Transformers trained via Reinforcement Learning (RL) with outcome-based supervision can spontaneously develop the ability to generate intermediate reasoning steps (Chain-of-Thought). Yet the mechanism by which sparse rewards drive policy gradient to discover such systematic reasoning remains poorly understood. We address this by analyzing the policy gradient dynamics of single-layer linear Transformers on a synthetic graph traversal task that cannot be solved without Chain-of-Thought but admits a simple iterative solution. We prove that despite training solely on final-answer correctness, policy gradient drives the Transformer to converge to a structured, interpretable algorithm that iteratively traverses the graph vertex-by-vertex. We characterize the distributional properties required for this emergence, identifying the critical role of "simple examples": instances requiring fewer reasoning steps. When the training distribution places sufficient mass on these simpler examples, the Transformer learns a generalizable traversal strategy that extrapolates to longer chains; when this mass vanishes, policy gradient learning becomes infeasible. We corroborate our theoretical results through experiments on synthetic data and with real-world language models on mathematical reasoning tasks, validating that our theoretical findings carry over to practical settings.
Global optimization of large-scale, complex systems such as multi-physics black-box simulations and real-world industrial systems is important but challenging. This work presents a novel Surrogate-Based Optimization framework based on Clustering, SBOC for global optimization of such systems, which can be used with any surrogate modeling technique. At each iteration, it uses a single surrogate model for the entire domain, employs k-means clustering to identify unexplored domain, and exploits a local region around the surrogate optimum to potentially add three new sample points in the domain. SBOC has been tested against sixteen promising benchmarking algorithms using 52 analytical test functions of varying input dimensionalities and shape profiles. It successfully identified a global minimum for most test functions with substantially lower computational effort than other algorithms. It worked especially well on test functions with four or more input variables. It was also among the top six algorithms in approaching a global minimum closely. Overall, SBOC is a robust, reliable, and efficient algorithm for global optimization of box-constrained systems.
Community detection is a fundamental task in data analysis, and block models provide an approach for identifying diverse community structures. The degree-corrected block model (DCBM) is an established model that captures node degree heterogeneity. However, inference methods are computationally costly and sensitive to initialization, while cheaper alternatives, such as spectral or modularity-based approaches, may be less effective at recovering certain non-assortative structures. In this work, we show that DCBM inference can be reformulated as a constrained nonnegative matrix trifactorization problem. Leveraging this insight, we propose a scalable community detection method with a theoretically grounded initialization providing an initial partition for inference algorithms. Our approach is agnostic to network structure and applies to any graph representable by a DCBM. Experiments on synthetic and real-world benchmark networks show that our method achieves community recovery comparable to, and sometimes better than, that achieved by the DCBM inference methods, while being faster: it processes a graph with 100,000 nodes and 500,000 edges in about 30 seconds. Moreover, the initialization significantly improves solution quality. Overall, this work provides a scalable and robust framework for community detection and highlights the benefits of a matrix-factorization perspective for the DCBM.
Wildfires, as an integral component of the Earth system, are governed by a complex interplay of atmospheric, oceanic, and terrestrial processes spanning a vast range of spatiotemporal scales. Modeling their global activity on large timescales is therefore a critical yet challenging task. While deep learning has recently achieved significant breakthroughs in global weather forecasting, its potential for global wildfire behavior prediction remains underexplored. In this work, we reframe this problem and introduce the Hierarchical Graph ODE (HiGO), a novel framework designed to learn the multi-scale, continuous-time dynamics of wildfires. Specifically, we represent the Earth system as a multi-level graph hierarchy and propose an adaptive filtering message passing mechanism for both intra- and inter-level information flow, enabling more effective feature extraction and fusion. Furthermore, we incorporate GNN-parameterized Neural ODE modules at multiple levels to explicitly learn the continuous dynamics inherent to each scale. Through extensive experiments on the SeasFire Cube dataset, we demonstrate that HiGO significantly outperforms state-of-the-art baselines on long-range wildfire forecasting. Moreover, its continuous-time predictions exhibit strong observational consistency, highlighting its potential for real-world applications.
