Inverse tasks can uncover potential reasoning gaps as Large Language Models (LLMs) scale up. In this work, we explore the redefinition task, in which we assign alternative values to well-known physical constants and units of measure, prompting LLMs to respond accordingly. Our findings show that not only does model performance degrade with scale, but its false confidence also rises. Moreover, while factors such as prompting strategies or response formatting are influential, they do not preclude LLMs from anchoring to memorized values.

Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a framework for metric MSTs that first (1) finds a forest of disconnected components using practical heuristics, and then (2) finds a small weight set of edges to connect disjoint components of the forest into a spanning tree. We prove that optimally solving the second step still takes $\Omega(n^2)$ time, but we provide a subquadratic 2.62-approximation algorithm. In the spirit of learning-augmented algorithms, we then show that if the forest found in step (1) overlaps with an optimal MST, we can approximate the original MST problem in subquadratic time, where the approximation factor depends on a measure of overlap. In practice, we find nearly optimal spanning trees for a wide range of metrics, while being orders of magnitude faster than exact algorithms.

Time series clustering poses a significant challenge with diverse applications across domains. A prominent drawback of existing solutions lies in their limited interpretability, often confined to presenting users with centroids. In addressing this gap, our work presents $k$-Graph, an unsupervised method explicitly crafted to augment interpretability in time series clustering. Leveraging a graph representation of time series subsequences, $k$-Graph constructs multiple graph representations based on different subsequence lengths. This feature accommodates variable-length time series without requiring users to predetermine subsequence lengths. Our experimental results reveal that $k$-Graph outperforms current state-of-the-art time series clustering algorithms in accuracy, while providing users with meaningful explanations and interpretations of the clustering outcomes.

In-silico material discovery and design have traditionally relied on high-fidelity first-principles methods such as density functional theory (DFT) [1] and ab-initio molecular dynamics (AIMD) [2] to accurately model atomic interactions and predict material properties. Despite their effectiveness, these methods face significant challenges due to their prohibitive computational cost, limiting their scalability for highthroughput screening across vast chemical spaces and for simulations over large length and time scales. Moreover, many advanced materials remain beyond the reach of widespread predictive theories due to a fundamental lack of mechanistic understanding. These challenges stem from the inherent complexity of their chemical composition, phase stability, and the intricate interplay of multiple order parameters, compounded by the lack of self-consistent integration between theoretical models and multi-modal experimental findings. As a result, breakthroughs in functional materials, such as new classes of correlated oxides, nitrides, and low-dimensional quantum materials, have largely been serendipitous or guided by phenomenological intuition rather than systematic, theory-driven design. Attempts to predict new materials and functionalities have often led to mixed results, with theoretically proposed systems failing to exhibit the desired properties when synthesized and tested.

Existing end-to-end autonomous driving (AD) algorithms typically follow the Imitation Learning (IL) paradigm, which faces challenges such as causal confusion and the open-loop gap. In this work, we establish a 3DGS-based closed-loop Reinforcement Learning (RL) training paradigm. By leveraging 3DGS techniques, we construct a photorealistic digital replica of the real physical world, enabling the AD policy to extensively explore the state space and learn to handle out-of-distribution scenarios through large-scale trial and error. To enhance safety, we design specialized rewards that guide the policy to effectively respond to safety-critical events and understand real-world causal relationships. For better alignment with human driving behavior, IL is incorporated into RL training as a regularization term. We introduce a closed-loop evaluation benchmark consisting of diverse, previously unseen 3DGS environments. Compared to IL-based methods, RAD achieves stronger performance in most closed-loop metrics, especially 3x lower collision rate. Abundant closed-loop results are presented at https://hgao-cv.github.io/RAD.

Selecting high-quality data can significantly improve the pretraining efficiency of large language models (LLMs). Existing methods generally rely on heuristic techniques and single-quality signals, limiting their ability to evaluate data quality comprehensively. In this work, we propose FIRE, a flexible and scalable framework for integrating multiple data quality raters, which allows for a comprehensive assessment of data quality across various dimensions. FIRE aligns multiple quality signals into a unified space, and integrates diverse data quality raters to provide a comprehensive quality signal for each data point. Further, we introduce a progressive data selection scheme based on FIRE that iteratively refines the selection of high-quality data points. Experiments on the SlimPajama dataset reveal that FIRE outperforms other data selection methods and significantly enhances the pretrained model across a wide range of downstream tasks, with a 2.9% average performance improvement over Random and reducing the FLOPs necessary to achieve a certain performance level by more than half.

