The T and Y spectral classes represent the coolest and lowest-mass population of brown dwarfs, yet their census remains incomplete due to limited statistics. Existing detection frameworks are often constrained to identifying M, L, and early T dwarfs, owing to the sparse observational sample of ultracool dwarfs (UCDs) at later types. This paper presents a novel machine learning framework capable of detecting and classifying late-T and Y dwarfs, trained entirely on synthetic photometry from atmospheric models. Utilizing grids from the ATMO 2020 and Sonora Bobcat models, I produce a training dataset over two orders of magnitude larger than any empirical set of >T6 UCDs. Polynomial color relations fitted to the model photometry are used to assign spectral types to these synthetic models, which in turn train an ensemble of classifiers to identify and classify the spectral type of late UCDs. The model is highly performant when validating on both synthetic and empirical datasets, verifying catalogs of known UCDs with object classification metrics >99% and an average spectral type precision within 0.35 +/- 0.37 subtypes. Application of the model to a 1.5 degree region around Pisces and the UKIDSS UDS field results in the discovery of one previously uncatalogued T8.2 candidate, demonstrating the ability of this model-trained approach in discovering faint, late-type UCDs from photometric catalogs.

Gaussian Processes (GPs) are widely used for regression and system identification due to their flexibility and ability to quantify uncertainty. However, their computational complexity limits their applicability to small datasets. Moreover in a streaming scenario, more and more datapoints accumulate which is intractable even for Sparse GPs. Online GPs aim to alleviate this problem by e.g. defining a maximum budget of datapoints and removing redundant datapoints. This work provides a unified comparison of several reduction criteria, analyzing both their computational complexity and reduction behavior. The criteria are evaluated on benchmark functions and real-world datasets, including dynamic system identification tasks. Additionally, acceptance criteria are proposed to further filter out redundant datapoints. This work yields practical guidelines for choosing a suitable criterion for an online GP algorithm.

We develop a rigorous framework for deterministic coreset construction in empirical risk minimization (ERM). Our central contribution is the Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm, which constructs a coreset by excising points with the lowest sensitivity bounds and applying a data-dependent uniform weight to the remainder. The method yields a uniform $(1\pm\varepsilon)$ relative-error approximation for the ERM objective over the entire hypothesis space. We provide complete analysis, including (i) a minimax characterization proving the optimality of the adaptive weight, (ii) an instance-dependent size analysis in terms of a \emph{Sensitivity Heterogeneity Index}, and (iii) tractable sensitivity oracles for kernel ridge regression, regularized logistic regression, and linear SVM. Reproducibility is supported by precise pseudocode for the algorithm, sensitivity oracles, and evaluation pipeline. Empirical results align with the theory. We conclude with open problems on instance-optimal oracles, deterministic streaming, and fairness-constrained ERM.

We propose a feature screening method that integrates both feature-feature and feature-target relationships. Inactive features are identified via a penalized minimum Redundancy Maximum Relevance (mRMR) procedure, which is the continuous version of the classic mRMR penalized by a non-convex regularizer, and where the parameters estimated as zero coefficients represent the set of inactive features. We establish the conditions under which zero coefficients are correctly identified to guarantee accurate recovery of inactive features. We introduce a multi-stage procedure based on the knockoff filter enabling the penalized mRMR to discard inactive features while controlling the false discovery rate (FDR). Our method performs comparably to HSIC-LASSO but is more conservative in the number of selected features. It only requires setting an FDR threshold, rather than specifying the number of features to retain. The effectiveness of the method is illustrated through simulations and real-world datasets. The code to reproduce this work is available on the following GitHub: https://github.com/PeterJackNaylor/SmRMR.

Although common in real-world applications, heterogeneous client label sets are rarely investigated in federated learning (FL). Furthermore, in the cases they are, clients are assumed to be willing to share their entire label sets with other clients. Federated learning with private label sets, shared only with the central server, adds further constraints on learning algorithms and is, in general, a more difficult problem to solve. In this work, we study the effects of label set heterogeneity on model performance, comparing the public and private label settings -- when the union of label sets in the federation is known to clients and when it is not. We apply classical methods for the classifier combination problem to FL using centralized tuning, adapt common FL methods to the private label set setting, and discuss the justification of both approaches under practical assumptions. Our experiments show that reducing the number of labels available to each client harms the performance of all methods substantially. Centralized tuning of client models for representational alignment can help remedy this, but often at the cost of higher variance. Throughout, our proposed adaptations of standard FL methods perform well, showing similar performance in the private label setting as the standard methods achieve in the public setting. This shows that clients can enjoy increased privacy at little cost to model accuracy.

