Recently, contrastive learning has risen to be a promising paradigm for extracting meaningful data representations. Among various special designs, adding a projection head on top of the encoder during training and removing it for downstream tasks has proven to significantly enhance the performance of contrastive learning. However, despite its empirical success, the underlying mechanism of the projection head remains under-explored. In this paper, we develop an in-depth theoretical understanding of the projection head from the information-theoretic perspective. By establishing the theoretical guarantees on the downstream performance of the features before the projector, we reveal that an effective projector should act as an information bottleneck, filtering out the information irrelevant to the contrastive objective. Based on theoretical insights, we introduce modifications to projectors with training and structural regularizations. We believe our theoretical understanding on the role of the projection head will inspire more principled and advanced designs in this field. In recent years, contrastive learning has emerged as a promising representation learning paradigm and exhibited impressive performance without supervised labels (Chen et al., 2020; He et al., 2020; Zbontar et al., 2021). The core idea of contrastive learning is quite simple, that is to pull the augmented views of the same samples (i.e., positive samples) together while pushing the independent samples (i.e., negative samples) away. To improve the downstream performance of contrastive learning, researchers have proposed various special training objectives and architecture designs (Grill et al., 2020; Wang et al., 2021; Guo et al., 2023; Wang et al., 2023; 2024; Du et al., 2024). Among them, one of the most widely-used techniques is the projection head (i.e., projector) (Chen et al., 2020), which is a shallow layer following the backbone during pretraining and is discarded in downstream tasks like image classification and object detection. It has been shown that the features before the projector (denoted as encoder features) exhibit much better downstream performance than the features after the projector (denoted as projector features) across various applications (Jing et al., 2021; Gupta et al., 2022). Inspired by the success of the projection head in contrastive learning, researchers also extend this architecture to other representation learning paradigms and achieve significant improvements (Sariyildiz et al., 2022; Zhou et al., 2021). However, although the projection head has been widely adopted, the understanding of the underlying mechanism behind it is still quite limited. In this paper, we aim to establish a theoretical analysis of the relationship between the projection head and the downstream performance of contrastive learning.

Large Language Models (LLMs) have demonstrated remarkable success across various NLP benchmarks. However, excelling in complex tasks that require nuanced reasoning and precise decision-making demands more than raw language proficiency--LLMs must reason, i.e., think logically, draw from past experiences, and synthesize information to reach conclusions and take action. To enhance reasoning abilities, approaches such as prompting and fine-tuning have been widely explored. While these methods have led to clear improvements in reasoning, their impact on LLM safety remains less understood. In this work, we investigate the interplay between reasoning and safety in LLMs. We highlight the latent safety risks that arise as reasoning capabilities improve, shedding light on previously overlooked vulnerabilities. At the same time, we explore how reasoning itself can be leveraged to enhance safety, uncovering potential mitigation strategies. By examining both the risks and opportunities in reasoning-driven LLM safety, our study provides valuable insights for developing models that are not only more capable but also more trustworthy in real-world deployments.

Chain-of-thought (CoT) reasoning enhances the multi-step reasoning capabilities of large language models (LLMs) by breaking complex tasks into smaller, manageable sub-tasks. Researchers have been exploring ways to guide models to generate more complex CoT processes to improve the reasoning ability of LLMs, such as long CoT and the test-time scaling law. However, for most models and tasks, does an increase in CoT length consistently lead to improved reasoning accuracy? In this paper, we observe a nuanced relationship: as the number of reasoning steps increases, performance initially improves but eventually decreases. To understand this phenomenon, we provide a piece of evidence that longer reasoning processes are increasingly susceptible to noise. We theoretically prove the existence of an optimal CoT length and derive a scaling law for this optimal length based on model capability and task difficulty. Inspired by our theory, we conduct experiments on both synthetic and real world datasets and propose Length-filtered Vote to alleviate the effects of excessively long or short CoTs. Our findings highlight the critical need to calibrate CoT length to align with model capabilities and task demands, offering a principled framework for optimizing multi-step reasoning in LLMs.

The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. This topic has been thoroughly explored for one-dimensional signals. Multidimensional signal recovery has also been studied, but primarily in scenarios where the driving operator is a convolution operator. In this work, we shift our focus to the dynamical sampling problem in the context of three-dimensional signal recovery, where the evolution system can be characterized by tensor products. Specifically, we provide a necessary condition for the sampling set that ensures successful recovery of the three-dimensional signal. Furthermore, we reformulate the reconstruction problem as an optimization task, which can be solved efficiently. To demonstrate the effectiveness of our approach, we include some straightforward numerical simulations that showcase the reconstruction performance.

As advancements in large language models (LLMs) continue and the demand for personalized models increases, parameter-efficient fine-tuning (PEFT) methods (e.g., LoRA) will become essential due to their efficiency in reducing computation costs. However, recent studies have raised alarming concerns that LoRA fine-tuning could potentially compromise the safety alignment in LLMs, posing significant risks for the model owner. In this paper, we first investigate the underlying mechanism by analyzing the changes in safety alignment related features before and after fine-tuning. Then, we propose a fixed safety module calculated by safety data and a task-specific initialization for trainable parameters in low-rank adaptations, termed Safety-alignment preserved Low-Rank Adaptation (SaLoRA). Unlike previous LoRA methods and their variants, SaLoRA enables targeted modifications to LLMs without disrupting their original alignments. Our experiments show that SaLoRA outperforms various adapters-based approaches across various evaluation metrics in different fine-tuning tasks.

