Test-time scaling improves the reasoning capabilities of large language models (LLMs) by allocating extra compute to generate longer Chains-of-Thoughts (CoTs). This enables models to tackle more complex problem by breaking them down into additional steps, backtracking, and correcting mistakes. Despite its strong performance--demonstrated by OpenAI's o1 and DeepSeek R1, the conditions in the training data under which long CoTs emerge, and when such long CoTs improve the performance, remain unclear. In this paper, we study the performance of test-time scaling for transformers trained on an in-context weight prediction task for linear regression. Our analysis provides a theoretical explanation for several intriguing observations: First, at any fixed test error, increasing test-time compute allows us to reduce the number of in-context examples (context length) in training prompts. Second, if the skills required to solve a downstream task are not sufficiently present in the training data, increasing test-time compute can harm performance. Finally, we characterize task hardness via the smallest eigenvalue of its feature covariance matrix and show that training on a diverse, relevant, and hard set of tasks results in best performance for test-time scaling. We confirm our findings with experiments on large, nonlinear transformer architectures.

Learning dynamics is essential for model-based control and Reinforcement Learning in engineering systems, such as robotics and power systems. However, limited system measurements, such as those from low-resolution sensors, demand sample-efficient learning. Symmetry provides a powerful inductive bias by characterizing equivariant relations in system states to improve sample efficiency. While recent methods attempt to discover symmetries from data, they typically assume a single global symmetry group and treat symmetry discovery and dynamic learning as separate tasks, leading to limited expressiveness and error accumulation. In this paper, we propose the Latent Mixture of Symmetries (Latent MoS), an expressive model that captures a mixture of symmetry-governed latent factors from complex dynamical measurements. Latent MoS focuses on dynamic learning while locally and provably preserving the underlying symmetric transformations. To further capture long-term equivariance, we introduce a hierarchical architecture that stacks MoS blocks. Numerical experiments in diverse physical systems demonstrate that Latent MoS outperforms state-of-the-art baselines in interpolation and extrapolation tasks while offering interpretable latent representations suitable for future geometric and safety-critical analyses.

Deep learning has gained attention for solving PDEs, but the black-box nature of neural networks hinders precise enforcement of boundary conditions. To address this, we propose a boundary condition-guaranteed evolutionary Kolmogorov-Arnold Network (KAN) with radial basis functions (BEKAN). In BEKAN, we propose three distinct and combinable approaches for incorporating Dirichlet, periodic, and Neumann boundary conditions into the network. For Dirichlet problem, we use smooth and global Gaussian RBFs to construct univariate basis functions for approximating the solution and to encode boundary information at the activation level of the network. To handle periodic problems, we employ a periodic layer constructed from a set of sinusoidal functions to enforce the boundary conditions exactly. For a Neumann problem, we devise a least-squares formulation to guide the parameter evolution toward satisfying the Neumann condition. By virtue of the boundary-embedded RBFs, the periodic layer, and the evolutionary framework, we can perform accurate PDE simulations while rigorously enforcing boundary conditions. For demonstration, we conducted extensive numerical experiments on Dirichlet, Neumann, periodic, and mixed boundary value problems. The results indicate that BEKAN outperforms both multilayer perceptron (MLP) and B-splines KAN in terms of accuracy. In conclusion, the proposed approach enhances the capability of KANs in solving PDE problems while satisfying boundary conditions, thereby facilitating advancements in scientific computing and engineering applications.

Generative models for sequential data often struggle with sparsely sampled and high-dimensional trajectories, typically reducing the learning of dynamics to pairwise transitions. We propose \textit{Interpolative Multi-Marginal Flow Matching} (IMMFM), a framework that learns continuous stochastic dynamics jointly consistent with multiple observed time points. IMMFM employs a piecewise-quadratic interpolation path as a smooth target for flow matching and jointly optimizes drift and a data-driven diffusion coefficient, supported by a theoretical condition for stable learning. This design captures intrinsic stochasticity, handles irregular sparse sampling, and yields subject-specific trajectories. Experiments on synthetic benchmarks and real-world longitudinal neuroimaging datasets show that IMMFM outperforms existing methods in both forecasting accuracy and further downstream tasks.

Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.

Kernel change-point detection (KCPD) has become a widely used tool for identifying structural changes in complex data. While existing theory establishes consistency under independence assumptions, real-world sequential data such as text exhibits strong dependencies. We establish new guarantees for KCPD under $m$-dependent data: specifically, we prove consistency in the number of detected change points and weak consistency in their locations under mild additional assumptions. We perform an LLM-based simulation that generates synthetic $m$-dependent text to validate the asymptotics. To complement these results, we present the first comprehensive empirical study of KCPD for text segmentation with modern embeddings. Across diverse text datasets, KCPD with text embeddings outperforms baselines in standard text segmentation metrics. We demonstrate through a case study on Taylor Swift's tweets that KCPD not only provides strong theoretical and simulated reliability but also practical effectiveness for text segmentation tasks.

Open-source data offers a scalable and transparent foundation for estimating vehicle activity and emissions in urban regions. In this study, we propose a data-driven framework that integrates MOVES and open-source GPS trajectory data, OpenStreetMap (OSM) road networks, regional traffic datasets and satellite imagery-derived feature vectors to estimate the link level operating mode distribution and traffic emissions. A neural network model is trained to predict the distribution of MOVES-defined operating modes using only features derived from readily available data. The proposed methodology was applied using open-source data related to 45 municipalities in the Boston Metropolitan area. The "ground truth" operating mode distribution was established using OSM open-source GPS trajectories. Compared to the MOVES baseline, the proposed model reduces RMSE by over 50% for regional scale traffic emissions of key pollutants including CO, NOx, CO2, and PM2.5. This study demonstrates the feasibility of low-cost, replicable, and data-driven emissions estimation using fully open data sources.

In the study, the social robot act as a patrol to recognize and notify illegal parking in real-time. Dual-model pipeline method and large multimodal model were compared, and the GPT-4o multimodal model was adopted in license plate recognition without preprocessing. For moving smoothly on a flat ground, the robot navigated in a simulated parking lot in the experiments. The robot changes angle view of the camera automatically to capture the images around with the format of license plate number. From the captured images of the robot, the numbers on the plate are recognized through the GPT-4o model, and identifies legality of the numbers. When an illegal parking is detected, the robot sends Line messages to the system manager immediately. The contribution of the work is that a novel multimodal deep learning method has validated with high accuracy in license plate recognition, and a social assistive robot is also provided for solving problems in a real scenario, and can be applied in an indoor parking lot.

Large-scale text-to-image diffusion models have become the backbone of modern image editing, yet text prompts alone do not offer adequate control over the editing process. Two properties are especially desirable: disentanglement, where changing one attribute does not unintentionally alter others, and continuous control, where the strength of an edit can be smoothly adjusted. W e introduce a method for disentangled and continuous editing through token-level manipulation of text embeddings. The edits are applied by manipulating the embeddings along carefully chosen directions, which control the strength of the target attribute. T o identify such directions, we employ a Sparse Autoencoder (SAE), whose sparse latent space exposes semantically isolated dimensions. Our method operates directly on text em-beddings without modifying the diffusion process, making it model agnostic and broadly applicable to various image synthesis backbones. Experiments show that it enables intuitive and efficient manipulations with continuous control across diverse attributes and domains.

Large language models (LLMs) are typically deployed under diverse memory and compute constraints. Existing approaches build model families by training each size independently, which is prohibitively expensive and provides only coarse-grained size options. In this work, we identify a novel phenomenon that we call boomerang distillation: starting from a large base model (the teacher), one first distills down to a small student and then progressively reconstructs intermediate-sized models by re-incorporating blocks of teacher layers into the student without any additional training. This process produces zero-shot interpolated models of many intermediate sizes whose performance scales smoothly between the student and teacher, often matching or surpassing pretrained or distilled models of the same size. We further analyze when this type of interpolation succeeds, showing that alignment between teacher and student through pruning and distillation is essential. Boomerang distillation thus provides a simple and efficient way to generate fine-grained model families, dramatically reducing training cost while enabling flexible adaptation across deployment environments. The code and models are available at https://github.com/dcml-lab/boomerang-distillation.