Digital twins have been actively explored in many engineering applications, such as manufacturing and autonomous systems. However, model discrepancy is ubiquitous in most digital twin models and has significant impacts on the performance of using those models. In recent years, data-driven modeling techniques have been demonstrated promising in characterizing the model discrepancy in existing models, while the training data for the learning of model discrepancy is often obtained in an empirical way and an active approach of gathering informative data can potentially benefit the learning of model discrepancy. On the other hand, Bayesian experimental design (BED) provides a systematic approach to gathering the most informative data, but its performance is often negatively impacted by the model discrepancy. In this work, we build on sequential BED and propose an efficient approach to iteratively learn the model discrepancy based on the data from the BED. The performance of the proposed method is validated by a classical numerical example governed by a convection-diffusion equation, for which full BED is still feasible. The proposed method is then further studied in the same numerical example with a high-dimensional model discrepancy, which serves as a demonstration for the scenarios where full BED is not practical anymore. An ensemble-based approximation of information gain is further utilized to assess the data informativeness and to enhance learning model discrepancy. The results show that the proposed method is efficient and robust to the active learning of high-dimensional model discrepancy, using data suggested by the sequential BED. We also demonstrate that the proposed method is compatible with both classical numerical solvers and modern auto-differentiable solvers.

Sign up for the Slatest to get the most insightful analysis, criticism, and advice out there, delivered to your inbox daily. Decades ago, when I was a new teacher, my colleagues and I used to joke about the constant barrage of changes. "Public education is a moving target you can never hit," a mentor teacher once told me. Huge shifts are coming again. "I'm afraid I'm going to be put in prison for being trans," one of my students said to me after class last week.

The paper starts by introducing the background and showing the contributions. The authors then use the Zhang and Ando result showing that SSL reduces to an equivalent kernel-based supervised learning problem for the rest of the paper. In section 2 and appendix, they provide an error bound showing that minimising the spectral norm of the graph kernel matrix is a good way to improve generalisation. In section 3, they add a spectral norm regularization term to the Zhang and Ando formulation, and provide links between the error convergence and the Lovasz number of the data graph. Section 4 proposes a proximal solver, where the specificity is that it deals with the projection step approximately to handle the constraint of a cone-polytope intersection.

Weaknesses: Unfortunately, the paper has several major weaknesses: * In the online multitask expert setting (Section 3), the authors claim that their framework is more general than the related work [1,3,4,7], by allowing switches between hypotheses for each class. Yet, the number m of modes is known in advance. So, for each task i \in [s], we know that there are at most m best hypotheses. Thus, unless I missed something, we can simply replace the s tasks by m \times s ones (i.e. each task in [s] consists of m different subtasks), and just apply the results obtained by [1] for the shifting multitask problem with expert advice (Corollary 1 in [1]) in order to get a bound that is essentially similar to (3). Still, I am aware that there are some differences between [1] and the present paper.

The paper concerns a multi-task version of a well-known online learning problem of switching with long-term memory. It considers two two types of the hypothesis spaces: a finite space, and an RKHS space of functions. In both cases, the authors first provide a regret bound for an exponential-time algorithm based on a reduction to a single-task problem using the idea of „meta-experts". These algorithms are then followed by their efficient (polynomial-time) versions, which achieve the same bound up to a small overhead. The paper received a very mixed set of scores, ranging from „reject" to „to 15% of accepted papers". The main strength of the paper is a novel, efficient long-term memory algorithms for a multi-task version of the prediction with expert advice problem, as well as kernel linear classification (with hinge loss, but written in terms of 0/1 loss by only considering interpolants on an instance sequence). In particular, the second part seems a significant extension of the „switching with long-term memory" framework to an infinite hypothesis space (even leaving the multitask extension aside).

