Zeen Song

Xingyu Zhang, Siyu Zhao, Zeen Song et al.

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. The code is available at https://github.com/Zh-XY22/FreDF.

Zeen Song, Xingzhe Su, Jingyao Wang et al.

In recent years, self-supervised learning (SSL) has emerged as a promising approach for extracting valuable representations from unlabeled data. One successful SSL method is contrastive learning, which aims to bring positive examples closer while pushing negative examples apart. Many current contrastive learning approaches utilize a parameterized projection head. Through a combination of empirical analysis and theoretical investigation, we provide insights into the internal mechanisms of the projection head and its relationship with the phenomenon of dimensional collapse. Our findings demonstrate that the projection head enhances the quality of representations by performing contrastive loss in a projected subspace. Therefore, we propose an assumption that only a subset of features is necessary when minimizing the contrastive loss of a mini-batch of data. Theoretical analysis further suggests that a sparse projection head can enhance generalization, leading us to introduce SparseHead - a regularization term that effectively constrains the sparsity of the projection head, and can be seamlessly integrated with any self-supervised learning (SSL) approaches. Our experimental results validate the effectiveness of SparseHead, demonstrating its ability to improve the performance of existing contrastive methods.

Zeen Song, Wenwen Qiang, Changwen Zheng et al.

Self-supervised learning (SSL) has recently shown notable success in various visual tasks. However, in terms of discriminability, SSL is still not on par with supervised learning (SL). This paper identifies a key issue, the ``crowding problem," where features from different classes are not well-separated, and there is high intra-class variance. In contrast, SL ensures clear class separation. Our analysis reveals that SSL objectives do not adequately constrain the relationships between samples and their augmentations, leading to poorer performance in complex tasks. We further establish a theoretical framework that connects SSL objectives to cross-entropy risk bounds, explaining how reducing intra-class variance and increasing inter-class separation can improve generalization. To address this, we propose the Dynamic Semantic Adjuster (DSA), a learnable regulator that enhances feature aggregation and separation while being robust to outliers. Comprehensive experiments conducted on diverse benchmark datasets validate that DSA leads to substantial gains in SSL performance, narrowing the performance gap with SL.

Jingyao Wang, Zeen Song, Wenwen Qiang et al.

The long-term goal of machine learning is to learn general visual representations from a small amount of data without supervision, mimicking three advantages of human cognition: i) no need for labels, ii) robustness to data scarcity, and iii) learning from experience. Self-supervised learning and meta-learning are two promising techniques to achieve this goal, but they both only partially capture the advantages and fail to address all the problems. Self-supervised learning struggles to overcome the drawbacks of data scarcity, while ignoring prior knowledge that can facilitate learning and generalization. Meta-learning relies on supervised information and suffers from a bottleneck of insufficient learning. To address these issues, we propose a novel Bootstrapped Meta Self-Supervised Learning (BMSSL) framework that aims to simulate the human learning process. We first analyze the close relationship between meta-learning and self-supervised learning. Based on this insight, we reconstruct tasks to leverage the strengths of both paradigms, achieving advantages i and ii. Moreover, we employ a bi-level optimization framework that alternates between solving specific tasks with a learned ability (first level) and improving this ability (second level), attaining advantage iii. To fully harness its power, we introduce a bootstrapped target based on meta-gradient to make the model its own teacher. We validate the effectiveness of our approach with comprehensive theoretical and empirical study.

Zeen Song, Zihao Ma, Wenwen Qiang et al.

Inference-time reasoning scaling has significantly advanced the capabilities of Large Language Models (LLMs) in complex problem-solving. A prevalent approach involves external search guided by Process Reward Models (PRMs). However, a fundamental limitation of this framework is the epistemic uncertainty of PRMs when evaluating reasoning paths that deviate from their training distribution. In this work, we conduct a systematic analysis of this challenge. We first provide empirical evidence that PRMs exhibit high uncertainty and unreliable scoring on out-of-distribution (OOD) samples. We then establish a theoretical framework proving that while standard search incurs linear regret accumulation, an uncertainty-aware strategy can achieve sublinear regret. Motivated by these findings, we propose Uncertainty-Aware Tree Search (UATS), a unified method that estimates uncertainty via Monte Carlo Dropout and dynamically allocates compute budget using a reinforcement learning-based controller. Extensive experiments demonstrate that our approach effectively mitigates the impact of OOD errors.