This study presents an explainable parallel transformer architecture for soil liquefaction prediction that integrates three distinct data streams: spectral seismic encoding, soil stratigraphy tokenization, and site-specific features. The architecture processes data from 165 case histories across 11 major earthquakes, employing Fast Fourier Transform for seismic waveform encoding and principles from large language models for soil layer tokenization. Interpretability is achieved through SHapley Additive exPlanations (SHAP), which decompose predictions into individual contributions from seismic characteristics, soil properties, and site conditions. The model achieves 93.75% prediction accuracy on cross-regional validation sets and demonstrates robust performance through sensitivity analysis of ground motion intensity and soil resistance parameters. Notably, validation against previously unseen ground motion data from the 2024 Noto Peninsula earthquake confirms the model's generalization capabilities and practical utility. Implementation as a publicly accessible web application enables rapid assessment of multiple sites simultaneously. This approach establishes a new framework in geotechnical deep learning where sophisticated multi-modal analysis meets practical engineering requirements through quantitative interpretation and accessible deployment.

Recently, inference-time scaling of chain-of-thought (CoT) has been demonstrated as a promising approach for addressing multi-modal reasoning tasks. While existing studies have predominantly centered on text-based thinking, the integration of both visual and textual modalities within the reasoning process remains unexplored. In this study, we pioneer the exploration of inference-time scaling with multi-modal thought, aiming to bridge this gap. To provide a comprehensive analysis, we systematically investigate popular sampling-based and tree search-based inference-time scaling methods on 10 challenging tasks spanning various domains. Besides, we uniformly adopt a consistency-enhanced verifier to ensure effective guidance for both methods across different thought paradigms. Results show that multi-modal thought promotes better performance against conventional text-only thought, and blending the two types of thought fosters more diverse thinking. Despite these advantages, multi-modal thoughts necessitate higher token consumption for processing richer visual inputs, which raises concerns in practical applications. We hope that our findings on the merits and drawbacks of this research line will inspire future works in the field.

Full-waveform inversion (FWI) is a method that utilizes seismic data to invert the physical parameters of subsurface media by minimizing the difference between simulated and observed waveforms. Due to its ill-posed nature, FWI is susceptible to getting trapped in local minima. Consequently, various research efforts have attempted to combine neural networks with FWI to stabilize the inversion process. This study presents a simple yet effective training framework that is independent of dataset reliance and requires only moderate pre-training on a simple initial model to stabilize network outputs. During the transfer learning phase, the conventional FWI gradients will simultaneously update both the neural network and the proposed adaptive residual learning module, which learns the residual mapping of large-scale distribution features in the network's output, rather than directly fitting the target mapping. Through this synergistic training paradigm, the proposed algorithm effectively infers the physically-informed prior knowledge into a global representation of stratigraphic distribution, as well as capturing subtle variations in inter-layer velocities within local details, thereby escaping local optima. Evaluating the method on two benchmark models under various conditions, including absent low-frequency data, noise interference, and differing initial models, along with corresponding ablation experiments, consistently demonstrates the superiority of the proposed approach.

Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and strongly coupled solutions. In this work, we present a novel Sharp-PINN framework to tackle complex phase field corrosion problems. Instead of minimizing all governing PDE residuals simultaneously, the Sharp-PINNs introduce a staggered training scheme that alternately minimizes the residuals of Allen-Cahn and Cahn-Hilliard equations, which govern the corrosion system. To further enhance its efficiency and accuracy, we design an advanced neural network architecture that integrates random Fourier features as coordinate embeddings, employs a modified multi-layer perceptron as the primary backbone, and enforces hard constraints in the output layer. This framework is benchmarked through simulations of corrosion problems with multiple pits, where the staggered training scheme and network architecture significantly improve both the efficiency and accuracy of PINNs. Moreover, in three-dimensional cases, our approach is 5-10 times faster than traditional finite element methods while maintaining competitive accuracy, demonstrating its potential for real-world engineering applications in corrosion prediction.