ICLR 2024 Papers

International Conference on Learning Representations

Decision breakdown

2,260papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    863.8%
  • Spotlight
    36716.2%
  • Poster
    1,80780.0%

Browse all papers

Alleviating Exposure Bias in Diffusion Models through Sampling with Shifted Time Steps

Mingxiao Li, Tingyu Qu, Ruicong Yao, Wei Sun, Marie-Francine Moens

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Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could exaggerate the problem of exposure bias due to the training and inference discrepancy. Previous work has attempted to mitigate this issue by perturbing inputs during training, which consequently mandates the retraining of the DPM. In this work, we conduct a systematic study of exposure bias in DPM and, intriguingly, we find that the exposure bias could be alleviated with a novel sampling method that we propose, without retraining the model. We empirically and theoretically show that, during inference, for each backward time step t and corresponding state ˆxt, there might exist another time step $t_s$ which exhibits superior coupling with $\hat{x}_t$. Based on this finding, we introduce a sampling method named Time-Shift Sampler. Our framework can be seamlessly integrated to existing sampling algorithms, such as DDPM, DDIM and other high-order solvers, inducing merely minimal additional computations. Experimental results show our method brings significant and consistent improvements in FID scores on different datasets and sampling methods. For example, integrating Time-Shift Sampler to F-PNDM yields a FID=3.88, achieving 44.49% improvements as compared to F-PNDM, on CIFAR-10 with 10 sampling steps, which is more performant than the vanilla DDIM with 100 sampling steps. Our code is available at https://github.com/Mingxiao-Li/TS-DPM.

Poster
Active Test-Time Adaptation: Theoretical Analyses and An Algorithm

Shurui Gui, Xiner Li, Shuiwang Ji

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Test-time adaptation (TTA) addresses distribution shifts for streaming test data in unsupervised settings. Currently, most TTA methods can only deal with minor shifts and rely heavily on heuristic and empirical studies. To advance TTA under domain shifts, we propose the novel problem setting of active test-time adaptation (ATTA) that integrates active learning within the fully TTA setting. We provide a learning theory analysis, demonstrating that incorporating limited labeled test instances enhances overall performances across test domains with a theoretical guarantee. We also present a sample entropy balancing for implementing ATTA while avoiding catastrophic forgetting (CF). We introduce a simple yet effective ATTA algorithm, known as SimATTA, using real-time sample selection techniques. Extensive experimental results confirm consistency with our theoretical analyses and show that the proposed ATTA method yields substantial performance improvements over TTA methods while maintaining efficiency and shares similar effectiveness to the more demanding active domain adaptation (ADA) methods. Our code is available at https://github.com/divelab/ATTA.

Poster
TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting

Defu Cao, Furong Jia, Sercan O Arik, Tomas Pfister, Yixiang Zheng, Wen Ye, Yan Liu

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The past decade has witnessed significant advances in time series modeling with deep learning. While achieving state-of-the-art results, the best-performing architectures vary highly across applications and domains. Meanwhile, for natural language processing, the Generative Pre-trained Transformer (GPT) has demonstrated impressive performance via training one general-purpose model across various textual datasets. It is intriguing to explore whether GPT-type architectures can be effective for time series, capturing the intrinsic dynamic attributes and leading to significant accuracy improvements. In this paper, we propose a novel framework, TEMPO, that can effectively learn time series representations. We focus on utilizing two essential inductive biases of the time series task for pre-trained models: (i) decomposition of the complex interaction between trend, seasonal and residual components; and (ii) introducing the design of prompts to facilitate distribution adaptation in different types of time series. TEMPO expands the capability for dynamically modeling real-world temporal phenomena from data within diverse domains. Our experiments demonstrate the superior performance of TEMPO over state-of-the-art methods on zero shot setting for a number of time series benchmark datasets. This performance gain is observed not only in scenarios involving previously unseen datasets but also in scenarios with multi-modal inputs. This compelling finding highlights TEMPO's potential to constitute a foundational model-building framework.

