A common challenge in the natural sciences is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual neurons from overlapping signals, and separating seismic events from an ambient background. Traditional analyses often rely on simplified source models that fail to accurately reproduce the data. Recent advances have shown that diffusion models can directly learn complex prior distributions from noisy, incomplete data. In this work, we show that diffusion models can solve the source separation problem without explicit assumptions about the source. Our method relies only on multiple views, or the property that different sets of observations contain different linear transformations of the unknown sources. We show that our method succeeds even when no source is individually observed and the observations are noisy, incomplete, and vary in resolution. The learned diffusion models enable us to sample from the source priors, evaluate the probability of candidate sources, and draw from the joint posterior of the source distribution given an observation. We demonstrate the effectiveness of our method on a range of synthetic problems as well as real-world galaxy observations.

Scaling laws motivate the development of Time Series Foundation Models (TSFMs) that pre-train vast parameters and achieve remarkable zero-shot forecasting performance. Surprisingly, even after fine-tuning, TSFMs cannot consistently outperform smaller, specialized models trained on full-shot downstream data. A key question is how to realize effective adaptation of TSFMs for a target forecasting task. Through empirical studies on various TSFMs, the pre-trained models often exhibit inherent sparsity and redundancy in computation, suggesting that TSFMs have learned to activate task-relevant network substructures to accommodate diverse forecasting tasks. To preserve this valuable prior knowledge, we propose a structured pruning method to regularize the subsequent fine-tuning process by focusing it on a more relevant and compact parameter space. Extensive experiments on seven TSFMs and six benchmarks demonstrate that fine-tuning a smaller, pruned TSFM significantly improves forecasting performance compared to fine-tuning original models. This "prune-then-finetune" paradigm often enables TSFMs to achieve state-of-the-art performance and surpass strong specialized baselines.

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.

Agricultural parcels serve as basic units for conducting agricultural practices and applications, which is vital for land ownership registration, food security assessment, soil erosion monitoring, etc. However, existing agriculture parcel extraction studies only focus on mid-resolution mapping or regular plain farmlands while lacking representation of complex terraced terrains due to the demands of precision agriculture. In this paper, we introduce a more fine-grained terraced parcel dataset named GTPBD (Global Terraced Parcel and Boundary Dataset), which is the first fine-grained dataset covering major worldwide terraced regions with more than 200,000 complex terraced parcels with manually annotation. GTPBD comprises 47,537 high-resolution images with three-level labels, including pixel-level boundary labels, mask labels, and parcel labels. It covers seven major geographic zones in China and transcontinental climatic regions around the world. Compared to the existing datasets, the GTPBD dataset brings considerable challenges due to the: (1) terrain diversity; (2) complex and irregular parcel objects; and (3) multiple domain styles. Our proposed GTPBD dataset is suitable for four different tasks, including semantic segmentation, edge detection, terraced parcel extraction and unsupervised domain adaptation (UDA) tasks.

Transformers have driven remarkable breakthroughs in natural language processing 2and computer vision, yet their standard attention mechanism still imposes O(N) complexity, hindering scalability to longer sequences. We introduce Circularconvolutional ATtention (CAT), a Fourier-based approach that efficiently applies circular power. CA con T volutions achieves to O reduce (N log comple N) computations, xity without requires sacrificing fewer representational learnable parameters by streamlining fully connected layers, and introduces no additional heavy operations, resulting in consistent accuracy improvements and about a 10% speedup in naive PyTorch implementations. Based on the Engineering-Isomorphic Transformers (EITs) framework, CAT's design not only offers practical efficiency and ease of implementation, but also provides insights to guide the development of

Finetuning large pretrained neural networks is known to be resource-intensive, both in terms of memory and computational cost. To mitigate this, a common approach is to restrict training to a subset of the model parameters. By analyzing the relationship between gradients and weights during finetuning, we observe a notable pattern: large gradients are often associated with small-magnitude weights. This correlation is more pronounced in finetuning settings than in training from scratch. Motivated by this observation, we propose NANOADAM, which dynamically updates only the small-magnitude weights during finetuning and offers several practical advantages: first, the criterion is gradient-free--the parameter subset can be determined without gradient computation; second, it preserves large-magnitude weights, which are likely to encode critical features learned during pretraining, thereby reducing the risk of catastrophic forgetting; thirdly, it permits the use of larger learning rates and consistently leads to better generalization performance in experiments. We demonstrate this for both NLP and vision tasks.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty -- often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NESYDMS), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols.

Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem.

Score 0 4 (normal) is most common across cohorts, while score 3 (severe) is rare--especially in PD-GaM 5 and 3DGait, highlighting class imbalance challenges. BMCLab offers a balanced ON/OFF medication split, 7 while E-LC is skewed toward ON-medication. DNE includes healthy, Parkinsonian, and other disease 8 groups for broader contrastive training. Figure A.3 shows label distributions for FoG-related cohorts. This artifact likely stems from the unusual top-down perspective--different from the front15 facing or side views seen in WHAM's training data [1]. While motion encoder-based models may be 16 robust to such distortions, feature-based gait classifiers rely on precise kinematic measurements and 17 thus require carefully corrected input data. To correct this slope artifact, we perform a frame-wise 18 rigid alignment of the reconstructed SMPL skeleton using the Kabsch algorithm [2]. The goal is to 19 rotate each frame so that anatomical directions align with canonical coordinate axes (up, forward), 20 while preserving natural gait structure. This motion 28 vector is then projected onto the ground plane (xz-plane) and used as the walking axis. In frames where the sacrum displacement is less than 30 4mm--indicating near-stationary posture--we fall back on a proxy direction: the cross product of 31 the hip vector (left hip to right hip) and the vertical vector.

Several recently introduced deep learning optimizers utilizing matrix-level preconditioning have shown promising speedups relative to the current dominant optimizer AdamW, particularly in relatively small-scale experiments. However, efforts to validate and replicate their successes have reported mixed results. To better understand the effectiveness of these optimizers at scale, in this work we investigate how to scale preconditioned optimizers via hyperparameter transfer, building on prior works such as µP. We study how the optimal learning rate and weight decay should scale with model width and depth for a wide range of optimizers, including Shampoo, SOAP, and Muon, accounting for the impact of commonly used techniques such as blocking and grafting. We find that scaling the learning rate according to µP improves transfer, but can still suffer from significant finite-width deviations that cause drifting optimal learning rates, which we show can be mitigated by blocking and explicit spectral normalization. For compute-optimal scaling, we find scaling independent weight decay as 1/width is nearly optimal across optimizers. Applying these scaling rules, we show Muon, SOAP and Shampoo consistently achieve near 1.4 speedup over AdamW for training Llama-architecture language models of sizes ranging from 190M to 1.4B, whereas the speedup vanishes rapidly with scale under incorrect scaling. Based on these results and further ablations, we argue that studying optimal hyperparameter transfer is essential for reliably comparing optimizers at scale given a realistic tuning budget.