The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum utility is achieved. Recently, this theory has incorporated constraints, i.e., the optimum is achieved when the utility is maximized while respecting some information-processing constraints. This is reminiscent of thermodynamic systems. As such, the study of intelligent systems has benefited from the tools of thermodynamics. The first aim of this thesis is to clarify the applicability of these results in the study of intelligent systems. We can think of the local transition steps in thermodynamic or intelligent systems as being driven by uncertainty. In fact, the transitions in both systems can be described in terms of majorization. Hence, real-valued uncertainty measures like Shannon entropy are simply a proxy for their more involved behaviour. More in general, real-valued functions are fundamental to study optimization and complexity in the order-theoretic approach to several topics, including economics, thermodynamics, and quantum mechanics. The second aim of this thesis is to improve on this classification. The basic similarity between thermodynamic and intelligent systems is based on an uncertainty notion expressed by a preorder. We can also think of the transitions in the steps of a computational process as a decision-making procedure. In fact, by adding some requirements on the considered order structures, we can build an abstract model of uncertainty reduction that allows to incorporate computability, that is, to distinguish the objects that can be constructed by following a finite set of instructions from those that cannot. The third aim of this thesis is to clarify the requirements on the order structure that allow such a framework.

A major challenge in materials science is the determination of the structure of nanometer sized objects. Here we present a novel approach that uses a generative machine learning model based on a Diffusion model that is trained on 45,229 known structures. The model factors both the measured diffraction pattern as well as relevant statistical priors on the unit cell of atomic cluster structures. Conditioned only on the chemical formula and the information-scarce finite-size broadened powder diffraction pattern, we find that our model, PXRDnet, can successfully solve simulated nanocrystals as small as 10 angstroms across 200 materials of varying symmetry and complexity, including structures from all seven crystal systems. We show that our model can determine structural solutions with up to $81.5\%$ accuracy, as measured by structural correlation. Furthermore, PXRDnet is capable of solving structures from noisy diffraction patterns gathered in real-world experiments. We suggest that data driven approaches, bootstrapped from theoretical simulation, will ultimately provide a path towards determining the structure of previously unsolved nano-materials.

Federated Graph Learning (FGL) has emerged as a promising way to learn high-quality representations from distributed graph data with privacy preservation. Despite considerable efforts have been made for FGL under either cross-device or cross-silo paradigm, how to effectively capture graph knowledge in a more complicated cross-silo cross-device environment remains an under-explored problem. However, this task is challenging because of the inherent hierarchy and heterogeneity of decentralized clients, diversified privacy constraints in different clients, and the cross-client graph integrity requirement. To this end, in this paper, we propose a Hierarchical Federated Graph Learning (HiFGL) framework for cross-silo cross-device FGL. Specifically, we devise a unified hierarchical architecture to safeguard federated GNN training on heterogeneous clients while ensuring graph integrity. Moreover, we propose a Secret Message Passing (SecMP) scheme to shield unauthorized access to subgraph-level and node-level sensitive information simultaneously. Theoretical analysis proves that HiFGL achieves multi-level privacy preservation with complexity guarantees. Extensive experiments on real-world datasets validate the superiority of the proposed framework against several baselines. Furthermore, HiFGL's versatile nature allows for its application in either solely cross-silo or cross-device settings, further broadening its utility in real-world FGL applications.

In this study, we delve into the realm of meta-learning to combine point base forecasts for probabilistic short-term electricity demand forecasting. Our approach encompasses the utilization of quantile linear regression, quantile regression forest, and post-processing techniques involving residual simulation to generate quantile forecasts. Furthermore, we introduce both global and local variants of meta-learning. In the local-learning mode, the meta-model is trained using patterns most similar to the query pattern. Through extensive experimental studies across 35 forecasting scenarios and employing 16 base forecasting models, our findings underscored the superiority of quantile regression forest over its competitors.

