Daily Papers

Accurate electricity load forecasting is essential for grid stability, resource optimization, and renewable energy integration. While transformer-based deep learning models like TimeGPT have gained traction in time-series forecasting, their effectiveness in long-term electricity load prediction remains uncertain. This study evaluates forecasting models ranging from classical regression techniques to advanced deep learning architectures using data from the ESD 2025 competition. The dataset includes two years of historical electricity load data, alongside temperature and global horizontal irradiance (GHI) across five sites, with a one-day-ahead forecasting horizon. Since actual test set load values remain undisclosed, leveraging predicted values would accumulate errors, making this a long-term forecasting challenge. We employ (i) Principal Component Analysis (PCA) for dimensionality reduction and (ii) frame the task as a regression problem, using temperature and GHI as covariates to predict load for each hour, (iii) ultimately stacking 24 models to generate yearly forecasts. Our results reveal that deep learning models, including TimeGPT, fail to consistently outperform simpler statistical and machine learning approaches due to the limited availability of training data and exogenous variables. In contrast, XGBoost, with minimal feature engineering, delivers the lowest error rates across all test cases while maintaining computational efficiency. This highlights the limitations of deep learning in long-term electricity forecasting and reinforces the importance of model selection based on dataset characteristics rather than complexity. Our study provides insights into practical forecasting applications and contributes to the ongoing discussion on the trade-offs between traditional and modern forecasting methods.

The variability of wind power supply can present substantial challenges to incorporating wind power into a grid system. Thus, Wind Power Forecasting (WPF) has been widely recognized as one of the most critical issues in wind power integration and operation. There has been an explosion of studies on wind power forecasting problems in the past decades. Nevertheless, how to well handle the WPF problem is still challenging, since high prediction accuracy is always demanded to ensure grid stability and security of supply. We present a unique Spatial Dynamic Wind Power Forecasting dataset: SDWPF, which includes the spatial distribution of wind turbines, as well as the dynamic context factors. Whereas, most of the existing datasets have only a small number of wind turbines without knowing the locations and context information of wind turbines at a fine-grained time scale. By contrast, SDWPF provides the wind power data of 134 wind turbines from a wind farm over half a year with their relative positions and internal statuses. We use this dataset to launch the Baidu KDD Cup 2022 to examine the limit of current WPF solutions. The dataset is released at https://aistudio.baidu.com/aistudio/competition/detail/152/0/datasets.

As smart grids (SG) increasingly rely on advanced technologies like sensors and communication systems for efficient energy generation, distribution, and consumption, they become enticing targets for sophisticated cyberattacks. These evolving threats demand robust security measures to maintain the stability and resilience of modern energy systems. While extensive research has been conducted, a comprehensive exploration of proactive cyber defense strategies utilizing Deep Learning (DL) in {SG} remains scarce in the literature. This survey bridges this gap, studying the latest DL techniques for proactive cyber defense. The survey begins with an overview of related works and our distinct contributions, followed by an examination of SG infrastructure. Next, we classify various cyber defense techniques into reactive and proactive categories. A significant focus is placed on DL-enabled proactive defenses, where we provide a comprehensive taxonomy of DL approaches, highlighting their roles and relevance in the proactive security of SG. Subsequently, we analyze the most significant DL-based methods currently in use. Further, we explore Moving Target Defense, a proactive defense strategy, and its interactions with DL methodologies. We then provide an overview of benchmark datasets used in this domain to substantiate the discourse.{ This is followed by a critical discussion on their practical implications and broader impact on cybersecurity in Smart Grids.} The survey finally lists the challenges associated with deploying DL-based security systems within SG, followed by an outlook on future developments in this key field.

Neural fields, mapping low-dimensional input coordinates to corresponding signals, have shown promising results in representing various signals. Numerous methodologies have been proposed, and techniques employing MLPs and grid representations have achieved substantial success. MLPs allow compact and high expressibility, yet often suffer from spectral bias and slow convergence speed. On the other hand, methods using grids are free from spectral bias and achieve fast training speed, however, at the expense of high spatial complexity. In this work, we propose a novel way for exploiting both MLPs and grid representations in neural fields. Unlike the prevalent methods that combine them sequentially (extract features from the grids first and feed them to the MLP), we inject spectral bias-free grid representations into the intermediate features in the MLP. More specifically, we suggest a Coordinate-Aware Modulation (CAM), which modulates the intermediate features using scale and shift parameters extracted from the grid representations. This can maintain the strengths of MLPs while mitigating any remaining potential biases, facilitating the rapid learning of high-frequency components. In addition, we empirically found that the feature normalizations, which have not been successful in neural filed literature, proved to be effective when applied in conjunction with the proposed CAM. Experimental results demonstrate that CAM enhances the performance of neural representation and improves learning stability across a range of signals. Especially in the novel view synthesis task, we achieved state-of-the-art performance with the least number of parameters and fast training speed for dynamic scenes and the best performance under 1MB memory for static scenes. CAM also outperforms the best-performing video compression methods using neural fields by a large margin.

