Oblique Decision Tree (ODT) separates the feature space by linear projections, as opposed to the conventional Decision Tree (DT) that forces axis-parallel splits. ODT has been proven to have a stronger representation ability than DT, as it provides a way to create shallower tree structures while still approximating complex decision boundaries. However, its learning efficiency is still insufficient, since the linear projections cannot be transmitted to the child nodes, resulting in a waste of model parameters. In this work, we propose an enhanced ODT method with Feature Concatenation (\texttt{FC-ODT}), which enables in-model feature transformation to transmit the projections along the decision paths. Theoretically, we prove that our method enjoys a faster consistency rate w.r.t. the tree depth, indicating that our method possesses a significant advantage in generalization performance, especially for shallow trees. Experiments show that \texttt{FC-ODT} can outperform the other state-of-the-art decision trees with a limited tree depth.

Self-distillation (SD), a technique where a model refines itself from its own predictions, has garnered attention as a simple yet powerful approach in machine learning. Despite its widespread use, the mechanisms underlying its effectiveness remain unclear. In this study, we investigate the efficacy of hyperparameter-tuned multi-stage SD in binary classification tasks with noisy labeled Gaussian mixture data, utilizing a replica theory. Our findings reveals that the primary driver of SD's performance improvement is denoising through hard pseudo-labels, with the most notable gains observed in moderately sized datasets. We also demonstrate the efficacy of practical heuristics, such as early stopping for extracting meaningful signal and bias fixation for imbalanced data. These results provide both theoretical guarantees and practical insights, advancing our understanding and application of SD in noisy settings.

As digital technologies advance, communication networks face challenges in handling the vast data generated by intelligent devices. Autonomous vehicles, smart sensors, and IoT systems necessitate new paradigms. This thesis addresses these challenges by integrating semantic communication and generative models for optimized image compression and edge network resource allocation. Unlike bit-centric systems, semantic communication prioritizes transmitting meaningful data specifically selected to convey the meaning rather than obtain a faithful representation of the original data. The communication infrastructure can benefit to significant improvements in bandwidth efficiency and latency reduction. Central to this work is the design of semantic-preserving image compression using Generative Adversarial Networks and Denoising Diffusion Probabilistic Models. These models compress images by encoding only semantically relevant features, allowing for high-quality reconstruction with minimal transmission. Additionally, a Goal-Oriented edge network optimization framework is introduced, leveraging the Information Bottleneck principle and stochastic optimization to dynamically allocate resources and enhance efficiency. By integrating semantic communication into edge networks, this approach balances computational efficiency and communication effectiveness, making it suitable for real-time applications. The thesis compares semantic-aware models with conventional image compression techniques using classical and semantic evaluation metrics. Results demonstrate the potential of combining generative AI and semantic communication to create more efficient semantic-goal-oriented communication networks that meet the demands of modern data-driven applications.

A novel hybrid Random Forest and Convolutional Neural Network (CNN) framework is presented for oil-water classification in hyperspectral images (HSI). To address the challenge of preserving spatial context, the images were divided into smaller, non-overlapping tiles, which served as the basis for training, validation, and testing. Random Forest demonstrated strong performance in pixel-wise classification, outperforming models such as XGBoost, Attention-Based U-Net, and HybridSN. However, Random Forest loses spatial context, limiting its ability to fully exploit the spatial relationships in hyperspectral data. To improve performance, a CNN was trained on the probability maps generated by the Random Forest, leveraging the CNN's capacity to incorporate spatial context. The hybrid approach achieved 7.6% improvement in recall (to 0.85), 2.4% improvement in F1 score (to 0.84), and 0.54% improvement in AUC (to 0.99) compared to the baseline. These results highlight the effectiveness of combining probabilistic outputs with spatial feature learning for context-aware analysis of hyperspectral images.

Pneumonia is a leading cause of illness and death in children, underscoring the need for early and accurate detection. In this study, we propose a novel lightweight ensemble model for detecting pneumonia in children using chest X-ray images. This ensemble model integrates two pre-trained convolutional neural networks (CNNs), MobileNetV2 and NASNetMobile, selected for their balance of computational efficiency and accuracy. These models were fine-tuned on a pediatric chest X-ray dataset and combined to enhance classification performance. Our proposed ensemble model achieved a classification accuracy of 98.63%, significantly outperforming individual models such as MobileNetV2 (97.10%) and NASNetMobile(96.25%) in terms of accuracy, precision, recall, and F1 score. Moreover, the ensemble model outperformed state-of-the-art architectures, including ResNet50, InceptionV3, and DenseNet201, while maintaining computational efficiency. The proposed lightweight ensemble model presents a highly effective and resource-efficient solution for pneumonia detection, making it particularly suitable for deployment in resource-constrained settings.

