论文检索

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Jindou Jia, Zihan Yang, Meng Wang, Kexin Guo, Jianfei Yang, Xiang Yu, Lei Guo

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments benefiting from real-time feedback mechanisms. Inspired by the feedback philosophy, we present feedback neural networks, showing that a feedback loop can flexibly correct the learned latent dynamics of neural ordinary differential equations (neural ODEs), leading to a prominent generalization improvement. The feedback neural network is a novel two-DOF neural network, which possesses robust performance in unseen scenarios with no loss of accuracy performance on previous tasks. A linear feedback form is presented to correct the learned latent dynamics firstly, with a convergence guarantee. Then, domain randomization is utilized to learn a nonlinear neural feedback form. Finally, extensive tests including trajectory prediction of a real irregular object and model predictive control of a quadrotor with various uncertainties, are implemented, indicating significant improvements over state-of-the-art model-based and learning-based methods.

Deep Learning · Sequential Models, Time series

Arkaprava Majumdar, M Anand Krishna, P. K. Srijith

Sequence labeling problems arise in several real-world applications such as healthcare and robotics. In many such applications, sequence data are irregularly sampled and are of varying complexities. Recently, efforts have been made to develop neural ODE-based architectures to model the evolution of hidden states continuously in time, to address irregularly sampled sequence data. However, they assume a fixed architectural depth and limit their flexibility to adapt to data sets with varying complexities. We propose the neural wave equation, a novel deep learning method inspired by the wave equation, to address this through continuous modeling of depth. Neural Wave Equation models the evolution of hidden states continuously across time as well as depth by using a non-homogeneous wave equation parameterized by a neural network. Through d'Alembert's analytical solution of the wave equation, we also show that the neural wave equation provides denser connections across the hidden states, allowing for better modeling capability. We conduct experiments on several sequence labeling problems involving irregularly sampled sequence data and demonstrate the superior performance of the proposed neural wave equation model.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

BO HU, Tat-Jen Cham

To predict future trajectories of pedestrians, scene is as important as the history trajectory since i) scene reflects the position of possible goals of the pedestrian ii) trajectories are affected by the semantic information of the scene. It requires the model to capture scene information and learn the relation between scenes and trajectories. However, existing methods either apply Convolutional Neural Networks (CNNs) to summarize the scene to a feature vector, which raises the feature misalignment issue, or convert trajectory to heatmaps to align with the scene map, which ignores the interactions among different pedestrians. In this work, we introduce the trajectory-scene-cell feature to represent both trajectories and scenes in one feature space. By decoupling the trajectory in temporal domain and the scene in spatial domain, trajectory feature and scene feature are re-organized in different types of cell feature, which well aligns trajectory and scene, and allows the framework to model both human-human and human-scene interactions. Moreover, the Trajectory-Scene-Cell Network (TSC-Net) with new trajectory prediction manner is proposed, where both goal and intermediate positions of the trajectory are predict by cell classification and offset regression. Comparative experiments show that TSC-Net achieves the SOTA performance on several datasets with most of the metrics. Especially for the goal estimation, TSC-Net is demonstrated better on predicting goals for trajectories with irregular speed.

Deep Learning · Sequential Models, Time series

Filip Matzner, František Mráz

Echo State Networks (ESNs) are a class of recurrent neural networks in which only a small readout regression layer is trained, while the weights of the recurrent network, termed the reservoir, are randomly assigned and remain fixed. Our work introduces the Locally Connected ESN (LCESN), a novel ESN variant with a locally connected reservoir, forced memory, and a weight adaptation strategy. LCESN significantly reduces the asymptotic time and space complexities compared to the conventional ESN, enabling substantially larger networks. LCESN also improves the memory properties of ESNs without affecting network stability. We evaluate LCESN's performance on the NARMA10 benchmark task and compare it to state-of-the-art models on nine real-world datasets. Despite the simplicity of our model and its one-shot training approach, LCESN achieves competitive results, even surpassing several state-of-the-art models. LCESN introduces a fresh approach to real-world time series forecasting and demonstrates that large, well-tuned random recurrent networks can rival complex gradient-trained feedforward models. We provide our GPU-based implementation of LCESN as an open-source library.

