Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on time-domain representations often limits their ability to capture long-term dependencies and periodic structures; second, the inherent mismatch between their continuous-time formulation and the discrete nature of real-world data can lead to loss of granularity and predictive accuracy. To address these limitations, we propose Fourier Ordinary Differential Equations (FODEs), an approach that embeds the dynamics in the Fourier domain. By transforming time-series data into the frequency domain using the Fast Fourier Transform (FFT), FODEs uncover global patterns and periodic behaviors that remain elusive in the time domain. Additionally, we introduce a learnable element-wise filtering mechanism that aligns continuous model outputs with discrete observations, preserving granularity and enhancing accuracy. Experiments on various time series datasets demonstrate that FODEs outperform existing methods in terms of both accuracy and efficiency. By effectively capturing both long- and short-term patterns, FODEs provide a robust framework for modeling time series dynamics.

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that predominantly affects the elderly population and currently has no cure. Magnetic Resonance Imaging (MRI), as a non-invasive imaging technique, is essential for the early diagnosis of AD. MRI inherently contains both spatial and frequency information, as raw signals are acquired in the frequency domain and reconstructed into spatial images via the Fourier transform. However, most existing AD diagnostic models extract features from a single domain, limiting their capacity to fully capture the complex neuroimaging characteristics of the disease. While some studies have combined spatial and frequency information, they are mostly confined to 2D MRI, leaving the potential of dual-domain analysis in 3D MRI unexplored. To overcome this limitation, we propose Spatio-Frequency Network (SFNet), the first end-to-end deep learning framework that simultaneously leverages spatial and frequency domain information to enhance 3D MRI-based AD diagnosis. SFNet integrates an enhanced dense convolutional network to extract local spatial features and a global frequency module to capture global frequency-domain representations. Additionally, a novel multi-scale attention module is proposed to further refine spatial feature extraction. Experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that SFNet outperforms existing baselines and reduces computational overhead in classifying cognitively normal (CN) and AD, achieving an accuracy of 95.1%.

Estimating brain effective connectivity (EC) from functional magnetic resonance imaging (fMRI) data can aid in comprehending the neural mechanisms underlying human behavior and cognition, providing a foundation for disease diagnosis. However, current spatiotemporal attention modules handle temporal and spatial attention separately, extracting temporal and spatial features either sequentially or in parallel. These approaches overlook the inherent spatiotemporal correlations present in real world fMRI data. Additionally, the presence of noise in fMRI data further limits the performance of existing methods. In this paper, we propose a novel brain effective connectivity estimation method based on Fourier spatiotemporal attention (FSTA-EC), which combines Fourier attention and spatiotemporal attention to simultaneously capture inter-series (spatial) dynamics and intra-series (temporal) dependencies from high-noise fMRI data. Specifically, Fourier attention is designed to convert the high-noise fMRI data to frequency domain, and map the denoised fMRI data back to physical domain, and spatiotemporal attention is crafted to simultaneously learn spatiotemporal dynamics. Furthermore, through a series of proofs, we demonstrate that incorporating learnable filter into fast Fourier transform and inverse fast Fourier transform processes is mathematically equivalent to performing cyclic convolution. The experimental results on simulated and real-resting-state fMRI datasets demonstrate that the proposed method exhibits superior performance when compared to state-of-the-art methods.

Abstract: This study offers a revolutionary strategy to developing wheelchairs based on the Brain-Computer Interface (BCI) that incorporates Artificial Intelligence (AI) using a The device uses electroencephalogram (EEG) data to mimic wheelchair navigation. Five different models were trained on a pre-filtered dataset that was divided into fixed-length windows using a sliding window technique. Each window contained statistical measurements, FFT coefficients for different frequency bands, and a label identifying the activity carried out during that window that was taken from an open-source Kaggle repository. The XGBoost model outperformed the other models, CatBoost, GRU, SVC, and XGBoost, with an accuracy of 60%. The CatBoost model with a major difference between training and testing accuracy shows overfitting, and similarly, the bestperforming model, with SVC, was implemented in a tkinter GUI. The wheelchair movement could be simulated in various directions, and a Raspberry Pi-powered wheelchair system for braincomputer interface is proposed here. Keywords: Brain Computer Interfacing, FFT (Fast Fourier Transform), Raspberry-pi, electroencephalogram 1. Introduction Brain-Computer Interfaces (BCIs) represent a cutting-edge technology that facilitates direct communication between the human brain and external devices. In recent years, BCIs have been widely explored for assisting individuals with mobility impairments. This paper focuses on a novel BCI-based wheelchair control system that leverages EEG signals associated with control using various movements related dataset. The system incorporates various machine learning models with various optimization techniques for hyper-parameter tuning and finally, shows an attention mechanism for enhancing the performance of Bi-directional Long Short-Term Memory (Bi-LSTM) networks, which are employed for EEG signal classification. To integrate the braincomputer interface (BCI) for the wheelchair, an analysis of brain activity is necessary-based on modern technology. The signs of brain activity can be obtained using a variety of techniques [1]. In order to help people with severe disabilities live their daily lives, new aids, gadgets, and assistive technologies are required, as demonstrated by the pandemic emergency of the coronavirus illness 2019 (COVID-19). Brain-Computer Interfaces (BCIs) that use electroencephalography (EEG) can help people who experience major health issues become more independent and participate in activities more easily. This can improve their general well-being and prevent deficits [2].