Poster
Learning to Embed Time Series Patches Independently

Seunghan Lee, Taeyoung Park, Kibok Lee

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Masked time series modeling has recently gained much attention as a self-supervised representation learning strategy for time series. Inspired by masked image modeling in computer vision, recent works first patchify and partially mask out time series, and then train Transformers to capture the dependencies between patches by predicting masked patches from unmasked patches. However, we argue that capturing such patch dependencies might not be an optimal strategy for time series representation learning; rather, learning to embed patches independently results in better time series representations. Specifically, we propose to use 1) the simple patch reconstruction task, which autoencode each patch without looking at other patches, and 2) the simple patch-wise MLP that embeds each patch independently. In addition, we introduce complementary contrastive learning to hierarchically capture adjacent time series information efficiently. Our proposed method improves time series forecasting and classification performance compared to state-of-the-art Transformer-based models, while it is more efficient in terms of the number of parameters and training time. Code is available at this repository: https://github.com/seunghan96/pits.

Poster
Time-LLM: Time Series Forecasting by Reprogramming Large Language Models

Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, Xiaoming Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, Qingsong Wen

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Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that \method is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios. The code is made available at https://github.com/KimMeen/Time-LLM.

Poster
TEST: Text Prototype Aligned Embedding to Activate LLM's Ability for Time Series

Chenxi Sun, Hongyan Li, Yaliang Li, Shenda Hong

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This work summarizes two ways to accomplish Time-Series (TS) tasks in today's Large Language Model (LLM) context: LLM-for-TS (model-centric) designs and trains a fundamental large model, or fine-tunes a pre-trained LLM for TS data; TS-for-LLM (data-centric) converts TS into a model-friendly representation to enable the pre-trained LLM to handle TS data. Given the lack of data, limited resources, semantic context requirements, and so on, this work focuses on TS-for-LLM, where we aim to activate LLM's ability for TS data by designing a TS embedding method suitable for LLM. The proposed method is named TEST. It first tokenizes TS, builds an encoder to embed TS via instance-wise, feature-wise, and text-prototype-aligned contrast, where the TS embedding space is aligned to LLM’s embedding layer space, then creates soft prompts to make LLM more open to that embeddings, and finally implements TS tasks using the frozen LLM. We also demonstrate the feasibility of TS-for-LLM through theory and experiments. Experiments are carried out on TS classification, forecasting, and representation tasks using eight frozen LLMs with various structures and sizes. The results show that the pre-trained LLM with TEST strategy can achieve better or comparable performance than today's SOTA TS models, and offers benefits for few-shot and generalization. By treating LLM as the pattern machine, TEST can endow LLM's ability to process TS data without compromising language ability. We hope that this study will serve as a foundation for future work to support TS+LLM progress.

Poster
Towards Transparent Time Series Forecasting

Krzysztof Kacprzyk, Tennison Liu, Mihaela van der Schaar

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Transparent machine learning (ML) models are essential for ensuring interpretability and trustworthiness in decision-making systems, particularly in high-stakes domains such as healthcare, finance, and criminal justice. While transparent machine learning models have been proposed for classification and regression, time series forecasting presents some unique challenges for ensuring transparency. In particular, currently used bottom-up approaches that focus on the values of the time series at specific time points (usually regularly spaced) do not provide a holistic understanding of the entire time series. This limits the applicability of ML in many critical areas. To open up these domains for ML, we propose a top-down framework of bi-level transparency, which involves understanding the higher-level trends and the lower-level properties of the predicted time series. Applying this framework, we develop TIMEVIEW, a transparent ML model for time series forecasting based on static features, complemented with an interactive visualization tool. Through a series of experiments, we demonstrate the efficacy and interpretability of our approach, paving the way for more transparent and reliable applications of ML in various domains.

Poster
Feature-aligned N-BEATS with Sinkhorn divergence

Joonhun Lee, Myeongho Jeon, Myungjoo Kang, Kyunghyun Park

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We propose Feature-aligned N-BEATS as a domain-generalized time series forecasting model. It is a nontrivial extension of N-BEATS with doubly residual stacking principle (Oreshkin et al. [45]) into a representation learning framework. In particular, it revolves around marginal feature probability measures induced by the intricate composition of residual and feature extracting operators of N-BEATS in each stack and aligns them stack-wise via an approximate of an optimal transport distance referred to as the Sinkhorn divergence. The training loss consists of an empirical risk minimization from multiple source domains, i.e., forecasting loss, and an alignment loss calculated with the Sinkhorn divergence, which allows the model to learn invariant features stack-wise across multiple source data sequences while retaining N-BEATS’s interpretable design and forecasting power. Comprehensive experimental evaluations with ablation studies are provided and the corresponding results demonstrate the proposed model’s forecasting and generalization capabilities.

