Domain-Aware Tensor Network Structure Search

Tensor networks (TNs) provide efficient representations of high-dimensional data, yet identification of the optimal TN structures, the so called tensor network structure search (TN-SS) problem, remains a challenge. Current state-of-the-art (SOTA) algorithms are computationally expensive as they require extensive function evaluations, which is prohibitive for real-world applications. In addition, existing methods ignore valuable domain information inherent in real-world tensor data and lack transparency in their identified TN structures. To this end, we propose a novel TN-SS framework, termed the tnLLM, which incorporates domain information about the data and harnesses the reasoning capabilities of large language models (LLMs) to directly predict suitable TN structures. The proposed framework involves a domain-aware prompting pipeline which instructs the LLM to infer suitable TN structures based on the real-world relationships between tensor modes. In this way, our approach is capable of not only iteratively optimizing the objective function, but also generating domain-aware explanations for the identified structures. Experimental results demonstrate that tnLLM achieves comparable TN-SS objective function values with much fewer function evaluations compared to SOTA algorithms. Furthermore, we demonstrate that the LLM-enabled domain information can be used to find good initializations in the search space for sampling-based SOTA methods to accelerate their convergence while preserving theoretical performance guarantees.

A Systematic Review of EEG-based Machine Intelligence Algorithms for Depression Diagnosis, and Monitoring

Depression disorder is a serious health condition that has affected the lives of millions of people around the world. Diagnosis of depression is a challenging practice that relies heavily on subjective studies and, in most cases, suffers from late findings. Electroencephalography (EEG) biomarkers have been suggested and investigated in recent years as a potential transformative objective practice. In this article, for the first time, a detailed systematic review of EEG-based depression diagnosis approaches is conducted using advanced machine learning techniques and statistical analyses. For this, 938 potentially relevant articles (since 1985) were initially detected and filtered into 139 relevant articles based on the review scheme 'preferred reporting items for systematic reviews and meta-analyses (PRISMA).' This article compares and discusses the selected articles and categorizes them according to the type of machine learning techniques and statistical analyses. Algorithms, preprocessing techniques, extracted features, and data acquisition systems are discussed and summarized. This review paper explains the existing challenges of the current algorithms and sheds light on the future direction of the field. This systematic review outlines the issues and challenges in machine intelligence for the diagnosis of EEG depression that can be addressed in future studies and possibly in future wearable technologies.

Relational Conformal Prediction for Correlated Time Series

We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our method, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known as a prior and can be applied on top of any pre-trained time series predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and archives state-of-the-art uncertainty quantification in relevant benchmarks.

Learning to Predict Global Atrial Fibrillation Dynamics from Sparse Measurements

Catheter ablation of Atrial Fibrillation (AF) consists of a one-size-fits-all treatment with limited success in persistent AF. This may be due to our inability to map the dynamics of AF with the limited resolution and coverage provided by sequential contact mapping catheters, preventing effective patient phenotyping for personalised, targeted ablation. Here we introduce FibMap, a graph recurrent neural network model that reconstructs global AF dynamics from sparse measurements. Trained and validated on 51 non-contact whole atria recordings, FibMap reconstructs whole atria dynamics from 10% surface coverage, achieving a 210% lower mean absolute error and an order of magnitude higher performance in tracking phase singularities compared to baseline methods. Clinical utility of FibMap is demonstrated on real-world contact mapping recordings, achieving reconstruction fidelity comparable to non-contact mapping. FibMap's state-spaces and patient-specific parameters offer insights for electrophenotyping AF. Integrating FibMap into clinical practice could enable personalised AF care and improve outcomes.

TensorLLM: Tensorising Multi-Head Attention for Enhanced Reasoning and Compression in LLMs

The reasoning abilities of Large Language Models (LLMs) can be improved by structurally denoising their weights, yet existing techniques primarily focus on denoising the feed-forward network (FFN) of the transformer block, and can not efficiently utilise the Multi-head Attention (MHA) block, which is the core of transformer architectures. To address this issue, we propose a novel intuitive framework that, at its very core, performs MHA compression through a multi-head tensorisation process and the Tucker decomposition. This enables both higher-dimensional structured denoising and compression of the MHA weights, by enforcing a shared higher-dimensional subspace across the weights of the multiple attention heads. We demonstrate that this approach consistently enhances the reasoning capabilities of LLMs across multiple benchmark datasets, and for both encoder-only and decoder-only architectures, while achieving compression rates of up to $\sim 250$ times in the MHA weights, all without requiring any additional data, training, or fine-tuning. Furthermore, we show that the proposed method can be seamlessly combined with existing FFN-only-based denoising techniques to achieve further improvements in LLM reasoning performance.