Explainable AI (XAI) methods often struggle to generate clear, interpretable outputs for users without domain expertise. We introduce Feature-Guided Neighbor Selection (FGNS), a post hoc method that enhances interpretability by selecting class-representative examples using both local and global feature importance. In a user study (N = 98) evaluating Kannada script classifications, FGNS significantly improved non-experts' ability to identify model errors while maintaining appropriate agreement with correct predictions. Participants made faster and more accurate decisions compared to those given traditional k-NN explanations. Quantitative analysis shows that FGNS selects neighbors that better reflect class characteristics rather than merely minimizing feature-space distance, leading to more consistent selection and tighter clustering around class prototypes. These results support FGNS as a step toward more human-aligned model assessment, although further work is needed to address the gap between explanation quality and perceived trust.

The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex M-estimation or stochastic optimization problem is solvable in such an assumption-free setting, providing a precise dividing line between solvable and unsolvable problems. The conditions we identify show, perhaps surprisingly, that Lipschitz continuity of the loss being minimized is not necessary for distribution free minimization, and they are also distinct from classical characterizations of learnability in machine learning.

Multimodal in-context learning (ICL) equips Large Vision-language Models (LVLMs) with the ability to adapt to new tasks via multiple user-provided demonstrations, without requiring any model parameter updates. However, its effectiveness is constrained by the token-intensive nature of multimodal inputs and the complexity of cross-modal few-shot reasoning, which together hinder LVLMs from extracting useful patterns from demonstrations. To address these challenges, we propose \textbf{M$^2$IV}, a novel representation engineering approach that replaces explicit token-level demonstrations with a set of learnable Multimodal In-context Vectors directly injected into the residual streams of LVLMs. By analyzing the distinct roles of multi-head attention (MHA) and multi-layer perceptrons (MLP) in the ICL process, we design a training strategy that enables M$^2$IV to perform fine-grained semantic distillation and robust cross-modal representation learning. M$^2$IV not only improves performance across diverse tasks and LVLMs but also significantly reduces token overhead, enabling graceful scaling to many-shot scenarios. To further enhance usability, we introduce \textbf{VLibrary}, a repository that stores trained M$^2$IVs for flexible retrieval and injection. With VLibrary, users can steer pre-trained LVLMs in a customized manner that meets diverse requirements. Extensive experiments demonstrate that M$^2$IV consistently outperforms vanilla ICL and prior representation engineering baselines, achieving an average accuracy gain of 3.74\% with substantial improvements in overall efficiency.

Contemporary artificial intelligence (AI) development largely centers on rational decision-making, valued for its measurability and suitability for objective evaluation. Y et in real-world contexts, an intelligent agent's decisions are shaped not only by logic but also by deeper influences such as beliefs, values, and preferences. The diversity of human decision-making styles emerges from these differences, highlighting that "style" is an essential but often overlooked dimension of intelligence. This dissertation introduces playstyle as an alternative lens for observing and analyzing the decision-making behavior of intelligent agents, and examines its foundational meaning and historical context from a philosophical perspective. By analyzing how beliefs and values drive intentions and actions, we construct a two-tier framework for style formation: the external interaction loop with the environment and the internal cognitive loop of deliberation. On this basis, we formalize style-related characteristics and propose measurable indicators such as style capacity, style popularity, and evolutionary dynamics. The study focuses on three core research directions: (1) Defining and measuring playstyle, proposing a general playstyle metric based on discretized state spaces, and extending it to quantify strategic diversity and competitive balance; (2) Expressing and generating playstyle, exploring how reinforcement learning and imitation learning can be used to train agents exhibiting specific stylistic tendencies, and introducing a novel approach for human-like style learning and modeling; and (3) Practical applications, analyzing the potential of these techniques in domains such as game design and interactive entertainment. Finally, the dissertation outlines future extensions, including the role of style as a core element in building artificial general intelligence (AGI). By investigating stylistic variation, we aim to rethink autonomy, value expression, and even offer a tangible perspective on the ultimate i philosophical question: What is the soul?

Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a piecewise-linear approximation of the given function, use the potential energy of springs to encode a desired mean squared error loss function, and converge to a minimum-energy configuration via dissipation. We apply the proposed simulation system to regression tasks and show that its performance is comparable to that of multi-layer perceptrons. In addition, we study the thermodynamic properties of the system and find a relation between the free energy change of the system and its ability to learn an underlying data distribution. We empirically find a \emph{thermodynamic learning barrier} for the system caused by the fluctuations of the environment, whereby the system cannot learn if its change in free energy hits such a barrier. We believe this simple model can help us better understand learning systems from a physical point of view.