Date/Time : 30 Oct 2024 16:45
Venue : S17 #04-06 (SR1)
Speaker : Desmond Lau,

We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical term model. We then demonstrate the usefulness of this framework by applying it to variants of the extended Namba problem, as well as to the analysis of models of certain theories with constraints in interpretation (TCIs). Separately, we look at small extensions of V as generalised degrees of computability over V. Using TCIs, we formalise and investigate the complexity of certain methods one can use to define, in V, subclasses of degrees over V. Finally, we give a characterisation of the complexity of forcing.

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Date/Time : 30 Oct 2024 16:30
Venue : S17 #05-11 (SR5)
Speaker : Wang Yangshuai, National University of Singapore

The success of molecular simulations hinges on the accuracy and efficiency of force fields. Recently, machine-learned interatomic potentials (MLIPs) have revolutionized the field by bridging the gap between high-accuracy ab initio models and classical force fields. MLIPs have quickly become an essential tool in computational atomic simulations, leading to numerous breakthroughs across various scientific domains. This talk will provide an overview of the latest advancements in MLIPs, with a focus on their applications in materials science. I will start by discussing the Atomic Cluster Expansion (ACE) method, a linear model known for its strong predictive performance in small systems. To address the limitations of linear models, I will introduce MACE, an advanced potential based on ACE and enhanced by Message Passing Neural Networks (MPNN), tailored for complex systems with superior generalization and robustness. The focus will then shift to MACE-MP-0, a pre-trained foundation model built on MACE, highlighting its predictive accuracy and the advantages of fine-tuning across diverse materials applications. I will conclude by discussing future MLIP extensions that could further enhance molecular modeling and simulation in materials science and chemistry.

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Date/Time : 29 Oct 2024 14:00
Venue : S17 #04-06 (SR1)
Speaker : Nathan Ross, University of Melbourne

Neural networks are random parametric functions, where the parameters are chosen according to stochastic gradient descent, based on the sample of training data. It has long been known that at initialisation, a neural network with “large” width and “fixed” depth can be well-approximated by a limiting Gaussian random field. But what quantities are well-approximated, and how wide does a neural network need to be for the approximation to be good? There has been a flurry of recent work trying to answer these and related questions, by deriving rates of convergence between the distribution of the neural network and the limiting Gaussian random field in various probability metrics, including some at the process level.

The aim of these lectures is to explain a general approach that can be applied to derive such rates at the process level, which uses Stein’s method, functional smoothing inequalities, and classical Gaussian process concepts such as Karhunen-Loeve expansion and Cameron-Martin/Reproducing Kernel Hilbert Space. The target audience is PhD students planning to do research in probability or statistics. In particular, the definitions and relevant properties of the concepts above will be covered in detail. Open questions and future directions will also be discussed.

The approach is based on joint work with (A.D. Barbour, K. Balasubramanian, L. Goldstein, A. Salim, and G. Zheng).

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Date/Time : 28 Oct 2024 16:00
Venue : S17 #04-06 (SR1)
Speaker : Nathan Ross, University of Melbourne

Neural networks are random parametric functions, where the parameters are chosen according to stochastic gradient descent, based on the sample of training data. It has long been known that at initialisation, a neural network with “large” width and “fixed” depth can be well-approximated by a limiting Gaussian random field. But what quantities are well-approximated, and how wide does a neural network need to be for the approximation to be good? There has been a flurry of recent work trying to answer these and related questions, by deriving rates of convergence between the distribution of the neural network and the limiting Gaussian random field in various probability metrics, including some at the process level.

The aim of these lectures is to explain a general approach that can be applied to derive such rates at the process level, which uses Stein’s method, functional smoothing inequalities, and classical Gaussian process concepts such as Karhunen-Loeve expansion and Cameron-Martin/Reproducing Kernel Hilbert Space. The target audience is PhD students planning to do research in probability or statistics. In particular, the definitions and relevant properties of the concepts above will be covered in detail. Open questions and future directions will also be discussed.

The approach is based on joint work with (A.D. Barbour, K. Balasubramanian, L. Goldstein, A. Salim, and G. Zheng).

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Date/Time : 28 Oct 2024 10:00
Venue : via Zoom
Speaker : Qijun Tan, Google DeepMind

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https://nus-sg.zoom.us/j/82351206827?pwd=L6NM7PEa9BfIlfHqeare8XkoY0IKnr.1

Meeting ID: 823 5120 6827
Passcode: 077539

In this talk, we will explain how Large Language Models (LLM) obtain their capability in solving difficult math problems. In particular, We will go over key techniques that unearth the reasoning potential of LLMs. We will also illustrate key challenges in LLM reasoning.

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Date/Time : 24 Oct 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Jimmy He, Ohio State University

The study of quantum groups and integrable systems have long been connected through the Yang-Baxter equation. Recently, these ideas have been introduced in probability to study integrable stochastic models. I will discuss a similar story for models with boundary, which are connected to quantum symmetric spaces through the reflection equation, as well as some applications to probability. The focus will be on illustrating the connections through illustrative examples and applications for a specific model called the six vertex model.

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Date/Time : 24 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Michael Pevzner, Université de Reims-Champagne-Ardenne

Inspired by classical concepts of generating functions for orthogonal polynomials, this talk will explore “generating operators” for a family of differential operators acting between two manifolds.

We will present a formula for these generating operators associated with Rankin–Cohen brackets and discuss their connection to infinite-dimensional representation theory. Joint work with T. Kobayashi.

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Date/Time : 23 Oct 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Jimmy He, Ohio State University

The study of quantum groups and integrable systems have long been connected through the Yang-Baxter equation. Recently, these ideas have been introduced in probability to study integrable stochastic models. I will discuss a similar story for models with boundary, which are connected to quantum symmetric spaces through the reflection equation, as well as some applications to probability. The focus will be on illustrating the connections through illustrative examples and applications for a specific model called the six vertex model.

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Date/Time : 23 Oct 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Wei Xin, University of Science and Technology of China

Separating hash families (SHFs) are useful combinatorial structures which generalize several well-studied objects in cryptography and coding theory, including perfect hash families, frameproof codes and parent-identifying codes. The classical upper and lower bounds for the extremum size of SHFs as a function of the alphabet size do not match. In 2008, Blackburn et al. conjectured that the upper bound has the correct exponent.Before our work, the only nontrivial known cases of this conjecture was by Shangguan and Ge in 2016, when the type sum of the SHF goes no larger than 4.

In this talk, I will discuss our recent proof of all the cases of Blackburn’s conjecture when the upper bound exponent is equal to 2. We do this by transforming the problem into finding a large common solution-free set of a large collection of related linear equations. The new idea is to use an algorithm to create a link from each equation to a class of equations with some good quality in finite many steps, while the good quality can be passed backwards through the link.

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