Beat and downbeat tracking, jointly referred to as Meter Tracking, is a fundamental task in Music Information Retrieval (MIR). Deep learning models have far surpassed traditional signal processing and classical machine learning approaches in this domain, particularly for Western (Eurogenetic) genres, where large annotated datasets are widely available. These systems, however, perform less reliably on underrepresented musical traditions. Carnatic music, a rich tradition from the Indian subcontinent, is renowned for its rhythmic intricacy and unique metrical structures (tālas). The most notable prior work on meter tracking in this context employed probabilistic Dynamic Bayesian Networks (DBNs). The performance of state-of-the-art (SOTA) deep learning models on Carnatic music, however, remains largely unexplored. In this study, we evaluate two models for meter tracking in Carnatic music: the Temporal Convolutional Network (TCN), a lightweight architecture that has been successfully adapted for Latin rhythms, and Beat This!, a transformer-based model designed for broad stylistic coverage without the need for post-processing. Replicating the experimental setup of the DBN baseline on the Carnatic Music Rhythm (CMR$_f$) dataset, we systematically assess the performance of these models in a directly comparable setting. We further investigate adaptation strategies, including fine-tuning the models on Carnatic data and the use of musically informed parameters. Results show that while off-the-shelf models do not always outperform the DBN, their performance improves substantially with transfer learning, matching or surpassing the baseline. These findings indicate that SOTA deep learning models can be effectively adapted to underrepresented traditions, paving the way for more inclusive and broadly applicable meter tracking systems.

We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using Bayesian inference for parameter estimation. These models are shown to be more robust to noise in the measurement results used to perform the parameter estimation as well as noise in the data used to train them. We also show that much less data is needed to achieve comparable performance to Bayesian inference based estimation, which is known to reach the ultimate precision limit as more data is collected, than was used in previous proposals.

Sequential fine-tuning of transformers is useful when new data arrive sequentially, especially with shifting distributions. Unlike batch learning, sequential learning demands that training be stabilized despite a small amount of data by balancing new information and previously learned knowledge in the pre-trained models. This challenge is further complicated when training is to be completed in latency-critical environments and learning must additionally quantify and be mediated by uncertainty. Motivated by these challenges, we propose a novel method that frames sequential fine-tuning as a posterior inference problem within a Bayesian framework. Our approach integrates closed-form moment propagation of random variables, Kalman Bayesian Neural Networks, and Taylor approximations of the moments of softmax functions. By explicitly accounting for pre-trained models as priors and adaptively balancing them against new information based on quantified uncertainty, our method achieves robust and data-efficient sequential learning. The effectiveness of our method is demonstrated through numerical simulations involving sequential adaptation of a decision transformer to tasks characterized by distribution shifts and limited memory resources.

Trajectory prediction serves as a critical functionality in autonomous driving, enabling the anticipation of future motion paths for traffic participants such as vehicles and pedestrians, which is essential for driving safety. Although conventional deep learning methods have improved accuracy, they remain hindered by inherent limitations, including lack of interpretability, heavy reliance on large-scale annotated data, and weak generalization in long-tail scenarios. The rise of Large Foundation Models (LFMs) is transforming the research paradigm of trajectory prediction. This survey offers a systematic review of recent advances in LFMs, particularly Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) for trajectory prediction. By integrating linguistic and scene semantics, LFMs facilitate interpretable contextual reasoning, significantly enhancing prediction safety and generalization in complex environments. The article highlights three core methodologies: trajectory-language mapping, multimodal fusion, and constraint-based reasoning. It covers prediction tasks for both vehicles and pedestrians, evaluation metrics, and dataset analyses. Key challenges such as computational latency, data scarcity, and real-world robustness are discussed, along with future research directions including low-latency inference, causality-aware modeling, and motion foundation models.

