Chain-of-Thought prompting has remarkably advanced LLM reasoning by generating explicit step-by-step tokens, yet its discrete nature inherently limits expressiveness and efficiency, struggling with abstract, ambiguous, or semantically divergent cognition beyond linguistic tokens. Latent reasoning offers a promising alternative by operating in the model’s internal continuous space for richer cognitive representations. However, existing methods typically rely on finetuning or token interpolation to bridge latent and input spaces, introducing training difficulty or semantic degradation. To this end, we propose Dynamic Latent Reasoning (DyLaR), a training-free framework that preserves semantic fidelity to latent space. DyLaR introduces a Semantic Residual Refinement module that progressively refines latent inputs by integrating semantic residuals from prior hidden states, thus capturing expressive semantic hierarchies that closely approximate continuous latent representations. To enhance flexibility, DyLaR further incorporates a dynamic switching policy that allows LLMs to alternate between discrete and latent reasoning based on model uncertainty, favoring explicit reasoning when confident and latent exploration under ambiguity. Empirical experiments across knowledge- and reasoning-intensive tasks demonstrate that DyLaR consistently outperforms strong baselines in both effectiveness and token efficiency. Qualitative analyses further illustrate its interpretability and flexibility in navigating complex reasoning scenarios.

Multimodal large language models excel across diverse domains but struggle with complex visual reasoning tasks. To enhance their reasoning capabilities, current approaches typically rely on explicit search or post-training techniques. However, search-based methods suffer from computational inefficiency due to extensive solution space exploration, while post-training methods demand substantial data, computational resources, and often exhibit training instability. To address these challenges, we propose **AStar**, a training-free, **A**utomatic **S**tructured **t**hinking paradigm for multimod**a**l **r**easoning. Specifically, we introduce novel "thought cards", a lightweight library of high-level reasoning patterns abstracted from prior samples. For each test problem, AStar adaptively retrieves the optimal thought cards and seamlessly integrates these external explicit guidelines with the model’s internal implicit reasoning capabilities. Compared to previous methods, AStar eliminates computationally expensive explicit search and avoids additional complex post-training processes, enabling a more efficient reasoning approach. Extensive experiments demonstrate that our framework achieves 53.9% accuracy on MathVerse (surpassing GPT-4o's 50.2%) and 32.7% on MathVision (outperforming GPT-4o's 30.4%). Further analysis reveals the remarkable transferability of our method: thought cards generated from mathematical reasoning can also be applied to other reasoning tasks, even benefiting general visual perception and understanding. AStar serves as a plug-and-play test-time inference method, compatible with other post-training techniques, providing an important complement to existing multimodal reasoning approaches.

Physics problems constitute a significant aspect of reasoning, necessitating complicated reasoning ability and abundant physics knowledge. However, existing large language models (LLMs) frequently fail due to a lack of knowledge or incorrect knowledge application. To mitigate these issues, we propose Physics Reasoner, a knowledge-augmented framework to solve physics problems with LLMs. Specifically, the proposed framework constructs a comprehensive formula set to provide explicit physics knowledge and utilizes checklists containing detailed instructions to guide effective knowledge application. Namely, given a physics problem, Physics Reasoner solves it through three stages: problem analysis, formula retrieval, and guided reasoning. During the process, checklists are employed to enhance LLMs’ self-improvement in the analysis and reasoning stages. Empirically, Physics Reasoner mitigates the issues of insufficient knowledge and incorrect application, achieving state-of-the-art performance on SciBench with an average accuracy improvement of 5.8%.