We develop a data-driven framework for discovering constitutive relations in models of fluid flow and scalar transport. Under the assumption that velocity and/or scalar fields are measured, our approach infers unknown closure terms in the governing equations as neural networks. The target to be discovered is the constitutive relations only, while the temporal derivative, convective transport terms, and pressure-gradient term in the governing equations are prescribed. The formulation is rooted in a variational principle from non-equilibrium thermodynamics, where the dynamics is defined by a free-energy functional and a dissipation functional. The unknown constitutive terms arise as functional derivatives of these functionals with respect to the state variables. To enable a flexible and structured model discovery, the free-energy and dissipation functionals are parameterized using neural networks, while their functional derivatives are obtained via automatic differentiation. This construction enforces thermodynamic consistency by design, guaranteeing monotonic decay of the total free energy and non-negative entropy production. The resulting method, termed GIMLET (Generalizable and Interpretable Model Learning through Embedded Thermodynamics), avoids reliance on a predefined library of candidate functions, unlike sparse regression or symbolic identification approaches. The learned models are generalizable in that functionals identified from one dataset can be transferred to distinct datasets governed by the same underlying equations. Moreover, the inferred free-energy and dissipation functions provide direct physical interpretability of the learned dynamics. The framework is demonstrated on several benchmark systems, including the viscous Burgers equation, the Kuramoto--Sivashinsky equation, and the incompressible Navier--Stokes equations for both Newtonian and non-Newtonian fluids.
Recent multimodal large language models (MLLMs) show great potential in natural image understanding. Yet, they perform well, mainly on reasoning in-view contents within the image frame. This paper presents the first study on out-of-view (OOV) understanding, i.e., the ability to reason about objects, activities, and scenes beyond the visible frame of a perspective view. Our technical contributions are threefold. First, we design OpenView, a four-stage pipeline that leverages panoramic imagery for large-scale and diverse multi-choice VQA synthesis, where full-scene coverage enables flexible view framing while preserving global scene awareness. Second, we curate OpenView-Dataset, a high-quality synthetic dataset from diverse real-world panoramas to empower MLLMs upon supervised fine-tuning. Third, we build OpenView-Bench, a benchmark that jointly measures choice and rationale accuracy for interpretable and diagnosable evaluation. Experimental results show that despite having a large gap from human performance in OOV VQA answer selection, multiple MLLMs, upon empowered by OpenView, can consistently boost their performance, uplifted from 48.3% to 62.3% on average. Code, benchmark, and data are available at https://github.com/q1xiangchen/OpenView.
Training high-performing language models which include medium- and lower-resource languages remains a challenge. Massively multilingual models still underperform language-specific adaptations, especially at smaller scales, due to the curse of multilinguality. In this work, we investigate scaling as an efficient strategy for adapting pretrained models to new target languages. Through comprehensive ablations matched for data and training FLOPs, we test whether upscaling from English base models enables more effective and resource-efficient adaptation than standard continued pretraining. We find that upscaling is an efficient strategy for improving target-language performance by relieving capacity constraints, especially for higher-resourced languages. An initial upscaling step in English is beneficial for low-resource languages. However, in higher-resource scenarios it is more compute-efficient to directly scale up on the target language, albeit slightly compromising data efficiency for most languages. For multilingual continued pre-training, we identify directly scaling up using the target data as the optimal setup for both data efficiency and reduced English forgetting.
Training end-to-end policies from image data to directly predict navigation actions for robotic systems has proven inherently difficult. Existing approaches often suffer from either the sim-to-real gap during policy transfer or limited action-labeled training data. To address this problem, we introduce Visual Learned Distance (VLD), a scalable framework for image-goal navigation that decouples perception learning from policy learning. We first train a self-supervised distance-to-goal predictor on about 3,000 hours of internet-scale and simulated video, providing a distance signal that a reinforcement learning (RL) policy can minimize. The RL policy is trained separately in simulation using privileged geometric distances perturbed by GeoNoise, a learned noise model that reproduces the viewpoint- and overlap-dependent errors of the trained distance predictor. At deployment, the policy consumes VLD predictions zero-shot, without retraining, inheriting ``where to go'' from large-scale visual training while retaining the robust navigation behaviors learned in simulation. This error modeling is key to the transfer: with VLD inputs, GeoNoise-trained policies reach $58.7\%$ success on HM3D and $76.2\%$ on Gibson, whereas policies trained with generic temporally correlated noise collapse to $4.9\%$ and $11.5\%$. On a physical robot, the VLD-driven policy succeeds in $88\%$ of trials, compared with $60\%$ for a strong end-to-end image-goal baseline that outperforms it in simulation. Our decoupled design thus provides an alternative and scalable path toward reliable navigation policies that transfer from simulation to the real world.