Accurate forecasts for day-ahead photovoltaic (PV) power generation are crucial to support a high PV penetration rate in the local electricity grid and to assure stability in the grid. We use state-of-the-art tree-based machine learning methods to produce such forecasts and, unlike previous studies, we hereby account for (i) the effects various meteorological as well as astronomical features have on PV power production, and this (ii) at coarse as well as granular spatial locations. To this end, we use data from Belgium and forecast day-ahead PV power production at an hourly resolution. The insights from our study can assist utilities, decision-makers, and other stakeholders in optimizing grid operations, economic dispatch, and in facilitating the integration of distributed PV power into the electricity grid.

We prove stability for a class of heterogeneous catalysis models in the L_p-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a reasonable condition on the involved parameters, we show that given equilibria are normally stable, i.e. solutions are attracted at an exponential rate. The potential incidence of instability is discussed as well.

We present an open-source Python library for simulating two-dimensional incompressible Kelvin-Helmholtz instabilities in stratified shear flows. The solver employs a fractional-step projection method with spectral Poisson solution via Fast Sine Transform, achieving second-order spatial accuracy. Implementation leverages NumPy, SciPy, and Numba JIT compilation for efficient computation. Four canonical test cases explore Reynolds numbers 1000--5000 and Richardson numbers 0.1--0.3: classical shear layer, double shear configuration, rotating flow, and forced turbulence. Statistical analysis using Shannon entropy and complexity indices reveals that double shear layers achieve 2.8times higher mixing rates than forced turbulence despite lower Reynolds numbers. The solver runs efficiently on standard desktop hardware, with 384times192 grid simulations completing in approximately 31 minutes. Results demonstrate that mixing efficiency depends on instability generation pathways rather than intensity measures alone, challenging Richardson number-based parameterizations and suggesting refinements for subgrid-scale representation in climate models.

Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global curvature and gradients of rotation for non-axisymmetric disturbances. We then examine the stability of differentially rotating disks for several rotation profiles and present the associated effective potential for the onset of these instabilities in the MHD regime. In particular, results for global axisymmetric magnetorotational instability (MRI) as well as local and global non-axisymmetric modes are presented. The latter constitute two distinct non-axisymmetric modes, a high frequency local MRI and a global low-frequency non-axisymmetric mode (the magneto-curvature mode, introduced in Ebrahimi&Pharr, ApJ 2022), confined either between two Alfv\'enic resonances or an Alfv\'enic resonance and a boundary.

Before deploying autonomous agents in the real world, we need to be confident they will perform safely in novel situations. Ideally, we would expose agents to a very wide range of situations during training, allowing them to learn about every possible danger, but this is often impractical. This paper investigates safety and generalization from a limited number of training environments in deep reinforcement learning (RL). We find RL algorithms can fail dangerously on unseen test environments even when performing perfectly on training environments. Firstly, in a gridworld setting, we show that catastrophes can be significantly reduced with simple modifications, including ensemble model averaging and the use of a blocking classifier. In the more challenging CoinRun environment we find similar methods do not significantly reduce catastrophes. However, we do find that the uncertainty information from the ensemble is useful for predicting whether a catastrophe will occur within a few steps and hence whether human intervention should be requested.

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

Most 3D object generators focus on aesthetic quality, often neglecting physical constraints necessary in applications. One such constraint is that the 3D object should be self-supporting, i.e., remains balanced under gravity. Prior approaches to generating stable 3D objects used differentiable physics simulators to optimize geometry at test-time, which is slow, unstable, and prone to local optima. Inspired by the literature on aligning generative models to external feedback, we propose Direct Simulation Optimization (DSO), a framework to use the feedback from a (non-differentiable) simulator to increase the likelihood that the 3D generator outputs stable 3D objects directly. We construct a dataset of 3D objects labeled with a stability score obtained from the physics simulator. We can then fine-tune the 3D generator using the stability score as the alignment metric, via direct preference optimization (DPO) or direct reward optimization (DRO), a novel objective, which we introduce, to align diffusion models without requiring pairwise preferences. Our experiments show that the fine-tuned feed-forward generator, using either DPO or DRO objective, is much faster and more likely to produce stable objects than test-time optimization. Notably, the DSO framework works even without any ground-truth 3D objects for training, allowing the 3D generator to self-improve by automatically collecting simulation feedback on its own outputs.

