Artificial intelligence (AI) is reshaping scientific discovery, evolving from specialized computational tools into autonomous research partners. We position Agentic Science as a pivotal stage within the broader AI for Science paradigm, where AI systems progress from partial assistance to full scientific agency. Enabled by large language models (LLMs), multimodal systems, and integrated research platforms, agentic AI shows capabilities in hypothesis generation, experimental design, execution, analysis, and iterative refinement -- behaviors once regarded as uniquely human. This survey provides a domain-oriented review of autonomous scientific discovery across life sciences, chemistry, materials science, and physics. We unify three previously fragmented perspectives -- process-oriented, autonomy-oriented, and mechanism-oriented -- through a comprehensive framework that connects foundational capabilities, core processes, and domain-specific realizations. Building on this framework, we (i) trace the evolution of AI for Science, (ii) identify five core capabilities underpinning scientific agency, (iii) model discovery as a dynamic four-stage workflow, (iv) review applications across the above domains, and (v) synthesize key challenges and future opportunities. This work establishes a domain-oriented synthesis of autonomous scientific discovery and positions Agentic Science as a structured paradigm for advancing AI-driven research.

Test-Time Scaling (TTS) improves the performance of Large Language Models (LLMs) by using additional inference-time computation to explore multiple reasoning paths through search. Yet how to allocate a fixed rollout budget most effectively during search remains underexplored, often resulting in inefficient use of compute at test time. To bridge this gap, we formulate test-time search as a resource allocation problem and derive the optimal allocation strategy that maximizes the probability of obtaining a correct solution under a fixed rollout budget. Within this formulation, we reveal a core limitation of existing search methods: solution-level allocation tends to favor reasoning directions with more candidates, leading to theoretically suboptimal and inefficient use of compute. To address this, we propose Direction-Oriented Resource Allocation (DORA), a provably optimal method that mitigates this bias by decoupling direction quality from candidate count and allocating resources at the direction level. To demonstrate DORA's effectiveness, we conduct extensive experiments on challenging mathematical reasoning benchmarks including MATH500, AIME2024, and AIME2025. The empirical results show that DORA consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art accuracy. We hope our findings contribute to a broader understanding of optimal TTS for LLMs.

We present a modular framework for solving a motion planning problem among a group of robots. The proposed framework utilizes a finite set of low level motion primitives to generate motions in a gridded workspace. The constraints on allowable sequences of motion primitives are formalized through a maneuver automaton. At the high level, a control policy determines which motion primitive is executed in each box of the gridded workspace. We state general conditions on motion primitives to obtain provably correct behavior so that a library of safe-by-design motion primitives can be designed. The overall framework yields a highly robust design by utilizing feedback strategies at both the low and high levels. We provide specific designs for motion primitives and control policies suitable for multi-robot motion planning; the modularity of our approach enables one to independently customize the designs of each of these components. Our approach is experimentally validated on a group of quadrocopters.

Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $\sqrt n$-convergence. In this work, we present two complementary results (with different proof strategies), establishing that the minimax lower bound of KSD estimation is $n^{-1/2}$ and settling the optimality of these estimators. Our first result focuses on KSD estimation on $\mathbb R^d$ with the Langevin-Stein operator; our explicit constant for the Gaussian kernel indicates that the difficulty of KSD estimation may increase exponentially with the dimensionality $d$. Our second result settles the minimax lower bound for KSD estimation on general domains.

Large language models (LLMs) are increasingly demonstrating strong capabilities as autonomous agents, with function calling serving as a core mechanism for interaction with the environment. Meanwhile, inference scaling has become a cutting-edge technique to enhance LLM performance by allocating more computational resources during the inference process. However, current research on inference scaling primarily focuses on unstructured output generation tasks, leaving its application in structured outputs, like function calling, largely underexplored. To bridge this gap, we propose an inference scaling framework that combines fine-grained beam search with a process reward model, ToolPRM, which scores the internal steps of each single function call. To train ToolPRM, we construct the first fine-grained intra-call process supervision dataset, automatically annotated with function-masking techniques to provide step-level rewards for structured tool-use reasoning. Extensive experiments demonstrate that ToolPRM beats the coarse-grained and outcome reward models in terms of predictive accuracy, indicating its stronger capability in supervising the function calling inference process. Inference scaling technique equipped with ToolPRM also significantly improves the backbone model performance across various function calling tasks and benchmarks. More importantly, we reveal a key principle for applying inference scaling techniques to structured outputs: "explore more but retain less" due to the unrecoverability characteristics of structured function calling generation.