Deep Learning · Sequential Models, Time series

Armand Foucault, Francois Malgouyres, Franck Mamalet

Binary and sparse ternary weights in neural networks enable faster computations and lighter representations, facilitating their use on edge devices with limited computational power. Meanwhile, vanilla RNNs are highly sensitive to changes in their recurrent weights, making the binarization and ternarization of these weights inherently challenging. To date, no method has successfully achieved binarizationor ternarization of vanilla RNN weights. We present a new approach leveraging the properties of Hadamard matrices to parameterize a subset of binary and sparse ternary orthogonal matrices. This method enables the training of orthogonal RNNs (ORNNs) with binary and sparse ternary recurrent weights, effectively creating a specific class of binary and sparse ternary vanilla RNNs. The resulting ORNNs, called HadamRNN and Block-HadamRNN, are evaluated on benchmarks such as the copy task, permuted and sequential MNIST tasks, and IMDB dataset. Despite binarization or sparse ternarization, these RNNs maintain performance levels comparable to state-of-the-art full-precision models, highlighting the effectiveness of our approach. Notably, our approach is the first solution with binary recurrent weights capable of tackling the copy task over 1000 timesteps.

Deep Learning · Sequential Models, Time series

Jiale Chen, Dingling Yao, Adeel Pervez, Dan Alistarh, Francesco Locatello

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.

Deep Learning · Sequential Models, Time series

Qinshuo Liu, Weiqin Zhao, Wei Huang, Yanwen Fang, Lequan Yu, Guodong Li

The depth of neural networks is a critical factor for their capability, with deeper models often demonstrating superior performance. Motivated by this, significant efforts have been made to enhance layer aggregation - reusing information from previous layers to better extract features at the current layer, to improve the representational power of deep neural networks. However, previous works have primarily addressed this problem from a discrete-state perspective which is not suitable as the number of network layers grows. This paper novelly treats the outputs from layers as states of a continuous process and considers leveraging the state space model (SSM) to design the aggregation of layers in very deep neural networks. Moreover, inspired by its advancements in modeling long sequences, the Selective State Space Models (S6) is employed to design a new module called Selective State Space Model Layer Aggregation (S6LA). This module aims to combine traditional CNN or transformer architectures within a sequential framework, enhancing the representational capabilities of state-of-the-art vision networks. Extensive experiments show that S6LA delivers substantial improvements in both image classification and detection tasks, highlighting the potential of integrating SSMs with contemporary deep learning techniques.

Deep Learning · Sequential Models, Time series

Woojin Cho, Minju Jo, Kookjin Lee, Noseong Park

As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding signal, facilitating the learning of continuous neural representations from discrete data points. Despite notable successes in learning diverse signal types, coordinate-based MLPs often face issues of overfitting and limited generalizability beyond the training region, resulting in subpar extrapolation performance. This study addresses scenarios where the underlying true signals exhibit periodic properties, either spatially or temporally. We propose a novel network architecture, which extracts periodic patterns from measurements and leverages this information to represent the signal, thereby enhancing generalization and improving extrapolation performance. We demonstrate the efficacy of the proposed method through comprehensive experiments, including the learning of the periodic solutions for differential equations, and time series imputation (interpolation) and forecasting (extrapolation) on real-world datasets.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Junxi Wu, Dongjian Hu, Yajie Bao, Shu-Tao Xia, Changliang Zou

Uncertainty quantification in time series prediction is challenging due to the temporal dependence and distribution shift on sequential data. Conformal prediction provides a pivotal and flexible instrument for assessing the uncertainty of machine learning models through prediction sets. Recently, a series of online conformal inference methods updated thresholds of prediction sets by performing online gradient descent on a sequence of quantile loss functions. A drawback of such methods is that they only use the information of revealed non-conformity scores via miscoverage indicators but ignore error quantification, namely the distance between the non-conformity score and the current threshold. To accurately leverage the dynamic of miscoverage error, we propose Error-quantified Conformal Inference (ECI) by smoothing the quantile loss function. ECI introduces a continuous and adaptive feedback scale with the miscoverage error, rather than simple binary feedback in existing methods. We establish a long-term coverage guarantee for ECI under arbitrary dependence and distribution shift. The extensive experimental results show that ECI can achieve valid miscoverage control and output tighter prediction sets than other baselines.