Stellarators are magnetic confinement devices under active development to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations and significant domain expertise. Recent advances in plasma physics and open-source tools have made stellarator optimization more accessible. However, broader community progress is currently bottlenecked by the lack of standardized optimization problems with strong baselines and datasets that enable data-driven approaches, particularly for quasi-isodynamic (QI) stellarator configurations, considered as a promising path to commercial fusion due to their inherent resilience to current-driven disruptions. Here, we release an open dataset of diverse QI-like stellarator plasma boundary shapes, paired with their ideal magnetohydrodynamic (MHD) equilibria and performance metrics. We generated this dataset by sampling a variety of QI fields and optimizing corresponding stellarator plasma boundaries. We introduce three optimization benchmarks of increasing complexity: (1) a single-objective geometric optimization problem, (2) a "simple-to-build" QI stellarator, and (3) a multi-objective ideal-MHD stable QI stellarator that investigates trade-offs between compactness and coil simplicity. For every benchmark, we provide reference code, evaluation scripts, and strong baselines based on classical optimization techniques. Finally, we show how learned models trained on our dataset can efficiently generate novel, feasible configurations without querying expensive physics oracles. By openly releasing the dataset along with benchmark problems and baselines, we aim to lower the entry barrier for optimization and machine learning researchers to engage in stellarator design and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.

We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative prediction~Perdomo et. al., 2020, we introduce the concept of performatively stable policy. We then consider a regularized version of the reinforcement learning problem and show that repeatedly optimizing this objective converges to a performatively stable policy under reasonable assumptions on the transition dynamics. Our proof utilizes the dual perspective of the reinforcement learning problem and may be of independent interest in analyzing the convergence of other algorithms with decision-dependent environments. We then extend our results for the setting where the learner just performs gradient ascent steps instead of fully optimizing the objective, and for the setting where the learner has access to a finite number of trajectories from the changed environment. For both settings, we leverage the dual formulation of performative reinforcement learning and establish convergence to a stable solution. Finally, through extensive experiments on a grid-world environment, we demonstrate the dependence of convergence on various parameters e.g. regularization, smoothness, and the number of samples.

The objective of this study is to develop a fully compressible magnetohydrodynamic solver for fast simulations of the global dynamo of the Sun using unstructured grids and GPUs. Accurate modeling of the Sun's convective layers is vital to predicting the Sun's behavior, including the solar dynamo and sunspot cycles. Currently, there are many efficient codes capable of conducting these large simulations; however, many assume an anealastic density distribution. The anelastic assumption is capable of producing accurate results for low mach numbers; however, it fails in regions with a higher mach number and a fully compressible flow must be considered. To avoid these issues, Wang et al. [1] created a Compressible High-ORder Unstructured Spectral difference (CHORUS) code for simulating fluid dynamics inside stars and planets. CHORUS++ augmented the CHORUS code to adopt a higher degree of polynomials by using cubed-sphere meshing and transfinite mapping to perform simulations on unstructured grids [2]. Recently, CHORUS++ was further developed for parallel magnetohydrodynamic (MHD) solutions on GPUs at Clarkson University. In this study the solar benchmark problems presented by Chen et al. [2] are extended to unsteady solar dynamo problems, with two different density scale heights. The CHORUS-MHD code is further accelerated by multiple GPUs and used to successfully solve these solar dynamo benchmark problems. [1] Wang, J., Liang, C., and Miesch, M. S., "A Compressible High-Order Unstructured Spectral Difference Code for Stratified Convection in Rotating Spherical Shells," Journal of Computational Physics, Vol. 290, 2015, pp. 90-111. [2] Chen, K., Liang, C., and Wan, M., "Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids," Physics of Fluids, Vol. 35, 2023, p. 086120.

