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Researcher profile

Andrew Y. K. Foong

Andrew Y. K. Foong contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceComputer Visionmath.STStatistics Theory

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Published work

6 published item(s)

preprint2026arXiv

Position: agentic AI orchestration should be Bayes-consistent

LLMs excel at predictive tasks and complex reasoning tasks, but many high-value deployments rely on decisions under uncertainty, for example, which tool to call, which expert to consult, or how many resources to invest. While the usefulness and feasibility of Bayesian approaches remain unclear for LLM inference, this position paper argues that the control layer of an agentic AI system (that orchestrates LLMs and tools) is a clear case where Bayesian principles should shine. Bayesian decision theory provides a framework for agentic systems that can help to maintain beliefs over task-relevant latent quantities, to update these beliefs from observed agentic and human-AI interactions, and to choose actions. Making LLMs themselves explicitly Bayesian belief-updating engines remains computationally intensive and conceptually nontrivial as a general modeling target. In contrast, this paper argues that coherent decision-making requires Bayesian principles at the orchestration level of the agentic system, not necessarily the LLM agent parameters. This paper articulates practical properties for Bayesian control that fit modern agentic AI systems and human-AI collaboration, and provides concrete examples and design patterns to illustrate how calibrated beliefs and utility-aware policies can improve agentic AI orchestration.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Note on the Chernoff Bound for Random Variables in the Unit Interval

The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the generalisation risk of a hypothesis in terms of its empirical risk on held-out data, for the case of a binary-valued loss function. However, the extension of this bound to the case of random variables taking values in the unit interval is less well known in the community. In this note we provide a proof of this extension for convenience and future reference.

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preprint2022arXiv

How Tight Can PAC-Bayes be in the Small Data Regime?

In this paper, we investigate the question: Given a small number of datapoints, for example N = 30, how tight can PAC-Bayes and test set bounds be made? For such small datasets, test set bounds adversely affect generalisation performance by withholding data from the training procedure. In this setting, PAC-Bayes bounds are especially attractive, due to their ability to use all the data to simultaneously learn a posterior and bound its generalisation risk. We focus on the case of i.i.d. data with a bounded loss and consider the generic PAC-Bayes theorem of Germain et al. While their theorem is known to recover many existing PAC-Bayes bounds, it is unclear what the tightest bound derivable from their framework is. For a fixed learning algorithm and dataset, we show that the tightest possible bound coincides with a bound considered by Catoni; and, in the more natural case of distributions over datasets, we establish a lower bound on the best bound achievable in expectation. Interestingly, this lower bound recovers the Chernoff test set bound if the posterior is equal to the prior. Moreover, to illustrate how tight these bounds can be, we study synthetic one-dimensional classification tasks in which it is feasible to meta-learn both the prior and the form of the bound to numerically optimise for the tightest bounds possible. We find that in this simple, controlled scenario, PAC-Bayes bounds are competitive with comparable, commonly used Chernoff test set bounds. However, the sharpest test set bounds still lead to better guarantees on the generalisation error than the PAC-Bayes bounds we consider.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

The Gaussian Neural Process

Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to train conditional NPs. Moreover, we propose a new member to the Neural Process family called the Gaussian Neural Process (GNP), which models predictive correlations, incorporates translation equivariance, provides universal approximation guarantees, and demonstrates encouraging performance.

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preprint2020arXiv

Convolutional Conditional Neural Processes

We introduce the Convolutional Conditional Neural Process (ConvCNP), a new member of the Neural Process family that models translation equivariance in the data. Translation equivariance is an important inductive bias for many learning problems including time series modelling, spatial data, and images. The model embeds data sets into an infinite-dimensional function space as opposed to a finite-dimensional vector space. To formalize this notion, we extend the theory of neural representations of sets to include functional representations, and demonstrate that any translation-equivariant embedding can be represented using a convolutional deep set. We evaluate ConvCNPs in several settings, demonstrating that they achieve state-of-the-art performance compared to existing NPs. We demonstrate that building in translation equivariance enables zero-shot generalization to challenging, out-of-domain tasks.

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preprint2020arXiv

Structured Weight Priors for Convolutional Neural Networks

Selection of an architectural prior well suited to a task (e.g. convolutions for image data) is crucial to the success of deep neural networks (NNs). Conversely, the weight priors within these architectures are typically left vague, e.g.~independent Gaussian distributions, which has led to debate over the utility of Bayesian deep learning. This paper explores the benefits of adding structure to weight priors. It initially considers first-layer filters of a convolutional NN, designing a prior based on random Gabor filters. Second, it considers adding structure to the prior of final-layer weights by estimating how each hidden feature relates to each class. Empirical results suggest that these structured weight priors lead to more meaningful functional priors for image data. This contributes to the ongoing discussion on the importance of weight priors.

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