Neural architecture search (NAS) in expressive search spaces is a computationally hard problem, but it also holds the potential to automatically discover completely novel and performant architectures. To achieve this we need effective search algorithms that can identify powerful components and reuse them in new candidate architectures. In this paper, we introduce two adapted variants of the Smith-Waterman algorithm for local sequence alignment and use them to compute the edit distance in a grammar-based evolutionary architecture search. These algorithms enable us to efficiently calculate a distance metric for neural architectures and to generate a set of hybrid offspring from two parent models. This facilitates the deployment of crossover-based search heuristics, allows us to perform a thorough analysis on the architectural loss landscape, and track population diversity during search. We highlight how our method vastly improves computational complexity over previous work and enables us to efficiently compute shortest paths between architectures. When instantiating the crossover in evolutionary searches, we achieve competitive results, outperforming competing methods. Future work can build upon this new tool, discovering novel components that can be used more broadly across neural architecture design, and broadening its applications beyond NAS.
Embodied agents are expected to assist humans by actively exploring unknown environments and reasoning about spatial contexts. When deployed in real life, agents often face sequential tasks where each new task follows the completion of the previous one and may include infeasible objectives, such as searching for non-existent objects. However, most existing research focuses on isolated goals, overlooking the core challenge of sequential tasks: the ability to reuse spatial knowledge accumulated from previous explorations to guide subsequent reasoning and exploration. In this work, we investigate this underexplored yet practically significant embodied AI challenge. Specifically, we propose 3DSPMR, a 3D SPatial Memory Reasoning framework that utilizes Field-of-View (FoV) coverage as an explicit geometric prior. By integrating FoV-based constraints, 3DSPMR significantly enhances an agent's memory, reasoning, and exploration capabilities across sequential tasks. To facilitate research in this area, we further introduce SEER-Bench, a novel Sequential Embodied Exploration and Reasoning Benchmark that spans two foundational tasks: Embodied Question Answering (EQA) and Embodied Multi-modal Navigation (EMN). SEER-Bench uniquely incorporates both feasible and infeasible tasks to provide a rigorous and comprehensive evaluation of agent performance. Extensive experiments verify that 3DSPMR achieves substantial performance gains on both sequential EQA and EMN tasks.
Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex operators, leading to substantial computational costs. Neural operators have recently emerged as a powerful framework for learning mappings between function spaces directly from data, enabling efficient surrogate models for PDE systems. Among these architectures, the Fourier Neural Operator (FNO) has become the most influential and widely adopted due to its elegant spectral formulation, which captures global correlations through learnable transformations in Fourier space while remaining invariant to discretization and resolution. Despite their success, the practical use of FNOs is often hindered by an incomplete understanding among practitioners of their theoretical foundations, practical constraints, and implementation details, which can lead to their incorrect or unreliable application. This work presents a comprehensive and practice-oriented guide to FNOs, unifying their mathematical principles with implementation strategies. We provide an intuitive exposition of the concepts of operator theory and signal processing that underlie the FNO, detail its spectral parameterization and the computational design of all its components, and address common misunderstandings encountered in the literature. The exposition is closely integrated with the NeuralOperator 2.0.0 library, offering modular state-of-the-art implementations that faithfully reflect the theory. By connecting rigorous foundations with practical insight, this guide aims to establish a clear and reliable framework for applying FNOs effectively across diverse scientific and engineering fields.
When the distributions of the training and test data do not coincide, the problem of understanding generalization becomes considerably more complex, prompting a variety of questions. Prior work has shown that, for some fixed learning methods, there are scenarios where training on a distribution different from the test distribution improves generalization. However, these results do not account for the possibility of choosing, for each training distribution, the optimal learning algorithm, leaving open whether the observed benefits stem from the mismatch itself or from suboptimality of the learner. In this work, we address this question. That is, we study whether it is always optimal for the training distribution to be identical to the test distribution when the learner is allowed to be optimally adapted to the training distribution. Surprisingly, when we restrict our attention to efficient learners, i.e., those running in polynomial time, and assume the existence of one-way functions, the answer is negative. In other words, matching the training and test distributions is not always optimal.