Enhancing node-level Out-Of-Distribution (OOD) generalization on graphs remains a crucial area of research. In this paper, we develop a Structural Causal Model (SCM) to theoretically dissect the performance of two prominent invariant learning methods -- Invariant Risk Minimization (IRM) and Variance-Risk Extrapolation (VREx) -- in node-level OOD settings. Our analysis reveals a critical limitation: due to the lack of class-conditional invariance constraints, these methods may struggle to accurately identify the structure of the predictive invariant ego-graph and consequently rely on spurious features. To address this, we propose Cross-environment Intra-class Alignment (CIA), which explicitly eliminates spurious features by aligning cross-environment representations conditioned on the same class, bypassing the need for explicit knowledge of the causal pattern structure. To adapt CIA to node-level OOD scenarios where environment labels are hard to obtain, we further propose CIA-LRA (Localized Reweighting Alignment) that leverages the distribution of neighboring labels to selectively align node representations, effectively distinguishing and preserving invariant features while removing spurious ones, all without relying on environment labels. We theoretically prove CIA-LRA's effectiveness by deriving an OOD generalization error bound based on PAC-Bayesian analysis. Experiments on graph OOD benchmarks validate the superiority of CIA and CIA-LRA, marking a significant advancement in node-level OOD generalization. The codes are available at https://github.com/NOVAglow646/NeurIPS24-Invariant-Learning-on-Graphs.

Learning from noisy labels is a critical challenge in machine learning, with vast implications for numerous real-world scenarios. While supervised contrastive learning has recently emerged as a powerful tool for navigating label noise, many existing solutions remain heuristic, often devoid of a systematic theoretical foundation for crafting robust supervised contrastive losses. To address the gap, in this paper, we propose a unified theoretical framework for robust losses under the pairwise contrastive paradigm. In particular, we for the first time derive a general robust condition for arbitrary contrastive losses, which serves as a criterion to verify the theoretical robustness of a supervised contrastive loss against label noise. The theory indicates that the popular InfoNCE loss is in fact non-robust, and accordingly inspires us to develop a robust version of InfoNCE, termed Symmetric InfoNCE (SymNCE). Moreover, we highlight that our theory is an inclusive framework that provides explanations to prior robust techniques such as nearest-neighbor (NN) sample selection and robust contrastive loss. Validation experiments on benchmark datasets demonstrate the superiority of SymNCE against label noise.

Unsupervised contrastive learning has shown significant performance improvements in recent years, often approaching or even rivaling supervised learning in various tasks. However, its learning mechanism is fundamentally different from that of supervised learning. Previous works have shown that difficult-to-learn examples (well-recognized in supervised learning as examples around the decision boundary), which are essential in supervised learning, contribute minimally in unsupervised settings. In this paper, perhaps surprisingly, we find that the direct removal of difficult-to-learn examples, although reduces the sample size, can boost the downstream classification performance of contrastive learning. To uncover the reasons behind this, we develop a theoretical framework modeling the similarity between different pairs of samples. Guided by this theoretical framework, we conduct a thorough theoretical analysis revealing that the presence of difficult-to-learn examples negatively affects the generalization of contrastive learning. Furthermore, we demonstrate that the removal of these examples, and techniques such as margin tuning and temperature scaling can enhance its generalization bounds, thereby improving performance. Empirically, we propose a simple and efficient mechanism for selecting difficult-to-learn examples and validate the effectiveness of the aforementioned methods, which substantiates the reliability of our proposed theoretical framework.

Graph Neural Networks (GNNs) have garnered significant attention from researchers due to their outstanding performance in handling graph-related tasks, such as social network analysis, protein design, and so on. Despite their widespread application, recent research has demonstrated that GNNs are vulnerable to backdoor attacks, implemented by injecting triggers into the training datasets. Trained on the poisoned data, GNNs will predict target labels when attaching trigger patterns to inputs. This vulnerability poses significant security risks for applications of GNNs in sensitive domains, such as drug discovery. While there has been extensive research into backdoor defenses for images, strategies to safeguard GNNs against such attacks remain underdeveloped. Furthermore, we point out that conventional backdoor defense methods designed for images cannot work well when directly implemented on graph data. In this paper, we first analyze the key difference between image backdoor and graph backdoor attacks. Then we tackle the graph defense problem by presenting a novel approach called MADE, which devises an adversarial mask generation mechanism that selectively preserves clean sub-graphs and further leverages masks on edge weights to eliminate the influence of triggers effectively. Extensive experiments across various graph classification tasks demonstrate the effectiveness of MADE in significantly reducing the attack success rate (ASR) while maintaining a high classification accuracy.

In this work, we explore the mechanism of in-context learning (ICL) on out-of-distribution (OOD) tasks that were not encountered during training. To achieve this, we conduct synthetic experiments where the objective is to learn OOD mathematical functions through ICL using a GPT-2 model. We reveal that Transformers may struggle to learn OOD task functions through ICL. Specifically, ICL performance resembles implementing a function within the pretraining hypothesis space and optimizing it with gradient descent based on the in-context examples. Additionally, we investigate ICL's well-documented ability to learn unseen abstract labels in context. We demonstrate that such ability only manifests in the scenarios without distributional shifts and, therefore, may not serve as evidence of new-task-learning ability. Furthermore, we assess ICL's performance on OOD tasks when the model is pretrained on multiple tasks. Both empirical and theoretical analyses demonstrate the existence of the \textbf{low-test-error preference} of ICL, where it tends to implement the pretraining function that yields low test error in the testing context. We validate this through numerical experiments. This new theoretical result, combined with our empirical findings, elucidates the mechanism of ICL in addressing OOD tasks.