While large language models like BERT demonstrate strong empirical performance on semantic tasks, whether this reflects true conceptual competence or surface-level statistical association remains unclear. I investigate whether BERT encodes abstract relational schemata by examining internal representations of concept pairs across taxonomic, mereological, and functional relations. I compare BERT's relational classification performance with representational structure in [CLS] token embeddings. Results reveal that pretrained BERT enables high classification accuracy, indicating latent relational signals. However, concept pairs organize by relation type in high-dimensional embedding space only after fine-tuning on supervised relation classification tasks. This indicates relational schemata are not emergent from pretraining alone but can be induced via task scaffolding. These findings demonstrate that behavioral performance does not necessarily imply structured conceptual understanding, though models can acquire inductive biases for grounded relational abstraction through appropriate training.

The relative balance between physics and data within any physics-informed machine learner is an important modelling consideration to ensure that the benefits of both physics and data-based approaches are maximised. An over reliance on physical knowledge can be detrimental, particularly when the physics-based component of a model may not accurately represent the true underlying system. An underutilisation of physical knowledge potentially wastes a valuable resource, along with benefits in model interpretability and reduced demand for expensive data collection. Achieving an optimal physics-data balance is a challenging aspect of model design, particularly if the level varies through time; for example, one might have a physical approximation, only valid within particular regimes, or a physical phenomenon may be known to only occur when given conditions are met (e.g. at high temperatures). This paper develops novel, physically-informed, change-point kernels for Gaussian processes, capable of dynamically varying the reliance upon available physical knowledge. A high level of control is granted to a user, allowing for the definition of conditions in which they believe a phenomena should occur and the rate at which the knowledge should be phased in and out of a model. In circumstances where users may be less certain, the switching reliance upon physical knowledge may be automatically learned and recovered from the model in an interpretable and intuitive manner. Variation of the modelled noise based on the physical phenomena occurring is also implemented to provide a more representative capture of uncertainty alongside predictions. The capabilities of the new kernel structures are explored through the use of two engineering case studies: the directional wind loading of a cable-stayed bridge and the prediction of aircraft wing strain during in-flight manoeuvring.

Multimodal large language models (MLLMs), which bridge the gap between audio-visual and natural language processing, achieve state-of-the-art performance on several audio-visual tasks. Despite the superior performance of MLLMs, the scarcity of high-quality audio-visual training data and computational resources necessitates the utilization of third-party data and open-source MLLMs, a trend that is increasingly observed in contemporary research. This prosperity masks significant security risks. Empirical studies demonstrate that the latest MLLMs can be manipulated to produce malicious or harmful content. This manipulation is facilitated exclusively through instructions or inputs, including adversarial perturbations and malevolent queries, effectively bypassing the internal security mechanisms embedded within the models. To gain a deeper comprehension of the inherent security vulnerabilities associated with audio-visual-based multimodal models, a series of surveys investigates various types of attacks, including adversarial and backdoor attacks. While existing surveys on audio-visual attacks provide a comprehensive overview, they are limited to specific types of attacks, which lack a unified review of various types of attacks. To address this issue and gain insights into the latest trends in the field, this paper presents a comprehensive and systematic review of audio-visual attacks, which include adversarial attacks, backdoor attacks, and jailbreak attacks. Furthermore, this paper also reviews various types of attacks in the latest audio-visual-based MLLMs, a dimension notably absent in existing surveys. Drawing upon comprehensive insights from a substantial review, this paper delineates both challenges and emergent trends for future research on audio-visual attacks and defense.

In-context learning (ICL) allows large language models (LLMs) to solve novel tasks without weight updates. Despite its empirical success, the mechanism behind ICL remains poorly understood, limiting our ability to interpret, improve, and reliably apply it. In this paper, we propose a new theoretical perspective that interprets ICL as an implicit form of knowledge distillation (KD), where prompt demonstrations guide the model to form a task-specific reference model during inference. Under this view, we derive a Rademacher complexity-based generalization bound and prove that the bias of the distilled weights grows linearly with the Maximum Mean Discrepancy (MMD) between the prompt and target distributions. This theoretical framework explains several empirical phenomena and unifies prior gradient-based and distributional analyses. To the best of our knowledge, this is the first to formalize inference-time attention as a distillation process, which provides theoretical insights for future prompt engineering and automated demonstration selection.

We present a technical evaluation of a new, disruptive cryptographic approach to data security, known as HbHAI (Hash-based Ho-momorphic Artificial Intelligence). HbHAI is based on a novel class of key-dependent hash functions that naturally preserve most similarity properties, most AI algorithms rely on. As a main claim, HbHAI makes now possible to analyse and process data in its cryptographically secure form while using existing native AI algorithms without modification, with unprecedented performances compared to existing homomorphic encryption schemes. We tested various HbHAI-protected datasets (non public preview) using traditional unsupervised and supervised learning techniques (clustering, classification, deep neural networks) with classical unmodified AI algorithms. This paper presents technical results from an independent analysis conducted with those different, off-the-shelf AI algorithms. The aim was to assess the security, operability and performance claims regarding HbHAI techniques. As a results, our results confirm most these claims, with only a few minor reservations.

