In recent decades, the main focus of computer modeling has been on supporting the design and development of engineering prototyes, but it is now ubiquitous in non-traditional areas such as medical rehabilitation. Conventional modeling approaches like the finite element~(FE) method are computationally costly when dealing with complex models, making them of limited use for purposes like real-time simulation or deployment on low-end hardware, if the model at hand cannot be simplified in a useful manner. Consequently, non-traditional approaches such as surrogate modeling using data-driven model order reduction are used to make complex high-fidelity models more widely available anyway. They often involve a dimensionality reduction step, in which the high-dimensional system state is transformed onto a low-dimensional subspace or manifold, and a regression approach to capture the reduced system behavior. While most publications focus on one dimensionality reduction, such as principal component analysis~(PCA) (linear) or autoencoder (nonlinear), we consider and compare PCA, kernel PCA, autoencoders, as well as variational autoencoders for the approximation of a structural dynamical system. In detail, we demonstrate the benefits of the surrogate modeling approach on a complex FE model of a human upper-arm. We consider both the models deformation and the internal stress as the two main quantities of interest in a FE context. By doing so we are able to create a computationally low cost surrogate model which captures the system behavior with high approximation quality and fast evaluations.

The Transformer architecture consists of self-attention and feed-forward networks (FFNs) which can be viewed as key-value memories according to previous works. However, FFN and traditional memory utilize different activation functions (i.e., ReLU and Softmax respectively), which makes them not equivalent. In this paper, we first rebuild the connections between FFN and key-value memory by conducting extensive studies on ReLU and Softmax, and find they are equivalent when adding an additional layer normalization module on Softmax. In addition, ReLU outperforms Softmax on both FFN and key-value memory when the number of value slots is large. We analyze the reasons and then explore this good property of ReLU on the self-attention network where the original Softmax activation performs poorly on long input sequences. We then propose a full ReLU architecture named ReLUFormer which performs better than the baseline Transformer on long sequence tasks such as document translation. This paper sheds light on the following points: 1) Softmax and ReLU use different normalization methods over elements which lead to different variances of results, and ReLU is good at dealing with a large number of key-value slots; 2) FFN and key-value memory are equivalent, and thus the Transformer can be viewed as a memory network where FFNs and self-attention networks are both key-value memories.

Abstract: Water is a necessary fluid to the human body and automatic checking of its quality and cleanness is an ongoing area of research. One such approach is to present the liquid to various types of signals and make the amount of signal attenuation an indication of the liquid category. In this article, we have utilized the Wi-Fi signal to distinguish clean water from poisoned water via training different machine learning algorithms. The Wi-Fi access points (WAPs) signal is acquired via equivalent smartphone-embedded Wi-Fi chipsets, and then Channel-State-Information CSI measures are extracted and converted into feature vectors to be used as input for machine learning classification algorithms. The measured amplitude and phase of the CSI data are selected as input features into four classifiers k-NN, SVM, LSTM, and Ensemble. The experimental results show that the model is adequate to differentiate poison water from clean water with a classification accuracy of 89% when LSTM is applied, while 92% classification accuracy is achieved when the AdaBoost-Ensemble classifier is applied.

Pretrained large language models (LLMs) are able to solve a wide variety of tasks through transfer learning. Various explainability methods have been developed to investigate their decision making process. TracIn (Pruthi et al., 2020) is one such gradient-based method which explains model inferences based on the influence of training examples. In this paper, we explore the use of TracIn to improve model performance in the parameter-efficient tuning (PET) setting. We develop conversational safety classifiers via the prompt-tuning PET method and show how the unique characteristics of the PET regime enable TracIn to identify the cause for certain misclassifications by LLMs. We develop a new methodology for using gradient-based explainability techniques to improve model performance, G-BAIR: gradient-based automated iterative recovery. We show that G-BAIR can recover LLM performance on benchmarks after manually corrupting training labels. This suggests that influence methods like TracIn can be used to automatically perform data cleaning, and introduces the potential for interactive debugging and relabeling for PET-based transfer learning methods.

Atrial Fibrillation is a common form of irregular heart rhythm that can be very dangerous. Our primary goal is to analyze Atrial Fibrillation data within ECGs to develop a model based only on RR-Intervals, or the length between heart-beats, to create a real time classification model for Atrial Fibrillation to be implemented in common heart-rate monitors on the market today. Physionet's MIT-BIH Atrial Fibrillation Database \cite{goldberger2000physiobank} and 2017 Challenge Database \cite{clifford2017af} were used to identify patterns of Atrial Fibrillation and test classification models on. These two datasets are very different. The MIT-BIH database contains long samples taken with a medical grade device, which is not useful for simulating a consumer device, but is useful for Atrial Fibrillation pattern detection. The 2017 Challenge database includes short ($<60sec$) samples taken with a portable device and reveals many of the challenges of Atrial Fibrillation classification in a real-time device. We developed multiple SVM models with three sets of extracted features as predictor variables which gave us moderately high accuracies with low computational intensity. With robust filtering techniques already applied in many Photoplethysmograph-based consumer heart-rate monitors, this method can be used to develop a reliable real time model for Atrial Fibrillation detection in consumer-grade heart-rate monitors.

