The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We propose a framework for bridging this gap, by using computational complexity theory to assess local and global perspectives of interpreting ML models. We begin by proposing proofs for two novel insights that are essential for our analysis: (1) a duality between local and global forms of explanations; and (2) the inherent uniqueness of certain global explanation forms. We then use these insights to evaluate the complexity of computing explanations, across three model types representing the extremes of the interpretability spectrum: (1) linear models; (2) decision trees; and (3) neural networks. Our findings offer insights into both the local and global interpretability of these models. For instance, under standard complexity assumptions such as P != NP, we prove that selecting global sufficient subsets in linear models is computationally harder than selecting local subsets. Interestingly, with neural networks and decision trees, the opposite is true: it is harder to carry out this task locally than globally. We believe that our findings demonstrate how examining explainability through a computational complexity lens can help us develop a more rigorous grasp of the inherent interpretability of ML models.

Time series classification (TSC) on multivariate time series is a critical problem. We propose a novel multi-view approach integrating frequency-domain and time-domain features to provide complementary contexts for TSC. Our method fuses continuous wavelet transform spectral features with temporal convolutional or multilayer perceptron features. We leverage the Mamba state space model for efficient and scalable sequence modeling. We also introduce a novel tango scanning scheme to better model sequence relationships. Experiments on 10 standard benchmark datasets demonstrate our approach achieves an average 6.45% accuracy improvement over state-of-the-art TSC models.

Realtime finite element modeling of bridges assists modern structural health monitoring systems by providing comprehensive insights into structural integrity. This capability is essential for ensuring the safe operation of bridges and preventing sudden catastrophic failures. However, FEM computational cost and the need for realtime analysis pose significant challenges. Additionally, the input data is a 7 dimensional vector, while the output is a 1017 dimensional vector, making accurate and efficient analysis particularly difficult. In this study, we propose a novel hybrid quantum classical Multilayer Perceptron pipeline leveraging Symmetric Positive Definite matrices and Riemannian manifolds for effective data representation. To maintain the integrity of the qubit structure, we utilize SPD matrices, ensuring data representation is well aligned with the quantum computational framework. Additionally, the method leverages polynomial feature expansion to capture nonlinear relationships within the data. The proposed pipeline combines classical fully connected neural network layers with quantum circuit layers to enhance model performance and efficiency. Our experiments focused on various configurations of such hybrid models to identify the optimal structure for accurate and efficient realtime analysis. The best performing model achieved a Mean Squared Error of 0.00031, significantly outperforming traditional methods.

Implicit neural representations have emerged as a powerful paradigm to represent signals such as images and sounds. This approach aims to utilize neural networks to parameterize the implicit function of the signal. However, when representing implicit functions, traditional neural networks such as ReLU-based multilayer perceptrons face challenges in accurately modeling high-frequency components of signals. Recent research has begun to explore the use of Fourier Neural Networks (FNNs) to overcome this limitation. In this paper, we propose Quantum Implicit Representation Network (QIREN), a novel quantum generalization of FNNs. Furthermore, through theoretical analysis, we demonstrate that QIREN possesses a quantum advantage over classical FNNs. Lastly, we conducted experiments in signal representation, image superresolution, and image generation tasks to show the superior performance of QIREN compared to state-of-the-art (SOTA) models. Our work not only incorporates quantum advantages into implicit neural representations but also uncovers a promising application direction for Quantum Neural Networks.

In the rapidly evolving field of artificial intelligence, transformer-based models have gained significant attention in the context of Sequential Recommender Systems (SRSs), demonstrating remarkable proficiency in capturing user-item interactions. However, such attention-based frameworks result in substantial computational overhead and extended inference time. To address this problem, this paper proposes a novel efficient sequential recommendation framework GLINT-RU that leverages dense selective Gated Recurrent Units (GRU) module to accelerate the inference speed, which is a pioneering work to further exploit the potential of efficient GRU modules in SRSs. The GRU module lies at the heart of GLINT-RU, playing a crucial role in substantially reducing both inference time and GPU memory usage. Through the integration of a dense selective gate, our framework adeptly captures both long-term and short-term item dependencies, enabling the adaptive generation of item scores. GLINT-RU further integrates a mixing block, enriching it with global user-item interaction information to bolster recommendation quality. Moreover, we design a gated Multi-layer Perceptron (MLP) for our framework where the information is deeply filtered. Extensive experiments on three datasets are conducted to highlight the effectiveness and efficiency of GLINT-RU. Our GLINT-RU achieves exceptional inference speed and prediction accuracy, outperforming existing baselines based on Recurrent Neural Network (RNN), Transformer, MLP and State Space Model (SSM). These results establish a new standard in sequential recommendation, highlighting the potential of GLINT-RU as a renewing approach in the realm of recommender systems.

