Multimodal representation learning is critical for a wide range of applications, such as multimodal sentiment analysis. Current multimodal representation learning methods mainly focus on the multimodal alignment or fusion strategies, such that the complementary and consistent information among heterogeneous modalities can be fully explored. However, they mistakenly treat the uncertainty noise within each modality as the complementary information, failing to simultaneously leverage both consistent and complementary information while eliminating the aleatoric uncertainty within each modality. To address this issue, we propose a plug-and-play feature causality decomposition method for multimodal representation learning from causality perspective, which can be integrated into existing models with no affects on the original model structures. Specifically, to deal with the heterogeneity and consistency, according to whether it can be aligned with other modalities, the unimodal feature is first disentangled into two parts: modality-invariant (the synergistic information shared by all heterogeneous modalities) and modality-specific part. To deal with complementarity and uncertainty, the modality-specific part is further decomposed into unique and redundant features, where the redundant feature is removed and the unique feature is reserved based on the backdoor-adjustment. The effectiveness of noise removal is supported by causality theory. Finally, the task-related information, including both synergistic and unique components, is further fed to the original fusion module to obtain the final multimodal representations. Extensive experiments show the effectiveness of our proposed strategies.

In recent years, the successor representation (SR) has attracted increasing attention in reinforcement learning (RL), and it has been used to address some of its key challenges, such as exploration, credit assignment, and generalization. The SR can be seen as representing the underlying credit assignment structure of the environment by implicitly encoding its induced transition dynamics. However, the SR is reward-agnostic. In this paper, we discuss a similar representation that also takes into account the reward dynamics of the problem. We study the default representation (DR), a recently proposed representation with limited theoretical (and empirical) analysis. Here, we lay some of the theoretical foundation underlying the DR in the tabular case by (1) deriving dynamic programming and (2) temporal-difference methods to learn the DR, (3) characterizing the basis for the vector space of the DR, and (4) formally extending the DR to the function approximation case through default features. Empirically, we analyze the benefits of the DR in many of the settings in which the SR has been applied, including (1) reward shaping, (2) option discovery, (3) exploration, and (4) transfer learning. Our results show that, compared to the SR, the DR gives rise to qualitatively different, reward-aware behaviour and quantitatively better performance in several settings.

Variational Quantum Algorithms (VQAs) are emerging as leading strategies with the potential to unlock practical applications and deliver significant advantages in the investigation of many-body quantum systems and quantum chemistry. A key challenge hindering the application of VQAs to large-scale problems is rooted in the no-cloning theorem in quantum mechanics, precluding standard backpropagation and leading to prohibitive quantum resource expenditure such as measurement cost. To address this challenge, we reformulate the training dynamics of VQAs as a non-linear partial differential equation and propose a novel protocol that leverages physics-informed neural networks (PINNs) to model this dynamical system efficiently. Given a small amount of training trajectory data collected from quantum devices, our protocol predicts the parameter updates of VQAs over multiple iterations on the classical side, dramatically reducing quantum resource costs. Through systematic numerical experiments, we demonstrate that our method achieves up to a 30x speedup compared to conventional methods and reduces quantum resource costs by as much as 90\% for tasks involving up to 40 qubits, including ground state preparation of different quantum systems, while maintaining competitive accuracy. Our approach complements existing techniques aimed at improving the efficiency of VQAs and further strengthens their potential for practical applications.

Advancing code reasoning in large language models (LLMs) is fundamentally limited by the scarcity of high-difficulty datasets, especially those with verifiable input-output test cases necessary for rigorous solution validation at scale. We introduce rStar-Coder, which significantly improves LLM code reasoning capabilities by constructing a large-scale, verified dataset of 418K competition-level code problems, 580K long-reasoning solutions along with rich test cases of varying difficulty. This is achieved through three core contributions: (1) we curate competitive programming code problems and solutions to synthesize new, solvable problems; (2) we introduce a reliable input-output test case synthesis pipeline that decouples the generation into a three-step input generation method and a mutual verification mechanism for effective output labeling; (3) we augment problems with high-quality, test-case-verified long-reasoning solutions. Extensive experiments on Qwen models (1.5B-14B) across various code reasoning benchmarks demonstrate the superiority of rStar-Coder dataset, achieving leading performance comparable to frontier reasoning LLMs with significantly smaller model sizes.

The process of editing an image can be naturally modeled as evaluating a counterfactual query: "What would an image look like if a particular feature had changed?" While recent advances in text-guided image editing leverage powerful pre-trained models to produce visually appealing images, they often lack counterfactual consistency -- ignoring how features are causally related and how changing one may affect others. In contrast, existing causal-based editing approaches offer solid theoretical foundations and perform well in specific settings, but remain limited in scalability and often rely on labeled data. In this work, we aim to bridge the gap between causal editing and large-scale text-to-image generation through two main contributions. First, we introduce Backdoor Disentangled Causal Latent Space (BD-CLS), a new class of latent spaces that allows for the encoding of causal inductive biases. One desirable property of this latent space is that, even under weak supervision, it can be shown to exhibit counterfactual consistency. Second, and building on this result, we develop BD-CLS-Edit, an algorithm capable of learning a BD-CLS from a (non-causal) pre-trained Stable Diffusion model. This enables counterfactual image editing without retraining. Our method ensures that edits respect the causal relationships among features, even when some features are unlabeled or unprompted and the original latent space is oblivious to the environment's underlying cause-and-effect relationships.