Online Graph Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation

Graph Signal Processing (GSP) provides a powerful framework for analysing complex, interconnected systems by modelling data as signals on graphs. Recent advances in GSP have enabled the learning of graph structures from observed signals, but these methods often struggle with time-varying systems and real-time applications. Adaptive filtering techniques, while effective for online learning, have seen limited application in graph topology estimation from a GSP perspective. To this end, we introduce AdaCGP, an online algorithm for adaptive estimation of the Graph Shift Operator (GSO) from multivariate time series. The GSO is estimated from an adaptive time-vertex autoregressive model through recursive update formulae designed to address sparsity, shift-invariance and bias. Through simulations, we show that AdaCGP performs consistently well across various graph topologies, and achieves improvements in excess of 82% for GSO estimation compared to baseline adaptive vector autoregressive models. In addition, our online variable splitting approach for enforcing sparsity enables near-perfect precision in identifying causal connections while maintaining low false positive rates upon optimisation of the forecast error. Finally, AdaCGP's ability to track changes in graph structure is demonstrated on recordings of ventricular fibrillation dynamics in response to an anti-arrhythmic drug. AdaCGP is shown to be able to identify the stability of critical conduction patterns that may be maintaining the arrhythmia in an intuitive way, together with its potential to support diagnosis and treatment strategies.

Towards LLM-guided Efficient and Interpretable Multi-linear Tensor Network Rank Selection

We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs, our approach offers enhanced interpretability of the rank choices and can effectively optimise the objective function. This framework enables users without specialised domain expertise to utilise tensor network decompositions and understand the underlying rationale within the rank selection process. Experimental results validate our method on financial higher-order datasets, demonstrating interpretable reasoning, strong generalisation to unseen test data, and its potential for self-enhancement over successive iterations. This work is placed at the intersection of large language models and higher-order data analysis.

RespDiff: An End-to-End Multi-scale RNN Diffusion Model for Respiratory Waveform Estimation from PPG Signals

Respiratory rate (RR) is a critical health indicator often monitored under inconvenient scenarios, limiting its practicality for continuous monitoring. Photoplethysmography (PPG) sensors, increasingly integrated into wearable devices, offer a chance to continuously estimate RR in a portable manner. In this paper, we propose RespDiff, an end-to-end multi-scale RNN diffusion model for respiratory waveform estimation from PPG signals. RespDiff does not require hand-crafted features or the exclusion of low-quality signal segments, making it suitable for real-world scenarios. The model employs multi-scale encoders, to extract features at different resolutions, and a bidirectional RNN to process PPG signals and extract respiratory waveform. Additionally, a spectral loss term is introduced to optimize the model further. Experiments conducted on the BIDMC dataset demonstrate that RespDiff outperforms notable previous works, achieving a mean absolute error (MAE) of 1.18 bpm for RR estimation while others range from 1.66 to 2.15 bpm, showing its potential for robust and accurate respiratory monitoring in real-world applications.

FinLlama: Financial Sentiment Classification for Algorithmic Trading Applications

There are multiple sources of financial news online which influence market movements and trader's decisions. This highlights the need for accurate sentiment analysis, in addition to having appropriate algorithmic trading techniques, to arrive at better informed trading decisions. Standard lexicon based sentiment approaches have demonstrated their power in aiding financial decisions. However, they are known to suffer from issues related to context sensitivity and word ordering. Large Language Models (LLMs) can also be used in this context, but they are not finance-specific and tend to require significant computational resources. To facilitate a finance specific LLM framework, we introduce a novel approach based on the Llama 2 7B foundational model, in order to benefit from its generative nature and comprehensive language manipulation. This is achieved by fine-tuning the Llama2 7B model on a small portion of supervised financial sentiment analysis data, so as to jointly handle the complexities of financial lexicon and context, and further equipping it with a neural network based decision mechanism. Such a generator-classifier scheme, referred to as FinLlama, is trained not only to classify the sentiment valence but also quantify its strength, thus offering traders a nuanced insight into financial news articles. Complementing this, the implementation of parameter-efficient fine-tuning through LoRA optimises trainable parameters, thus minimising computational and memory requirements, without sacrificing accuracy. Simulation results demonstrate the ability of the proposed FinLlama to provide a framework for enhanced portfolio management decisions and increased market returns. These results underpin the ability of FinLlama to construct high-return portfolios which exhibit enhanced resilience, even during volatile periods and unpredictable market events.

Tensor Star Decomposition

A novel tensor decomposition framework, termed Tensor Star (TS) decomposition, is proposed which represents a new type of tensor network decomposition based on tensor contractions. This is achieved by connecting the core tensors in a ring shape, whereby the core tensors act as skip connections between the factor tensors and allow for direct correlation characterisation between any two arbitrary dimensions. Uniquely, this makes it possible to decompose an order-$N$ tensor into $N$ order-$3$ factor tensors $\{\mathcal{G}_{k}\}_{k=1}^{N}$ and $N$ order-$4$ core tensors $\{\mathcal{C}_{k}\}_{k=1}^{N}$, which are arranged in a star shape. Unlike the class of Tensor Train (TT) decompositions, these factor tensors are not directly connected to one another. The so obtained core tensors also enable consecutive factor tensors to have different latent ranks. In this way, the TS decomposition alleviates the "curse of dimensionality" and controls the "curse of ranks", exhibiting a storage complexity which scales linearly with the number of dimensions and as the fourth power of the ranks.