Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training of deep neural networks in artificial intelligence (AI) systems. Despite the popularity and the success of Adam it remains an \emph{open research problem} to provide a rigorous convergence analysis for Adam even for the class of strongly convex SOPs. In one of the main results of this work we establish convergence rates for Adam in terms of the number of gradient steps (convergence rate \nicefrac{1}{2} w.r.t. the size of the learning rate), the size of the mini-batches (convergence rate 1 w.r.t. the size of the mini-batches), and the size of the second moment parameter of Adam (convergence rate 1 w.r.t. the distance of the second moment parameter to 1) for the class of strongly convex SOPs. In a further main result of this work, which we refer to as \emph{Adam symmetry theorem}, we illustrate the optimality of the established convergence rates by proving for a special class of simple quadratic strongly convex SOPs that Adam converges as the number of gradient steps increases to infinity to the solution of the SOP (the unique minimizer of the strongly convex objective function) if and \emph{only} if the random variables in the SOP (the data in the SOP) are \emph{symmetrically distributed}. In particular, in the standard case where the random variables in the SOP are not symmetrically distributed we \emph{disprove} that Adam converges to the minimizer of the SOP as the number of Adam steps increases to infinity. We also complement the conclusions of our convergence analysis and the Adam symmetry theorem by several numerical simulations that indicate the sharpness of the established convergence rates and that illustrate the practical appearance of the phenomena revealed in the \emph{Adam symmetry theorem}.

In the fast-moving consumer goods (FMCG) industry, deciding where to place physical assets, such as commercial beverage coolers, can directly impact revenue growth and execution efficiency. Although churn prediction and demand forecasting have been widely studied in B2B contexts, the use of machine learning to guide asset allocation remains relatively unexplored. This paper presents a framework focused on predicting which beverage clients are most likely to deliver strong returns in volume after receiving a cooler. Using a private dataset from a well-known Central American brewing and beverage company of 3,119 B2B traditional trade channel clients that received a cooler from 2022-01 to 2024-07, and tracking 12 months of sales transactions before and after cooler installation, three growth thresholds were defined: 10%, 30% and 50% growth in sales volume year over year. The analysis compares results of machine learning models such as XGBoost, LightGBM, and CatBoost combined with SHAP for interpretable feature analysis in order to have insights into improving business operations related to cooler allocation; the results show that the best model has AUC scores of 0.857, 0.877, and 0.898 across the thresholds on the validation set. Simulations suggest that this approach can improve ROI because it better selects potential clients to grow at the expected level and increases cost savings by not assigning clients that will not grow, compared to traditional volume-based approaches with substantial business management recommendations

The non-rival nature of data creates a dilemma for firms: sharing data unlocks value but risks eroding competitive advantage. Existing data synthesis methods often exacerbate this problem by creating data with symmetric utility, allowing any party to extract its value. This paper introduces the Encapsulation-Forging (EnFo) framework, a novel approach to generate rival synthetic data with asymmetric utility. EnFo operates in two stages: it first encapsulates predictive knowledge from the original data into a designated ``key'' model, and then forges a synthetic dataset by optimizing the data to intentionally overfit this key model. This process transforms non-rival data into a rival product, ensuring its value is accessible only to the intended model, thereby preventing unauthorized use and preserving the data owner's competitive edge. Our framework demonstrates remarkable sample efficiency, matching the original data's performance with a fraction of its size, while providing robust privacy protection and resistance to misuse. EnFo offers a practical solution for firms to collaborate strategically without compromising their core analytical advantage.

The identification of high-dimensional nonlinear dynamical systems via the Volterra series has significant potential, but has been severely hindered by the curse of dimensionality. Tensor Network (TN) methods such as the Modified Alternating Linear Scheme (MVMALS) have been a breakthrough for the field, offering a tractable approach by exploiting the low-rank structure in Volterra kernels. However, these techniques still encounter prohibitive computational and memory bottlenecks due to high-order polynomial scaling with respect to input dimension. To overcome this barrier, we introduce the Tensor Head Averaging (THA) algorithm, which significantly reduces complexity by constructing an ensemble of localized MVMALS models trained on small subsets of the input space. In this paper, we present a theoretical foundation for the THA algorithm. We establish observable, finite-sample bounds on the error between the THA ensemble and a full MVMALS model, and we derive an exact decomposition of the squared error. This decomposition is used to analyze the manner in which subset models implicitly compensate for omitted dynamics. We quantify this effect, and prove that correlation between the included and omitted dynamics creates an optimization incentive which drives THA's performance toward accuracy superior to a simple truncation of a full MVMALS model. THA thus offers a scalable and theoretically grounded approach for identifying previously intractable high-dimensional systems.

Abstract--A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UA V) trajectories, can be naturally represented as graphs, often exhibiting non-Euclidean structures. These graph representations may evolve over time, forming time-varying graphs. Effectively modeling and analyzing such dynamic graph data is critical for tasks like predicting graph evolution and reconstructing missing graph data. In this paper, we propose a framework based on the Koopman autoencoder (KAE) to handle time-varying graph data. Specifically, we assume the existence of a hidden non-linear dynamical system, where the state vector corresponds to the graph embedding of the time-varying graph signals. T o capture the evolving graph structures, the graph data is first converted into a vector time series through graph embedding, representing the structural information in a finite-dimensional latent space. In this latent space, the KAE is applied to learn the underlying non-linear dynamics governing the temporal evolution of graph features, enabling both prediction and reconstruction tasks. A. Motivation Graphs are fundamental data structures for modeling the structure and interactions within complex systems [1] across a variety of domains, including, but not limited to, social networks [2], biological systems [3], transportation networks [4], and communication systems [5]. These data structures provide a versatile framework for representing relationships and dependencies, enabling insights into the organization and behavior of complex systems. In many real-world applications, the underlying graph data is not static; instead they evolve over time. Time-varying graphs [6] are a type of graph data characterized by temporal variations in their components or overall configuration. Unlike the commonly studied static graph structures, analyzing time-varying graph data introduces additional challenges. While the reconstruction of graph signals is necessary for recovering missing information, which is common in real-world sensor networks or data transmission scenarios, prediction, on the other hand, enables forecasting the future states of the systems and thus supports planning, decision-making, and control in dynamical environments. S. Krishnan and J. Choi are with the School of Electrical and Mechanical Engineering, The University of Adelaide, Australia (Emails:{jinho.choi,sivaram.krishan}@adelaide.edu.au), and J. Park is with the Information Systems Technology and Design Pillar, Singapore University of Technology and Design, Singapore (Email: jihong park@sutd.edu.sg).