This work presents a custom approach to developing a domain specific knowledge assistant for sustainability reporting using the International Financial Reporting Standards (IFRS). In this domain, there is no publicly available question-answer dataset, which has impeded the development of a high-quality chatbot to support companies with IFRS reporting. The two key contributions of this project therefore are: (1) A high-quality synthetic question-answer (QA) dataset based on IFRS sustainability standards, created using a novel generation and evaluation pipeline leveraging Large Language Models (LLMs). This comprises 1,063 diverse QA pairs that address a wide spectrum of potential user queries in sustainability reporting. Various LLM-based techniques are employed to create the dataset, including chain-of-thought reasoning and few-shot prompting. A custom evaluation framework is developed to assess question and answer quality across multiple dimensions, including faithfulness, relevance, and domain specificity. The dataset averages a score range of 8.16 out of 10 on these metrics. (2) Two architectures for question-answering in the sustainability reporting domain - a RAG pipeline and a fully LLM-based pipeline. The architectures are developed by experimenting, fine-tuning, and training on the QA dataset. The final pipelines feature an LLM fine-tuned on domain specific data and an industry classification component to improve the handling of complex queries. The RAG architecture achieves an accuracy of 85.32% on single-industry and 72.15% on cross-industry multiple-choice questions, outperforming the baseline approach by 4.67 and 19.21 percentage points, respectively. The LLM-based pipeline achieves an accuracy of 93.45% on single-industry and 80.30% on cross-industry multiple-choice questions, an improvement of 12.80 and 27.36 percentage points over the baseline, respectively.

Recent Large Language Models (LLMs) have demonstrated satisfying general instruction following ability. However, small LLMs with about 7B parameters still struggle fine-grained format following (e.g., JSON format), which seriously hinder the advancements of their applications. Most existing methods focus on benchmarking general instruction following while overlook how to improve the specific format following ability for small LLMs. Besides, these methods often rely on evaluations based on advanced LLMs (e.g., GPT-4), which can introduce the intrinsic bias of LLMs and be costly due to the API calls. In this paper, we first curate a fully verifiable format following dataset VFF. In contrast to existing works often adopting external LLMs for instruction-following validations, every sample of VFF can be easily validated with a Python function. Further, we propose to leverage this verifiable feature to synthesize massive data for progressively training small LLMs, in order to improve their format following abilities. Experimental results highlight the prevalent limitations in the format following capabilities of 7B level open-source LLMs and demonstrate the effectiveness of our method in enhancing this essential ability.

Knowledge distillation (KD) is a popular method of transferring knowledge from a large "teacher" model to a small "student" model. KD can be divided into two categories: prediction matching and intermediate-layer matching. We explore an intriguing phenomenon: layer-selection strategy does not matter (much) in intermediate-layer matching. In this paper, we show that seemingly nonsensical matching strategies such as matching the teacher's layers in reverse still result in surprisingly good student performance. We provide an interpretation for this phenomenon by examining the angles between teacher layers viewed from the student's perspective.

We consider learning underlying laws of dynamical systems governed by ordinary differential equations (ODE). A key challenge is how to discover intrinsic dynamics across multiple environments while circumventing environment-specific mechanisms. Unlike prior work, we tackle more complex environments where changes extend beyond function coefficients to entirely different function forms. For example, we demonstrate the discovery of ideal pendulum's natural motion $\alpha^2 \sin{\theta_t}$ by observing pendulum dynamics in different environments, such as the damped environment $\alpha^2 \sin(\theta_t) - \rho \omega_t$ and powered environment $\alpha^2 \sin(\theta_t) + \rho \frac{\omega_t}{\left|\omega_t\right|}$. Here, we formulate this problem as an \emph{invariant function learning} task and propose a new method, known as \textbf{D}isentanglement of \textbf{I}nvariant \textbf{F}unctions (DIF), that is grounded in causal analysis. We propose a causal graph and design an encoder-decoder hypernetwork that explicitly disentangles invariant functions from environment-specific dynamics. The discovery of invariant functions is guaranteed by our information-based principle that enforces the independence between extracted invariant functions and environments. Quantitative comparisons with meta-learning and invariant learning baselines on three ODE systems demonstrate the effectiveness and efficiency of our method. Furthermore, symbolic regression explanation results highlight the ability of our framework to uncover intrinsic laws.

Large language models have been increasing in size due to their success in a wide range of applications. This calls for a pressing need to reduce memory usage to make them more accessible. Post-training quantization is a popular technique which uses fewer bits (e.g., 4--8 bits) to represent the model without retraining it. However, it remains a challenging task to perform quantization in an ultra-low-bit setup (e.g., 2 bits). In this paper, we propose InvarExplore, a unified framework that systematically explores different model invariance at the same time, allowing us to take advantage of the synergy between each type of invariance. Importantly, InvarExplore features a discrete search algorithm that enables us to explore permutation invariance, which is under-studied as it cannot be optimized with gradient-based methods. Results show that InvarExplore is compatible with existing state-of-the-art methods, achieving an add-on performance improvement over strong competing methods.