The performance gains of LLMs have historically been driven by scaling up model size and training data. However, the rapidly diminishing availability of high-quality training data is introducing a fundamental bottleneck, shifting the focus of research toward inference-time scaling. This paradigm uses additional computation at the time of deployment to substantially improve LLM performance on downstream tasks without costly model re-training. This review systematically surveys the diverse techniques contributing to this new era of inference-time scaling, organizing the rapidly evolving field into two comprehensive perspectives: Output-focused and Input-focused methods. Output-focused techniques encompass complex, multi-step generation strategies, including reasoning (e.g., CoT, ToT, ReAct), various search and decoding methods (e.g., MCTS, beam search), training for long CoT (e.g., RLVR, GRPO), and model ensemble methods. Input-focused techniques are primarily categorized by few-shot and RAG, with RAG as the central focus. The RAG section is further detailed through a structured examination of query expansion, data, retrieval and reranker, LLM generation methods, and multi-modal RAG.

Deep learning has generated diverse perspectives in astronomy, with ongoing discussions between proponents and skeptics motivating this review. We examine how neural networks complement classical statistics, extending our data analytical toolkit for modern surveys. Astronomy offers unique opportunities through encoding physical symmetries, conservation laws, and differential equations directly into architectures, creating models that generalize beyond training data. Yet challenges persist as unlabeled observations number in billions while confirmed examples with known properties remain scarce and expensive. This review demonstrates how deep learning incorporates domain knowledge through architectural design, with built-in assumptions guiding models toward physically meaningful solutions. We evaluate where these methods offer genuine advances versus claims requiring careful scrutiny. - Neural architectures overcome trade-offs between scalability, expressivity, and data efficiency by encoding physical symmetries and conservation laws into network structure, enabling learning from limited labeled data. - Simulation-based inference and anomaly detection extract information from complex, non-Gaussian distributions where analytical likelihoods fail, enabling field-level cosmological analysis and systematic discovery of rare phenomena. - Multi-scale neural modeling bridges resolution gaps in astronomical simulations, learning effective subgrid physics from expensive high-fidelity runs to enhance large-volume calculations where direct computation remains prohibitive. - Emerging paradigms-reinforcement learning for telescope operations, foundation models learning from minimal examples, and large language model agents for research automation-show promise though are still developing in astronomical applications.

User mobility trajectory and mobile traffic data are essential for a wide spectrum of applications including urban planning, network optimization, and emergency management. However, large-scale and fine-grained mobility data remains difficult to obtain due to privacy concerns and collection costs, making it essential to simulate realistic mobility and traffic patterns. User trajectories and mobile traffic are fundamentally coupled, reflecting both physical mobility and cyber behavior in urban environments. Despite this strong interdependence, existing studies often model them separately, limiting the ability to capture cross-modal dynamics. Therefore, a unified framework is crucial. In this paper, we propose MSTDiff, a Multi-Scale Diffusion Transformer for joint simulation of mobile traffic and user trajectories. First, MSTDiff applies discrete wavelet transforms for multi-resolution traffic decomposition. Second, it uses a hybrid denoising network to process continuous traffic volumes and discrete location sequences. A transition mechanism based on urban knowledge graph embedding similarity is designed to guide semantically informed trajectory generation. Finally, a multi-scale Transformer with cross-attention captures dependencies between trajectories and traffic. Experiments show that MSTDiff surpasses state-of-the-art baselines in traffic and trajectory generation tasks, reducing Jensen-Shannon divergence (JSD) across key statistical metrics by up to 17.38% for traffic generation, and by an average of 39.53% for trajectory generation. The source code is available at: https://github.com/tsinghua-fib-lab/MSTDiff .

Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an internal, emergent valuation induced by network structure. Beliefs are nodes in a directed, signed, weighted graph whose edges encode support and contradiction. Confidence is obtained by a contractive propagation process that mixes a stated prior with structure-aware influence and guarantees a unique, stable solution. Within this dynamics, we define reasoning zones: high-confidence, structurally balanced subgraphs on which classical inference is safe despite global contradictions. We provide a near-linear procedure that seeds zones by confidence, tests balance using a parity-based coloring, and applies a greedy, locality-preserving repair with Jaccard de-duplication to build a compact atlas. To model belief change, we introduce shock updates that locally downscale support and elevate targeted contradictions while preserving contractivity via a simple backtracking rule. Re-propagation yields localized reconfiguration-zones may shrink, split, or collapse--without destabilizing the entire graph. We outline an empirical protocol on synthetic signed graphs with planted zones, reporting zone recovery, stability under shocks, and runtime. The result is a principled foundation for contradiction-tolerant reasoning that activates classical logic precisely where structure supports it.

Hybrid locomotion of wheeled-legged robots has recently attracted increasing attention due to their advantages of combining the agility of legged locomotion and the efficiency of wheeled motion. But along with expanded performance, the whole-body control of wheeled-legged robots remains challenging for hybrid locomotion. In this paper, we present ATRos, a reinforcement learning (RL)-based hybrid locomotion framework to achieve hybrid walking-driving motions on the wheeled-legged robot. Without giving predefined gait patterns, our planner aims to intelligently coordinate simultaneous wheel and leg movements, thereby achieving improved terrain adaptability and improved energy efficiency. Based on RL techniques, our approach constructs a prediction policy network that could estimate external environmental states from proprioceptive sensory information, and the outputs are then fed into an actor critic network to produce optimal joint commands. The feasibility of the proposed framework is validated through both simulations and real-world experiments across diverse terrains, including flat ground, stairs, and grassy surfaces. The hybrid locomotion framework shows robust performance over various unseen terrains, highlighting its generalization capability.

Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. However, in practice, the goal of inverse problem solving is not to cover the posterior but to recover the most accurate reconstruction, where optimization-based diffusion solvers often excel despite lacking a clear probabilistic foundation. We introduce Local MAP Sampling (LMAPS), a new inference framework that iteratively solving local MAP subproblems along the diffusion trajectory. This perspective clarifies their connection to global MAP estimation and DPS, offering a unified probabilistic interpretation for optimization-based methods. Building on this foundation, we develop practical algorithms with a probabilistically interpretable covariance approximation, a reformulated objective for stability and interpretability, and a gradient approximation for non-differentiable operators. Across a broad set of image restoration and scientific tasks, LMAPS achieves state-of-the-art performance, including $\geq 2$ dB gains on motion deblurring, JPEG restoration, and quantization, and $>1.5$ dB improvements on inverse scattering benchmarks.

Physical vulnerability and mortality are often seen as obstacles to be avoided in the development of artificial agents, which struggle to adapt to open-ended environments and provide aligned care. Meanwhile, biological organisms survive, thrive, and care for each other in an open-ended physical world with relative ease and efficiency. Understanding the role of the conditions of life in this disparity can aid in developing more robust, adaptive, and caring artificial agents. Here we define two minimal conditions for physical embodiment inspired by the existentialist phenomenology of Martin Heidegger: being-in-the-world (the agent is a part of the environment) and being-towards-death (unless counteracted, the agent drifts toward terminal states due to the second law of thermodynamics). We propose that from these conditions we can obtain both a homeostatic drive - aimed at maintaining integrity and avoiding death by expending energy to learn and act - and an intrinsic drive to continue to do so in as many ways as possible. Drawing inspiration from Friedrich Nietzsche's existentialist concept of will-to-power, we examine how intrinsic drives to maximize control over future states, e.g., empowerment, allow agents to increase the probability that they will be able to meet their future homeostatic needs, thereby enhancing their capacity to maintain physical integrity. We formalize these concepts within a reinforcement learning framework, which enables us to examine how intrinsically driven embodied agents learning in open-ended multi-agent environments may cultivate the capacities for open-endedness and care.

This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wherein learnt sampling policies and value functions define proposal kernels and twist functions. Exploiting this connection, we introduce an off-policy RL training procedure for the sampler that uses samples from SMC -- using the learnt sampler as a proposal -- as a behaviour policy that better explores the target distribution. We describe techniques for stable joint training of proposals and twist functions and an adaptive weight tempering scheme to reduce training signal variance. Furthermore, building upon past attempts to use experience replay to guide the training of neural samplers, we derive a way to combine historical samples with annealed importance sampling weights within a replay buffer. On synthetic multi-modal targets (in both continuous and discrete spaces) and the Boltzmann distribution of alanine dipeptide conformations, we demonstrate improvements in approximating the true distribution as well as training stability compared to both amortised and Monte Carlo methods.

Conditional sampling is a fundamental task in Bayesian statistics and generative modeling. Consider the problem of sampling from the posterior distribution $P_{X|Y=y^*}$ for some observation $y^*$, where the likelihood $P_{Y|X}$ is known, and we are given $n$ i.i.d. samples $D=\{X_i\}_{i=1}^n$ drawn from an unknown prior distribution $π_X$. Suppose that $f(\hatπ_{X^n})$ is the distribution of a posterior sample generated by an algorithm (e.g. a conditional generative model or the Bayes rule) when $\hatπ_{X^n}$ is the empirical distribution of the training data. Although averaging over the randomness of the training data $D$, we have $\mathbb{E}_D\left(\hatπ_{X^n}\right)= π_X$, we do not have $\mathbb{E}_D\left\{f(\hatπ_{X^n})\right\}= f(π_X)$ due to the nonlinearity of $f$, leading to a bias. In this paper we propose a black-box debiasing scheme that improves the accuracy of such a naive plug-in approach. For any integer $k$ and under boundedness of the likelihood and smoothness of $f$, we generate samples $\hat{X}^{(1)},\dots,\hat{X}^{(k)}$ and weights $w_1,\dots,w_k$ such that $\sum_{i=1}^kw_iP_{\hat{X}^{(i)}}$ is a $k$-th order approximation of $f(π_X)$, where the generation process treats $f$ as a black-box. Our generation process achieves higher accuracy when averaged over the randomness of the training data, without degrading the variance, which can be interpreted as improving memorization without compromising generalization in generative models.

This paper develops a finite-sample statistical theory for in-context learning (ICL), analyzed within a meta-learning framework that accommodates mixtures of diverse task types. We introduce a principled risk decomposition that separates the total ICL risk into two orthogonal components: Bayes Gap and Posterior Variance. The Bayes Gap quantifies how well the trained model approximates the Bayes-optimal in-context predictor. For a uniform-attention Transformer, we derive a non-asymptotic upper bound on this gap, which explicitly clarifies the dependence on the number of pretraining prompts and their context length. The Posterior Variance is a model-independent risk representing the intrinsic task uncertainty. Our key finding is that this term is determined solely by the difficulty of the true underlying task, while the uncertainty arising from the task mixture vanishes exponentially fast with only a few in-context examples. Together, these results provide a unified view of ICL: the Transformer selects the optimal meta-algorithm during pretraining and rapidly converges to the optimal algorithm for the true task at test time.