Time series prediction is a fundamental problem in scientific exploration and artificial intelligence (AI) technologies have substantially bolstered its efficiency and accuracy. A well-established paradigm in AI-driven time series prediction is injecting physical knowledge into neural networks through signal decomposition methods, and sustaining progress in numerous scenarios has been reported. However, we uncover non-negligible evidence that challenges the effectiveness of signal decomposition in AI-based time series prediction. We confirm that improper dataset processing with subtle future label leakage is unfortunately widely adopted, possibly yielding abnormally superior but misleading results. By processing data in a strictly causal way without any future information, the effectiveness of additional decomposed signals diminishes. Our work probably identifies an ingrained and universal error in time series modeling, and the de facto progress in relevant areas is expected to be revisited and calibrated to prevent future scientific detours and minimize practical losses.

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database dimensions, with a focus on computational efficiency and overcoming the curse of dimensionality. We introduce a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context. By demonstrating its utility across various AI domains, including Retrieval-Augmented Generation (RAG) models and image processing, this FFT-based approach promises to improve data retrieval processes and enhance the efficiency and scalability of AI solutions. The incorporation of FFT may not only optimize operations in real-time processing and recommendation systems but also extend to advanced image processing techniques, where dimensionality reduction can significantly improve performance and analysis efficiency. This paper advocates for the broader adoption of FFT in vector database management, marking a significant stride towards addressing the challenges of data volume and complexity in AI research and applications. Unlike many existing approaches, we directly handle the embedding vectors produced by the model after processing a test input.

Human Activity Recognition is a subject of great research today and has its applications in remote healthcare, activity tracking of the elderly or the disables, calories burnt tracking etc. In our project, we have created an Android application that recognizes the daily human activities and calculate the calories burnt in real time. We first captured labeled triaxial acceleration readings for different daily human activities from the smartphone's embedded accelerometer. These readings were preprocessed using a median filter. 42 features were extracted using various methods. We then tested various machine learning algorithms along with dimensionality reduction. Finally, in our Android application, we used the machine learning algorithm and a subset of features that provided maximum accuracy and minimum model building time. This is used for real-time activity recognition and calculation of calories burnt using a formula based on Metabolic Equivalent.

Over 1.5 billion people worldwide live with hearing impairment. Despite various technologies that have been created for individuals with such disabilities, most of these technologies are either extremely expensive or inaccessible for everyday use in low-medium income countries. In order to combat this issue, we have developed a new assistive device, EchoVest, for blind/deaf people to intuitively become more aware of their environment. EchoVest transmits vibrations to the user's body by utilizing transcutaneous electric nerve stimulation (TENS) based on the source of the sounds. EchoVest also provides various features, including sound localization, sound classification, noise reduction, and depth perception. We aimed to outperform CNN-based machine-learning models, the most commonly used machine learning model for classification tasks, in accuracy and computational costs. To do so, we developed and employed a novel audio pipeline that adapts the Audio Spectrogram Transformer (AST) model, an attention-based model, for our sound classification purposes, and Fast Fourier Transforms for noise reduction. The application of Otsu's Method helped us find the optimal thresholds for background noise sound filtering and gave us much greater accuracy. In order to calculate direction and depth accurately, we applied Complex Time Difference of Arrival algorithms and SOTA localization. Our last improvement was to use blind source separation to make our algorithms applicable to multiple microphone inputs. The final algorithm achieved state-of-the-art results on numerous checkpoints, including a 95.7\% accuracy on the ESC-50 dataset for environmental sound classification.

While Fourier Transform has seen many applications in data compression and signal processing, it's applications in Deep Neural Networks are limited. They are often only used for Medical Imaging based applications. Here, I discuss three approaches of scaling up Neural Networks for computer vision using Fast Fourier Transform (FFT). Note: python libraries were used for FFT as they provide extremely efficient cuda-based approaches for FFT on the GPU. The report only contains part of the code; the entire code-base is very large and includes the dataloaders, hyperparameter configurations, scripts to test fps, datasets, training and validation engines, and the model implementations themselves.