Recent years have seen an exponential increase in the application of machine learning (ML) techniques to several fields, including physics and astrophysics (Nguyen et al., 2019; Zhou et al., 2021; Reiss et al., 2021; Rüdisser et al., 2022). ML-based tools provide predictions more accurate than other models due to their generalisation properties. Furthermore, the current availability of computational power makes feasible building complex and prediction-effective predictors. These are the main reasons behind the heavy application of ML algorithms, even though they usually require a huge amount of training data to be provided. This need of large training data sets may be challenging in some scenarios, but it does not constitute a limitation when ML predictors rely on observations gathered on beam experiments in high-energy physics and by long-lasting space missions, for instance. Predictive tools in general, and ML models in particular, are precious resources for space missions to achieve several goals, as time series missing data filling and pattern recognition (Villani et al., 2022).

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\mathbf{x},y)$ from an unknown distribution on $\mathbb{R}^n \times \{ \pm 1\}$, whose marginal distribution on $\mathbf{x}$ is the standard Gaussian and the labels $y$ can be arbitrary, the goal is to output a hypothesis with 0-1 loss $\mathrm{OPT}+\epsilon$, where $\mathrm{OPT}$ is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required temporal dependencies. However, most existing sequential models operate within finite-dimensional Euclidean spaces which offer limited functionality when employed in modelling physics relevant data. Alternatively recent work with neural operator learning within the Fourier space has shown efficient strategies for parameterising Partial Differential Equations (PDE). In this work, we propose a novel sequential model, built to handle Physics relevant data by way of amalgamating the conventional RNN architecture with that of the Fourier Neural Operators (FNO). The Fourier-RNN allows for learning the mappings from the input to the output as well as to the hidden state within the Fourier space associated with the temporal data. While the Fourier-RNN performs identical to the FNO when handling PDE data, it outperforms the FNO and the conventional RNN when deployed in modelling noisy, non-Markovian data.

This work considers the problem of finding a first-order stationary point of a non-convex function with potentially unbounded smoothness constant using a stochastic gradient oracle. We focus on the class of $(L_0,L_1)$-smooth functions proposed by Zhang et al. (ICLR'20). Empirical evidence suggests that these functions more closely captures practical machine learning problems as compared to the pervasive $L_0$-smoothness. This class is rich enough to include highly non-smooth functions, such as $\exp(L_1 x)$ which is $(0,\mathcal{O}(L_1))$-smooth. Despite the richness, an emerging line of works achieves the $\widetilde{\mathcal{O}}(\frac{1}{\sqrt{T}})$ rate of convergence when the noise of the stochastic gradients is deterministically and uniformly bounded. This noise restriction is not required in the $L_0$-smooth setting, and in many practical settings is either not satisfied, or results in weaker convergence rates with respect to the noise scaling of the convergence rate. We develop a technique that allows us to prove $\mathcal{O}(\frac{\mathrm{poly}\log(T)}{\sqrt{T}})$ convergence rates for $(L_0,L_1)$-smooth functions without assuming uniform bounds on the noise support. The key innovation behind our results is a carefully constructed stopping time $\tau$ which is simultaneously "large" on average, yet also allows us to treat the adaptive step sizes before $\tau$ as (roughly) independent of the gradients. For general $(L_0,L_1)$-smooth functions, our analysis requires the mild restriction that the multiplicative noise parameter $\sigma_1 < 1$. For a broad subclass of $(L_0,L_1)$-smooth functions, our convergence rate continues to hold when $\sigma_1 \geq 1$. By contrast, we prove that many algorithms analyzed by prior works on $(L_0,L_1)$-smooth optimization diverge with constant probability even for smooth and strongly-convex functions when $\sigma_1 > 1$.

Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a graph kernel approach, however this local average construction is known to be cursed by the high-dimension d. In this article, we build a different estimator of the Laplacian, via a reproducing kernel Hilbert space method, which adapts naturally to the regularity of the problem. We provide non-asymptotic statistical rates proving that the kernel estimator we build can circumvent the curse of dimensionality. Finally we discuss techniques (Nystr\"om subsampling, Fourier features) that enable to reduce the computational cost of the estimator while not degrading its overall performance.