into rankings and combine them into an aggregate ranking. We have carried out experiments on five chosen locations to analyze the behavior of this ranking-based methodology. The results show that the specific performance is dependent on the location and season, which is expected, and that this selection technique works properly with Random Forest models but can also improve simpler regression models such as Bayesian Ridge. This work also contributes with an extensive analysis of the results. We can conclude that this selection based on the top-k ranked variables seems promising for this real problem, and it could also be applied in other domains.

Yield forecasting, the science of predicting agricultural productivity before the crop harvest occurs, helps a wide range of stakeholders make better decisions around agricultural planning. This study aims to investigate whether machine learning-based yield prediction models can capably predict Kharif season rice yields at the district level in India several months before the rice harvest takes place. The methodology involved training 19 machine learning models such as CatBoost, LightGBM, Orthogonal Matching Pursuit, and Extremely Randomized Trees on 20 years of climate, satellite, and rice yield data across 247 of Indian rice-producing districts. In addition to model-building, a dynamic dashboard was built understand how the reliability of rice yield predictions varies across districts. The results of the proof-of-concept machine learning pipeline demonstrated that rice yields can be predicted with a reasonable degree of accuracy, with out-of-sample R2, MAE, and MAPE performance of up to 0.82, 0.29, and 0.16 respectively. These results outperformed test set performance reported in related literature on rice yield modeling in other contexts and countries. In addition, SHAP value analysis was conducted to infer both the importance and directional impact of the climate and remote sensing variables included in the model. Important features driving rice yields included temperature, soil water volume, and leaf area index. In particular, higher temperatures in August correlate with increased rice yields, particularly when the leaf area index in August is also high. Building on the results, a proof-of-concept dashboard was developed to allow users to easily explore which districts may experience a rise or fall in yield relative to the previous year.

Gate sizing plays an important role in timing optimization after physical design. Existing machine learning-based gate sizing works cannot optimize timing on multiple timing paths simultaneously and neglect the physical constraint on layouts. They cause sub-optimal sizing solutions and low-efficiency issues when compared with commercial gate sizing tools. In this work, we propose a learning-driven physically-aware gate sizing framework to optimize timing performance on large-scale circuits efficiently. In our gradient descent optimization-based work, for obtaining accurate gradients, a multi-modal gate sizing-aware timing model is achieved via learning timing information on multiple timing paths and physical information on multiple-scaled layouts jointly. Then, gradient generation based on the sizing-oriented estimator and adaptive back-propagation are developed to update gate sizes. Our results demonstrate that our work achieves higher timing performance improvements in a faster way compared with the commercial gate sizing tool.

Transformer-based language models are trained on large datasets to predict the next token given an input sequence. Despite this simple training objective, they have led to revolutionary advances in natural language processing. Underlying this success is the self-attention mechanism. In this work, we ask: $\textit{What}$ $\textit{does}$ $\textit{a}$ $\textit{single}$ $\textit{self-attention}$ $\textit{layer}$ $\textit{learn}$ $\textit{from}$ $\textit{next-token}$ $\textit{prediction?}$ We show that training self-attention with gradient descent learns an automaton which generates the next token in two distinct steps: $\textbf{(1)}$ $\textbf{Hard}$ $\textbf{retrieval:}$ Given input sequence, self-attention precisely selects the $\textit{high-priority}$ $\textit{input}$ $\textit{tokens}$ associated with the last input token. $\textbf{(2)}$ $\textbf{Soft}$ $\textbf{composition:}$ It then creates a convex combination of the high-priority tokens from which the next token can be sampled. Under suitable conditions, we rigorously characterize these mechanics through a directed graph over tokens extracted from the training data. We prove that gradient descent implicitly discovers the strongly-connected components (SCC) of this graph and self-attention learns to retrieve the tokens that belong to the highest-priority SCC available in the context window. Our theory relies on decomposing the model weights into a directional component and a finite component that correspond to hard retrieval and soft composition steps respectively. This also formalizes a related implicit bias formula conjectured in [Tarzanagh et al. 2023]. We hope that these findings shed light on how self-attention processes sequential data and pave the path toward demystifying more complex architectures.

