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A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for…

Recent advances such as self-consistency and test-time reinforcement learning (TTRL) improve the reliability of large language models (LLMs) without additional supervision, yet their underlying mechanisms and statistical guarantees remain…

Recursive learning -- where models are trained on data generated by previous versions of themselves -- is increasingly common in large language models, autonomous agents, and self-supervised systems. However, standard performance metrics…

Temporally indexed data are essential in a wide range of fields and of interest to machine learning researchers. Time series data, however, are often scarce or highly sensitive, which precludes the sharing of data between researchers and…

Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of…

Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random…

Aligned Large Language Models (LLMs) have attracted significant attention for their safety, particularly in the context of jailbreak attacks that attempt to bypass guardrails via adversarial prompts. Among existing approaches, the Greedy…

Agentic LLM frameworks promise autonomous behavior via task decomposition, tool use, and iterative planning, but most deployed systems remain brittle. They lack runtime introspection, cannot diagnose their own failure modes, and do not…

Gradient Boosting Machines (GBM) are hugely popular for solving tabular data problems. However, practitioners are not only interested in point predictions, but also in probabilistic predictions in order to quantify the uncertainty of the…

We present an approach for efficiently training Gaussian Mixture Model (GMM) by Stochastic Gradient Descent (SGD) with non-stationary, high-dimensional streaming data. Our training scheme does not require data-driven parameter…

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework…

Frontier AI models have achieved remarkable progress, yet recent studies suggest they struggle with compositional reasoning, often performing at or below random chance on established benchmarks. We revisit this problem and show that widely…

The alignment of Large Language Models (LLMs) for complex reasoning heavily relies on Reinforcement Learning with Verifiable Rewards (RLVR). However, standard algorithms like GRPO apply sequence-level rewards uniformly to all tokens,…

LLM-based prompt optimization, that uses LLM-provided "textual gradients" (feedback) to refine prompts, has emerged an effective method for automatic prompt engineering. However, its scalability and stability are unclear when using more…

Sign-based optimization algorithms, such as SignSGD, have garnered significant attention for their remarkable performance in distributed learning and training large foundation models. Despite their empirical superiority, SignSGD is known to…

Residual bootstrap is a classical method for statistical inference in regression settings. With massive data sets becoming increasingly common, there is a demand for computationally efficient alternatives to residual bootstrap. We propose a…

Recently, Reinforcement Learning from Verifiable Rewards (RLVR) has been established as a highly effective technique for augmenting the math reasoning skills of Large Language Models (LLMs) based on a single instance. Current…

Whenever data-based systems are employed in engineering applications, defining an optimal statistical representation is subject to the problem of model selection. This paper focusses on how well models can generalise in Structural Health…

Large Language Models (LLMs) have achieved remarkable success across a wide range of natural language tasks, but often exhibit overconfidence and generate plausible yet incorrect answers. This overconfidence, especially in models undergone…

The increasing use of generative ML foundation models for image restoration tasks such as super-resolution calls for robust and interpretable uncertainty quantification methods. We address this need by presenting a novel approach based on…