Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators

The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle distribution functions (PDFs). Despite its success, solving the LBE numerically remains computationally intensive due to strict time-step restrictions imposed by collision kernels. Here, we introduce a physics-informed neural operator framework for the LBE that enables prediction over large time horizons without step-by-step integration, effectively bypassing the need to explicitly solve the collision kernel. We incorporate intrinsic moment-matching constraints of the LBE, along with global equivariance of the full distribution field, enabling the model to capture the complex dynamics of the underlying kinetic system. Our framework is discretization-invariant, enabling models trained on coarse lattices to generalise to finer ones (kinetic super-resolution). In addition, it is agnostic to the specific form of the underlying collision model, which makes it naturally applicable across different kinetic datasets regardless of the governing dynamics. Our results demonstrate robustness across complex flow scenarios, including von Karman vortex shedding, ligament breakup, and bubble adhesion. This establishes a new data-driven pathway for modelling kinetic systems.

Towards Community-Driven Agents for Machine Learning Engineering

Large language model-based machine learning (ML) agents have shown great promise in automating ML research. However, existing agents typically operate in isolation on a given research problem, without engaging with the broader research community, where human researchers often gain insights and contribute by sharing knowledge. To bridge this gap, we introduce MLE-Live, a live evaluation framework designed to assess an agent's ability to communicate with and leverage collective knowledge from a simulated Kaggle research community. Building on this framework, we propose CoMind, a novel agent that excels at exchanging insights and developing novel solutions within a community context. CoMind achieves state-of-the-art performance on MLE-Live and outperforms 79.2% human competitors on average across four ongoing Kaggle competitions. Our code is released at https://github.com/comind-ml/CoMind.

Towards an Introspective Dynamic Model of Globally Distributed Computing Infrastructures

Large-scale scientific collaborations like ATLAS, Belle II, CMS, DUNE, and others involve hundreds of research institutes and thousands of researchers spread across the globe. These experiments generate petabytes of data, with volumes soon expected to reach exabytes. Consequently, there is a growing need for computation, including structured data processing from raw data to consumer-ready derived data, extensive Monte Carlo simulation campaigns, and a wide range of end-user analysis. To manage these computational and storage demands, centralized workflow and data management systems are implemented. However, decisions regarding data placement and payload allocation are often made disjointly and via heuristic means. A significant obstacle in adopting more effective heuristic or AI-driven solutions is the absence of a quick and reliable introspective dynamic model to evaluate and refine alternative approaches. In this study, we aim to develop such an interactive system using real-world data. By examining job execution records from the PanDA workflow management system, we have pinpointed key performance indicators such as queuing time, error rate, and the extent of remote data access. The dataset includes five months of activity. Additionally, we are creating a generative AI model to simulate time series of payloads, which incorporate visible features like category, event count, and submitting group, as well as hidden features like the total computational load-derived from existing PanDA records and computing site capabilities. These hidden features, which are not visible to job allocators, whether heuristic or AI-driven, influence factors such as queuing times and data movement.

Maximal Update Parametrization and Zero-Shot Hyperparameter Transfer for Fourier Neural Operators

Fourier Neural Operators (FNOs) offer a principled approach for solving complex partial differential equations (PDEs). However, scaling them to handle more complex PDEs requires increasing the number of Fourier modes, which significantly expands the number of model parameters and makes hyperparameter tuning computationally impractical. To address this, we introduce $\mu$Transfer-FNO, a zero-shot hyperparameter transfer technique that enables optimal configurations, tuned on smaller FNOs, to be directly applied to billion-parameter FNOs without additional tuning. Building on the Maximal Update Parametrization ($\mu$P) framework, we mathematically derive a parametrization scheme that facilitates the transfer of optimal hyperparameters across models with different numbers of Fourier modes in FNOs, which is validated through extensive experiments on various PDEs. Our empirical study shows that Transfer-FNO reduces computational cost for tuning hyperparameters on large FNOs while maintaining or improving accuracy.

RelTopo: Enhancing Relational Modeling for Driving Scene Topology Reasoning

Accurate road topology reasoning is critical for autonomous driving, enabling effective navigation and adherence to traffic regulations. Central to this task are lane perception and topology reasoning. However, existing methods typically focus on either lane detection or Lane-to-Lane (L2L) topology reasoning, often \textit{neglecting} Lane-to-Traffic-element (L2T) relationships or \textit{failing} to optimize these tasks jointly. Furthermore, most approaches either overlook relational modeling or apply it in a limited scope, despite the inherent spatial relationships among road elements. We argue that relational modeling is beneficial for both perception and reasoning, as humans naturally leverage contextual relationships for road element recognition and their connectivity inference. To this end, we introduce relational modeling into both perception and reasoning, \textit{jointly} enhancing structural understanding. Specifically, we propose: 1) a relation-aware lane detector, where our geometry-biased self-attention and \curve\ cross-attention refine lane representations by capturing relational dependencies; 2) relation-enhanced topology heads, including a geometry-enhanced L2L head and a cross-view L2T head, boosting reasoning with relational cues; and 3) a contrastive learning strategy with InfoNCE loss to regularize relationship embeddings. Extensive experiments on OpenLane-V2 demonstrate that our approach significantly improves both detection and topology reasoning metrics, achieving +3.1 in DET$_l$, +5.3 in TOP$_{ll}$, +4.9 in TOP$_{lt}$, and an overall +4.4 in OLS, setting a new state-of-the-art. Code will be released.