Large language models (LLMs) exhibit powerful reasoning capacity, as evidenced by prior studies focusing on objective topics that with unique standard answer such as arithmetic and commonsense reasoning.However, the reasoning to definite answers emphasizes more on logical thinking, and falls short in effectively reflecting the comprehensive, reflective, and creative thinking that is also critical for the overall reasoning prowess of LLMs.In light of this, we build a dataset SJTP comprising diverse SubJective ToPics with free responses, as well as three evaluation indicators to fully explore LLM's reasoning ability.We observe that a sole emphasis on logical thinking falls short in effectively tackling subjective challenges.Therefore, we introduce a framework grounded in the principle of the Negation of Negation (NeoN) to unleash the potential comprehensive, reflective, and creative thinking abilities of LLMs.Comprehensive experiments on SJTP demonstrate the efficacy of NeoN, and the enhanced performance on various objective reasoning tasks unequivocally underscores the benefits of stimulating LLM's subjective thinking in augmenting overall reasoning capabilities.

Domain generalization (DG) tends to alleviate the poor generalization capability of deep neural networks by learning model with multiple source domains. A classical solution to DG is domain augmentation, the common belief of which is that diversifying source domains will be conducive to the out-of-distribution generalization. However, these claims are understood intuitively, rather than mathematically. Our explorations empirically reveal that the correlation between model generalization and the diversity of domains may be not strictly positive, which limits the effectiveness of domain augmentation. This work therefore aim to guarantee and further enhance the validity of this strand. To this end, we propose a new perspective on DG that recasts it as a convex game between domains. We first encourage each diversified domain to enhance model generalization by elaborately designing a regularization term based on supermodularity. Meanwhile, a sample filter is constructed to eliminate low-quality samples, thereby avoiding the impact of potentially harmful information. Our framework presents a new avenue for the formal analysis of DG, heuristic analysis and extensive experiments demonstrate the rationality and effectiveness.11Code is available at “https://github.com/BIT-DA/DCG”.

Unsupervised domain adaptation (UDA) aims to utilize knowledge from a label-rich source domain to understand a similar yet distinct unlabeled target domain. Notably, global distribution statistics across domains and local semantic characteristics across samples, are two essential factors of data analysis that should be fully explored. Most existing UDA approaches either harness only one of them or fail to closely associate them for efficient adaptation. In this work, we propose a unified framework, called Collaborative Alignment Framework (CAF), which simultaneously reduces the global domain discrepancy and preserves the local semantic consistency for cross-domain knowledge transfer in a collaborative manner. Specifically, for domain-oriented alignment, we utilize adversarial training or minimize the Wasserstein distance between the two distributions to learn domain-level invariant representations. For semantic-oriented matching, we capture the semantic discrepancy between the predictions of two diverse task-specific classifiers and enhance the features of target data to be near the support of the source data class-wisely, which promotes semantic consistency across domains effectively. These two adaptation processes can be deeply intertwined in CAF via collaborative training, thus CAF can learn domain-invariant and semantic-consistent feature representations. Extensive experiments on four popular benchmarks, including DomainNet, VisDA-2017, Office-31, and ImageCLEF, demonstrate the proposed methods significantly outperform the existing methods, especially on the large-scale dataset. The code is available athttps://github.com/BIT-DA/CAF.

Domain generalization (DG) is essentially an out-of-distribution problem, aiming to generalize the knowledge learned from multiple source domains to an unseen target domain. The mainstream is to leverage statistical models to model the dependence between data and labels, intending to learn representations independent of domain. Nevertheless, the statistical models are superficial descriptions of reality since they are only required to model dependence instead of the intrinsic causal mechanism. When the dependence changes with the target distribution, the statistic models may fail to generalize. In this regard, we introduce a general structural causal model to formalize the DG problem. Specifically, we assume that each input is constructed from a mix of causal factors (whose relationship with the label is invariant across domains) and non-causal factors (category-independent), and only the former cause the classification judgments. Our goal is to extract the causal factors from inputs and then reconstruct the invariant causal mechanisms. However, the theoretical idea is far from practical of DG since the required causal/non-causal factors are unobserved. We highlight that ideal causal factors should meet three basic properties: separated from the non-causal ones, jointly independent, and causally sufficient for the classification. Based on that, we propose a Causality Inspired Representation Learning (CIRL) algorithm that enforces the representations to satisfy the above properties and then uses them to simulate the causal factors, which yields improved generalization ability. Extensive experimental results on several widely used datasets verify the effectiveness of our approach.11Code is available at “https://github.com/BIT-DA/CIRL”.

