Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov-Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov-Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Despite the remarkable success achieved by neural networks, particularly those represented by MLP and Transformer, we reveal that they exhibit potential flaws in the modeling and reasoning of periodicity, i.e., they tend to memorize the periodic data rather than genuinely understanding the underlying principles of periodicity. However, periodicity is a crucial trait in various forms of reasoning and generalization, underpinning predictability across natural and engineered systems through recurring patterns in observations. In this paper, we propose FAN, a novel network architecture based on Fourier Analysis, which empowers the ability to efficiently model and reason about periodic phenomena. By introducing Fourier Series, the periodicity is naturally integrated into the structure and computational processes of the neural network, thus achieving a more accurate expression and prediction of periodic patterns. As a promising substitute to multi-layer perceptron (MLP), FAN can seamlessly replace MLP in various models with fewer parameters and FLOPs. Through extensive experiments, we demonstrate the effectiveness of FAN in modeling and reasoning about periodic functions, and the superiority and generalizability of FAN across a range of real-world tasks, including symbolic formula representation, time series forecasting, and language modeling.

Given the computational cost and technical expertise required to train machine learning models, users may delegate the task of learning to a service provider. We show how a malicious learner can plant an undetectable backdoor into a classifier. On the surface, such a backdoored classifier behaves normally, but in reality, the learner maintains a mechanism for changing the classification of any input, with only a slight perturbation. Importantly, without the appropriate "backdoor key", the mechanism is hidden and cannot be detected by any computationally-bounded observer. We demonstrate two frameworks for planting undetectable backdoors, with incomparable guarantees. First, we show how to plant a backdoor in any model, using digital signature schemes. The construction guarantees that given black-box access to the original model and the backdoored version, it is computationally infeasible to find even a single input where they differ. This property implies that the backdoored model has generalization error comparable with the original model. Second, we demonstrate how to insert undetectable backdoors in models trained using the Random Fourier Features (RFF) learning paradigm or in Random ReLU networks. In this construction, undetectability holds against powerful white-box distinguishers: given a complete description of the network and the training data, no efficient distinguisher can guess whether the model is "clean" or contains a backdoor. Our construction of undetectable backdoors also sheds light on the related issue of robustness to adversarial examples. In particular, our construction can produce a classifier that is indistinguishable from an "adversarially robust" classifier, but where every input has an adversarial example! In summary, the existence of undetectable backdoors represent a significant theoretical roadblock to certifying adversarial robustness.

Contemporary machine learning models, such as language models, are powerful, but come with immense resource requirements both at training and inference time. It has been shown that decoder-only language models can be trained to a competitive state with ternary weights (1.58 bits per weight), facilitating efficient inference. Here, we start our exploration with non-transformer model architectures, investigating 1.58-bit training for multi-layer perceptrons and graph neural networks. Then, we explore 1.58-bit training in other transformer-based language models, namely encoder-only and encoder-decoder models. Our results show that in all of these settings, 1.58-bit training is on par with or sometimes even better than the standard 32/16-bit models.

For the last decade, the Perceptron [1] has served as the defacto building block of deep neural networks that utilize a fully connected layer in their architecture. Recent breakthroughs in large language models are due partly to large stacks of Transformer [2] units, which also utilize Perceptrons as part of their internal machinery. The popularity of Perceptron based architectures can be attributed mainly to two things: flexibility for learning non-linear functions [3], and an inherent ability to parallelize on modern GPU architecture [4]. While Perceptron-free architectures have been shown to display impressive performance [5], the fully-connected Perceptron layer remains a staple in high performing models. Recently, a viable alternative to the Perceptron unit for fully connected layers has been proposed - the Kolmogorov-Arnold unit [6].

Coordinate-based Multi-Layer Perceptrons (MLPs) are known to have difficulty reconstructing high frequencies of the training data. A common solution to this problem is Positional Encoding (PE), which has become quite popular. However, PE has drawbacks. It has high-frequency artifacts and adds another hyper-hyperparameter, just like batch normalization and dropout do. We believe that under certain circumstances PE is not necessary, and a smarter construction of the network architecture together with a smart training method is sufficient to achieve similar results. In this paper, we show that very simple MLPs can quite easily output a frequency when given input of the half-frequency and quarter-frequency. Using this, we design a network architecture in blocks, where the input to each block is the output of the two previous blocks along with the original input. We call this a {\it Fibonacci Network}. By training each block on the corresponding frequencies of the signal, we show that Fibonacci Networks can reconstruct arbitrarily high frequencies.