This paper proposes a novel, node-splitting support vector machine (SVM) for creating survival trees. This approach is capable of non-linearly partitioning survival data which includes continuous, right-censored outcomes. Our method improves on an existing non-parametric method, which uses at most oblique splits to induce survival regression trees. In the prior work, these oblique splits were created via a non-SVM approach, by minimizing a piece-wise linear objective, called a dipole splitting criterion, constructed from pairs of covariates and their associated survival information. We extend this method by enabling splits from a general class of non-linear surfaces. We achieve this by ridge regularizing the dipole-splitting criterion to enable application of kernel methods in a manner analogous to classical SVMs. The ridge regularization provides robustness and can be tuned. Using various kernels, we induce both linear and non-linear survival trees to compare their sizes and predictive powers on real and simulated data sets. We compare traditional univariate log-rank splits, oblique splits using the original dipole-splitting criterion and a variety of non-linear splits enabled by our method. In these tests, trees created by non-linear splits, using polynomial and Gaussian kernels show similar predictive power while often being of smaller sizes compared to trees created by univariate and oblique splits. This approach provides a novel and flexible array of survival trees that can be applied to diverse survival data sets.

With the recent rise of generative Artificial Intelligence (AI), the need of selecting high-quality dataset to improve machine learning models has garnered increasing attention. However, some part of this topic remains underexplored, even for simple prediction models. In this work, we study the problem of developing practical algorithms that select appropriate dataset to minimize population loss of our prediction model with high probability. Broadly speaking, we investigate when datasets from different sources can be effectively merged to enhance the predictive model's performance, and propose a practical algorithm with theoretical guarantees. By leveraging an oracle inequality and data-driven estimators, the algorithm reduces population loss with high probability. Numerical experiments demonstrate its effectiveness in both standard linear regression and broader machine learning applications. Code is available at https://github.com/kkrokii/collaborative_prediction.

This is a course project report with complete methodology, experiments, references and mathematical derivations. Matrix factorization [1] is a widely used technique in recommendation systems. Probabilistic Matrix Factorization (PMF) [2] extends traditional matrix factorization by incorporating probability distributions over latent factors, allowing for uncertainty quantification. However, computing the posterior distribution is intractable due to the high-dimensional integral. To address this, we employ two Bayesian inference methods: Markov Chain Monte Carlo (MCMC) [3, 4] and Variational Inference (VI) [5, 6] to approximate the posterior. We evaluate their performance on MovieLens dataset [7] and compare their convergence speed, predictive accuracy, and computational efficiency. Experimental results demonstrate that VI offers faster convergence, while MCMC provides more accurate posterior estimates.

In this paper, we introduce a new approach to proving the convergence of the Stochastic Approximation (SA) and the Stochastic Gradient Descent (SGD) algorithms. The new approach is based on a concept called GSLLN (Generalized Strong Law of Large Numbers), which extends the traditional SLLN. Using this concept, we provide sufficient conditions for convergence, which effectively decouple the properties of the function whose zero we are trying to find, from the properties of the measurement errors (noise sequence). The new approach provides an alternative to the two widely used approaches, namely the ODE approach and the martingale approach, and also permits a wider class of noise signals than either of the two known approaches. In particular, the ``noise'' or measurement error \textit{need not} have a finite second moment, and under suitable conditions, not even a finite mean. By adapting this method of proof, we also derive sufficient conditions for the convergence of zero-order SGD, wherein the stochastic gradient is computed using $2d$ function evaluations, but no gradient computations. The sufficient conditions derived here are the weakest to date, thus leading to a considerable expansion of the applicability of SA and SGD theory.

In this paper, we present a unified algorithm for stochastic optimization that makes use of a "momentum" term; in other words, the stochastic gradient depends not only on the current true gradient of the objective function, but also on the true gradient at the previous iteration. Our formulation includes the Stochastic Heavy Ball (SHB) and the Stochastic Nesterov Accelerated Gradient (SNAG) algorithms as special cases. In addition, in our formulation, the momentum term is allowed to vary as a function of time (i.e., the iteration counter). The assumptions on the stochastic gradient are the most general in the literature, in that it can be biased, and have a conditional variance that grows in an unbounded fashion as a function of time. This last feature is crucial in order to make the theory applicable to "zero-order" methods, where the gradient is estimated using just two function evaluations. We present a set of sufficient conditions for the convergence of the unified algorithm. These conditions are natural generalizations of the familiar Robbins-Monro and Kiefer-Wolfowitz-Blum conditions for standard stochastic gradient descent. We also analyze another method from the literature for the SHB algorithm with a time-varying momentum parameter, and show that it is impracticable.