Unsupervised domain adaptation challenges the problem of transferring knowledge from a well-labelled source domain to an unlabelled target domain. Recently, adversarial learning with bi-classifier has been proven effective in pushing cross-domain distributions close. Prior approaches typically leverage the disagreement between bi-classifier to learn transferable representations, however, they often neglect the classifier determinacy in the target domain, which could result in a lack of feature discriminability. In this paper, we present a simple yet effective method, namely Bi-Classifier Determinacy Maximization (BCDM), to tackle this problem. Motivated by the observation that target samples cannot always be separated distinctly by the decision boundary, here in the proposed BCDM, we design a novel classifier determinacy disparity (CDD) metric, which formulates classifier discrepancy as the class relevance of distinct target predictions and implicitly introduces constraint on the target feature discriminability. To this end, the BCDM can generate discriminative representations by encouraging target predictive outputs to be consistent and determined, meanwhile, preserve the diversity of predictions in an adversarial manner. Furthermore, the properties of CDD as well as the theoretical guarantees of BCDM's generalization bound are both elaborated. Extensive experiments show that BCDM compares favorably against the existing state-of-the-art domain adaptation methods.

Domain adaptation (DA) paves the way for label annotation and dataset bias issues by the knowledge transfer from a label-rich source domain to a related but unlabeled target domain. A mainstream of DA methods is to align the feature distributions of the two domains. However, the majority of them focus on the entire image features where irrelevant semantic information, e.g., the messy background, is inevitably embedded. Enforcing feature alignments in such case will negatively influence the correct matching of objects and consequently lead to the semantically negative transfer due to the confusion of irrelevant semantics. To tackle this issue, we propose Semantic Concentration for Domain Adaptation (SCDA), which encourages the model to concentrate on the most principal features via the pair-wise adversarial alignment of prediction distributions. Specifically, we train the classifier to class-wisely maximize the prediction distribution divergence of each sample pair, which enables the model to find the region with large differences among the same class of samples. Meanwhile, the feature extractor attempts to minimize that discrepancy, which suppresses the features of dissimilar regions among the same class of samples and accentuates the features of principal parts. As a general method, SCDA can be easily integrated into various DA methods as a regularizer to further boost their performance. Extensive experiments on the cross-domain benchmarks show the efficacy of SCDA.

Domain adaptation (DA) attempts to transfer the knowledge from a labeled source domain to an unlabeled target domain that follows different distribution from the source. To achieve this, DA methods include a source classification objective to extract the source knowledge and a domain alignment objective to diminish the domain shift, ensuring knowledge transfer. Typically, former DA methods adopt some weight hyper-parameters to linearly combine the training objectives to form an overall objective. However, the gradient directions of these objectives may conflict with each other due to domain shift. Under such circumstances, the linear optimization scheme might decrease the overall objective value at the expense of damaging one of the training objectives, leading to restricted solutions. In this paper, we rethink the optimization scheme for DA from a gradient-based perspective. We propose a Pareto Domain Adaptation (ParetoDA) approach to control the overall optimization direction, aiming to cooperatively optimize all training objectives. Specifically, to reach a desirable solution on the target domain, we design a surrogate loss mimicking target classification. To improve target-prediction accuracy to support the mimicking, we propose a target-prediction refining mechanism which exploits domain labels via Bayes’ theorem. On the other hand, since prior knowledge of weighting schemes for objectives is often unavailable to guide optimization to approach the optimal solution on the target domain, we propose a dynamic preference mechanism to dynamically guide our cooperative optimization by the gradient of the surrogate loss on a held-out unlabeled target dataset. Our theoretical analyses show that the held-out data can guide but will not be over-fitted by the optimization. Extensive experiments on image classification and semantic segmentation benchmarks demonstrate the effectiveness of ParetoDA