We present GeoGrid-Bench, a benchmark designed to evaluate the ability of foundation models to understand geo-spatial data in the grid structure. Geo-spatial datasets pose distinct challenges due to their dense numerical values, strong spatial and temporal dependencies, and unique multimodal representations including tabular data, heatmaps, and geographic visualizations. To assess how foundation models can support scientific research in this domain, GeoGrid-Bench features large-scale, real-world data covering 16 climate variables across 150 locations and extended time frames. The benchmark includes approximately 3,200 question-answer pairs, systematically generated from 8 domain expert-curated templates to reflect practical tasks encountered by human scientists. These range from basic queries at a single location and time to complex spatiotemporal comparisons across regions and periods. Our evaluation reveals that vision-language models perform best overall, and we provide a fine-grained analysis of the strengths and limitations of different foundation models in different geo-spatial tasks. This benchmark offers clearer insights into how foundation models can be effectively applied to geo-spatial data analysis and used to support scientific research.

Generative adversarial networks (GANs) have proven successful in image generation tasks. However, GAN training is inherently unstable. Although many works try to stabilize it by manually modifying GAN architecture, it requires much expertise. Neural architecture search (NAS) has become an attractive solution to search GANs automatically. The early NAS-GANs search only generators to reduce search complexity but lead to a sub-optimal GAN. Some recent works try to search both generator (G) and discriminator (D), but they suffer from the instability of GAN training. To alleviate the instability, we propose an efficient two-stage evolutionary algorithm-based NAS framework to search GANs, namely EAGAN. We decouple the search of G and D into two stages, where stage-1 searches G with a fixed D and adopts the many-to-one training strategy, and stage-2 searches D with the optimal G found in stage-1 and adopts the one-to-one training and weight-resetting strategies to enhance the stability of GAN training. Both stages use the non-dominated sorting method to produce Pareto-front architectures under multiple objectives (e.g., model size, Inception Score (IS), and Fr\'echet Inception Distance (FID)). EAGAN is applied to the unconditional image generation task and can efficiently finish the search on the CIFAR-10 dataset in 1.2 GPU days. Our searched GANs achieve competitive results (IS=8.81pm0.10, FID=9.91) on the CIFAR-10 dataset and surpass prior NAS-GANs on the STL-10 dataset (IS=10.44pm0.087, FID=22.18). Source code: https://github.com/marsggbo/EAGAN.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

Image restoration in adverse weather conditions is a difficult task in computer vision. In this paper, we propose a novel transformer-based framework called GridFormer which serves as a backbone for image restoration under adverse weather conditions. GridFormer is designed in a grid structure using a residual dense transformer block, and it introduces two core designs. First, it uses an enhanced attention mechanism in the transformer layer. The mechanism includes stages of the sampler and compact self-attention to improve efficiency, and a local enhancement stage to strengthen local information. Second, we introduce a residual dense transformer block (RDTB) as the final GridFormer layer. This design further improves the network's ability to learn effective features from both preceding and current local features. The GridFormer framework achieves state-of-the-art results on five diverse image restoration tasks in adverse weather conditions, including image deraining, dehazing, deraining & dehazing, desnowing, and multi-weather restoration. The source code and pre-trained models will be released.

Existing diffusion-based text-to-3D generation methods primarily focus on producing visually realistic shapes and appearances, often neglecting the physical constraints necessary for downstream tasks. Generated models frequently fail to maintain balance when placed in physics-based simulations or 3D printed. This balance is crucial for satisfying user design intentions in interactive gaming, embodied AI, and robotics, where stable models are needed for reliable interaction. Additionally, stable models ensure that 3D-printed objects, such as figurines for home decoration, can stand on their own without requiring additional supports. To fill this gap, we introduce Atlas3D, an automatic and easy-to-implement method that enhances existing Score Distillation Sampling (SDS)-based text-to-3D tools. Atlas3D ensures the generation of self-supporting 3D models that adhere to physical laws of stability under gravity, contact, and friction. Our approach combines a novel differentiable simulation-based loss function with physically inspired regularization, serving as either a refinement or a post-processing module for existing frameworks. We verify Atlas3D's efficacy through extensive generation tasks and validate the resulting 3D models in both simulated and real-world environments.