Brain tumor detection and classification are critical tasks in medical image analysis, particularly in early-stage diagnosis, where accurate and timely detection can significantly improve treatment outcomes. In this study, we apply various statistical and machine learning models to detect and classify brain tumors using brain MRI images. We explore a variety of statistical models including linear, logistic, and Bayesian regressions, and the machine learning models including decision tree, random forest, single-layer perceptron, multi-layer perceptron, convolutional neural network (CNN), recurrent neural network, and long short-term memory. Our findings show that CNN outperforms other models, achieving the best performance. Additionally, we confirm that the CNN model can also work for multi-class classification, distinguishing between four categories of brain MRI images such as normal, glioma, meningioma, and pituitary tumor images. This study demonstrates that machine learning approaches are suitable for brain tumor detection and classification, facilitating real-world medical applications in assisting radiologists with early and accurate diagnosis.

Common challenges in fault diagnosis include the lack of labeled data and the need to build models for each domain, resulting in many models that require supervision. Transfer learning can help tackle these challenges by learning cross-domain knowledge. Many approaches still require at least some labeled data in the target domain, and often provide unexplainable results. To this end, we propose a supervised transfer learning framework for fault diagnosis in wind turbines that operates in an Anomaly-Space. This space was created using SCADA data and vibration data and was built and provided to us by our research partner. Data within the Anomaly-Space can be interpreted as anomaly scores for each component in the wind turbine, making each value intuitive to understand. We conducted cross-domain evaluation on the train set using popular supervised classifiers like Random Forest, Light-Gradient-Boosting-Machines and Multilayer Perceptron as metamodels for the diagnosis of bearing and sensor faults. The Multilayer Perceptron achieved the highest classification performance. This model was then used for a final evaluation in our test set. The results show, that the proposed framework is able to detect cross-domain faults in the test set with a high degree of accuracy by using one single classifier, which is a significant asset to the diagnostic team.

Graph Convolutional Network (GCN) are widely used in Graph Anomaly Detection (GAD) due to their natural compatibility with graph structures, resulting in significant performance improvements. However, most researchers approach GAD as a graph node classification task and often rely on low-pass filters or feature aggregation from neighboring nodes. This paper proposes a novel approach by introducing a High-Pass Graph Convolution Network (HP-GCN) for GAD. The proposed HP-GCN leverages high-frequency components to detect anomalies, as anomalies tend to increase high-frequency signals within the network of normal nodes. Additionally, isolated nodes, which lack interactions with other nodes, present a challenge for Graph Neural Network (GNN). To address this, the model segments the graph into isolated nodes and nodes within connected subgraphs. Isolated nodes learn their features through Multi-Layer Perceptron (MLP), enhancing detection accuracy. The model is evaluated and validated on YelpChi, Amazon, T-Finance, and T-Social datasets. The results showed that the proposed HP-GCN can achieve anomaly detection accuracy of 96.10%, 98.16%, 96.46%, and 98.94%, respectively. The findings demonstrate that the HP-GCN outperforms existing GAD methods based on spatial domain GNN as well as those using low-pass and band-pass filters in spectral domain GCN. The findings underscore the effectiveness of this method in improving anomaly detection performance. Source code can be found at: https://github.com/meteor0033/High-pass_GAD.git.

Privacy-preserving machine learning (PPML) solutions are gaining widespread popularity. Among these, many rely on homomorphic encryption (HE) that offers confidentiality of the model and the data, but at the cost of large latency and memory requirements. Pruning neural network (NN) parameters improves latency and memory in plaintext ML but has little impact if directly applied to HE-based PPML. We introduce a framework called HE-PEx that comprises new pruning methods, on top of a packing technique called tile tensors, for reducing the latency and memory of PPML inference. HE-PEx uses permutations to prune additional ciphertexts, and expansion to recover inference loss. We demonstrate the effectiveness of our methods for pruning fully-connected and convolutional layers in NNs on PPML tasks, namely, image compression, denoising, and classification, with autoencoders, multilayer perceptrons (MLPs) and convolutional neural networks (CNNs). We implement and deploy our networks atop a framework called HElayers, which shows a 10-35% improvement in inference speed and a 17-35% decrease in memory requirement over the unpruned network, corresponding to 33-65% fewer ciphertexts, within a 2.5% degradation in inference accuracy over the unpruned network. Compared to the state-of-the-art pruning technique for PPML, our techniques generate networks with 70% fewer ciphertexts, on average, for the same degradation limit.