Large Language Models are Demonstration Pre-Selectors for Themselves

In-context learning (ICL) with large language models (LLMs) delivers strong few-shot performance by choosing few-shot demonstrations from the entire training data. However, existing ICL methods, which rely on similarity or diversity scores to choose demonstrations, incur high computational costs due to repeatedly retrieval from large-scale datasets for each query. To this end, we propose FEEDER (FEw yet Essential Demonstration prE-selectoR), a novel pre-selection framework that identifies a representative subset of demonstrations containing the most representative examples in the training data, tailored to specific LLMs. To construct this subset, we introduce the "sufficiency" and "necessity" metrics in the pre-selection stage and design a tree-based algorithm to identify representative examples efficiently. Once pre-selected, this representative subset can effectively replace the full training data, improving efficiency while maintaining comparable performance in ICL. Additionally, our pre-selected subset also benefits fine-tuning LLMs, where we introduce a bi-level optimization method that enhances training efficiency without sacrificing performance. Experiments with LLMs ranging from 300M to 8B parameters show that FEEDER can reduce training data size by over 20% while maintaining performance and seamlessly integrating with various downstream demonstration selection strategies in ICL.

Sample Complexity and Representation Ability of Test-time Scaling Paradigms

Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $\Theta(1/\Delta^2)$ samples to produce the correct answer, while best-of-$n$ only needs $\Theta(1/\Delta)$, where $\Delta < 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods.

Do Large Language Models Think Like the Brain? Sentence-Level Evidence from fMRI and Hierarchical Embeddings

Understanding whether large language models (LLMs) and the human brain converge on similar computational principles remains a fundamental and important question in cognitive neuroscience and AI. Do the brain-like patterns observed in LLMs emerge simply from scaling, or do they reflect deeper alignment with the architecture of human language processing? This study focuses on the sentence-level neural mechanisms of language models, systematically investigating how hierarchical representations in LLMs align with the dynamic neural responses during human sentence comprehension. By comparing hierarchical embeddings from 14 publicly available LLMs with fMRI data collected from participants, who were exposed to a naturalistic narrative story, we constructed sentence-level neural prediction models to precisely identify the model layers most significantly correlated with brain region activations. Results show that improvements in model performance drive the evolution of representational architectures toward brain-like hierarchies, particularly achieving stronger functional and anatomical correspondence at higher semantic abstraction levels.

Enhancing Training Data Attribution with Representational Optimization

Training data attribution (TDA) methods aim to measure how training data impacts a model's predictions. While gradient-based attribution methods, such as influence functions, offer theoretical grounding, their computational costs make them impractical for large-scale applications. Representation-based approaches are far more scalable, but typically rely on heuristic embeddings that are not optimized for attribution, limiting their fidelity. To address these challenges, we propose AirRep, a scalable, representation-based approach that closes this gap by learning task-specific and model-aligned representations optimized explicitly for TDA. AirRep introduces two key innovations: a trainable encoder tuned for attribution quality, and an attention-based pooling mechanism that enables accurate estimation of group-wise influence. We train AirRep using a ranking objective over automatically constructed training subsets labeled by their empirical effect on target predictions. Experiments on instruction-tuned LLMs demonstrate that AirRep achieves performance on par with state-of-the-art gradient-based approaches while being nearly two orders of magnitude more efficient at inference time. Further analysis highlights its robustness and generalization across tasks and models. Our code is available at https://github.com/sunnweiwei/AirRep.

A Comprehensive Evaluation of Contemporary ML-Based Solvers for Combinatorial Optimization

Machine learning (ML) has demonstrated considerable potential in supporting model design and optimization for combinatorial optimization (CO) problems. However, much of the progress to date has been evaluated on small-scale, synthetic datasets, raising concerns about the practical effectiveness of ML-based solvers in real-world, large-scale CO scenarios. Additionally, many existing CO benchmarks lack sufficient training data, limiting their utility for evaluating data-driven approaches. To address these limitations, we introduce FrontierCO, a comprehensive benchmark that covers eight canonical CO problem types and evaluates 16 representative ML-based solvers--including graph neural networks and large language model (LLM) agents. FrontierCO features challenging instances drawn from industrial applications and frontier CO research, offering both realistic problem difficulty and abundant training data. Our empirical results provide critical insights into the strengths and limitations of current ML methods, helping to guide more robust and practically relevant advances at the intersection of machine learning and combinatorial optimization. Our data is available at https://huggingface.co/datasets/CO-Bench/FrontierCO.