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an explicit unnormalised density for the target. To mitigate this difficulty, we introduce a novel measure of suboptimality called 'gradient discrepancy', and in particular a 'kernel gradient discrepancy' (KGD) that can be explicitly computed. In the standard Bayesian context, KGD coincides with the kernel Stein discrepancy (KSD), and we obtain a novel charasterisation of KSD as measuring the size of a variational gradient. Outside this familiar setting, KGD enables novel sampling algorithms to be developed and compared, even when unnormalised densities cannot be obtained. To illustrate this point several novel algorithms are proposed, including a natural generalisation of Stein variational gradient descent, with applications to mean-field neural networks and prediction-centric uncertainty quantification presented. On the theoretical side, our principal contribution is to establish sufficient conditions for desirable properties of KGD, such as continuity and convergence control.

Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses a novel and conservative method to avoid potential inconsistencies in the input IT2 MFs that otherwise might produce invalid output results. We then describe a novel and flexible algorithm for encoding SME-provided intervals into IT2 fuzzy membership functions (MFs), which we can use to specify the input probabilities in Bayes Theorem. Our algorithm generalizes and extends previous work on this problem that primarily addressed the encoding of intervals into word MFs for Computing with Words applications.

Modern neural networks (NNs) often achieve high predictive accuracy but are poorly calibrated, producing overconfident predictions even when wrong. This miscalibration poses serious challenges in applications where reliable uncertainty estimates are critical. In this work, we investigate how human perceptual uncertainty compares to uncertainty estimated by NNs. Using three vision benchmarks annotated with both human disagreement and crowdsourced confidence, we assess the correlation between model-predicted uncertainty and human-perceived uncertainty. Our results show that current methods only weakly align with human intuition, with correlations varying significantly across tasks and uncertainty metrics. Notably, we find that incorporating human-derived soft labels into the training process can improve calibration without compromising accuracy. These findings reveal a persistent gap between model and human uncertainty and highlight the potential of leveraging human insights to guide the development of more trustworthy AI systems.

The increasing availability of personal data has enabled significant advances in fields such as machine learning, healthcare, and cybersecurity. However, this data abundance also raises serious privacy concerns, especially in light of powerful re-identification attacks and growing legal and ethical demands for responsible data use. Differential privacy (DP) has emerged as a principled, mathematically grounded framework for mitigating these risks. This review provides a comprehensive survey of DP, covering its theoretical foundations, practical mechanisms, and real-world applications. It explores key algorithmic tools and domain-specific challenges - particularly in privacy-preserving machine learning and synthetic data generation. The report also highlights usability issues and the need for improved communication and transparency in DP systems. Overall, the goal is to support informed adoption of DP by researchers and practitioners navigating the evolving landscape of data privacy.

We present a novel recursive Bayesian estimation framework using B-splines for continuous-time 6-DoF dynamic motion estimation. The state vector consists of a recurrent set of position control points and orientation control point increments, enabling efficient estimation via a modified iterated extended Kalman filter without involving error-state formulations. The resulting recursive spline estimator (RESPLE) is further leveraged to develop a versatile suite of direct LiDAR-based odometry solutions, supporting the integration of one or multiple LiDARs and an IMU. We conduct extensive real-world evaluations using public datasets and our own experiments, covering diverse sensor setups, platforms, and environments. Compared to existing systems, RESPLE achieves comparable or superior estimation accuracy and robustness, while attaining real-time efficiency. Our results and analysis demonstrate RESPLE's strength in handling highly dynamic motions and complex scenes within a lightweight and flexible design, showing strong potential as a universal framework for multi-sensor motion estimation. We release the source code and experimental datasets at https://github.com/ASIG-X/RESPLE .

The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the component of interest, such as the location of the optimum. Nuisance parameters are eliminated via profile likelihood, which naturally handles constraints. As a direct instantiation, we develop a MINimalist Thompson Sampling (MINTS) algorithm. Our framework accommodates structured problems, including continuum-armed Lipschitz bandits and dynamic pricing. It also provides a probabilistic lens on classical convex optimization algorithms such as the center of gravity and ellipsoid methods. We further analyze MINTS for multi-armed bandits and establish near-optimal regret guarantees.