Open-source foundation models have seen rapid adoption and development, enabling powerful general-purpose capabilities across diverse domains. However, fine-tuning large foundation models for domain-specific or personalized tasks remains prohibitively expensive for most users due to the significant memory overhead beyond that of inference. We introduce EMLoC, an Emulator-based Memory-efficient fine-tuning framework with LoRACorrection, which enables model fine-tuning within the same memory budget required for inference. EMLoC constructs a task-specific light-weight emulator using activation-aware singular value decomposition (SVD) on a small downstream calibration set. Fine-tuning then is performed on this lightweight emulator via LoRA. To tackle the misalignment between the original model and the compressed emulator, we propose a novel compensation algorithm to correct the fine-tuned LoRA module, which thus can be merged into the original model for inference. EMLoC supports flexible compression ratios and standard training pipelines, making it adaptable to a wide range of applications. Extensive experiments demonstrate that EMLoC outperforms other baselines across multiple datasets and modalities. Moreover, without quantization, EMLoC enables fine-tuning of a 38B model, which originally required 95GB of memory, on a single 24GB consumer GPU--bringing efficient and practical model adaptation to individual users.

Understanding how individual edges influence the behavior of graph neural networks (GNNs) is essential for improving their interpretability and robustness. Graph influence functions have emerged as promising tools to efficiently estimate the effects of edge deletions without retraining. However, existing influence prediction methods rely on strict convexity assumptions, exclusively consider the influence of edge deletions while disregarding edge insertions, and fail to capture changes in message propagation caused by these modifications. In this work, we propose a proximal Bregman response function specifically tailored for GNNs, relaxing the convexity requirement and enabling accurate influence prediction for standard neural network architectures. Furthermore, our method explicitly accounts for message propagation effects and extends influence prediction to both edge deletions and insertions in a principled way. Experiments with real-world datasets demonstrate accurate influence predictions for different characteristics of GNNs. We further demonstrate that the influence function is versatile in applications such as graph rewiring and adversarial attacks.

Anomaly detection is a crucial task in data mining, focusing on identifying data points that deviate significantly from the main patterns in the data. This paper introduces Anomaly Detection by an Ensemble of Random Pairs of Hyperspheres (ADERH), a new isolation-based technique leveraging two key observations: (i) anomalies are comparatively rare, and (ii) they typically deviate stronger from general patterns than normal data points. Drawing on a δ-separation argument, ADERH constructs an ensemble of multi-scale hyperspheres built upon randomly paired data points to identify anomalies. To address inevitable overlaps between anomalous and normal regions in the feature space, ADERH integrates two complementary concepts: Pitch, which highlights points near hypersphere boundaries, and NDensity, which down-weights hyperspheres centered on sparse (and often anomalous) regions.

Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current largescale reasoning models primarily rely on scaling up training datasets with diverse mathematical problems and long thinking chains, which raises questions about whether LLMs genuinely acquire mathematical concepts and reasoning principles or merely remember the training data. In contrast, humans tend to break down complex problems into multiple fundamental atomic capabilities. Inspired by this, we propose a new paradigm for evaluating mathematical atomic capabilities.

Understanding the 3D world from 2D monocular videos is a crucial ability for AI. Recently, to tackle this underdetermined task, end-to-end 3D geometry priors have been sought after, such as pre-trained point map models at scale. These models enable robust 3D understanding from casually taken videos, providing accurate object shapes disentangled from uncertain camera parameters. However, they still struggle when affected by object deformation and dynamics, failing to establish consistent correspondence over the frames. Furthermore, their architectures are typically limited to pairwise frame processing, which is insufficient for capturing complex motion dynamics over extended sequences. To address these limitations, we introduce Track3R, a novel framework that integrates a new architecture and task to jointly predict point map and motion trajectories across multiple frames from video input. Specifically, our key idea is modeling two disentangled trajectories for each point: one representing object motion and the other camera poses. This design not only can enable understanding of the 3D object dynamics, but also facilitates the learning of more robust priors for 3D shapes in dynamic scenes. In our experiments, Track3R demonstrates significant improvements in a joint point mapping and 3D motion estimation task for dynamic scenes, such as 25.8% improvements in the motion estimation, and 15.7% in the point mapping accuracy.

