PAC-Bayes learning is a comprehensive setting for (i) studying the generalisation ability of learning algorithms and (ii) deriving new learning algorithms by optimising a generalisation bound. However, optimising generalisation bounds might not always be viable for tractable or computational reasons, or both. For example, iteratively querying the empirical risk might prove computationally expensive. In response, we introduce a novel principled strategy for building an iterative learning algorithm via the optimisation of a sequence of surrogate training objectives, inherited from PAC-Bayes generalisation bounds. The key argument is to replace the empirical risk (seen as a function of hypotheses) in the generalisation bound by its projection onto a constructible low dimensional functional space: these projections can be queried much more efficiently than the initial risk. On top of providing that generic recipe for learning via surrogate PAC-Bayes bounds, we (i) contribute theoretical results establishing that iteratively optimising our surrogates implies the optimisation of the original generalisation bounds, (ii) instantiate this strategy to the framework of meta-learning, introducing a meta-objective offering a closed form expression for meta-gradient, (iii) illustrate our approach with numerical experiments inspired by an industrial biochemical problem.

Debugging is an essential skill when learning to program, yet its instruction and emphasis often vary widely across introductory courses. In the era of code-generating large language models (LLMs), the ability for students to reason about code and identify errors is increasingly important. However, students frequently resort to trial-and-error methods to resolve bugs without fully understanding the underlying issues. Developing the ability to identify and hypothesize the cause of bugs is crucial but can be time-consuming to teach effectively through traditional means. This paper introduces BugSpotter, an innovative tool that leverages an LLM to generate buggy code from a problem description and verify the synthesized bugs via a test suite. Students interact with BugSpotter by designing failing test cases, where the buggy code's output differs from the expected result as defined by the problem specification. This not only provides opportunities for students to enhance their debugging skills, but also to practice reading and understanding problem specifications. We deployed BugSpotter in a large classroom setting and compared the debugging exercises it generated to exercises hand-crafted by an instructor for the same problems. We found that the LLM-generated exercises produced by BugSpotter varied in difficulty and were well-matched to the problem specifications. Importantly, the LLM-generated exercises were comparable to those manually created by instructors with respect to student performance, suggesting that BugSpotter could be an effective and efficient aid for learning debugging.

This paper explores a new black-box, zero-shot language model inversion problem and proposes an innovative framework for prompt reconstruction using only text outputs from a language model. Leveraging a large language model alongside an optimization algorithm, the proposed method effectively recovers prompts with minimal resources. Experimental results on several datasets derived from public sources indicate that the proposed approach achieves high-quality prompt recovery and generates prompts more similar to the originals than current state-of-the-art methods. Additionally, the use-case study demonstrates the method's strong potential for generating high-quality text data.

Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described simply and intuitively, and it also helps to understand the essence of tensor products. In fact, most of matrix/tensor products including inner product, outer product, Hadamard product, Kronecker product, and Khatri-Rao product can be written in graphical notation. These matrix/tensor operations are essential building blocks for the use of matrix/tensor decompositions in signal processing and machine learning. The purpose of this lecture note is to learn the very basics of tensors and how to represent them in mathematical symbols and graphical notation. Many papers using tensors omit these detailed definitions and explanations, which can be difficult for the reader. I hope this note will be of help to such readers.

This tutorial investigates the convergence of statistical mechanics and learning theory, elucidating the potential enhancements in machine learning methodologies through the integration of foundational principles from physics. The tutorial delves into advanced techniques like entropy, free energy, and variational inference which are utilized in machine learning, illustrating their significant contributions to model efficiency and robustness. By bridging these scientific disciplines, we aspire to inspire newer methodologies in researches, demonstrating how an in-depth comprehension of physical systems' behavior can yield more effective and dependable machine learning models, particularly in contexts characterized by uncertainty.