Qihe Huang, Zhengyang Zhou, Kuo Yang, Gengyu Lin, Zhongchao Yi, Yang Wang

Time series forecasting (TSF) plays a pivotal role in many real-world applications. Recently, the utilization of Large Language Models (LLM) in TSF has demonstrated exceptional predictive performance, surpassing most task-specific forecasting models. The success of LLM-based forecasting methods underscores the importance of causal dependence modeling and pre-trained knowledge transfer. However, challenges persist in directly applying LLM to TSF, i.e., the unacceptable parameter scales for resource-intensive model optimization, and the significant gap of feature space between structural numerical time series and natural language. To this end, we propose LeRet, a Language-empowered Retentive network for TSF. Technically, inspired by the causal extraction in LLM, we propose a causal dependence learner, enhanced by a patch-level pre-training task, to capture sequential causal evolution. To minimize the gap between numeric and language, we initialize a language description protocol for time series and design a TS-related language knowledge extractor to learn from language description, avoiding training with large-scale parameters. Finally, we dedicatedly achieve a Language-TS Modality Integrator for the fusion of two types data, and enable language-empowered sequence forecasting. Extensive evaluations demonstrate the effectiveness of our LeRet, especially reveal superiority on few-shot, and zero-shot forecasting tasks. Code is available at https://github.com/hqh0728/LeRet.

Mingrui Liu

The current analysis of federated optimization algorithms for training deep neural networks assumes that the data is non-sequential (e.g., images), which incurs a smooth loss objective. In contrast, edge devices generate lots of sequential data every day, where these sequences exhibit significant sequential correlation at different time stamps (e.g., text messages). In order to learn from such sequential data, people typically use a class of neural networks that is inherently nonsmooth, with a potentially unbounded smoothness parameter. Examples include recurrent neural networks, long-short-term memory networks, and transformers. It remains unclear how to design provably efficient algorithms for training these neural networks to learn from sequential data. My goal is to lay the algorithmic foundation of federated learning with sequential data, which contributes novel algorithms for learning from a range of real-world sequential data (e.g., natural language, electronic health record, transportation, time series, etc.) using state-of-the-art deep neural networks. In this talk, I will first motivate the problem by showing that the transformer, which is widely used for sequential data learning, has an unbounded smooth landscape. Then, I will introduce provably efficient federated deep learning algorithms in the presence of unbounded smoothness. In particular, I will introduce a few efficient algorithms for various settings of federated learning, including homogeneous data, heterogeneous data, and partial client participation. The main result is twofold. First, we show that the designed algorithms provably small computational and communication complexities. Second, we establish fundamental hardness results in the unbounded smoothness setting. Ultimately, I will discuss the future challenges of extending our research framework from small-scale neural networks to large language models.

Jingge Xiao, Leonie Basso, Wolfgang Nejdl, Niloy Ganguly, Sandipan Sikdar

Continuous-time models such as Neural ODEs and Neural Flows have shown promising results in analyzing irregularly sampled time series frequently encountered in electronic health records. Based on these models, time series are typically processed with a hybrid of an initial value problem (IVP) solver and a recurrent neural network within the variational autoencoder architecture. Sequentially solving IVPs makes such models computationally less efficient. In this paper, we propose to model time series purely with continuous processes whose state evolution can be approximated directly by IVPs. This eliminates the need for recurrent computation and enables multiple states to evolve in parallel. We further fuse the encoder and decoder with one IVP solver utilizing its invertibility, which leads to fewer parameters and faster convergence. Experiments on three real-world datasets show that the proposed method can systematically outperform its predecessors, achieve state-of-the-art results, and have significant advantages in terms of data efficiency.

