Large Language Models (LLMs) have demonstrated exceptional capabilities in natural language understanding and generation. Based on these LLMs, businesses have started to provide Embeddings-as-a-Service (EaaS), offering feature extraction capabilities (in the form of text embeddings) that benefit downstream natural language processing tasks. However, prior research has demonstrated that EaaS is vulnerable to imitation attacks, where an attacker clones the service's model in a black-box manner without access to the model's internal workings. In response, watermarks have been added to the text embeddings to protect the intellectual property of EaaS providers by allowing them to check for model ownership. This thesis focuses on defending against imitation attacks by investigating EaaS watermarks. To achieve this goal, we unveil novel attacks and propose and validate new watermarking techniques. Firstly, we show that existing EaaS watermarks can be removed through paraphrasing the input text when attackers clone the model during imitation attacks. Our study illustrates that paraphrasing can effectively bypass current state-of-the-art EaaS watermarks across various attack setups (including different paraphrasing techniques and models) and datasets in most instances. This demonstrates a new vulnerability in recent EaaS watermarking techniques. Subsequently, as a countermeasure, we propose a novel watermarking technique, WET (Watermarking EaaS with Linear Transformation), which employs linear transformation of the embeddings. Watermark verification is conducted by applying a reverse transformation and comparing the similarity between recovered and original embeddings. We demonstrate its robustness against paraphrasing attacks with near-perfect verifiability. We conduct detailed ablation studies to assess the significance of each component and hyperparameter in WET.

Tilted (entropic) risk, obtained by applying a log-exponential transform to a base loss, is a well established tool in statistics and machine learning for emphasizing rare or high loss events while retaining a tractable optimization problem. In this work, our aim is to interpret its structure for Flow Matching (FM). FM learns a velocity field that transports samples from a simple source distribution to data by integrating an ODE. In rectified FM, training pairs are obtained by linearly interpolating between a source sample and a data sample, and a neural velocity field is trained to predict the straight line displacement using a mean squared error loss. This squared loss collapses all velocity targets that reach the same space-time point into a single conditional mean, thereby ignoring higher order conditional information (variance, skewness, multi-modality) that encodes fine geometric structure about the data manifold and minority branches. We apply the standard risk-sensitive (log-exponential) transform to the conditional FM loss and show that the resulting tilted risk loss is a natural upper-bound on a meaningful conditional entropic FM objective defined at each space-time point. Furthermore, we show that a small order expansion of the gradient of this conditional entropic objective yields two interpretable first order corrections: covariance preconditioning of the FM residual, and a skew tail term that favors asymmetric or rare branches. On synthetic data designed to probe ambiguity and tails, the resulting risk-sensitive loss improves statistical metrics and recovers geometric structure more faithfully than standard rectified FM.

Continual reinforcement learning (continual RL) seeks to formalize the notions of lifelong learning and endless adaptation in RL. In particular, the aim of continual RL is to develop RL agents that can maintain a careful balance between retaining useful information and adapting to new situations. To date, continual RL has been explored almost exclusively through the lens of risk-neutral decision-making, in which the agent aims to optimize the expected long-run performance. In this work, we present the first formal theoretical treatment of continual RL through the lens of risk-aware decision-making, in which the behaviour of the agent is directed towards optimizing a measure of long-run performance beyond the mean. In particular, we show that the classical theory of risk measures, widely used as a theoretical foundation in non-continual risk-aware RL, is, in its current form, incompatible with continual learning. Then, building on this insight, we extend risk measure theory into the continual setting by introducing a new class of ergodic risk measures that are compatible with continual learning. Finally, we provide a case study of risk-aware continual learning, along with empirical results, which show the intuitive appeal of ergodic risk measures in continual settings.

The blockchain oracle problem, which refers to the challenge of injecting reliable external data into decentralized systems, remains a fundamental limitation to the development of trustless applications. While recent years have seen a proliferation of architectural, cryptographic, and economic strategies to mitigate this issue, no one has yet fully resolved the fundamental question of how a blockchain can gain knowledge about the off-chain world. In this position paper, we critically assess the role artificial intelligence (AI) can play in tackling the oracle problem. Drawing from both academic literature and practitioner implementations, we examine how AI techniques such as anomaly detection, language-based fact extraction, dynamic reputation modeling, and adversarial resistance can enhance oracle systems. We observe that while AI introduces powerful tools for improving data quality, source selection, and system resilience, it cannot eliminate the reliance on unverifiable off-chain inputs. Therefore, this study supports the idea that AI should be understood as a complementary layer of inference and filtering within a broader oracle design, not a substitute for trust assumptions.

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the tempered Bayes filter, improving estimation performance through both of the aforementioned, and one newly introduced, modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that -- besides the well-known fact in the field of Bayesian inference that likelihood tempering affects the balance between prior and likelihood -- full-posterior tempering tunes the level of entropy in the final belief distribution. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter achieves improved predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance propagation. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.