Urban spatio-temporal (ST) forecasting is crucial for various urban applications such as intelligent scheduling and trip planning. Previous studies focus on modeling ST correlations among urban locations in offline settings, which often neglect the non-stationary nature of urban ST data, particularly, distribution shifts over time. This oversight can lead to degraded performance in real-world scenarios. In this paper, we first analyze the distribution shifts in urban ST data, and then introduce DOST, a novel online continual learning framework tailored for ST data characteristics. DOST employs an adaptive ST network equipped with a variable-independent adapter to address the unique distribution shifts at each urban location dynamically. Further, to accommodate the gradual nature of these shifts, we also develop an awake-hibernate learning strategy that intermittently fine-tunes the adapter during the online phase to reduce computational overhead. This strategy integrates a streaming memory update mechanism designed for urban ST sequential data, enabling effective network adaptation to new patterns while preventing catastrophic forgetting. Experimental results confirm DOST's superiority over state-of-the-art models on four real-world datasets, providing online forecasts within an average of 0.1 seconds and achieving a 12.89% reduction in forecast errors compared to baseline models.

Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for formal theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully proves 155 theorems previously unproved formally by humans across 23 diverse Lean repositories, many from advanced mathematics. It performs significantly better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem-proving performance.

Traditional drug discovery processes are both time-consuming and require extensive professional expertise. With the accumulation of drug-target interaction (DTI) data from experimental studies, leveraging modern machine-learning techniques to discern patterns between drugs and target proteins has become increasingly feasible. In this paper, we introduce the Multi-channel Interaction Network (MIN), a novel framework designed to predict DTIs through two primary components: a representation learning module and a multi-channel interaction module. The representation learning module features a C-Score Predictor-assisted screening mechanism, which selects critical residues to enhance prediction accuracy and reduce noise. The multi-channel interaction module incorporates a structure-agnostic channel, a structure-aware channel, and an extended-mixture channel, facilitating the identification of interaction patterns at various levels for optimal complementarity. Additionally, contrastive learning is utilized to harmonize the representations of diverse data types. Our experimental evaluations on public datasets demonstrate that MIN surpasses other strong DTI prediction methods. Furthermore, the case study reveals a high overlap between the residues selected by the C-Score Predictor and those in actual binding pockets, underscoring MIN's explainability capability. These findings affirm that MIN is not only a potent tool for DTI prediction but also offers fresh insights into the prediction of protein binding sites.

Federated Learning (FL) is a decentralized machine learning approach that has gained attention for its potential to enable collaborative model training across clients while protecting data privacy, making it an attractive solution for the chemical industry. This work aims to provide the chemical engineering community with an accessible introduction to the discipline. Supported by a hands-on tutorial and a comprehensive collection of examples, it explores the application of FL in tasks such as manufacturing optimization, multimodal data integration, and drug discovery while addressing the unique challenges of protecting proprietary information and managing distributed datasets. The tutorial was built using key frameworks such as $\texttt{Flower}$ and $\texttt{TensorFlow Federated}$ and was designed to provide chemical engineers with the right tools to adopt FL in their specific needs. We compare the performance of FL against centralized learning across three different datasets relevant to chemical engineering applications, demonstrating that FL will often maintain or improve classification performance, particularly for complex and heterogeneous data. We conclude with an outlook on the open challenges in federated learning to be tackled and current approaches designed to remediate and improve this framework.

Multimodal Learning Analytics (MMLA) leverages advanced sensing technologies and artificial intelligence to capture complex learning processes, but integrating diverse data sources into cohesive insights remains challenging. This study introduces a novel methodology for integrating latent class analysis (LCA) within MMLA to map monomodal behavioural indicators into parsimonious multimodal ones. Using a high-fidelity healthcare simulation context, we collected positional, audio, and physiological data, deriving 17 monomodal indicators. LCA identified four distinct latent classes: Collaborative Communication, Embodied Collaboration, Distant Interaction, and Solitary Engagement, each capturing unique monomodal patterns. Epistemic network analysis compared these multimodal indicators with the original monomodal indicators and found that the multimodal approach was more parsimonious while offering higher explanatory power regarding students' task and collaboration performances. The findings highlight the potential of LCA in simplifying the analysis of complex multimodal data while capturing nuanced, cross-modality behaviours, offering actionable insights for educators and enhancing the design of collaborative learning interventions. This study proposes a pathway for advancing MMLA, making it more parsimonious and manageable, and aligning with the principles of learner-centred education.