On the Generalization and Causal Explanation in Self-Supervised Learning

Self-supervised learning (SSL) methods learn from unlabeled data and achieve high generalization performance on downstream tasks. However, they may also suffer from overfitting to their training data and lose the ability to adapt to new tasks. To investigate this phenomenon, we conduct experiments on various SSL methods and datasets and make two observations: (1) Overfitting occurs abruptly in later layers and epochs, while generalizing features are learned in early layers for all epochs; (2) Coding rate reduction can be used as an indicator to measure the degree of overfitting in SSL models. Based on these observations, we propose Undoing Memorization Mechanism (UMM), a plug-and-play method that mitigates overfitting of the pre-trained feature extractor by aligning the feature distributions of the early and the last layers to maximize the coding rate reduction of the last layer output. The learning process of UMM is a bi-level optimization process. We provide a causal analysis of UMM to explain how UMM can help the pre-trained feature extractor overcome overfitting and recover generalization. We also demonstrate that UMM significantly improves the generalization performance of SSL methods on various downstream tasks.

Rethinking Meta-Learning from a Learning Lens

Meta-learning has emerged as a powerful approach for leveraging knowledge from previous tasks to solve new tasks. The mainstream methods focus on training a well-generalized model initialization, which is then adapted to different tasks with limited data and updates. However, it pushes the model overfitting on the training tasks. Previous methods mainly attributed this to the lack of data and used augmentations to address this issue, but they were limited by sufficient training and effective augmentation strategies. In this work, we focus on the more fundamental ``learning to learn'' strategy of meta-learning to explore what causes errors and how to eliminate these errors without changing the environment. Specifically, we first rethink the algorithmic procedure of meta-learning from a ``learning'' lens. Through theoretical and empirical analyses, we find that (i) this paradigm faces the risk of both overfitting and underfitting and (ii) the model adapted to different tasks promote each other where the effect is stronger if the tasks are more similar. Based on this insight, we propose using task relations to calibrate the optimization process of meta-learning and propose a plug-and-play method called Task Relation Learner (TRLearner) to achieve this goal. Specifically, it first obtains task relation matrices from the extracted task-specific meta-data. Then, it uses the obtained matrices with relation-aware consistency regularization to guide optimization. Extensive theoretical and empirical analyses demonstrate the effectiveness of TRLearner.

On the Causal Sufficiency and Necessity of Multi-Modal Representation Learning

An effective paradigm of multi-modal learning (MML) is to learn unified representations among modalities. From a causal perspective, constraining the consistency between different modalities can mine causal representations that convey primary events. However, such simple consistency may face the risk of learning insufficient or unnecessary information: a necessary but insufficient cause is invariant across modalities but may not have the required accuracy; a sufficient but unnecessary cause tends to adapt well to specific modalities but may be hard to adapt to new data. To address this issue, in this paper, we aim to learn representations that are both causal sufficient and necessary, i.e., Causal Complete Cause ($C^3$), for MML. Firstly, we define the concept of $C^3$ for MML, which reflects the probability of being causal sufficiency and necessity. We also propose the identifiability and measurement of $C^3$, i.e., $C^3$ risk, to ensure calculating the learned representations' $C^3$ scores in practice. Then, we theoretically prove the effectiveness of $C^3$ risk by establishing the performance guarantee of MML with a tight generalization bound. Based on these theoretical results, we propose a plug-and-play method, namely Causal Complete Cause Regularization ($C^3$R), to learn causal complete representations by constraining the $C^3$ risk bound. Extensive experiments conducted on various benchmark datasets empirically demonstrate the effectiveness of $C^3$R.

