Time series analysis is crucial in various fields such as healthcare and finance. However, environmental variations and the inherent non-stationarity of time series data often lead to out-of-distribution (OOD) scenarios, consequently causing model performance degradation. Most existing OOD generalization methods primarily focus on images or text, leaving time series analysis relatively underexplored. In this paper, we propose COGS, a novel framework that incorporates causal representation learning into the OOD generalization of time series. By imposing structural priors, our method identifies latent variables and learns a causal graph to disentangle causal variables from non-causal ones. These causal variables are then used to learn domain-invariant representations for stable prediction. Moreover, to tackle the challenge of the absence of domain labels, we further introduce a prototype-based domain discovery algorithm that infers domain labels in an unsupervised manner. The entire framework is optimized in a two-phase iterative manner, resulting in robust OOD performance. Extensive experiments on multiple real-world time series datasets demonstrate that our method achieves competitive performance compared to baseline methods.

Functional Magnetic Resonance Imaging (fMRI) data is a widely used kind of four-dimensional biomedical data, which requires effective compression. However, fMRI compressing poses unique challenges due to its intricate temporal dynamics, low signal-to-noise ratio, and complicated underlying redundancies. This paper reports a novel compression paradigm specifically tailored for fMRI data based on Implicit Neural Representation (INR). The proposed approach focuses on removing the various redundancies among the time series by employing several methods, including (i) conducting spatial correlation modeling for intra-region dynamics, (ii) decomposing reusable neuronal activation patterns, and (iii) using proper initialization together with nonlinear fusion to describe the inter-region similarity. This scheme appropriately incorporates the unique features of fMRI data, and experimental results on publicly available datasets demonstrate the effectiveness of the proposed method, surpassing state-of-the-art algorithms in both conventional image quality evaluation metrics and fMRI downstream tasks. This work in this paper paves the way for sharing massive fMRI data at low bandwidth and high fidelity.

Scientific discovery serves as the cornerstone for advances in various fields, from the fundamental laws of physics to the intricate mechanisms of biology. However, two existing mainstream methods---symbolic regression and dimensional analysis, are significantly limited in this task: the former suffers from low computational efficiency due to the vast search space and often results in formulas without physical meaning; the latter provides a useful theoretical framework but also struggles in searching in a huge space because of lacking effective analysis for the latent variables. To address this issue, here we propose a framework for efficiently discovering underlying formulas in data, named FIND. We draw inspiration from Buckingham’s Pi theorem, imposing dimensional constraints on the input and output, thereby ensuring discovered expressions possess physical meaning. Additionally, we propose a theoretical scheme for identifying the latent structure as well as a coarse-to-fine framework, significantly reducing the search space of latent variables. This framework not only improves computational efficiency but also enhances model interpretability. From comprehensive experimental validation, FIND showcases its potential to uncover meaningful scientific insights across various domains, providing a robust tool for advancing our understanding of unknown systems.

Recent advancements in computer vision have seen Implicit Neural Representations (INR) becoming a dominant representation form for data due to their compactness and expressive power. To solve various vision tasks with INR data, vision networks can either be purely INR-based, but are thereby limited by simplistic operations and performance constraints, or include raster-based methods, which then tend to lose crucial structural information of the INR during the conversion process. To address these issues, we propose DVI, a novel Derivative-based Vision network for INR, capable of handling a variety of vision tasks across various data modalities, while achieving the best performance among the existing methods by incorporating state of the art raster-based methods into a INR based architecture. DVI excels by extracting semantic information from the high order derivative map of the INR, then seamlessly fusing it into a pre-existing raster-based vision network, enhancing its performance with deeper, task-relevant semantic insights. Extensive experiments on five vision tasks across three data modalities demonstrate DVI's superiority over existing methods. Additionally, our study encompasses comprehensive ablation studies to affirm the efficacy of each element of DVI, the influence of different derivative computation techniques and the impact of derivative orders. Reproducible codes are provided in the supplementary materials.

Causal discovery in time-series is a fundamental problem in the machine learning community, enabling causal reasoning and decision-making in complex scenarios. Recently, researchers successfully discover causality by combining neural networks with Granger causality, but their performances degrade largely when encountering high-dimensional data because of the highly redundant network design and huge causal graphs. Moreover, the missing entries in the observations further hamper the causal structural learning. To overcome these limitations, We propose CUTS+, which is built on the Granger-causality-based causal discovery method CUTS and raises the scalability by introducing a technique called Coarse-to-fine-discovery (C2FD) and leveraging a message-passing-based graph neural network (MPGNN). Compared to previous methods on simulated, quasi-real, and real datasets, we show that CUTS+ largely improves the causal discovery performance on high-dimensional data with different types of irregular sampling.