The electric power sector is a leading source of air pollutant emissions, impacting the public health of nearly every community. Although regulatory measures have reduced air pollutants, fossil fuels remain a significant component of the energy supply, highlighting the need for more advanced demand-side approaches to reduce the public health impacts. To enable health-informed demand-side management, we introduce HealthPredictor, a domain-specific AI model that provides an end-to-end pipeline linking electricity use to public health outcomes. The model comprises three components: a fuel mix predictor that estimates the contribution of different generation sources, an air quality converter that models pollutant emissions and atmospheric dispersion, and a health impact assessor that translates resulting pollutant changes into monetized health damages. Across multiple regions in the United States, our health-driven optimization framework yields substantially lower prediction errors in terms of public health impacts than fuel mix-driven baselines. A case study on electric vehicle charging schedules illustrates the public health gains enabled by our method and the actionable guidance it can offer for health-informed energy management. Overall, this work shows how AI models can be explicitly designed to enable health-informed energy management for advancing public health and broader societal well-being. Our datasets and code are released at: https://github.com/Ren-Research/Health-Impact-Predictor.
Practical LLM agents often operate over multi-turn conversations where success is determined only after the full interaction ends. Most multi-turn RL methods train via on-policy rollouts, but unlike in single-turn RL, the policy cannot produce a trajectory alone, since an external environment must respond after each agent turn. For conversational agents, this environment is a user, but real users are generally unavailable inside the training loop and simulated users are difficult to build faithfully. Separately, real-world deployment is rarely fully online or fully offline. The common production pattern is called batch online, where the current policy is deployed to collect a batch of interaction data, then retrained on that batch and redeployed. We show that this batch-online setting creates an opportunity for applying the classical approximate policy iteration algorithm. Our central observation is that running standard token-level, single-turn GRPO with a learned turn-level $Q$-function as the reward model is a policy improvement step for the multi-turn problem. Building on this, we present Iterative Policy Optimization (IterPO), which alternates between fitting $Q^\pi$ from logged Monte Carlo returns via standard reward modeling (policy evaluation) and running single-turn GRPO against $Q^\pi$ (policy improvement). During policy improvement, the learned $Q^\pi$ scores candidate responses by their expected downstream return, avoiding the need for simulator rollouts of the remaining conversation. Overall, this allows us to do principled multi-turn RL using only single-turn RL methods without an interactive environment or user simulator inside the training loop. We demonstrate the effectiveness of IterPO on six multi-turn negotiation environments.
Foundation models trained on text and images have been shown to develop abstract internal features that align with human concepts and that can be directly manipulated via activation steering to alter model behaviour. Whether scientific foundation models learn similarly abstract and domain-general representations has remained an open question. Inspired by recent work identifying single directions in activation space that control complex behaviours in large language models, we show that Walrus, a large physics foundation model, learns linearly steerable representations of physical phenomena. By computing the difference between activations representing contrasting physical regimes, we identify single directions in activation space that correspond to vorticity, diffusion, and even temporal progression. We find that injecting these concept directions back into the model during inference enables fine-grained causal control: vortices can be induced or removed, diffusion enhanced or suppressed, and simulations sped up or slowed down. Moreover, directions derived from one physical system also steer the behaviour of other physical systems, suggesting that they are domain-general. These results provide early evidence that scientific foundation models can learn general representations of physical principles, and further support for the Linear Representation Hypothesis.
Learning embodied manipulation from egocentric human data offers a scalable path, reducing the cost of collecting robot-specific demonstrations. However, existing representation learning methods largely stop at perceptual understanding, such as extracting what a scene contains or what an action is. A capable embodied agent is more than understanding: it predicts the next motion. We propose that forecasting 3D human hand motion is one suitable pretraining task, as the representation jointly learns how to manipulate objects and how the motion will unfold next. Building on this hypothesis, we introduce SFHand, the first representation learning method via streaming egocentric 3D hand forecasting. SFHand learns by autoregressively predicting future 3D hand states, including hand type, 2D bounding box, 3D pose, and trajectory, from a continuous stream of video and language instructions. Its autoregressive architecture is equipped with an ROI-enhanced memory layer, capturing temporal context while focusing on salient hand-centric regions. To enable this research, we also introduce SFHand, the first open-source large-scale dataset pairing synchronized 3D hand poses with fine-grained language instructions (247K clips, 3.95M frames). Transferred to downstream embodied control, the learned representation shows state-of-the-art performance on both simulation and real-world manipulation benchmarks, improving success rate by up to 13.4%. Our method also achieves leading 3D hand forecasting accuracy, with 35.8% lower ADE than baseline methods. These results suggest that forecasting hand motion is a better pretraining task for representation learning in embodied manipulation. Projec page: https://ruicongliu.github.io/sfhand/.