On the Discriminability of Self-Supervised Representation Learning

Self-supervised learning (SSL) has recently achieved significant success in downstream visual tasks. However, a notable gap still exists between SSL and supervised learning (SL), especially in complex downstream tasks. In this paper, we show that the features learned by SSL methods suffer from the crowding problem, where features of different classes are not distinctly separated, and features within the same class exhibit large intra-class variance. In contrast, SL ensures a clear separation between classes. We analyze this phenomenon and conclude that SSL objectives do not constrain the relationships between different samples and their augmentations. Our theoretical analysis delves into how SSL objectives fail to enforce the necessary constraints between samples and their augmentations, leading to poor performance in complex tasks. We provide a theoretical framework showing that the performance gap between SSL and SL mainly stems from the inability of SSL methods to capture the aggregation of similar augmentations and the separation of dissimilar augmentations. To address this issue, we propose a learnable regulator called Dynamic Semantic Adjuster (DSA). DSA aggregates and separates samples in the feature space while being robust to outliers. Through extensive empirical evaluations on multiple benchmark datasets, we demonstrate the superiority of DSA in enhancing feature aggregation and separation, ultimately closing the performance gap between SSL and SL.

Not All Frequencies Are Created Equal:Towards a Dynamic Fusion of Frequencies in Time-Series Forecasting

Long-term time series forecasting is a long-standing challenge in various applications. A central issue in time series forecasting is that methods should expressively capture long-term dependency. Furthermore, time series forecasting methods should be flexible when applied to different scenarios. Although Fourier analysis offers an alternative to effectively capture reusable and periodic patterns to achieve long-term forecasting in different scenarios, existing methods often assume high-frequency components represent noise and should be discarded in time series forecasting. However, we conduct a series of motivation experiments and discover that the role of certain frequencies varies depending on the scenarios. In some scenarios, removing high-frequency components from the original time series can improve the forecasting performance, while in others scenarios, removing them is harmful to forecasting performance. Therefore, it is necessary to treat the frequencies differently according to specific scenarios. To achieve this, we first reformulate the time series forecasting problem as learning a transfer function of each frequency in the Fourier domain. Further, we design Frequency Dynamic Fusion (FreDF), which individually predicts each Fourier component, and dynamically fuses the output of different frequencies. Moreover, we provide a novel insight into the generalization ability of time series forecasting and propose the generalization bound of time series forecasting. Then we prove FreDF has a lower bound, indicating that FreDF has better generalization ability. Extensive experiments conducted on multiple benchmark datasets and ablation studies demonstrate the effectiveness of FreDF.

Teleporter Theory: A General and Simple Approach for Modeling Cross-World Counterfactual Causality

Leveraging the development of structural causal model (SCM), researchers can establish graphical models for exploring the causal mechanisms behind machine learning techniques. As the complexity of machine learning applications rises, single-world interventionism causal analysis encounters theoretical adaptation limitations. Accordingly, cross-world counterfactual approach extends our understanding of causality beyond observed data, enabling hypothetical reasoning about alternative scenarios. However, the joint involvement of cross-world variables, encompassing counterfactual variables and real-world variables, challenges the construction of the graphical model. Twin network is a subtle attempt, establishing a symbiotic relationship, to bridge the gap between graphical modeling and the introduction of counterfactuals albeit with room for improvement in generalization. In this regard, we demonstrate the theoretical breakdowns of twin networks in certain cross-world counterfactual scenarios. To this end, we propose a novel teleporter theory to establish a general and simple graphical representation of counterfactuals, which provides criteria for determining teleporter variables to connect multiple worlds. In theoretical application, we determine that introducing the proposed teleporter theory can directly obtain the conditional independence between counterfactual variables and real-world variables from the cross-world SCM without requiring complex algebraic derivations. Accordingly, we can further identify counterfactual causal effects through cross-world symbolic derivation. We demonstrate the generality of the teleporter theory to the practical application. Adhering to the proposed theory, we build a plug-and-play module, and the effectiveness of which are substantiated by experiments on benchmarks.