Department of Multidisciplinary Engineering (AI & DS) Vishwakarma Institute of Technology, Pune, 411037, Maharashtra, India Abstract - Sepsis is a potentially fatal medical disorder that needs to be identified and treated right away to avoid fatalities. It must be quickly identified and treated in order to stop it from developing into severe sepsis, septic shock, and multi-organ failure. Sepsis remains a significant problem for doctors despite advancements in medical technology and treatment methods. The beginning of the disease has been successfully predicted by machine learning models in recent years, but due to their black-box character, it is challenging to interpret these predictions and comprehend the underlying illness mechanisms. In this research, we propose a comprehensible AI method for sepsis analysis that combines machine learning with clinical knowledge and expertise in the domain. Our method allows clinicians to understand and verify the model's predictions based on clinical expertise and preexisting beliefs, in addition to providing precise predictions of the onset of sepsis. Keywords - Sepsis, Artificial Intelligence, Machine Learning, Explainable AI, Sensitivity Analysis I. INTRODUCTION As the world continues to advance in technology, the potential of artificial intelligence (AI) in healthcare is becoming more apparent.

Recently, optimizers that explicitly treat weights as matrices, rather than flattened vectors, have demonstrated their effectiveness. This perspective naturally leads to structured approximations of the Fisher matrix as preconditioners, where the matrix view induces a Kronecker-factorized form that enables memory-efficient representation. However, constructing such approximations both efficiently and accurately remains an open challenge, since obtaining the optimal factorization is resource-intensive and practical methods therefore rely on heuristic design choices. In this work, we introduce a novel approach that leverages projector-splitting integrators to construct effective preconditioners. Our optimizer, DyKAF (Dynamical Kronecker Approximation of the Fisher Matrix), consistently improves the Fisher matrix approximation quality. Experiments on large language model pre-training and fine-tuning demonstrate that DyKAF outperforms existing optimizers across a range of evaluation metrics.

Drug-target interaction (DTI) prediction is of great significance for drug discovery and drug repurposing. With the accumulation of a large volume of valuable data, data-driven methods have been increasingly harnessed to predict DTIs, reducing costs across various dimensions. Therefore, this paper proposes a $\textbf{L}$arge $\textbf{L}$anguage $\textbf{M}$odel and $\textbf{M}$ulti-$\textbf{M}$odel data co-powered $\textbf{D}$rug $\textbf{T}$arget $\textbf{I}$nteraction prediction framework, named LLM$^3$-DTI. LLM$^3$-DTI constructs multi-modal data embedding to enhance DTI prediction performance. In this framework, the text semantic embeddings of drugs and targets are encoded by a domain-specific LLM. To effectively align and fuse multi-modal embedding. We propose the dual cross-attention mechanism and the TSFusion module. Finally, these multi-modal data are utilized for the DTI task through an output network. The experimental results indicate that LLM$^3$-DTI can proficiently identify validated DTIs, surpassing the performance of the models employed for comparison across diverse scenarios. Consequently, LLM$^3$-DTI is adept at fulfilling the task of DTI prediction with excellence. The data and code are available at https://github.com/chaser-gua/LLM3DTI.

Abstract--This paper studies optimization proxies--machine learning (ML) models trained to efficiently predict optimal solutions for AC Optimal Power Flow (ACOPF) problems. While promising, optimization proxy performance heavily depends on training data quality. T o address this limitation, this paper introduces a novel active sampling framework for ACOPF optimization proxies designed to generate realistic and diverse training data. The framework actively explores varied, flexible problem specifications reflecting plausible operational realities. More importantly, the approach uses optimization-specific quantities (active constraint sets) that better capture the salient features of an ACOPF that lead to the optimal solution. Numerical results show superior generalization over existing sampling methods with an equivalent training budget, significantly advancing the state-of-practice for trustworthy ACOPF optimization proxies.

In-context learning (ICL) enables large language models to adapt to new tasks from demonstrations without parameter updates. Despite extensive empirical studies, a principled understanding of ICL emergence at scale remains more elusive. We present a unified theoretical framework connecting scaling laws to ICL emergence in transformers. Our analysis establishes that ICL performance follows power-law relationships with model depth $L$, width $d$, context length $k$, and training data $D$, with exponents determined by task structure. We show that under specific conditions, transformers implement gradient-based metalearning in their forward pass, with an effective learning rate $η_{\text{eff}} = Θ(1/\sqrt{Ld})$. We demonstrate sharp phase transitions at critical scales and derive optimal depth-width allocations favoring $L^* \propto N^{2/3}$, $d^* \propto N^{1/3}$ for the fixed parameter budget $N = Ld$. Systematic experiments on synthetic tasks validate our predictions, with measured scaling exponents closely matching theory. This work provides both necessary and sufficient conditions for the emergence of ICLs and establishes fundamental computational limits on what transformers can learn in-context.