Yucheng Wang, Yuecong Xu, Jianfei Yang, Min Wu, Xiaoli Li, Lihua Xie, Zhenghua Chen

Multivariate Time-Series (MTS) data is crucial in various application fields. With its sequential and multi-source (multiple sensors) properties, MTS data inherently exhibits Spatial-Temporal (ST) dependencies, involving temporal correlations between timestamps and spatial correlations between sensors in each timestamp. To effectively leverage this information, Graph Neural Network-based methods (GNNs) have been widely adopted. However, existing approaches separately capture spatial dependency and temporal dependency and fail to capture the correlations between Different sEnsors at Different Timestamps (DEDT). Overlooking such correlations hinders the comprehensive modelling of ST dependencies within MTS data, thus restricting existing GNNs from learning effective representations. To address this limitation, we propose a novel method called Fully-Connected Spatial-Temporal Graph Neural Network (FC-STGNN), including two key components namely FC graph construction and FC graph convolution. For graph construction, we design a decay graph to connect sensors across all timestamps based on their temporal distances, enabling us to fully model the ST dependencies by considering the correlations between DEDT. Further, we devise FC graph convolution with a moving-pooling GNN layer to effectively capture the ST dependencies for learning effective representations. Extensive experiments show the effectiveness of FC-STGNN on multiple MTS datasets compared to SOTA methods. The code is available at https://github.com/Frank-Wang-oss/FCSTGNN.

Jihyeon Seong, Jungmin Kim, Jaesik Choi

In Time Series Classification (TSC), temporal pooling methods that consider sequential information have been proposed. However, we found that each temporal pooling has a distinct mechanism, and can perform better or worse depending on time series data. We term this fixed pooling mechanism a single perspective of temporal poolings. In this paper, we propose a novel temporal pooling method with diverse perspective learning: Selection over Multiple Temporal Poolings (SoM-TP). SoM-TP dynamically selects the optimal temporal pooling among multiple methods for each data by attention. The dynamic pooling selection is motivated by the ensemble concept of Multiple Choice Learning (MCL), which selects the best among multiple outputs. The pooling selection by SoM-TP's attention enables a non-iterative pooling ensemble within a single classifier. Additionally, we define a perspective loss and Diverse Perspective Learning Network (DPLN). The loss works as a regularizer to reflect all the pooling perspectives from DPLN. Our perspective analysis using Layer-wise Relevance Propagation (LRP) reveals the limitation of a single perspective and ultimately demonstrates diverse perspective learning of SoM-TP. We also show that SoM-TP outperforms CNN models based on other temporal poolings and state-of-the-art models in TSC with extensive UCR/UEA repositories.

Time Series

Yuxin Jia, Youfang Lin, Jing Yu, Shuo Wang, Tianhao Liu, Huaiyu Wan

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to $\mathcal{O}(1)$, effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of $\mathcal{O}(\sqrt{L})$, ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: https://github.com/Water2sea/TPGN.

Neuroscience, Cognitive Science

Changze Lv, Dongqi Han, Yansen Wang, Xiaoqing Zheng, Xuanjing Huang, Dongsheng Li

Spiking neural networks (SNNs) represent a promising approach to developing artificial neural networks that are both energy-efficient and biologically plausible.However, applying SNNs to sequential tasks, such as text classification and time-series forecasting, has been hindered by the challenge of creating an effective and hardware-friendly spike-form positional encoding (PE) strategy.Drawing inspiration from the central pattern generators (CPGs) in the human brain, which produce rhythmic patterned outputs without requiring rhythmic inputs, we propose a novel PE technique for SNNs, termed CPG-PE.We demonstrate that the commonly used sinusoidal PE is mathematically a specific solution to the membrane potential dynamics of a particular CPG.Moreover, extensive experiments across various domains, including time-series forecasting, natural language processing, and image classification, show that SNNs with CPG-PE outperform their conventional counterparts.Additionally, we perform analysis experiments to elucidate the mechanism through which SNNs encode positional information and to explore the function of CPGs in the human brain.This investigation may offer valuable insights into the fundamental principles of neural computation.