Recent advances in machine learning have been achieved by using overparametrized models trained until near interpolation of the training data. It was shown, e.g., through the double descent phenomenon, that the number of parameters is a poor proxy for the model complexity and generalization capabilities. This leaves open the question of understanding the impact of parametrization on the performance of these models. How does model complexity and generalization depend on the number of parameters $p$? How should we choose $p$ relative to the sample size $n$ to achieve optimal test error? In this paper, we investigate the example of random feature ridge regression (RFRR). This model can be seen either as a finite-rank approximation to kernel ridge regression (KRR), or as a simplified model for neural networks trained in the so-called lazy regime. We consider covariates uniformly distributed on the $d$-dimensional sphere and compute sharp asymptotics for the RFRR test error in the high-dimensional polynomial scaling, where $p,n,d \to \infty$ while $p/ d^{\kappa_1}$ and $n / d^{\kappa_2}$ stay constant, for all $\kappa_1 , \kappa_2 \in \mathbb{R}_{>0}$. These asymptotics precisely characterize the impact of the number of random features and regularization parameter on the test performance. In particular, RFRR exhibits an intuitive trade-off between approximation and generalization power. For $n = o(p)$, the sample size $n$ is the bottleneck and RFRR achieves the same performance as KRR (which is equivalent to taking $p = \infty$). On the other hand, if $p = o(n)$, the number of random features $p$ is the limiting factor and RFRR test error matches the approximation error of the random feature model class (akin to taking $n = \infty$). Finally, a double descent appears at $n= p$, a phenomenon that was previously only characterized in the linear scaling $\kappa_1 = \kappa_2 = 1$.

Neural networks have achieved remarkable success across various tasks, yet the precise mechanism driving this success remains theoretically elusive. The training of neural networks involve optimizing a non-convex loss function, where the training algorithm typically is a first-order methods such as gradient descent or its variants. A particularly puzzling aspect is how these training algorithms succeed in finding a solution with good generalization capabilities despite the non-convexity of the loss landscape. In addition to the choice of the training algorithm, the choice of initialization in these algorithms play a crucial role in determining the neural network performance. Indeed, recent works have made increasingly clear the benefit of small initializations, revealing that neural networks trained using (stochastic) gradient descent with small initializations exhibit feature learning [2] and also generalize better for various tasks [3, 4, 5]; see Section 2 for more details into the impact of initialization scale. However, for small initializations, the training dynamics of neural networks is extremely non-linear and not well understood so far. Our focus in this paper is on understanding the effect of small initialization on the training dynamics of neural networks. In pursuit of a deeper understanding of the training mechanism for small initializations, researchers have uncovered the phenomenon of directional convergence in the neural network weights during early phases of training [6, 7]. In [6], authors study the gradient flow dynamics of training two-layer Rectified Linear Unit (ReLU) neural networks.

Surrogate modelling techniques have seen growing attention in recent years when applied to both modelling and optimisation of industrial design problems. These techniques are highly relevant when assessing the performance of a particular design carries a high cost, as the overall cost can be mitigated via the construction of a model to be queried in lieu of the available high-cost source. The construction of these models can sometimes employ other sources of information which are both cheaper and less accurate. The existence of these sources however poses the question of which sources should be used when constructing a model. Recent studies have attempted to characterise harmful data sources to guide practitioners in choosing when to ignore a certain source. These studies have done so in a synthetic setting, characterising sources using a large amount of data that is not available in practice. Some of these studies have also been shown to potentially suffer from bias in the benchmarks used in the analysis. In this study, we present a characterisation of harmful low-fidelity sources using only the limited data available to train a surrogate model. We employ recently developed benchmark filtering techniques to conduct a bias-free assessment, providing objectively varied benchmark suites of different sizes for future research. Analysing one of these benchmark suites with the technique known as Instance Space Analysis, we provide an intuitive visualisation of when a low-fidelity source should be used and use this analysis to provide guidelines that can be used in an applied industrial setting.