Multi-output Gaussian process (MOGP) regression allows modelling dependencies among multiple correlated response variables. Similarly to standard Gaussian processes (GPs), MOGPs are sensitive to model misspecification and outliers, which can distort predictions within individual outputs. In the multi-output case, this situation can be further exacerbated as anomalous observations in one response can adversely influence predictions for other correlated outputs. To handle this situation, we propose R-MOGP, an MOGP that is provably robust to outliers in any individual response. Our approach preserves conjugacy, achieving robustness without sacrificing computational efficiency, and integrates naturally with sparse variational inference for scalability. Empirically, we show that R-MOGP achieves performance comparable to existing state-of-the-art robust MOGPs at a fraction of their computational costs.
We study in-context learning problems where a Transformer is pretrained on tasks drawn from a mixture distribution $\pi=\sum_{\alpha\in\mathcal{A}} \lambda_{\alpha} \pi_{\alpha}$, called the pretraining prior, in which each mixture component $\pi_{\alpha}$ is a distribution on tasks of a specific difficulty level indexed by $\alpha$. Our goal is to understand the performance of the pretrained Transformer when evaluated on a different test distribution $\mu$, consisting of tasks of fixed difficulty $\beta\in\mathcal{A}$, and with potential distribution shift relative to $\pi_\beta$, subject to the chi-squared divergence $\chi^2(\mu,\pi_{\beta})$ being at most $\kappa$. In particular, we consider nonparametric regression problems with random smoothness, and multi-index models with both random smoothness and random effective dimension. We prove that a large Transformer pretrained on sufficient data achieves the optimal rate of convergence corresponding to the difficulty level $\beta$, uniformly over test distributions $\mu$ in the chi-squared divergence ball. Thus, the pretrained Transformer is able to achieve faster rates of convergence on easier tasks and is robust to distribution shift at test time. Finally, we prove that even if an estimator had access to the test distribution $\mu$, the convergence rate of its expected risk over $\mu$ could not be faster than that of our pretrained Transformers, thereby providing a more appropriate optimality guarantee than minimax lower bounds.
Large language models (LLMs) now support context windows of hundreds of thousands to millions of tokens, enabling applications such as long-document summarization, large-scale code synthesis, multi-document question answering and persistent multi-turn dialogue. However, such extended contexts exacerbate the quadratic cost of self-attention, leading to severe latency in autoregressive decoding. Existing sparse attention methods reduce these costs by attending to only a subset of key-value (KV) tokens, but fixed or coarse-grained selection strategies can miss important tokens or retain substantial redundancy under constrained token budgets. We introduce \textbf{Adamas}, an accurate and efficient token-level sparse attention mechanism for long-context inference. Adamas applies the Hadamard transform, bucketization and 2-bit compression to produce compact representations, and uses lightweight distance-based estimation for efficient top-$k$ candidate selection. The selected positions are then used to gather the corresponding original KV states for sparse attention. Comprehensive evaluations show that Adamas maintains near-lossless performance within the effective context length of Llama-3.1-8B-Instruct. In efficiency evaluations, Adamas achieves up to $6.5\times$ self-attention speedup and $1.7\times$ end-to-end decoding speedup at a 32K context length. Adamas also maintains performance comparable to full attention on challenging long-form reasoning benchmarks, including AIME 2024 and AIME 2025.
Coral reef monitoring requires scalable recognition of visually similar taxa across heterogeneous underwater surveys. We introduce ReefNet, a public dataset that aligns approximately 925K hard-coral point annotations from 76 CoralNet sources and an independently collected Al-Wajh dataset with the World Register of Marine Species taxonomy. A stratified expert audit of 8,962 patches guides filtering to a 479,027-annotation benchmark with 39 labels: 38 genera and the family Fungiidae. Expert agreement is 92% on the retained audit subset, rather than an exhaustive accuracy estimate. We evaluate pretrained models through zero-shot recognition, few-shot adaptation, and full fine-tuning, each on within-source ReefNet and held-out-source Al-Wajh tests. Biological vision-language pretraining provides the strongest zero-shot results; supervised adaptation substantially improves recognition, with DINOv2 reaching 65.79% macro recall on Al-Wajh. Matched text-description experiments improve all four evaluated MLLMs on Al-Wajh, while a GPT-5.4 reasoning ablation does not improve over direct classification. Long-tail recognition, label uncertainty, and geographic imbalance remain challenges. ReefNet provides a taxonomically grounded resource for studying these challenges; the Al-Wajh test is a regional stress test rather than evidence of global robustness. Public data and resource links are documented in the supplement.