Yao Zhou, Zeen Song, Wenwen Qiang et al.

Safety alignment mechanisms in Large Language Models (LLMs) often operate as latent internal states, obscuring the model's inherent capabilities. Building on this observation, we model the safety mechanism as an unobserved confounder from a causal perspective. Then, we propose the Causal Front-Door Adjustment Attack (CFA{$^2$}) to jailbreak LLM, which is a framework that leverages Pearl's Front-Door Criterion to sever the confounding associations for robust jailbreaking. Specifically, we employ Sparse Autoencoders (SAEs) to physically strip defense-related features, isolating the core task intent. We further reduce computationally expensive marginalization to a deterministic intervention with low inference complexity. Experiments demonstrate that CFA{$^2$} achieves state-of-the-art attack success rates while offering a mechanistic interpretation of the jailbreaking process.

Shuyi Zhou, Zeen Song, Wenwen Qiang et al.

Large Language Models remain vulnerable to adversarial prefix attacks (e.g., ``Sure, here is'') despite robust standard safety. We diagnose this vulnerability as Shallow Safety Alignment, stemming from a pathology we term semantic representation decay: as the model generates compliant prefixes, its internal malicious intent signal fades. To address this, we propose Two-Stage Causal-GRPO (TSC-GRPO), a framework designed to achieve intent pinning. First, grounded in causal identifiability theory, we train a causal intent probe to disentangle invariant intent from stylistic perturbations. Second, we internalize this causal awareness into the policy via Group Relative Policy Optimization. By employing a cumulative causal penalty within ``fork-in-the-road'' training scenarios, we force the model to learn that accumulating harmful tokens monotonically decreases reward, enabling robust late-stage refusals. Experiments show that TSC-GRPO significantly outperforms baselines in defending against jailbreak attacks while preserving general utility.

Zeen Song, Wenwen Qiang, Changwen Zheng et al.

Video contrastive learning (V-CL) has emerged as a popular framework for unsupervised video representation learning, demonstrating strong results in tasks such as action classification and detection. Yet, to harness these benefits, it is critical for the learned representations to fully capture both static and dynamic semantics. However, our experiments show that existing V-CL methods fail to effectively learn either type of feature. Through a rigorous theoretical analysis based on the Structural Causal Model and gradient update, we find that in a given dataset, certain static semantics consistently co-occur with specific dynamic semantics. This phenomenon creates spurious correlations between static and dynamic semantics in the dataset. However, existing V-CL methods do not differentiate static and dynamic similarities when computing sample similarity. As a result, learning only one type of semantics is sufficient for the model to minimize the contrastive loss. Ultimately, this causes the V-CL pre-training process to prioritize learning the easier-to-learn semantics. To address this limitation, we propose Bi-level Optimization with Decoupling for Video Contrastive Learning. (BOD-VCL). In BOD-VCL, we model videos as linear dynamical systems based on Koopman theory. In this system, all frame-to-frame transitions are represented by a linear Koopman operator. By performing eigen-decomposition on this operator, we can separate time-variant and time-invariant components of semantics, which allows us to explicitly separate the static and dynamic semantics in the video. By modeling static and dynamic similarity separately, both types of semantics can be fully exploited during the V-CL training process. BOD-VCL can be seamlessly integrated into existing V-CL frameworks, and experimental results highlight the significant improvements achieved by our method.

Wenwen Qiang, Jingyao Wang, Zeen Song et al.