Current frameworks for consensus statement generation with large language models lack the inherent structure needed to provide provable fairness guarantees when aggregating diverse free-form opinions. We model the task as a multi-objective, token-level Markov Decision Process (MDP), where each objective corresponds to an agent's preference. Token-level rewards for each agent are derived from their policy (e.g., a personalized language model). This approach utilizes the finding that such policies implicitly define optimal Q-functions, providing a principled way to quantify rewards at each generation step without a value function (Rafailov et al., 2024). This MDP formulation creates a formal structure amenable to analysis using principles from social choice theory. We propose two approaches grounded in social choice theory. First, we propose a stochastic generation policy guaranteed to be in the ex-ante core, extending core stability concepts from voting theory to text generation. This policy is derived from an underlying distribution over complete statements that maximizes proportional fairness (Nash Welfare). Second, for generating a single statement, we target the maximization of egalitarian welfare using search algorithms within the MDP framework. Empirically, experiments using language models to instantiate agent policies show that search guided by the egalitarian objective generates consensus statements with improved worst-case agent alignment compared to baseline methods, including the Habermas Machine (Tessler et al., 2024).

Adapting to diverse user needs at test time is a key challenge in controllable multi-objective generation. Existing methods are insufficient: merging-based approaches provide indirect, suboptimal control at the parameter level, often disregarding the impacts of multiple objectives. While decoding-based guidance is more direct, it typically requires aggregating logits from multiple expert models, incurring significant space overhead and relying heavily on individual model capacity. To address these issues, we introduce Merge-And-GuidE (MAGE), a two-stage framework that leverages model merging for guided decoding. We first identify a critical compatibility problem between the guidance and base models. In Stage 1, MAGE resolves this by dynamically constructing a more robust base model, merging a series of backbone models that account for multiple objectives. In Stage 2, we merge explicit and implicit value models into a unified guidance proxy, which then steers the decoding of the base model from Stage 1. Our analysis empirically validates Linear Mode Connectivity (LMC) in value models, explores the relationship between model merging and prediction ensembling, and demonstrates the enhanced controllability afforded by our approach. Extensive experiments show that our method outperforms existing approaches, achieving superior controllability, Pareto-optimal performance, and enhanced adaptability.

Long-horizon embodied planning is challenging because the world does not only change through an agent's actions: exogenous processes (e.g., water heating, dominoes cascading) unfold concurrently with the agent's actions. We propose a framework for abstract world models that jointly learns (i) symbolic state representations and (ii) causal processes for both endogenous actions and exogenous mechanisms. Each causal process models the time course of a stochastic cause-effect relation. We learn these world models from limited data via variational Bayesian inference combined with LLM proposals. Across five simulated tabletop robotics environments, the learned models enable fast planning that generalizes to held-out tasks with more objects and more complex goals, outperforming a range of baselines.

We address the bin packing problem (BPP), which aims to maximize bin utilization when packing a variety of items. The offline problem, where the complete information about the item set and their sizes is known in advance, is proven to be NP-hard. The semi-online and online variants are even more challenging, as full information about incoming items is unavailable. While existing methods have tackled both 2D and 3D BPPs, the 2D BPP remains underexplored in terms of fully maximizing utilization. We propose a hierarchical approach for solving the 2D online and semi-online BPP by combining deep reinforcement learning (RL) with heuristic search. The heuristic search selects which item to pack or unpack, determines the packing order, and chooses the orientation of each item, while the RL agent decides the precise position within the bin. Our method is capable of handling diverse scenarios, including repacking, varying levels of item information, differing numbers of accessible items, and coordination of dual manipulators. Experimental results demonstrate that our approach achieves near-optimal utilization across various practical scenarios, largely due to its repacking capability. In addition, the algorithm is evaluated in a physics-based simulation environment, where execution time is measured to assess its real-world performance.

Boosting methods often achieve excellent classification accuracy, but can experience notable performance degradation in the presence of label noise. Existing robust methods for boosting provide theoretical robustness guarantees for certain types of label noise, and can exhibit only moderate performance degradation. However, previous theoretical results do not account for realistic types of noise and finite training sizes, and existing robust methods can provide unsatisfactory accuracies, even without noise. This paper presents methods for robust minimax boosting (RMBoost) that minimize worst-case error probabilities and are robust to general types of label noise. In addition, we provide finite-sample performance guarantees for RMBoost with respect to the error obtained without noise and with respect to the best possible error (Bayes risk). The experimental results corroborate that RMBoost is not only resilient to label noise but can also provide strong classification accuracy.