In recent decades, machine learning has provided valuable models and algorithms for processing and extracting knowledge from time-series surveys. Different classifiers have been proposed and performed to an excellent standard. Nevertheless, few papers have tackled the data shift problem in labeled training sets, which occurs when there is a mismatch between the data distribution in the training set and the testing set. This drawback can damage the prediction performance in unseen data. Consequently, we propose a scalable and easily adaptable approach based on an informative regularization and an ad-hoc training procedure to mitigate the shift problem during the training of a multi-layer perceptron for RR Lyrae classification. We collect ranges for characteristic features to construct a symbolic representation of prior knowledge, which was used to model the informative regularizer component. Simultaneously, we design a two-step back-propagation algorithm to integrate this knowledge into the neural network, whereby one step is applied in each epoch to minimize classification error, while another is applied to ensure regularization. Our algorithm defines a subset of parameters (a mask) for each loss function. This approach handles the forgetting effect, which stems from a trade-off between these loss functions (learning from data versus learning expert knowledge) during training. Experiments were conducted using recently proposed shifted benchmark sets for RR Lyrae stars, outperforming baseline models by up to 3\% through a more reliable classifier. Our method provides a new path to incorporate knowledge from characteristic features into artificial neural networks to manage the underlying data shift problem.

We propose a novel architecture called MLP-SRGAN, which is a single-dimension Super Resolution Generative Adversarial Network (SRGAN) that utilizes Multi-Layer Perceptron Mixers (MLP-Mixers) along with convolutional layers to upsample in the slice direction. MLP-SRGAN is trained and validated using high resolution (HR) FLAIR MRI from the MSSEG2 challenge dataset. The method was applied to three multicentre FLAIR datasets (CAIN, ADNI, CCNA) of images with low spatial resolution in the slice dimension to examine performance on held-out (unseen) clinical data. Upsampled results are compared to several state-of-the-art SR networks. For images with high resolution (HR) ground truths, peak-signal-to-noise-ratio (PSNR) and structural similarity index (SSIM) are used to measure upsampling performance. Several new structural, no-reference image quality metrics were proposed to quantify sharpness (edge strength), noise (entropy), and blurriness (low frequency information) in the absence of ground truths. Results show MLP-SRGAN results in sharper edges, less blurring, preserves more texture and fine-anatomical detail, with fewer parameters, faster training/evaluation time, and smaller model size than existing methods. Code for MLP-SRGAN training and inference, data generators, models and no-reference image quality metrics will be available at https://github.com/IAMLAB-Ryerson/MLP-SRGAN.

Transformers flexibly operate over sets of real-valued vectors representing taskspecific entities and their attributes, where each vector might encode one wordpiece token and its position in a sequence, or some piece of information that carries no position at all. But as set processors, standard transformers are at a disadvantage in reasoning over more general graph-structured data where nodes represent entities and edges represent relations between entities. To address this shortcoming, we generalize transformer attention to consider and update edge vectors in each transformer layer. We evaluate this relational transformer on a diverse array of graph-structured tasks, including the large and challenging CLRS Algorithmic Reasoning Benchmark. There, it dramatically outperforms state-of-theart graph neural networks expressly designed to reason over graph-structured data. Our analysis demonstrates that these gains are attributable to relational attention's inherent ability to leverage the greater expressivity of graphs over sets. Graph-structured problems turn up in many domains, including knowledge bases (Hu et al., 2021; Bordes et al., 2013), communication networks (Leskovec et al., 2010), citation networks (McCallum et al., 2000), and molecules (Debnath et al., 1991; Zhang et al., 2020b). One example is predicting the bioactive properties of a molecule, where the atoms of the molecule are the nodes of the graph and the bonds are the edges. Along with their ubiquity, graph-structured problems vary widely in difficulty. For example, certain graph problems can be solved with a simple multi-layer perceptron, while others are quite challenging and require explicit modeling of relational characteristics. Graph Neural Networks (GNNs) are designed to process graphstructured data, including the graph's (possibly directed) edge Figure 1: The relational transformer structure and (in some cases) features associated with the edges. Standard transformers lack the relational inductive biases (Battaglia et al., 2018) that are explicitly built into the most commonly used GNNs. This allows entities carrying domain-specific attributes (like position) to be encoded as vectors for input to the same transformer architecture applied to different domains. Work was done during an internship at Microsoft Research. Figure 2: Categories of GNNs and Transformers, compared in terms of transformer machinery and edge vector incorporation.

Learning halfspaces from random labeled examples is a classical task in machine learning, with history going back to the Perceptron algorithm [Ros58]. In the realizable PAC model [Val84] (i.e., with consistent labels), the class of halfspaces is known to be efficiently learnable without distributional assumptions. On the other hand, in the agnostic (or adversarial label noise) model [Hau92, KSS94] even weak learning is computationally intractable in the distribution-free setting [Dan16, DKMR22, Tie22]. These intractability results have served as a motivation for the study of agnostic learning in the distribution-specific setting, i.e., when the marginal distribution on examples is assumed to be wellbehaved. In this context, a number of algorithmic results are known.