Spotlight
Test-time Adaptation against Multi-modal Reliability Bias

Mouxing Yang, Yunfan Li, Changqing Zhang, Peng Hu, Xi Peng

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Test-time adaptation (TTA) has emerged as a new paradigm for reconciling distribution shifts across domains without accessing source data. However, existing TTA methods mainly concentrate on uni-modal tasks, overlooking the complexity of multi-modal scenarios. In this paper, we delve into the multi-modal test-time adaptation and reveal a new challenge named reliability bias. Different from the definition of traditional distribution shifts, reliability bias refers to the information discrepancies across different modalities derived from intra-modal distribution shifts. To solve the challenge, we propose a novel method, dubbed REliable fusion and robust ADaptation (READ). On the one hand, unlike the existing TTA paradigm that mainly repurposes the normalization layers, READ employs a new paradigm that modulates the attention between modalities in a self-adaptive way, supporting reliable fusion against reliability bias. On the other hand, READ adopts a novel objective function for robust multi-modal adaptation, where the contributions of confident predictions could be amplified and the negative impacts of noisy predictions could be mitigated. Moreover, we introduce two new benchmarks to facilitate comprehensive evaluations of multi-modal TTA under reliability bias. Extensive experiments on the benchmarks verify the effectiveness of our method against multi-modal reliability bias. The code and benchmarks are available at https://github.com/XLearning-SCU/2024-ICLR-READ.

Poster
Weakly Supervised Virus Capsid Detection with Image-Level Annotations in Electron Microscopy Images

Hannah Kniesel, Leon Sick, Tristan Payer, Tim Bergner, Kavitha Shaga Devan, Clarissa Read, Paul Walther, Timo Ropinski, Pedro Hermosilla

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Current state-of-the-art methods for object detection rely on annotated bounding boxes of large data sets for training. However, obtaining such annotations is expensive and can require up to hundreds of hours of manual labor. This poses a challenge, especially since such annotations can only be provided by experts, as they require knowledge about the scientific domain. To tackle this challenge, we propose a domain-specific weakly supervised object detection algorithm that only relies on image-level annotations, which are significantly easier to acquire. Our method distills the knowledge of a pre-trained model, on the task of predicting the presence or absence of a virus in an image, to obtain a set of pseudo-labels that can be used to later train a state-of-the-art object detection model. To do so, we use an optimization approach with a shrinking receptive field to extract virus particles directly without specific network architectures. Through a set of extensive studies, we show how the proposed pseudo-labels are easier to obtain, and, more importantly, are able to outperform other existing weak labeling methods, and even ground truth labels, in cases where the time to obtain the annotation is limited.

Poster
Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement

Kai Xu, Rongyu Chen, Gianni Franchi, Angela Yao

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Activation shaping has proven highly effective for identifying out-of-distribution (OOD) samples post-hoc. Activation shaping prunes and scales network activations before estimating the OOD energy score; such an extremely simple approach achieves state-of-the-art OOD detection with minimal in-distribution (ID) accuracy drops. This paper analyzes the working mechanism behind activation shaping. We directly show that the benefits for OOD detection derive only from scaling, while pruning is detrimental. Based on our analysis, we propose SCALE, an even simpler yet more effective post-hoc network enhancement method for OOD detection. SCALE attains state-of-the-art OOD detection performance without any compromises on ID accuracy. Furthermore, we integrate scaling concepts into learning and propose Intermediate Tensor SHaping (ISH) for training-time OOD detection enhancement. ISH achieves significant AUROC improvements for both near- and far-OOD, highlighting the importance of activation distributions in emphasizing ID data characteristics. Our code and models are available at https://github.com/kai422/SCALE.