We study the tradeoff between sample complexity and round complexity in ondemand sampling, where the learning algorithm adaptively samples from k distributions over a limited number of rounds. In the realizable setting of MultiDistribution Learning (MDL), we show that the optimal sample complexity of an r-round algorithm scales approximately as dkΘ(1/r)/ε. For the general agnostic case, we present an algorithm that achieves near-optimal sample complexity of eO((d + k)/ε2) within eO( k) rounds. Of independent interest, we introduce a new framework, Optimization via On-Demand Sampling (OODS), which abstracts the sample-adaptivity tradeoff and captures most existing MDL algorithms. We establish nearly tight bounds on the round complexity in the OODS setting. The upper bounds directly yield the eO( k)-round algorithm for agnostic MDL, while the lower bounds imply that achieving sub-polynomial round complexity would require fundamentally new techniques that bypass the inherent hardness of OODS.

Surface electromyography (sEMG) at the wrists could enable natural, keyboard-free text entry, yet the state-of-the-art emg2qwertybaseline still misrecognizes 51.8% of characters zero-shot on unseen users and 7.0% after user-specific fine-tuning. We trace much of these errors to mismatched cross-user signal statistics, fragile reliance on high-order feature dependencies, and the absence of architectural inductive biases aligned with the bilateral nature of typing. To address these issues, we introduce three simple modifications: (i) Rolling Time Normalization which adaptively aligns input distributions across users; (ii) Aggressive Channel Masking, which encourages reliance on low-order feature combinations more likely to generalize across users; and (iii) a Split-and-Share encoder that processes each hand independently with weight-shared streams to reflect the bilateral symmetry of the neuromuscular system. Combined with a five-fold reduction in spectral resolution (33 6 frequency bands), these components yield a compact Splitand-Share model, SplashNet-mini, which uses only the parameters and 0.6 the FLOPs of the baseline while reducing character error rate (CER) to 36.4% zero-shot and 5.9% after fine-tuning. An upscaled variant, SplashNet ( parameters, 1.15 FLOPs of the baseline), further lowers error to 35.7% and 5.5%, representing 31% and 21% relative improvements in the zero-shot and finetuned settings, respectively. SplashNet therefore establishes a new state-of-the-art without requiring additional data.

We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear programs, we characterize when a dataset is sufficient to recover an optimal decision, given an uncertainty set on the cost vector. Our main contribution is a sharp geometric characterization that identifies the directions of the cost vector that matter for optimality, relative to the task constraints and uncertainty set. We further develop a practical algorithm that, for a given task, constructs a minimal or least-costly sufficient dataset. Our results reveal that small, well-chosen datasets can often fully determine optimal decisions--offering a principled foundation for task-aware data selection.

We propose the first framework capable of computing a 4D spatio-temporal grid of video architecture.

While visual autoregressive modeling (VAR) strategies have shed light on image generation with the autoregressive models, their potential for segmentation, a task that requires precise low-level spatial perception, remains unexplored. Inspired by the multi-scale modeling of classic Mask2Former-based models, we propose SegVAR, a novel framework that rethinks segmentation as a conditional autoregressive mask generation problem. This is achieved by replacing the discriminative learning with the latent learning process. Specifically, our method incorporates three core components: (1) an image encoder generating latent priors from input images, (2) a spatial-aware seglat (a latent expression of segmentation mask) encoder that maps segmentation masks into discrete latent tokens using a location-sensitive color mapping to distinguish instances, and (3) a decoder reconstructing masks from these latents. A multi-stage training strategy is introduced: first learning seglat representations via image-seglat joint training, then refining latent transformations, and finally aligning image-encoder-derived latents with seglat distributions. Experiments show Seg-VAR outperforms previous discriminative and generative methods on various segmentation tasks and validation benchmarks. By framing segmentation as a sequential hierarchical prediction task, Seg-VAR opens new avenues for integrating autoregressive reasoning into spatial-aware vision systems.