Figure 1: Overview of RL Prompt for discrete prompt optimization. All language models (LMs) are frozen. We build our policy network by training a task-specific multi-layer perceptron (MLP) network inserted into a frozen pre-trained LM. The figure above illustrates 1) generation of a prompt (left), 2) example usages in a masked LM for classification (top right) and a left-to-right LM for generation (bottom right), and 3) update of the MLP using RL reward signals (red arrows). TL;DR: Prompting enables large language models (LLMs) to perform various NLP tasks without changing the model.

The gradient information of multilayer perceptron with a linear neuron is modified with functional derivative for the global minimum search benchmarking problems. From this approach, we show that the landscape of the gradient derived from given continuous function using functional derivative can be the MLP-like form with ax+b neurons. In this extent, the suggested algorithm improves the availability of the optimization process to deal all the parameters in the problem set simultaneously. The functionality of this method could be improved through intentionally designed convex function with Kullack-Liebler divergence applied to cost value as well.

While preserving the privacy of federated learning (FL), differential privacy (DP) inevitably degrades the utility (i.e., accuracy) of FL due to model perturbations caused by DP noise added to model updates. Existing studies have considered exclusively noise with persistent root-mean-square amplitude and overlooked an opportunity of adjusting the amplitudes to alleviate the adverse effects of the noise. This paper presents a new DP perturbation mechanism with a time-varying noise amplitude to protect the privacy of FL and retain the capability of adjusting the learning performance. Specifically, we propose a geometric series form for the noise amplitude and reveal analytically the dependence of the series on the number of global aggregations and the $(\epsilon,\delta)$-DP requirement. We derive an online refinement of the series to prevent FL from premature convergence resulting from excessive perturbation noise. Another important aspect is an upper bound developed for the loss function of a multi-layer perceptron (MLP) trained by FL running the new DP mechanism. Accordingly, the optimal number of global aggregations is obtained, balancing the learning and privacy. Extensive experiments are conducted using MLP, supporting vector machine, and convolutional neural network models on four public datasets. The contribution of the new DP mechanism to the convergence and accuracy of privacy-preserving FL is corroborated, compared to the state-of-the-art Gaussian noise mechanism with a persistent noise amplitude.

While classical in many theoretical settings - and in particular in statistical physics-inspired works - the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we redeem this line of work in the case of generalized linear classification, a.k.a. the perceptron model, with random labels. We argue that there is a large universality class of high-dimensional input data for which we obtain the same minimum training loss as for Gaussian data with corresponding data covariance. In the limit of vanishing regularization, we further demonstrate that the training loss is independent of the data covariance. On the theoretical side, we prove this universality for an arbitrary mixture of homogeneous Gaussian clouds. Empirically, we show that the universality holds also for a broad range of real datasets.

We present a novel loss formulation for efficient learning of complex dynamics from governing physics, typically described by partial differential equations (PDEs), using physics-informed neural networks (PINNs). In our experiments, existing versions of PINNs are seen to learn poorly in many problems, especially for complex geometries, as it becomes increasingly difficult to establish appropriate sampling strategy at the near boundary region. Overly dense sampling can adversely impede training convergence if the local gradient behaviors are too complex to be adequately modelled by PINNs. On the other hand, if the samples are too sparse, existing PINNs tend to overfit the near boundary region, leading to incorrect solution. To prevent such issues, we propose a new Boundary Connectivity (BCXN) loss function which provides linear local structure approximation (LSA) to the gradient behaviors at the boundary for PINN. Our BCXN-loss implicitly imposes local structure during training, thus facilitating fast physics-informed learning across entire problem domains with order of magnitude sparser training samples. This LSA-PINN method shows a few orders of magnitude smaller errors than existing methods in terms of the standard L2-norm metric, while using dramatically fewer training samples and iterations. Our proposed LSA-PINN does not pose any requirement on the differentiable property of the networks, and we demonstrate its benefits and ease of implementation on both multi-layer perceptron and convolutional neural network versions as commonly used in current PINN literature.

We propose a novel framework for the regularised inversion of deep neural networks. The framework is based on the authors' recent work on training feed-forward neural networks without the differentiation of activation functions. The framework lifts the parameter space into a higher dimensional space by introducing auxiliary variables, and penalises these variables with tailored Bregman distances. We propose a family of variational regularisations based on these Bregman distances, present theoretical results and support their practical application with numerical examples. In particular, we present the first convergence result (to the best of our knowledge) for the regularised inversion of a single-layer perceptron that only assumes that the solution of the inverse problem is in the range of the regularisation operator, and that shows that the regularised inverse provably converges to the true inverse if measurement errors converge to zero.