Poster
Biased Temporal Convolution Graph Network for Time Series Forecasting with Missing Values

Xiaodan Chen, Xiucheng Li, Bo Liu, Zhijun Li

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Multivariate time series forecasting plays an important role in various applications ranging from meteorology study, traffic management to economics planning. In the past decades, many efforts have been made toward accurate and reliable forecasting methods development under the assumption of intact input data. However, the time series data from real-world scenarios is often partially observed due to device malfunction or costly data acquisition, which can seriously impede the performance of the existing approaches. A naive employment of imputation methods unavoidably involves error accumulation and leads to suboptimal solutions. Motivated by this, we propose a Biased Temporal Convolution Graph Network that jointly captures the temporal dependencies and spatial structure. In particular, we inject bias into the two carefully developed modules, the Multi-Scale Instance PartialTCN and Biased GCN, to account for missing patterns. The experimental results show that our proposed model is able to achieve up to $9.93$\% improvements over the existing methods on five real-world benchmark datasets. Our code is available at: https://github.com/chenxiaodanhit/BiTGraph.

Poster
CNN Kernels Can Be the Best Shapelets

Eric Qu, Yansen Wang, Xufang Luo, Wenqiang He, Kan Ren, Dongsheng Li

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Shapelets and CNN are two typical approaches to model time series. Shapelets aim at finding a set of sub-sequences that extract feature-based interpretable shapes, but may suffer from accuracy and efficiency issues. CNN performs well by encoding sequences with a series of hidden representations, but lacks interpretability. In this paper, we demonstrate that shapelets are essentially equivalent to a specific type of CNN kernel with a squared norm and pooling. Based on this finding, we propose ShapeConv, an interpretable CNN layer with its kernel serving as shapelets to conduct time-series modeling tasks in both supervised and unsupervised settings. By incorporating shaping regularization, we enforce the similarity for maximum interpretability. We also find human knowledge can be easily injected to ShapeConv by adjusting its initialization and model performance is boosted with it. Experiments show that ShapeConv can achieve state-of-the-art performance on time-series benchmarks without sacrificing interpretability and controllability.

Poster
MOTOR: A Time-to-Event Foundation Model For Structured Medical Records

Ethan Steinberg, Jason Alan Fries, Yizhe Xu, Nigam Shah

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We present a self-supervised, time-to-event (TTE) foundation model called MOTOR (Many Outcome Time Oriented Representations) which is pretrained on timestamped sequences of events in electronic health records (EHR) and health insurance claims. TTE models are used for estimating the probability distribution of the time until a specific event occurs, which is an important task in medical settings. TTE models provide many advantages over classification using fixed time horizons, including naturally handling censored observations, but are challenging to train with limited labeled data. MOTOR addresses this challenge by pretraining on up to 55M patient records (9B clinical events). We evaluate MOTOR's transfer learning performance on 19 tasks, across 3 patient databases (a private EHR system, MIMIC-IV, and Merative claims data). Task-specific models adapted from MOTOR improve time-dependent C statistics by 4.6\% over state-of-the-art, improve label efficiency by up to 95\%, and are more robust to temporal distributional shifts. We further evaluate cross-site portability by adapting our MOTOR foundation model for six prediction tasks on the MIMIC-IV dataset, where it outperforms all baselines. MOTOR is the first foundation model for medical TTE predictions and we release a 143M parameter pretrained model for research use at https://huggingface.co/StanfordShahLab/motor-t-base.

Spotlight
TESTAM: A Time-Enhanced Spatio-Temporal Attention Model with Mixture of Experts

Hyunwook Lee, Sungahn Ko

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Accurate traffic forecasting is challenging due to the complex dependency on road networks, various types of roads, and the abrupt speed change due to the events. Recent works mainly focus on dynamic spatial modeling with adaptive graph embedding or graph attention having less consideration for temporal characteristics and in-situ modeling. In this paper, we propose a novel deep learning model named TESTAM, which individually models recurring and non-recurring traffic patterns by a mixture-of-experts model with three experts on temporal modeling, spatio-temporal modeling with static graph, and dynamic spatio-temporal dependency modeling with dynamic graph. By introducing different experts and properly routing them, TESTAM could better model various circumstances, including spatially isolated nodes, highly related nodes, and recurring and non-recurring events. For the proper routing, we reformulate a gating problem into a classification problem with pseudo labels. Experimental results on three public traffic network datasets, METR-LA, PEMS-BAY, and EXPY-TKY, demonstrate that TESTAM achieves a better indication and modeling of recurring and non-recurring traffic.

