--Inherent in virtually every iterative machine learning algorithm is the problem of hyper-parameter tuning which includes three major design parameters: (a) the complexity of the model, e.g., the number of neurons in a neural network, (b) the initial conditions, which heavily affect the behavior of the algorithm, and (c) the dissimilarity measure used to quantify its performance. We introduce an online prototype-based learning algorithm that can be viewed as a progressively growing competitive-learning neural network architecture for classification and clustering. The learning rule of the proposed approach is formulated as an online gradient-free stochastic approximation algorithm that solves a sequence of appropriately defined optimization problems, simulating an annealing process. The annealing nature of the algorithm contributes to avoiding poor local minima, offers robustness with respect to the initial conditions, and provides a means to progressively increase the complexity of the learning model, through an intuitive bifurcation phenomenon. The proposed approach is interpretable, requires minimal hyper-parameter tuning, and allows online control over the performance-complexity trade-off. Finally, we show that Bregman divergences appear naturally as a family of dissimilarity measures that play a central role in both the performance and the computational complexity of the learning algorithm. EARNING from data samples has become an important component of artificial intelligence. While virtually all learning problems can be formulated as constrained stochastic optimization problems, the optimization methods can be intractable, typically dealing with mixed constraints and very large, or even infinite-dimensional spaces [1]. For this reason, feature extraction, model selection and design, and analysis of optimization methods, have been the cornerstone of machine learning algorithms from their genesis until today. Deep learning methods, currently dominating the field of machine learning due to their performance in multiple applications, attempt to learn feature representations from data, using biologically-inspired models in artificial neural networks [2], [3]. Manuscript published in the IEEE Transactions on Neural Networks and Learning Systems (TNNLS).

A deep dive into the open literature shows that there are t hree fundamental limitations to current ML approaches, namely blackbox brittleness (which renders models uninterpretable and unreliable under distribution shift [2]), causal blindness (which conflates correlation with causation [3]), and alignment failures (which produce systems optimizing objectives misaligned with human values [4]) . These deficiencies stem from a profound philosophical poverty in how ML conceptualizes knowledge, reasoning, and values. The first fundamental limitation, b lackbox brittleness, manifests when trained models fail on seemingly trivial variations of their training distribution. For example, a vision model that accurately identifies stop signs under normal conditions might misclassify them entirely when small adversarial perturbations are applied [5] . Not surprisingly, t h e same brittleness extends beyond adversarial examples to everyday distribution shifts (e.g., natural language processing models exhibit performance degradation when processing text from different cultural contexts, etc.) [6] .

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic regression. However, existing approaches are dominated by heuristic algorithms or data-hungry black-box methods, which often demand low-noise settings and lack principled uncertainty quantification. Motivated by interpretable Statistical Artificial Intelligence, we develop a hierarchical Bayesian framework for symbolic regression that represents scientific laws as ensembles of tree-structured symbolic expressions endowed with a regularized tree prior. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior-based criterion adhering to the Occam's window principle and further quantify structural fidelity to ground truth through a tailored expression-distance metric. On the theoretical front, we establish near-minimax rate of Bayesian posterior concentration, providing the first rigorous guarantee in context of symbolic regression. Empirical evaluation demonstrates robust performance of our proposed methodology against state-of-the-art competing modules on a simulated example, a suite of canonical Feynman equations, and single-atom catalysis dataset.

Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard baseline methods such as model logits and elicited probabilities produce overconfident and poorly calibrated estimates. In this work, we propose Approximate Bayesian Computation (ABC), a likelihood-free Bayesian inference, based approach that treats LLMs as a stochastic simulator to infer posterior distributions over predictive probabilities. We evaluate our ABC approach on two clinically relevant benchmarks: a synthetic oral lesion diagnosis dataset and the publicly available GretelAI symptom-to-diagnosis dataset. Compared to standard baselines, our approach improves accuracy by up to 46.9\%, reduces Brier scores by 74.4\%, and enhances calibration as measured by Expected Calibration Error (ECE) and predictive entropy.

Traffic accidents remain a major global concern, with lane-change maneuvers recognized as one of the significant contributors to collision risk. Anticipating these maneuvers has become an important research focus, supporting both traffic safety and the safe integration of autonomous and assisted driving technologies. Over the past decade, numerous models have been developed for lane-change prediction. However, most existing works have been designed and validated using simulation environments or pre-recorded datasets. While these settings allow for benchmarking and controlled evaluation, they often rely on simplified assumptions about sensing, communication, and vehicle behavior that do not fully capture the complexity of real-world operation. Real-world deployments of lane-change prediction systems are relatively rare, and when they are reported, their practical challenges, limitations, and insights remain under-documented. To illustrate the setting more concretely, consider the left lane change scenario shown in Figure 1. The Ego Vehicle (EV) is driving in the left lane, while the Target Vehicle (TV) is moving in the right lane behind a Preceding Vehicle (PV). When the PV suddenly brakes, the TV must change lanes to avoid a collision.

Advanced reasoning models with agentic capabilities (AI agents) are deployed to interact with humans and to solve sequential decision-making problems under (approximate) utility functions and internal models. When such problems have resource or failure constraints where action sequences may be forcibly terminated once resources are exhausted, agents face implicit trade-offs that reshape their utility-driven (rational) behaviour. Additionally, since these agents are typically commissioned by a human principal to act on their behalf, asymmetries in constraint exposure can give rise to previously unanticipated misalignment between human objectives and agent incentives. We formalise this setting through a survival bandit framework, provide theoretical and empirical results that quantify the impact of survival-driven preference shifts, identify conditions under which misalignment emerges and propose mechanisms to mitigate the emergence of risk-seeking or risk-averse behaviours. As a result, this work aims to increase understanding and interpretability of emergent behaviours of AI agents operating under such survival pressure, and offer guidelines for safely deploying such AI systems in critical resource-limited environments.

This paper presents a lidar-only state estimation and tracking framework, along with a roadside sensing unit for integration with existing urban infrastructure. Urban deployments demand scalable, real-time tracking solutions, yet traditional remote sensing remains costly and computationally intensive, especially under perceptually degraded conditions. Our sensor node couples a single lidar with an edge computing unit and runs a computationally efficient, GPU-free observer that simultaneously estimates object state, class, dimensions, and existence probability. The pipeline performs: (i) state updates via an extended Kalman filter, (ii) dimension estimation using a 1D grid-map/Bayesian update, (iii) class updates via a lookup table driven by the most probable footprint, and (iv) existence estimation from track age and bounding-box consistency. Experiments in dynamic urban-like scenes with diverse traffic participants demonstrate real-time performance and high precision: The complete end-to-end pipeline finishes within \SI{100}{\milli\second} for \SI{99.88}{\%} of messages, with an excellent detection rate. Robustness is further confirmed under simulated wind and sensor vibration. These results indicate that reliable, real-time roadside tracking is feasible on CPU-only edge hardware, enabling scalable, privacy-friendly deployments within existing city infrastructure. The framework integrates with existing poles, traffic lights, and buildings, reducing deployment costs and simplifying large-scale urban rollouts and maintenance efforts.