This paper adds uncertainty modelling and an external memory to prototypical networks and achieves good performance gains as a result. The paper is above the bar for acceptance. There were a number of extra details, clarifications, and related work that was brought up in the reviews and rebuttal that should be incorporated into the final camera ready version. The authors should also compare to the DKM model and try to quantify the benefit of uncertainty modelling, as promised in the rebuttal.

This paper proposes a Curriculum-Transfer-Learning based physics-informed neural network (CTL-PINN) for long-term simulation of physical and mechanical behaviors. The main innovation of CTL-PINN lies in decomposing long-term problems into a sequence of short-term subproblems. Initially, the standard PINN is employed to solve the first sub-problem. As the simulation progresses, subsequent time-domain problems are addressed using a curriculum learning approach that integrates information from previous steps. Furthermore, transfer learning techniques are incorporated, allowing the model to effectively utilize prior training data and solve sequential time domain transfer problems. CTL-PINN combines the strengths of curriculum learning and transfer learning, overcoming the limitations of standard PINNs, such as local optimization issues, and addressing the inaccuracies over extended time domains encountered in CL-PINN and the low computational efficiency of TL-PINN. The efficacy and robustness of CTL-PINN are demonstrated through applications to nonlinear wave propagation, Kirchhoff plate dynamic response, and the hydrodynamic model of the Three Gorges Reservoir Area, showcasing its superior capability in addressing long-term computational challenges.

Consider the problem of improving the estimation of conditional average treatment effects (CATE) for a target domain of interest by leveraging related information from a source domain with a different feature space. This heterogeneous transfer learning problem for CATE estimation is ubiquitous in areas such as healthcare where we may wish to evaluate the effectiveness of a treatment for a new patient population for which different clinical covariates and limited data are available. In this paper, we address this problem by introducing several building blocks that use representation learning to handle the heterogeneous feature spaces and a flexible multi-task architecture with shared and private layers to transfer information between potential outcome functions across domains. Then, we show how these building blocks can be used to recover transfer learning equivalents of the standard CATE learners. On a new semi-synthetic data simulation benchmark for heterogeneous transfer learning, we not only demonstrate performance improvements of our heterogeneous transfer causal effect learners across datasets, but also provide insights into the differences between these learners from a transfer perspective.

We study a multitask learning problem in which each task is parametrized by a weight vector and indexed by a pair of indices, which can be e.g, (consumer, time). The weight vectors can be collected into a tensor and the (multilinear-)rank of the tensor controls the amount of sharing of information among tasks. Two types of convex relaxations have recently been proposed for the tensor multilinear rank. However, we argue that both of them are not optimal in the context of multitask learning in which the dimensions or multilinear rank are typically heterogeneous. We propose a new norm, which we call the scaled latent trace norm and analyze the excess risk of all the three norms. The results apply to various settings including matrix and tensor completion, multitask learning, and multilinear multitask learning. Both the theory and experiments support the advantage of the new norm when the tensor is not equal-sized and we do not a priori know which mode is low rank.

Transfer learning algorithms are used when one has sufficient training data for one supervised learning task (the source/training domain) but only very limited training data for a second task (the target/test domain) that is similar but not identical to the first. Previous work on transfer learning has focused on relatively restricted settings, where specific parts of the model are considered to be carried over between tasks. Recent work on covariate shift focuses on matching the marginal distributions on observations X across domains. Similarly, work on target/conditional shift focuses on matching marginal distributions on labels Y and adjusting conditional distributions P (X|Y), such that P (X) can be matched across domains. However, covariate shift assumes that the support of test P (X) is contained in the support of training P (X), i.e., the training set is richer than the test set. Target/conditional shift makes a similar assumption for P (Y).

The reviewers seem to agree that there is value in proposed work. After a discussion, based on the rebuttal, the consensus is that given that the authors integrate in the camera ready the details of the rebuttal (particularly the comments of R4) and *toning down* or being more precise in the claims being made, I think this work would be very interesting and useful to the community. Please do take into account this advice, as it will help the work to have maximal impact in the community and to not be misinterpreted or its claims to be abused.

Surrogate models are frequently employed as efficient substitutes for the costly execution of real-world processes. However, constructing a high-quality surrogate model often demands extensive data acquisition. A solution to this issue is to transfer pre-trained surrogate models for new tasks, provided that certain invariances exist between tasks. This study focuses on transferring non-differentiable surrogate models (e.g., random forest) from a source function to a target function, where we assume their domains are related by an unknown affine transformation, using only a limited amount of transfer data points evaluated on the target. Previous research attempts to tackle this challenge for differentiable models, e.g., Gaussian process regression, which minimizes the empirical loss on the transfer data by tuning the affine transformations. In this paper, we extend the previous work to the random forest model and assess its effectiveness on a widely-used artificial problem set - Black-Box Optimization Benchmark (BBOB) testbed, and on four real-world transfer learning problems. The results highlight the significant practical advantages of the proposed method, particularly in reducing both the data requirements and computational costs of training surrogate models for complex real-world scenarios.

Fingerprint recognition remains one of the most reliable biometric technologies due to its high accuracy and uniqueness. Traditional systems rely on contact-based scanners, which are prone to issues such as image degradation from surface contamination and inconsistent user interaction. To address these limitations, contactless fingerprint recognition has emerged as a promising alternative, providing non-intrusive and hygienic authentication. This study evaluates the impact of image enhancement tech-niques on the performance of pre-trained deep learning models using transfer learning for touchless fingerprint recognition. The IIT-Bombay Touchless and Touch-Based Fingerprint Database, containing data from 200 subjects, was employed to test the per-formance of deep learning architectures such as VGG-16, VGG-19, Inception-V3, and ResNet-50. Experimental results reveal that transfer learning methods with fingerprint image enhance-ment (indirect method) significantly outperform those without enhancement (direct method). Specifically, VGG-16 achieved an accuracy of 98% in training and 93% in testing when using the enhanced images, demonstrating superior performance compared to the direct method. This paper provides a detailed comparison of the effectiveness of image enhancement in improving the accuracy of transfer learning models for touchless fingerprint recognition, offering key insights for developing more efficient biometric systems.

In recent years, Graph Neural Network (GNN) based models have shown promising results in simulating physics of complex systems. However, training dedicated graph network based physics simulators can be costly, as most models are confined to fully supervised training, which requires extensive data generated from traditional physics simulators. To date, how transfer learning could improve the model performance and training efficiency has remained unexplored. In this work, we introduce a pre-training and transfer learning paradigm for graph network simulators. We propose the scalable graph U-net (SGUNET). Incorporating an innovative depth-first search (DFS) pooling, the SGUNET is adaptable to different mesh sizes and resolutions for various simulation tasks. To enable the transfer learning between differently configured SGUNETs, we propose a set of mapping functions to align the parameters between the pre-trained model and the target model. An extra normalization term is also added into the loss to constrain the difference between the pre-trained weights and target model weights for better generalization performance. To pre-train our physics simulator we created a dataset which includes 20,000 physical simulations of randomly selected 3D shapes from the open source A Big CAD (ABC) dataset. We show that our proposed transfer learning methods allow the model to perform even better when fine-tuned with small amounts of training data than when it is trained from scratch with full extensive dataset. On the 2D Deformable Plate benchmark dataset, our pre-trained model fine-tuned on 1/16 of the training data achieved an 11.05\% improvement in position RMSE compared to the model trained from scratch.

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.