In this paper, we focus on the out-of-distribution (OOD) generalization of self-supervised learning (SSL). By analyzing the mini-batch construction during the SSL training phase, we first give one plausible explanation for SSL having OOD generalization. Then, from the perspective of data generation and causal inference, we analyze and conclude that SSL learns spurious correlations during the training process, which leads to a reduction in OOD generalization. To address this issue, we propose a post-intervention distribution (PID) grounded in the Structural Causal Model. PID offers a scenario where the spurious variable and label variable is mutually independent. Besides, we demonstrate that if each mini-batch during SSL training satisfies PID, the resulting SSL model can achieve optimal worst-case OOD performance. This motivates us to develop a batch sampling strategy that enforces PID constraints through the learning of a latent variable model. Through theoretical analysis, we demonstrate the identifiability of the latent variable model and validate the effectiveness of the proposed sampling strategy. Experiments conducted on various downstream OOD tasks demonstrate the effectiveness of the proposed sampling strategy.

Jingyao Wang, Wenwen Qiang, Zeen Song et al.

Large language models (LLMs) excel at complex tasks thanks to advances in their reasoning abilities. However, existing methods overlook the trade-off between reasoning effectiveness and efficiency, often encouraging unnecessarily long reasoning chains and wasting tokens. To address this, we propose Learning to Think (L2T), an information-theoretic reinforcement fine-tuning framework for LLMs to make the models achieve optimal reasoning with fewer tokens. Specifically, L2T treats each query-response interaction as a hierarchical session of multiple episodes and proposes a universal dense process reward, i.e., quantifies the episode-wise information gain in parameters, requiring no extra annotations or task-specific evaluators. We propose a method to quickly estimate this reward based on PAC-Bayes bounds and the Fisher information matrix. Theoretical analyses show that it significantly reduces computational complexity with high estimation accuracy. By immediately rewarding each episode's contribution and penalizing excessive updates, L2T optimizes the model via reinforcement learning to maximize the use of each episode and achieve effective updates. Empirical results on various reasoning benchmarks and base models demonstrate the advantage of L2T across different tasks, boosting both reasoning effectiveness and efficiency.

Zeen Song, Siyu Zhao, Xingyu Zhang et al.

Contrastive Language-Image Pretraining (CLIP) has achieved remarkable success, but its performance can degrade when fine-tuned in out-of-distribution (OOD) scenarios. We model the prediction process using a Structural Causal Model (SCM) and show that the causal mechanism involving both invariant and variant factors in training environments differs from that in test environments. In contrast, the causal mechanism with solely invariant factors remains consistent across environments. We theoretically prove the existence of a linear mapping from CLIP embeddings to invariant factors, which can be estimated using interventional data. Additionally, we provide a condition to guarantee low OOD risk of the invariant predictor. Based on these insights, we propose the Invariant Causal Mechanism of CLIP (CLIP-ICM) framework. CLIP-ICM involves collecting interventional data, estimating a linear projection matrix, and making predictions within the invariant subspace. Experiments on several OOD datasets show that CLIP-ICM significantly improves the performance of CLIP. Our method offers a simple but powerful enhancement, boosting the reliability of CLIP in real-world applications.

Xingyu Zhang, Hanyun Du, Zeen Song et al.

Large Language Models (LLMs) have recently shown exceptional potential in time series forecasting, leveraging their inherent sequential reasoning capabilities to model complex temporal dynamics. However, existing approaches typically employ a naive autoregressive generation strategy. We identify a critical theoretical flaw in this paradigm: during inference, the model operates in an open-loop manner, consuming its own generated outputs recursively. This leads to inevitable error accumulation (exposure bias), where minor early deviations cascade into significant trajectory drift over long horizons. In this paper, we reformulate autoregressive forecasting through the lens of control theory, proposing \textbf{F-LLM} (Feedback-driven LLM), a novel closed-loop framework. Unlike standard methods that passively propagate errors, F-LLM actively stabilizes the trajectory via a learnable residual estimator (Observer) and a feedback controller. Furthermore, we provide a theoretical guarantee that our closed-loop mechanism ensures uniformly bounded error, provided the base model satisfies a local Lipschitz constraint. Extensive experiments demonstrate that F-LLM significantly mitigates error propagation, achieving good performance on time series benchmarks.