Solving partial differential equations (PDEs) has been a fundamental problem in computational science and of wide applications for both scientific and engineering research. Due to its universal approximation property, neural network is widely used to approximate the solutions of PDEs. However, existing works are incapable of solving high-order PDEs due to insufficient calculation accuracy of higher-order derivatives, and the final network is a black box without explicit explanation. To address these issues, we propose a deep learning framework to solve high-order PDEs, named SHoP. Specifically, we derive the high-order derivative rule for neural network, to get the derivatives quickly and accurately; moreover, we expand the network into a Taylor series, providing an explicit solution for the PDEs. We conduct experimental validations four high-order PDEs with different dimensions, showing that we can solve high-order PDEs efficiently and accurately. The source code can be found at https://github.com/HarryPotterXTX/SHoP.git.

Time-series causal discovery (TSCD) is a fundamental problem of machine learning. However, existing synthetic datasets cannot properly evaluate or predict the algorithms' performance on real data. This study introduces the CausalTime pipeline to generate time-series that highly resemble the real data and with ground truth causal graphs for quantitative performance evaluation. The pipeline starts from real observations in a specific scenario and produces a matching benchmark dataset. Firstly, we harness deep neural networks along with normalizing flow to accurately capture realistic dynamics. Secondly, we extract hypothesized causal graphs by performing importance analysis on the neural network or leveraging prior knowledge. Thirdly, we derive the ground truth causal graphs by splitting the causal model into causal term, residual term, and noise term. Lastly, using the fitted network and the derived causal graph, we generate corresponding versatile time-series proper for algorithm assessment. In the experiments, we validate the fidelity of the generated data through qualitative and quantitative experiments, followed by a benchmarking of existing TSCD algorithms using these generated datasets. CausalTime offers a feasible solution to evaluating TSCD algorithms in real applications and can be generalized to a wide range of fields. For easy use of the proposed approach, we also provide a user-friendly website, hosted on www.causaltime.cc.

Despite their remarkable performance, deep neural networks remain mostly "black boxes", suggesting inexplicability and hindering their wide applications in fields requiring making rational decisions. Here we introduce HOPE (High-order Polynomial Expansion), a method for expanding a network into a high-order Taylor polynomial on a reference input. Specifically, we derive the high-order derivative rule for composite functions and extend the rule to neural networks to obtain their high-order derivatives quickly and accurately. From these derivatives, we can then derive the Taylor polynomial of the neural network, which provides an explicit expression of the network's local interpretations. We combine the Taylor polynomials obtained under different reference inputs to obtain the global interpretation of the neural network. Numerical analysis confirms the high accuracy, low computational complexity, and good convergence of the proposed method. Moreover, we demonstrate HOPE's wide applications built on deep learning, including function discovery, fast inference, and feature selection. We compared HOPE with other XAI methods and demonstrated our advantages.

Massive collection and explosive growth of biomedical data, demands effective compression for efficient storage, transmission and sharing. Readily available visual data compression techniques have been studied extensively but tailored for natural images/videos, and thus show limited performance on biomedical data which are of different features and larger diversity. Emerging implicit neural representation (INR) is gaining momentum and demonstrates high promise for fitting diverse visual data in target-data-specific manner, but a general compression scheme covering diverse biomedical data is so far absent. To address this issue, we firstly derive a mathematical explanation for INR's spectrum concentration property and an analytical insight on the design of INR based compressor. Further, we propose a Spectrum Concentrated Implicit neural compression (SCI) which adaptively partitions the complex biomedical data into blocks matching INR's concentrated spectrum envelop, and design a funnel shaped neural network capable of representing each block with a small number of parameters. Based on this design, we conduct compression via optimization under given budget and allocate the available parameters with high representation accuracy. The experiments show SCI's superior performance to state-of-the-art methods including commercial compressors, data-driven ones, and INR based counterparts on diverse biomedical data. The source code can be found at https://github.com/RichealYoung/ImplicitNeuralCompression.git.