Deep Learning · Sequential Models, Time series

Antonio Orvieto, Soham De, Caglar Gulcehre, Razvan Pascanu, Samuel Smith

Deep neural networks based on linear RNNs interleaved with position-wise MLPs are gaining traction as competitive approaches for sequence modeling. Examples of such architectures include state-space models (SSMs) like S4, LRU, and Mamba: recently proposed models that achieve promising performance on text, genetics, and other data that require long-range reasoning. Despite experimental evidence highlighting these architectures' effectiveness and computational efficiency, their expressive power remains relatively unexplored, especially in connection to specific choices crucial in practice - e.g., carefully designed initialization distribution and potential use of complex numbers. In this paper, we show that combining MLPs with both real or complex linear diagonal recurrences leads to arbitrarily precise approximation of regular causal sequence-to-sequence maps. At the heart of our proof, we rely on a separation of concerns: the linear RNN provides a lossless encoding of the input sequence, and the MLP performs non-linear processing on this encoding. While we show that real diagonal linear recurrences are enough to achieve universality in this architecture, we prove that employing complex eigenvalues near unit disk - i.e., empirically the most successful strategy in S4 - greatly helps the RNN in storing information. We connect this finding with the vanishing gradient issue and provide experiments supporting our claims.

Deep Learning · Sequential Models, Time series

Sangjun Park, JinYeong Bak

Making neural networks remember over the long term has been a longstanding issue. Although several external memory techniques have been introduced, most focus on retaining recent information in the short term. Regardless of its importance, information tends to be fatefully forgotten over time. We present Memoria, a memory system for artificial neural networks, drawing inspiration from humans and applying various neuroscientific and psychological theories. The experimental results prove the effectiveness of Memoria in the diverse tasks of sorting, language modeling, and classification, surpassing conventional techniques. Engram analysis reveals that Memoria exhibits the primacy, recency, and temporal contiguity effects which are characteristics of human memory.

Deep Learning · Sequential Models, Time series

Saya Higuchi, Sebastian Kairat, Sander Bohte, Sebastian Otte

The resonate-and-fire (RF) neuron, introduced over two decades ago, is a simple, efficient, yet biologically plausible spiking neuron model, which can extract frequency patterns within the time domain due to its resonating membrane dynamics. However, previous RF formulations suffer from intrinsic shortcomings that limit effective learning and prevent exploiting the principled advantage of RF neurons. Here, we introduce the balanced RF (BRF) neuron, which alleviates some of the intrinsic limitations of vanilla RF neurons and demonstrates its effectiveness within recurrent spiking neural networks (RSNNs) on various sequence learning tasks. We show that networks of BRF neurons achieve overall higher task performance, produce only a fraction of the spikes, and require significantly fewer parameters as compared to modern RSNNs. Moreover, BRF-RSNN consistently provide much faster and more stable training convergence, even when bridging many hundreds of time steps during backpropagation through time (BPTT). These results underscore that our BRF-RSNN is a strong candidate for future large-scale RSNN architectures, further lines of research in SNN methodology, and more efficient hardware implementations.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Xiuheng Wang, Ricardo Borsoi, Cédric Richard

Non-parametric detection of change points in streaming time series data that belong to Euclidean spaces has been extensively studied in the literature. Nevertheless, when the data belongs to a Riemannian manifold, existing approaches are no longer applicable as they fail to account for the structure and geometry of the manifold. In this paper, we introduce a non-parametric algorithm for online change point detection in manifold-valued data streams. This algorithm monitors the generalized Karcher mean of the data, computed using stochastic Riemannian optimization. We provide theoretical bounds on the detection and false alarm rate performances of the algorithm, using a new result on the non-asymptotic convergence of the stochastic Riemannian gradient descent. We apply our algorithm to two different Riemannian manifolds. Experimental results with both synthetic and real data illustrate the performance of the proposed method.