Poster
Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Time

Yuzhou Gu, Zhao Song, Junze Yin, Lichen Zhang

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Given a matrix $M\in \mathbb{R}^{m\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\top$ for $U\in \mathbb{R}^{m\times k}$ and $V\in \mathbb{R}^{n\times k}$ by only observing a few entries specified by a set of entries $\Omega\subseteq [m]\times [n]$. In particular, we examine an approach that is widely used in practice --- the alternating minimization framework. Jain, Netrapalli and Sanghavi showed that if $M$ has incoherent rows and columns, then alternating minimization provably recovers the matrix $M$ by observing a nearly linear in $n$ number of entries. While the sample complexity has been subsequently improved, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate a moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time $\widetilde O(|\Omega| k)$, which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require $\widetilde O(|\Omega| k^2)$ time.

Poster
CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting

Xue Wang, Tian Zhou, Qingsong Wen, Jinyang Gao, Bolin Ding, Rong Jin

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Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., **C**hannel **A**ligned **R**obust Blen**d** Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository: https://github.com/wxie9/CARD.

Poster
SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations

Xuan Zhang, Jacob Helwig, Yuchao Lin, Yaochen Xie, Cong Fu, Stephan Wojtowytsch, Shuiwang Ji

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We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model’s performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Poster
Online GNN Evaluation Under Test-time Graph Distribution Shifts

Xin Zheng, Dongjin Song, Qingsong Wen, Bo Du, Shirui Pan

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Evaluating the performance of a well-trained GNN model on real-world graphs is a pivotal step for reliable GNN online deployment and serving. Due to a lack of test node labels and unknown potential training-test graph data distribution shifts, conventional model evaluation encounters limitations in calculating performance metrics (e.g., test error) and measuring graph data-level discrepancies, particularly when the training graph used for developing GNNs remains unobserved during test time. In this paper, we study a new research problem, online GNN evaluation, which aims to provide valuable insights into the well-trained GNNs's ability to effectively generalize to real-world unlabeled graphs under the test-time graph distribution shifts. Concretely, we develop an effective learning behavior discrepancy score, dubbed LeBeD, to estimate the test-time generalization errors of well-trained GNN models. Through a novel GNN re-training strategy with a parameter-free optimality criterion, the proposed LeBeD comprehensively integrates learning behavior discrepancies from both node prediction and structure reconstruction perspectives. This enables the effective evaluation of the well-trained GNNs' ability to capture test node semantics and structural representations, making it an expressive metric for estimating the generalization error in online GNN evaluation. Extensive experiments on real-world test graphs under diverse graph distribution shifts could verify the effectiveness of the proposed method, revealing its strong correlation with ground-truth test errors on various well-trained GNN models.

Spotlight
Towards Enhancing Time Series Contrastive Learning: A Dynamic Bad Pair Mining Approach

Xiang Lan, Hanshu Yan, Shenda Hong, Mengling Feng

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*Not all positive pairs are beneficial to time series contrastive learning*. In this paper, we study two types of bad positive pairs that can impair the quality of time series representation learned through contrastive learning: the noisy positive pair and the faulty positive pair. We observe that, with the presence of noisy positive pairs, the model tends to simply learn the pattern of noise (Noisy Alignment). Meanwhile, when faulty positive pairs arise, the model wastes considerable amount of effort aligning non-representative patterns (Faulty Alignment). To address this problem, we propose a Dynamic Bad Pair Mining (DBPM) algorithm, which reliably identifies and suppresses bad positive pairs in time series contrastive learning. Specifically, DBPM utilizes a memory module to dynamically track the training behavior of each positive pair along training process. This allows us to identify potential bad positive pairs at each epoch based on their historical training behaviors. The identified bad pairs are subsequently down-weighted through a transformation module, thereby mitigating their negative impact on the representation learning process. DBPM is a simple algorithm designed as a lightweight **plug-in** without learnable parameters to enhance the performance of existing state-of-the-art methods. Through extensive experiments conducted on four large-scale, real-world time series datasets, we demonstrate DBPM's efficacy in mitigating the adverse effects of bad positive pairs.

Poster