Retrieval-augmented generation (RAG) enhances large language models (LLMs) by integrating external knowledge, yet traditional RAG systems struggle with static workflows and limited adaptability for complex, multistep reasoning tasks. Agentic RAG systems, such as DeepResearch, address these issues through dynamic retrieval, iterative context refinement, and adaptive workflows. However, recent methods like Search-R1, which rely on outcome-based reinforcement learning, face challenges such as low exploration efficiency, gradient conflict, and sparse reward signals. To tackle these limitations, we introduce ReasonRAG, a novel method that leverages RAG-ProGUIDE--a high-quality dataset providing fine-grained, process-level rewards for query generation, evidence extraction, and answer generation. By employing process-supervised reinforcement learning, ReasonRAG enhances LLMs' autonomous capabilities in search, query generation, evidence extraction, and answer synthesis. Experimental results show that ReasonRAG, utilizing RAG-ProGUIDE, outperforms existing approaches like Search-R1 and traditional RAG systems, achieving superior performance on five benchmark datasets with only 5k training instances--significantly fewer than the 90k required by Search-R1.

Pretrained vision-language models such as CLIP achieve strong zero-shot generalization but remain vulnerable to distribution shifts caused by input corruptions. In this work, we investigate how corruptions affect CLIP's image embeddings and uncover a consistent phenomenon we term as embedding variance collapse, where both intra-class and inter-class variances shrink as corruption severity increases. We find that this collapse is closely tied to performance degradation, with inter-class variance strongly correlated with classification accuracy. To explain this phenomenon, we analyze how corruptions alter the structure of the embedding space. Our theoretical results suggest that the visual encoder tends to encode corruption-related signals, which dilute class-discriminative features and compress the representation geometry. We further show that maximizing inter-class variance, even when estimated from pseudo-labels, can provably enhance embedding quality. Based on this insight, we propose Mint, a simple test-time adaptation method that maximizes pseudo-label-based inter-class variance on the fly using a mean accumulator and a gradient accumulator. Mint operates effectively with small batch sizes and consistently improves performance across multiple corruption benchmarks and CLIP architectures. Our code is available at https://github.com/baowenxuan/Mint.

One of the major bottlenecks for deploying popular first-order differentially private (DP) machine learning algorithms (e.g., DP-SGD) lies in their high computation and memory cost, despite the existence of optimized implementations. Zeroth-order methods have promise in mitigating the overhead, as they leverage function evaluations to approximate the gradients, hence significantly easier to privatize. While recent works have explored zeroth-order approaches in both private and non-private settings, they still suffer from relatively low utilities compared with DP-SGD, and have only been evaluated in limited application domains. In this work, we propose to leverage public information to guide and improve gradient approximation of private zeroth-order algorithms.

Local SGD, or Federated Averaging, is one of the most widely used algorithms for distributed optimization. Although it often outperforms alternatives such as mini-batch SGD, existing theory has not fully explained this advantage under realistic assumptions about data heterogeneity. Recent work has suggested that a second-order heterogeneity assumption may suffice to justify the empirical gains of local SGD. We confirm this conjecture by establishing new upper and lower bounds on the convergence of local SGD. These bounds demonstrate how a low second-order heterogeneity, combined with third-order smoothness, enables local SGD to interpolate between heterogeneous and homogeneous regimes while maintaining communication efficiency. Our main technical contribution is a refined analysis of the consensus error, a central quantity in such results. We validate our theory with experiments on a distributed linear regression task.

While end-to-end adaptive graph learning methods have demonstrated promising results in capturing latent spatiotemporal dependencies, they often suffer from high computational complexity and limited expressive capacity. In this paper, we propose MAGE for efficient spatiotemporal forecasting. We first conduct a theoretical analysis demonstrating that the ReLU activation function employed in existing methods amplifies edge-level noise during graph topology learning, thereby compromising the fidelity of the learned graph structures. To enhance model expressiveness, we introduce a sparse yet balanced mixture-of-experts strategy, where each expert perceives the unique underlying graph through kernel-based functions and operates with linear complexity relative to the number of nodes. The sparsity mechanism ensures that each node interacts exclusively with compatible experts, while the balancing mechanism promotes uniform activation across all experts, enabling diverse and adaptive graph representations. Furthermore, we theoretically establish that a single graph convolution using the learned graph in MAGE is mathematically equivalent to multiple convolutional steps under conventional graphs. We evaluate MAGE against advanced baselines on multiple real-world spatiotemporal datasets. MAGE achieves competitive performance while maintaining strong computational efficiency.