## 1 Introduction  
Time series data, collected from diverse sources such as personal devices, clinical centers, and financial institutions, have a wide range of applications such as sleep stage classification, human activity recognition, and epilepsy seizure prediction [1; 2; 3; 4; 5]. Representation learning is crucial for reducing dimensionality and constructing effective representations of time series data, enabling tasks such as classification, forecasting, and clustering. Consequently, representation learning methods for time series have gained significant attention [6; 7; 8; 9]. However, challenges arise in designing supervised representation methods due to labeling limitations and difficulties in capturing context. These challenges necessitate improved generalization ability and the availability of more labeled data. In this context, [PERSON]. [10] compares heuristics and event detection algorithms to determine optimal window sizes for time representation, highlighting the reliable estimation provided by the false nearest neighbors method. Additionally, [PERSON]. [11] refines feature representations for time series using instance-level augmentation, dropout, and iterative bilinear temporal-spectral fusion. Moreover, [PERSON]. [12] proposes a novel framework for multivariate time series representation learning using the transformer encoder architecture and unsupervised pre-training. Unlabeled time series data are frequently encountered in practical situations, leading to increased attention on unsupervised and self-supervised time series representation learning [11]. Contrastive learning, initially proposed for representation learning in computer vision and natural language processing, has also found applications in unsupervised time series representation learning [13; 14; 15]. For example, [PERSON]. [16] presents a universal representation learning framework for time series using hierarchical contrasting to learn scale-invariant representations within augmented context views. Furthermore, [PERSON]. [17] proposes a contrastive learning framework for learning domain-invariant semantics in multivariate time series through nearest-neighbor contrastive learning. This approach constructs positive and negative pairs via data augmentation and aims to maximize the similarity of positive pairs while minimizing the similarity of negative pairs. Additionally, [PERSON]. [9] combines adversarial training with self-supervised learning for emotion recognition, optimizing classifiers using diverse simulated time series samples. Another contrasting approach introduced by [18] utilizes expert features to encourage desirable properties in learned representations. Various augmentation methods are specifically designed to construct positive and negative pairs. For instance, Ref. [19] considers sampled subseries as augmentation pairs, while Ref. [11] adopts a dropout strategy to randomly mask parts of the original data. Ref. [20] transforms time series into the frequency domain, and Ref. [7] selects various transformations, such as scaling and permutation, to learn transformation-invariant representations. Contrastive learning methods typically employ two variants of the same augmentation [21], aiming to improve robustness and convergence efficiency. However, most contrastive methods overlook the representation biases introduced by augmentation techniques. Most of the previous frameworks only train encoders using augmented views [22], leading to a misunderstanding of the underlying data distribution when real data are absent. This gap between the representations learned from augmented data in contrastive learning and those learned from supervised learning is referred to as the data augmentation bias (DAB). The DAB represents the disparity between representations learned from augmented data in contrastive learning and those obtained from supervised learning.