Solving mathematics problems has been an intriguing capability of large language models, and many efforts have been made to improve reasoning by extending reasoning length, such as through self-correction and extensive long chain-of-thoughts. While promising in problem-solving, advanced long reasoning chain models exhibit an undesired single-modal behavior, where trivial questions require unnecessarily tedious long chains of thought. In this work, we propose a way to allow models to be aware of inference budgets by formulating it as utility maximization with respect to an inference budget constraint, hence naming our algorithm Inference Budget-Constrained Policy Optimization (IBPO). In a nutshell, models fine-tuned through IBPO learn to ``understand'' the difficulty of queries and allocate inference budgets to harder ones. With different inference budgets, our best models are able to have a $4.14$\% and $5.74$\% absolute improvement ($8.08$\% and $11.2$\% relative improvement) on MATH500 using $2.16$x and $4.32$x inference budgets respectively, relative to LLaMA3.1 8B Instruct. These improvements are approximately $2$x those of self-consistency under the same budgets.

Conformal prediction has emerged as a widely used framework for constructing valid prediction sets in classification and regression tasks. In this work, we extend the split conformal prediction framework to hierarchical classification, where prediction sets are commonly restricted to internal nodes of a predefined hierarchy, and propose two computationally efficient inference algorithms. The first algorithm returns internal nodes as prediction sets, while the second relaxes this restriction, using the notion of representation complexity, yielding a more general and combinatorial inference problem, but smaller set sizes. Empirical evaluations on several benchmark datasets demonstrate the effectiveness of the proposed algorithms in achieving nominal coverage.

Many real-world problems, such as those with fairness constraints, involve complex expectation constraints and large datasets, necessitating the design of efficient stochastic methods to solve them. Most existing research focuses on cases with no {constraint} or easy-to-project constraints or deterministic constraints. In this paper, we consider nonconvex nonsmooth stochastic optimization problems with expectation constraints, for which we build a novel exact penalty model. We first show the relationship between the penalty model and the original problem. Then on solving the penalty problem, we present a single-loop SPIDER-type stochastic subgradient method, which utilizes the subgradients of both the objective and constraint functions, as well as the constraint function value at each iteration. Under certain regularity conditions (weaker than Slater-type constraint qualification or strong feasibility assumed in existing works), we establish an iteration complexity result of $O(\epsilon^{-4})$ to reach a near-$\epsilon$ stationary point of the penalized problem in expectation, matching the lower bound for such tasks. Building on the exact penalization, an $(\epsilon,\epsilon)$-KKT point of the original problem is obtained. For a few scenarios, our complexity of either the {objective} sample subgradient or the constraint sample function values can be lower than the state-of-the-art results by a factor of $\epsilon^{-2}$. Moreover, on solving two fairness-constrained problems, our method is significantly (up to 466 times) faster than the state-of-the-art algorithms, including switching subgradient method and inexact proximal point methods.

Transformer models are challenging to optimize with SGD and typically require adaptive optimizers such as Adam. However, the reasons behind the superior performance of Adam over SGD remain unclear. In this study, we investigate the optimization of transformer models by focusing on \emph{gradient heterogeneity}, defined as the disparity in gradient norms among parameters. Our analysis shows that gradient heterogeneity hinders gradient-based optimization, including SGD, while sign-based optimization, a simplified variant of Adam, is less affected. We further examine gradient heterogeneity in transformer models and show that it is influenced by the placement of layer normalization. Additionally, we show that the momentum term in sign-based optimization is important for preventing the excessive growth of linear-head parameters in tasks with many classes. Experimental results from fine-tuning transformer models in both NLP and vision domains validate our theoretical analyses. This study provides insights into the optimization challenges of transformer models and offers guidance for designing future optimization algorithms. Code is available at \url{https://github.com/tom4649/gradient-heterogeneity}.

We show that learning-rate schedules for large model training behave surprisingly similar to a performance bound from non-smooth convex optimization theory. We provide a bound for the constant schedule with linear cooldown; in particular, the practical benefit of cooldown is reflected in the bound due to the absence of logarithmic terms. Further, we show that this surprisingly close match between optimization theory and practice can be exploited for learning-rate tuning: we achieve noticeable improvements for training 124M and 210M Llama-type models by (i) extending the schedule for continued training with optimal learning-rate, and (ii) transferring the optimal learning-rate across schedules.