Continual Test-Time Adaptation (TTA) seeks to adapt a source pre-trained model to continually changing, unlabeled target domains. Existing TTA methods are typically designed for environments where domain changes occur gradually and can struggle in more dynamic scenarios. Inspired by the principles of online K-Means, this paper introduces a novel approach to continual TTA through visual prompting. We propose a Dynamic Prompt Coreset that not only preserves knowledge from previously visited domains but also accommodates learning from new potential domains. This is complemented by a distance-based weight updating mechanism that ensures the coreset remains current and relevant. Our approach employs a fixed model architecture alongside the coreset and an innovative updating system to effectively mitigate challenges such as catastrophic forgetting and error accumulation. Extensive testing across various benchmarks-including ImageNet-C, CIFAR100-C, and CIFAR10-C-demonstrates that our method consistently outperforms state-of-the-art (SOTA) alternatives, particularly excelling in dynamically changing environments.

Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic gradient-descent-ascent (OGDA). While both algorithms enjoy $O(1/T)$ ergodic convergence to Nash equilibrium in two-player zero-sum games, OMWU offers several advantages including logarithmic dependence on the size of the payoff matrix and $\widetilde{O}(1/T)$ convergence to coarse correlated equilibria even in general-sum games. However, in terms of last-iterate convergence in two-player zero-sum games, an increasingly popular topic in this area, OGDA guarantees that the duality gap shrinks at a rate of $O(1/\sqrt{T})$, while the best existing last-iterate convergence for OMWU depends on some game-dependent constant that could be arbitrarily large. This begs the question: is this potentially slow last-iterate convergence an inherent disadvantage of OMWU, or is the current analysis too loose? Somewhat surprisingly, we show that the former is true. More generally, we prove that a broad class of algorithms that do not forget the past quickly all suffer the same issue: for any arbitrarily small $\delta>0$, there exists a $2\times 2$ matrix game such that the algorithm admits a constant duality gap even after $1/\delta$ rounds. This class of algorithms includes OMWU and other standard optimistic follow-the-regularized-leader algorithms.

Deep Learning is often depicted as a trio of data-architecture-loss. Yet, recent Self Supervised Learning (SSL) solutions have introduced numerous additional design choices, e.g., a projector network, positive views, or teacher-student networks. These additions pose two challenges. First, they limit the impact of theoretical studies that often fail to incorporate all those intertwined designs. Second, they slow-down the deployment of SSL methods to new domains as numerous hyper-parameters need to be carefully tuned. In this study, we bring forward the surprising observation that--at least for pretraining datasets of up to a few hundred thousands samples--the additional designs introduced by SSL do not contribute to the quality of the learned representations. That finding not only provides legitimacy to existing theoretical studies, but also simplifies the practitioner's path to SSL deployment in numerous small and medium scale settings. Our finding answers a long-lasting question: the often-experienced sensitivity to training settings and hyper-parameters encountered in SSL come from their design, rather than the absence of supervised guidance.

Identifying gene splicing is a core and significant task confronted in modern collaboration between artificial intelligence and bioinformatics. Past decades have witnessed great efforts on this concern, such as the bio-plausible splicing pattern AT-CG and the famous SpliceAI. In this paper, we propose a novel framework for the task of gene splicing identification, named Horizon-wise Gene Splicing Identification (H-GSI). The proposed H-GSI follows the horizon-wise identification paradigm and comprises four components: the pre-processing procedure transforming string data into tensors, the sliding window technique handling long sequences, the SeqLab model, and the predictor. In contrast to existing studies that process gene information with a truncated fixed-length sequence, H-GSI employs a horizon-wise identification paradigm in which all positions in a sequence are predicted with only one forward computation, improving accuracy and efficiency. The experiments conducted on the real-world Human dataset show that our proposed H-GSI outperforms SpliceAI and achieves the best accuracy of 97.20\%. The source code is available from this link.

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

The study seeks to develop an effective strategy based on the novel framework of statistical arbitrage based on graph clustering algorithms. Amalgamation of quantitative and machine learning methods, including the Kelly criterion, and an ensemble of machine learning classifiers have been used to improve risk-adjusted returns and increase immunity to transaction costs over existing approaches. The study seeks to provide an integrated approach to optimal signal detection and risk management. As a part of this approach, innovative ways of optimizing take profit and stop loss functions for daily frequency trading strategies have been proposed and tested. All of the tested approaches outperformed appropriate benchmarks. The best combinations of the techniques and parameters demonstrated significantly better performance metrics than the relevant benchmarks. The results have been obtained under the assumption of realistic transaction costs, but are sensitive to changes in some key parameters.