Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, yet generating reliable reasoning processes remains a significant challenge. We present a unified probabilistic framework that formalizes LLM reasoning through a novel graphical model incorporating latent thinking processes and evaluation signals. Our framework addresses two critical questions: (1) how to generate high-quality reasoning processes during inference automatically, and (2) how to integrate these processes into post-training. We propose the Bootstrapping Reinforced Thinking Process (BRiTE) algorithm and demonstrate its theoretical convergence at a rate of $1/T$, where $T$ is the number of iterations. The algorithm operates in two steps. First, it generates high-quality rationales by approximating the desired posterior distribution using a reinforcement learning approach with a novel reward shaping mechanism. Second, it fine-tunes the base LLM by maximizing the joint probability of rationale generation with respect to LLM parameters. Empirical evaluation on GSM8K and MATH benchmarks demonstrates that our approach consistently improves performance across different model sizes without requiring human-annotated thinking processes, outperforming standard chain-of-thought prompting while enhancing existing post-training methods.

Cross-domain few-shot learning (FSL) has demonstrated remarkable new classes recognition capabilities in hyperspectral image classification tasks. However, existing domain adaptation methods face two critical challenges in the cross-domain feature alignment process: first, the domain shift leads to misaligned feature transfer and diminished classification accuracy; second, the intra-class feature dispersion and inter-class boundary blurring in few-shot tasks result in degraded classification performance for novel classes. Moreover, the impact of redundant and noisy data on model discriminability is rarely considered in existing approaches. To solve these issues, this article proposes a cross-domain FSL hyperspectral image classification method based on diffusion-augmented prototype knowledge distillation (DAPKD-CFSL). Firstly, we introduce a diffusion-augmented unsupervised domain adaptation pre-training (DA-PT) framework to address the domain shift by performing a domain-adversarial denoising and reconstruction task using visible source data and masked target data. Second, our dual-branch spatial-spectral attention (DB-SSA) captures global and local spectral-spatial dependencies to enhance feature representation. Then, the proposed global-local prototype knowledge distillation (GL-PKD) performs global prototype alignment while conducting local contrastive learning, addressing feature dispersion and boundary ambiguity. Finally, a dynamic learning strategy prioritizes feature alignment early and gradually strengthens classification supervision through adaptive loss weights, and incorporates an SNR-enhanced loss to effectively mitigate noise interference. The experimental results on three HSI datasets demonstrate the superiority and effectiveness of the proposed DAPKD-CFSL.

Hindsight experience replay and goal relabeling are successful in reinforcement learning (RL) since they enable agents to learn from failures. Despite their successes, we lack a theoretical understanding, such as (i) why hindsight experience replay improves sample efficiency and (ii) how to design a relabeling method that achieves sample efficiency. To this end, we construct an example to show the information-theoretical improvement in sample efficiency achieved by goal relabeling. Our example reveals that goal relabeling can enhance sample efficiency and exploit the rich information in observations through better hypothesis elimination. Based on these insights, we develop an RL algorithm called GOALIVE. To analyze the sample complexity of GOALIVE, we introduce a complexity measure, the goal-conditioned Bellman-Eluder (GOAL-BE) dimension, which characterizes the sample complexity of goal-conditioned RL problems. Compared to the Bellman-Eluder dimension, the goal-conditioned version offers an exponential improvement in the best case. To the best of our knowledge, our work provides the first characterization of the theoretical improvement in sample efficiency achieved by goal relabeling.

In recent years, active learning (AL) methods have provided a feasible approach to alleviate the problem of limited labeled samples in deep learning projects. Existing AL algorithms generally tend to select sample without labeled, whose category is difficult to distinguish. However, the sample in the category center is difficult to determine in AL operations, resulting in inaccurate category measuring and inaccurate sample selection. In addition, hyperspectral images (HSIs) have rich spectral reflective bands with strong correlations, which leads to the phenomenon that the spatial distribution between different categories in HSIs characterizes staggered distribution, which undoubtedly influences the HSI classification effect. In this article, we propose a new AL method (called PLGCN) which combines prototype learning (PL) and graph convolution network (GCN) to solve few-shot HSI classification tasks, and this method can add into existing deep learning-based HSI classification models. It includes two advantages: 1) the prototype of each category is iteratively updated to ensure the optimality of prototype in each sampling stage and 2) the spatial distribution of unlabeled samples is extracted via graph convolution neural network in order to obtain the better features in new space for easier discriminating. Experimental results on three commonly used benchmark HSI datasets demonstrate the effectiveness of the PLGCN in HSI classification tasks with limited labeled samples.

In reinforcement learning (RL), balancing exploration and exploitation is crucial for achieving an optimal policy in a sample-efficient way. To this end, existing sample- efficient algorithms typically consist of three components: estimation, planning, and exploration. However, to cope with general function approximators, most of them involve impractical algorithmic components to incentivize exploration, such as data-dependent level-set constraints or complicated sampling procedures. To address this challenge, we propose an easy-to-implement RL framework called Maximize to Explore (MEX), which only needs to optimize unconstrainedly a single objective that integrates the estimation and planning components while balancing exploration and exploitation automatically. Theoretically, we prove that the MEX achieves a sublinear regret with general function approximators and is extendable to the zero-sum Markov game setting. Meanwhile, we adapt deep RL baselines to design practical versions of MEX in both the model-based and model-free settings, which outperform baselines in various MuJoCo environments with sparse reward by a stable margin. Compared with existing sample-efficient algorithms with general function approximators, MEX achieves similar sample efficiency while also enjoying a lower computational cost and is more compatible with modern deep RL methods.