Multi-layer perceptrons (MLP's) have been extensively utilized in discovering Deep Koopman operators for linearizing nonlinear dynamics. With the emergence of Kolmogorov-Arnold Networks (KANs) as a more efficient and accurate alternative to the MLP Neural Network, we propose a comparison of the performance of each network type in the context of learning Koopman operators with control. In this work, we propose a KANs-based deep Koopman framework with applications to an orbital Two-Body Problem (2BP) and the pendulum for data-driven discovery of linear system dynamics. KANs were found to be superior in nearly all aspects of training; learning 31 times faster, being 15 times more parameter efficiency, and predicting 1.25 times more accurately as compared to the MLP Deep Neural Networks (DNNs) in the case of the 2BP. Thus, KANs shows potential for being an efficient tool in the development of Deep Koopman Theory.

Neural networks readily learn a subset of the modular arithmetic tasks, while failing to generalize on the rest. This limitation remains unmoved by the choice of architecture and training strategies. On the other hand, an analytical solution for the weights of Multi-layer Perceptron (MLP) networks that generalize on the modular addition task is known in the literature. In this work, we (i) extend the class of analytical solutions to include modular multiplication as well as modular addition with many terms. Additionally, we show that real networks trained on these datasets learn similar solutions upon generalization (grokking).

The Univer sity of Texas at Arlington, 2015 Sup ervising Professor: Michael Manry There is always an ambiguity in deciding the number of learning factors that is really required for training a Multi - Layer Perceptron. This thesis solves this problem by introducing a new method of adaptively changing the number of learning factors computed based on the error change created per multiply. A new method is introduced for computing learning factors for weights grouped based on the curvature of the objective function. A method for linearly compressing large ill - conditioned Newton's Hessian matrices to smaller well - conditioned ones is shown. This thesis also shows that the proposed training algorithm adapts itself between two other algorithms in order to produce a better error decrease per multiply. The performanc e of the proposed algorithm is shown to be better than OWO - MOLF and Levenberg Marquardt for most of the data sets.

This work proposes an incremental learning (IL) framework for wearable sensor human activity recognition (HAR) that tackles two challenges simultaneously: catastrophic forgetting and non-uniform inputs. The scalable framework, iKAN, pioneers IL with Kolmogorov-Arnold Networks (KAN) to replace multi-layer perceptrons as the classifier that leverages the local plasticity and global stability of splines. To adapt KAN for HAR, iKAN uses task-specific feature branches and a feature redistribution layer. Unlike existing IL methods that primarily adjust the output dimension or the number of classifier nodes to adapt to new tasks, iKAN focuses on expanding the feature extraction branches to accommodate new inputs from different sensor modalities while maintaining consistent dimensions and the number of classifier outputs. Continual learning across six public HAR datasets demonstrated the iKAN framework's incremental learning performance, with a last performance of 84.9\% (weighted F1 score) and an average incremental performance of 81.34\%, which significantly outperforms the two existing incremental learning methods, such as EWC (51.42\%) and experience replay (59.92\%).

Recent progress in Graph Neural Networks (GNNs) has greatly enhanced the ability to model complex molecular structures for predicting properties. Nevertheless, molecular data encompasses more than just graph structures, including textual and visual information that GNNs do not handle well. To bridge this gap, we present an innovative framework that utilizes multimodal molecular data to extract insights from Large Language Models (LLMs). We introduce GALLON (Graph Learning from Large Language Model Distillation), a framework that synergizes the capabilities of LLMs and GNNs by distilling multimodal knowledge into a unified Multilayer Perceptron (MLP). This method integrates the rich textual and visual data of molecules with the structural analysis power of GNNs. Extensive experiments reveal that our distilled MLP model notably improves the accuracy and efficiency of molecular property predictions.