Revisiting Spurious Correlation in Domain Generalization

Without loss of generality, existing machine learning techniques may learn spurious correlation dependent on the domain, which exacerbates the generalization of models in out-of-distribution (OOD) scenarios. To address this issue, recent works build a structural causal model (SCM) to describe the causality within data generation process, thereby motivating methods to avoid the learning of spurious correlation by models. However, from the machine learning viewpoint, such a theoretical analysis omits the nuanced difference between the data generation process and representation learning process, resulting in that the causal analysis based on the former cannot well adapt to the latter. To this end, we explore to build a SCM for representation learning process and further conduct a thorough analysis of the mechanisms underlying spurious correlation. We underscore that adjusting erroneous covariates introduces bias, thus necessitating the correct selection of spurious correlation mechanisms based on practical application scenarios. In this regard, we substantiate the correctness of the proposed SCM and further propose to control confounding bias in OOD generalization by introducing a propensity score weighted estimator, which can be integrated into any existing OOD method as a plug-and-play module. The empirical results comprehensively demonstrate the effectiveness of our method on synthetic and large-scale real OOD datasets.

Interventional Imbalanced Multi-Modal Representation Learning via $β$-Generalization Front-Door Criterion

Multi-modal methods establish comprehensive superiority over uni-modal methods. However, the imbalanced contributions of different modalities to task-dependent predictions constantly degrade the discriminative performance of canonical multi-modal methods. Based on the contribution to task-dependent predictions, modalities can be identified as predominant and auxiliary modalities. Benchmark methods raise a tractable solution: augmenting the auxiliary modality with a minor contribution during training. However, our empirical explorations challenge the fundamental idea behind such behavior, and we further conclude that benchmark approaches suffer from certain defects: insufficient theoretical interpretability and limited exploration capability of discriminative knowledge. To this end, we revisit multi-modal representation learning from a causal perspective and build the Structural Causal Model. Following the empirical explorations, we determine to capture the true causality between the discriminative knowledge of predominant modality and predictive label while considering the auxiliary modality. Thus, we introduce the $\beta$-generalization front-door criterion. Furthermore, we propose a novel network for sufficiently exploring multi-modal discriminative knowledge. Rigorous theoretical analyses and various empirical evaluations are provided to support the effectiveness of the innate mechanism behind our proposed method.

Learning Invariant Causal Mechanism from Vision-Language Models

Pre-trained large-scale models have become a major research focus, but their effectiveness is limited in real-world applications due to diverse data distributions. In contrast, humans excel at decision-making across various domains by learning reusable knowledge that remains invariant despite environmental changes in a complex world. Although CLIP, as a successful vision-language pre-trained model, demonstrates remarkable performance in various visual downstream tasks, our experiments reveal unsatisfactory results in specific domains. Our further analysis with causal inference exposes the current CLIP model's inability to capture the invariant causal mechanisms across domains, attributed to its deficiency in identifying latent factors generating the data. To address this, we propose the Invariant Causal Mechanism of CLIP (CLIP-ICM), an algorithm designed to provably identify invariant latent factors with the aid of interventional data, and perform accurate prediction on various domains. Theoretical analysis demonstrates that our method has a lower generalization bound in out-of-distribution (OOD) scenarios. Experimental results showcase the outstanding performance of CLIP-ICM.

Explicitly Modeling Generality into Self-Supervised Learning

The goal of generality in machine learning is to achieve excellent performance on various unseen tasks and domains. Recently, self-supervised learning (SSL) has been regarded as an effective method to achieve this goal. It can learn high-quality representations from unlabeled data and achieve promising empirical performance on multiple downstream tasks. Existing SSL methods mainly constrain generality from two aspects: (i) large-scale training data, and (ii) learning task-level shared knowledge. However, these methods lack explicit modeling of the SSL generality in the learning objective, and the theoretical understanding of SSL's generality remains limited. This may cause SSL models to overfit in data-scarce situations and generalize poorly in the real world, making it difficult to achieve true generality. To address these issues, we provide a theoretical definition of generality in SSL and define a $\sigma$-measurement to help quantify it. Based on this insight, we explicitly model generality into self-supervised learning and further propose a novel SSL framework, called GeSSL. It introduces a self-motivated target based on $\sigma$-measurement, which enables the model to find the optimal update direction towards generality. Extensive theoretical and empirical evaluations demonstrate the superior performance of the proposed GeSSL.