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Statistical learning is the process of estimating an unknown probabilistic input-output relationship of a system using a limited number of observations. A statistical learning machine (SLM) is the algorithm, function, model, or rule, that…

The limited reasoning capabilities of small language models (SLMs) cast doubt on their suitability for tasks demanding deep, multi-step logical deduction. This paper introduces a framework called Small Reasons, Large Hints (SMART), which…

Support matrix machine (SMM) is a successful supervised classification model for matrix-type samples. Unlike support vector machines, it employs low-rank regularization on the regression matrix to effectively capture the intrinsic structure…

Large language models (LLMs) with enormous pre-training tokens and parameters emerge diverse abilities, including math reasoning, code generation, and instruction following. These abilities are further enhanced by supervised fine-tuning…

Small language models (SLMs) enable low-cost, private, on-device inference, but they often fail on problems that require specialized domain knowledge or multi-step reasoning. Existing approaches for improving reasoning either rely on scale…

Explicit chain-of-thought (CoT) reasoning substantially improves the reasoning ability of large language models (LLMs), but incurs high inference cost due to lengthy autoregressive traces. Existing latent reasoning methods offer a promising…

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…

Large language models (LLMs) are often equipped with multi-sample decoding strategies. An LLM implicitly defines an arithmetic code book, facilitating efficient and embarrassingly parallelizable \textbf{arithmetic sampling} to produce…

The Minimal Learning Machine (MLM) is a nonlinear supervised approach based on learning a linear mapping between distance matrices computed in the input and output data spaces, where distances are calculated using a subset of points called…

Current large language models (LLMs) primarily rely on linear sequence generation and massive parameter counts, yet they severely struggle with complex algorithmic reasoning. While recent reasoning architectures, such as the Hierarchical…

Large Language Models (LLM) exhibit zero-shot mathematical reasoning capacity as a behavior emergent with scale, commonly manifesting as chain-of-thoughts (CoT) reasoning. However, multiple empirical findings suggest that this prowess is…

Spiking Neural Networks (SNN) have gained increasing attention for its low power consumption. But training SNN is challenging. Liquid State Machine (LSM), as a major type of Reservoir computing, has been widely recognized for its low…

Statistical Machine Learning (SML) refers to a body of algorithms and methods by which computers are allowed to discover important features of input data sets which are often very large in size. The very task of feature discovery from data…

Test-time scaling (TTS) improves large language models (LLMs) by allocating additional compute at inference time. In practice, TTS is often achieved through parallel scaling: generating multiple candidate responses and selecting the best…

Code explanation plays a crucial role in the software engineering domain, aiding developers in grasping code functionality efficiently. Recent work shows that the performance of LLMs for code explanation improves in a few-shot setting,…

The prevailing approach to distilling reasoning from Large Language Models (LLMs)-behavioral cloning from textual rationales-is fundamentally limited. It teaches Small Language Models (SLMs) to mimic surface-level patterns rather than the…

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…

As a promising area in artificial intelligence, a new learning paradigm, called Small Sample Learning (SSL), has been attracting prominent research attention in the recent years. In this paper, we aim to present a survey to comprehensively…

Reconstruction and joint embedding have emerged as two leading paradigms in Self Supervised Learning (SSL). Reconstruction methods focus on recovering the original sample from a different view in input space. On the other hand, joint…

Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…