To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without incurring exponential computational cost. However, extending this model to a fully probabilistic formulation introduces several design challenges. In particular, for tensor train (TT) models, it is unclear which TT-core should be treated in a Bayesian manner. We introduce a Bayesian tensor train kernel machine that applies Laplace approximation to estimate the posterior distribution over a selected TT-core and employs variational inference (VI) for precision hyperparameters. Experiments show that core selection is largely independent of TT-ranks and feature structure, and that VI replaces cross-validation while offering up to 65x faster training. The method's effectiveness is demonstrated on an inverse dynamics problem.

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More accurate learning typically requires Markov chain Monte Carlo (MCMC) Boltzmann sampling, but it is time-consuming due to the difficulty of parallelization for more expressive models. To address this limitation, we first propose a new Boltzmann sampler inspired by a quantum-inspired combinatorial optimization called simulated bifurcation (SB). This SB-inspired approach, which we name Langevin SB (LSB), enables parallelized sampling while maintaining accuracy comparable to MCMC. Furthermore, this is applicable not only to RBMs but also to BMs with general couplings. However, LSB cannot control the inverse temperature of the output Boltzmann distribution, which hinders learning and degrades performance. To overcome this limitation, we also developed an efficient method for estimating the inverse temperature during the learning process, which we call conditional expectation matching (CEM). By combining LSB and CEM, we establish an efficient learning framework for BMs with greater expressive power than RBMs. We refer to this framework as sampler-adaptive learning (SAL). SAL opens new avenues for energy-based generative modeling beyond RBMs.

Algorithms developed under stationary Markov Decision Processes (MDPs) often face challenges in non-stationary environments, and infinite-horizon formulations may not directly apply to finite-horizon tasks. To address these limitations, we introduce the Non-stationary and Varying-discounting MDP (NVMDP) framework, which naturally accommodates non-stationarity and allows discount rates to vary with time and transitions. Infinite-horizon, stationary MDPs emerge as special cases of NVMDPs for identifying an optimal policy, and finite-horizon MDPs are also subsumed within the NVMDP formulations. Moreover, NVMDPs provide a flexible mechanism to shape optimal policies, without altering the state space, action space, or the reward structure. We establish the theoretical foundations of NVMDPs, including assumptions, state- and action-value formulation and recursion, matrix representation, optimality conditions, and policy improvement under finite state and action spaces. Building on these results, we adapt dynamic programming and generalized Q-learning algorithms to NVMDPs, along with formal convergence proofs. For problems requiring function approximation, we extend the Policy Gradient Theorem and the policy improvement bound in Trust Region Policy Optimization (TRPO), offering proofs in both scalar and matrix forms. Empirical evaluations in a non-stationary gridworld environment demonstrate that NVMDP-based algorithms successfully recover optimal trajectories under multiple reward and discounting schemes, whereas original Q-learning fails. These results collectively show that NVMDPs provide a theoretically sound and practically effective framework for reinforcement learning, requiring only minor algorithmic modifications while enabling robust handling of non-stationarity and explicit optimal policy shaping.

Thinking Large Language Models (LLMs) used as judges for pairwise preferences remain noisy at the single-sample level, and common aggregation rules (majority vote, soft self-consistency, or instruction-based self-aggregation) are inconsistent when ties are allowed. We study inference-time compute (ITC) for evaluators that generate n independent thinking-rating samples per item, and propose a principled, distribution-calibrated aggregation scheme. Our method models three-way preferences with a Bradley-Terry-Davidson formulation on rating counts, leveraging both polarity (margin among non-ties) and decisiveness (non-tie rate) to distinguish narrow margins from strong consensus. Across various evaluation benchmarks, our approach consistently reduces MAE and increases pairwise accuracy versus standard baselines, and when evaluated against human-consensus meta-labels, matches or exceeds individual human raters. These results show that carefully allocating ITC and aggregating with distribution-aware methods turns noisy individual model judgments into reliable ratings for evaluation. Thinking large language models (LLMs) are increasingly being employed as automated judges for evaluating the output of other generative systems, a paradigm known as "Thinking-LLM-as-a-Judge" (Saha et al., 2025). This approach offers a scalable and cost-effective alternative to human evaluation, which is often slow and expensive. To mitigate the inherent stochasticity and noise of single-pass judgments, a common strategy is to leverage inference-time compute (ITC) Snell et al. (2024) by generating multiple independent reasoning and rating samples for each item being evaluated. However, the reliability of the final judgment hinges critically on how these multiple outputs are aggregated. Current aggregation methods, such as majority voting (Self-Consistency (Wang et al., 2023b)) or heuristics based on model confidence scores or LLM generated aggregators, are often brittle and statistically suboptimal.