Ziyin Gu, Jingyao Wang, Ran Zuo et al.

Recent advances in large language models (LLMs) have broadened their applicability across diverse tasks, yet specialized domains still require targeted post training. Among existing methods, Group Relative Policy Optimization (GRPO) stands out for its efficiency, leveraging groupwise relative rewards while avoiding costly value function learning. However, GRPO treats candidate responses as independent, overlooking semantic interactions such as complementarity and contradiction. To address this challenge, we first introduce a Structural Causal Model (SCM) that reveals hidden dependencies among candidate responses induced by conditioning on a final integrated output forming a collider structure. Then, our causal analysis leads to two insights: (1) projecting responses onto a causally informed subspace improves prediction quality, and (2) this projection yields a better baseline than query only conditioning. Building on these insights, we propose Group Causal Policy Optimization (GCPO), which integrates causal structure into optimization through two key components: a causally informed reward adjustment and a novel KL regularization term that aligns the policy with a causally projected reference distribution. Comprehensive experimental evaluations demonstrate that GCPO consistently surpasses existing methods, including GRPO across multiple reasoning benchmarks.

Ruike Song, Zeen Song, Huijie Guo et al.

External reasoning systems combine language models with process reward models (PRMs) to select high-quality reasoning paths for complex tasks such as mathematical problem solving. However, these systems are prone to reward hacking, where high-scoring but logically incorrect paths are assigned high scores by the PRMs, leading to incorrect answers. From a causal inference perspective, we attribute this phenomenon primarily to the presence of confounding semantic features. To address it, we propose Causal Reward Adjustment (CRA), a method that mitigates reward hacking by estimating the true reward of a reasoning path. CRA trains sparse autoencoders on the PRM's internal activations to recover interpretable features, then corrects confounding by using backdoor adjustment. Experiments on math solving datasets demonstrate that CRA mitigates reward hacking and improves final accuracy, without modifying the policy model or retraining PRM.

Zeen Song, Wenwen Qiang, Siyu Zhao et al.

External test-time reasoning enhances large language models (LLMs) by decoupling generation and selection. At inference time, the model generates multiple reasoning paths, and an auxiliary process reward model (PRM) is used to score and select the best one. A central challenge in this setting is test-time compute optimality (TCO), i.e., how to maximize answer accuracy under a fixed inference budget. In this work, we establish a theoretical framework to analyze how the generalization error of the PRM affects compute efficiency and reasoning performance. Leveraging PAC-Bayes theory, we derive generalization bounds and show that a lower generalization error of PRM leads to fewer samples required to find correct answers. Motivated by this analysis, we propose Compute-Aware Tree Search (CATS), an actor-critic framework that dynamically controls search behavior. The actor outputs sampling hyperparameters based on reward distributions and sparsity statistics, while the critic estimates their utility to guide budget allocation. Experiments on the MATH and AIME benchmarks with various LLMs and PRMs demonstrate that CATS consistently outperforms other external TTS methods, validating our theoretical predictions.

Jingyao Wang, Yi Ren, Zeen Song et al.

Meta-learning enables rapid generalization to new tasks by learning knowledge from various tasks. It is intuitively assumed that as the training progresses, a model will acquire richer knowledge, leading to better generalization performance. However, our experiments reveal an unexpected result: there is negative knowledge transfer between tasks, affecting generalization performance. To explain this phenomenon, we conduct Structural Causal Models (SCMs) for causal analysis. Our investigation uncovers the presence of spurious correlations between task-specific causal factors and labels in meta-learning. Furthermore, the confounding factors differ across different batches. We refer to these confounding factors as "Task Confounders". Based on these findings, we propose a plug-and-play Meta-learning Causal Representation Learner (MetaCRL) to eliminate task confounders. It encodes decoupled generating factors from multiple tasks and utilizes an invariant-based bi-level optimization mechanism to ensure their causality for meta-learning. Extensive experiments on various benchmark datasets demonstrate that our work achieves state-of-the-art (SOTA) performance.