Chain-of-Thought (CoT) reasoning is a critical capability for large language models (LLMs), enabling them to tackle complex multi-step tasks. While base LLMs, pre-trained on general text corpora, often struggle with reasoning due to a lack of specialized training, recent studies reveal their latent reasoning potential tied to hidden states. However, existing hidden state manipulation methods, such as linear activation steering, suffer from limitations due to their rigid and unconstrained nature, often leading to distribution shifts and degraded text quality. In this work, we propose a novel approach for eliciting CoT reasoning from base LLMs through hidden state manipulation grounded in probabilistic conditional generation. By reformulating the challenge as an optimization problem with a balanced likelihood and prior regularization framework, our method guides hidden states toward reasoning-oriented trajectories while preserving linguistic coherence. Extensive evaluations across mathematical, commonsense, and logical reasoning benchmarks demonstrate that our approach consistently outperforms existing steering methods, offering a theoretically principled and effective solution for enhancing reasoning capabilities in base LLMs.

With the growing potential of large language models (LLMs) in the legal domain, domain-specific finetuning and retrieval-augmented generation (RAG) methods have received widespread attention. However, current methods still suffer from hallucination risk and failing to resolve semantic drift and adapt to varying citation numbers. To address this, we propose Authoritative and Accurate Lawyer (AALawyer), a complementary dual-retriever framework based on the Legal Syllogism and the nature of different legal data. First, we introduce Symbolic Constrained Retrieval (SCR) for closed-set article retrieval, by constraining retrieval to the generative prediction. Second, we build Analogical Precedent Retrieval (APR) to retrieve open-set judicial precedents for reasoning with a newly collected large criminal dataset.Extensive experiments, including LawBench, our Hallucination Risk-Benchmark, and comprehensive ablation studies, demonstrate the effectiveness of AALawyer, which mitigates hallucinations while improving the explainability of legal reasoning.

Masked autoencoders (MAEs) represent a prominent self-supervised learning paradigm in computer vision. Despite their empirical success, the underlying mechanisms of MAEs remain insufficiently understood. Recent studies have attempted to elucidate the functioning of MAEs through contrastive learning and feature representation analysis, yet these approaches often provide only implicit insights. In this paper, we propose a new perspective for understanding MAEs by leveraging the information bottleneck principle in information theory. Our theoretical analyses reveal that optimizing the latent features to balance relevant and irrelevant information is key to improving MAE performance. Building upon our proofs, we introduce MI-MAE, a novel method that optimizes MAEs through mutual information maximization and minimization. By enhancing latent features to retain maximal relevant information between them and the output, and minimizing irrelevant information between them and the input, our approach achieves better performance. Extensive experiments on standard benchmarks show that MI-MAE significantly outperforms MAE models in tasks such as image classification, object detection, and semantic segmentation. Our findings validate the theoretical framework and highlight the practical advantages of applying the information bottleneck principle to MAEs, offering deeper insights for developing more powerful self-supervised learning models.

Random defense represents a promising strategy to protect neural networks from adversarial attacks. Most of these methods enhance robustness by injecting randomness into the data, increasing uncertainty for attackers. However, this randomness could reduce the generalization capacity of defense, as defense performance could be sensitive to the hyperparameters of noise added to the data, making it difficult to generalize across different datasets. Additionally, the involvement of randomness always comes with a reduction of natural accuracy, which leads to a delicate trade-off between them, which is seldom studied in random defense. In this work, we propose incorporating randomness into the network structure instead of data input by designing stochastic deformable convolution, where a random mask replaces the convolutional offset. This process promotes data independence, enhancing generalization across datasets. To study the trade-off, we conduct a theoretical analysis of both robust and clean accuracy, from a perspective of gradient cosine similarity and natural inference. Based on the analysis, we reformulate the adversarial training in our random defense framework. Extensive experiments show that our method achieves SOTA adversarial robustness and clean accuracy compared with other random defense methods.

Deep neural networks have been found to be vulnerable in a variety of tasks. Adversarial attacks can manipulate network outputs, resulting in incorrect predictions. Adversarial defense methods aim to improve the adversarial robustness of networks by countering potential attacks. In addition to traditional defense approaches, randomized defense mechanisms have recently received increasing attention from researchers. These methods introduce different types of perturbations during the inference phase to destabilize adversarial attacks. Although promising empirical results have been demonstrated by these approaches, the defense performance is quite sensitive to the randomness parameters, which are always manually tuned without further analysis. On the contrary, we propose incorporating random weights into the optimization to fully exploit the potential of randomized defense. To perform better optimization of randomness parameters, we conduct a theoretical analysis of the connections between randomness parameters and gradient similarity as well as natural performance. From these two aspects, we suggest imposing theoretically-guided constraints on random weights during optimizations, as these weights play a critical role in balancing natural performance and adversarial robustness. We derive both the upper and lower bounds of random weight parameters by considering prediction bias and gradient similarity. In this study, we introduce the Constrained Trainable Random Weight (CTRW), which adds random weight parameters to the optimization and includes a constraint guided by the upper and lower bounds to achieve better trade-offs between natural and robust accuracy. We evaluate the effectiveness of CTRW on several datasets and benchmark convolutional neural networks. Our results indicate that our model achieves a robust accuracy approximately 16% to 17% higher than the baseline model under PGD-20 and 22% to 25% higher on Auto Attack.