We consider an improper reinforcement learning setting where a learner is given M base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an cartpole; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to 2/eta, where eta denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

The Jovian atmosphere contains a wide diversity of vortices, which have a large range of sizes, colors and forms in different dynamical regimes. The formation processes for these vortices is poorly understood, and aside from a few known, long-lived ovals, such as the Great Red Spot, and Oval BA, vortex stability and their temporal evolution are currently largely unknown. In this study, we use JunoCam data and a citizen-science project on Zooniverse to derive a catalog of vortices, some with repeated observations, through May 2018 to Sep 2021, and analyze their associated properties, such as size, location and color. We find that different colored vortices (binned as white, red, brown and dark), follow vastly different distributions in terms of their sizes and where they are found on the planet. We employ a simplified stability criterion using these vortices as a proxy, to derive a minimum Rossby deformation length for the planet of sim1800 km. We find that this value of L_d is largely constant throughout the atmosphere, and does not have an appreciable meridional gradient.

Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been commonly employed in existing approaches. However, these methods typically use the grid as an index for uniformly scattering point features. Compared with the irregular point features, the regular grid features may sacrifice some reconstruction details but improve efficiency. To take full advantage of these two types of features, we introduce a novel and high-efficiency attention mechanism between the grid and point features named Point-Grid Transformer (GridFormer). This mechanism treats the grid as a transfer point connecting the space and point cloud. Our method maximizes the spatial expressiveness of grid features and maintains computational efficiency. Furthermore, optimizing predictions over the entire space could potentially result in blurred boundaries. To address this issue, we further propose a boundary optimization strategy incorporating margin binary cross-entropy loss and boundary sampling. This approach enables us to achieve a more precise representation of the object structure. Our experiments validate that our method is effective and outperforms the state-of-the-art approaches under widely used benchmarks by producing more precise geometry reconstructions. The code is available at https://github.com/list17/GridFormer.

Stable locomotion in precipitous environments is an essential capability of quadruped robots, demanding the ability to resist various external disturbances. However, recent learning-based policies only use basic domain randomization to improve the robustness of learned policies, which cannot guarantee that the robot has adequate disturbance resistance capabilities. In this paper, we propose to model the learning process as an adversarial interaction between the actor and a newly introduced disturber and ensure their optimization with H_{infty} constraint. In contrast to the actor that maximizes the discounted overall reward, the disturber is responsible for generating effective external forces and is optimized by maximizing the error between the task reward and its oracle, i.e., "cost" in each iteration. To keep joint optimization between the actor and the disturber stable, our H_{infty} constraint mandates the bound of ratio between the cost to the intensity of the external forces. Through reciprocal interaction throughout the training phase, the actor can acquire the capability to navigate increasingly complex physical disturbances. We verify the robustness of our approach on quadrupedal locomotion tasks with Unitree Aliengo robot, and also a more challenging task with Unitree A1 robot, where the quadruped is expected to perform locomotion merely on its hind legs as if it is a bipedal robot. The simulated quantitative results show improvement against baselines, demonstrating the effectiveness of the method and each design choice. On the other hand, real-robot experiments qualitatively exhibit how robust the policy is when interfering with various disturbances on various terrains, including stairs, high platforms, slopes, and slippery terrains. All code, checkpoints, and real-world deployment guidance will be made public.

In many real-world applications, deep neural networks are retrained from scratch as a dataset grows in size. Given the computational expense for retraining networks, it has been argued that continual learning could make updating networks more efficient. An obstacle to achieving this goal is the stability gap, which refers to an observation that when updating on new data, performance on previously learned data degrades before recovering. Addressing this problem would enable learning new data with fewer network updates, resulting in increased computational efficiency. We study how to mitigate the stability gap. We test a variety of hypotheses to understand why the stability gap occurs. This leads us to discover a method that vastly reduces this gap. In large-scale class incremental learning experiments, we are able to significantly reduce the number of network updates needed for continual learning. Our work has the potential to advance the state-of-the-art in continual learning for real-world applications along with reducing the carbon footprint required to maintain updated neural networks.

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For n axis-aligned rectangles inside an axis-aligned bounding box B, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches B and the density k is minimized, where k is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box B. REP is NP-hard for k>1. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a 2-approximation algorithm for SEP with kgeq2 with time complexity O(n^{3/2}k^2). This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for kgeq 3 is 3/2 which is tight. We also give a 8-approximation algorithm for REP with time complexity O(nlog n+nk) and give a MPC version of this algorithm for k=O(1) which is the first parallel algorithm for this problem.

We present the design, implementation and engineering experience in building and deploying MegaScale, a production system for training large language models (LLMs) at the scale of more than 10,000 GPUs. Training LLMs at this scale brings unprecedented challenges to training efficiency and stability. We take a full-stack approach that co-designs the algorithmic and system components across model block and optimizer design, computation and communication overlapping, operator optimization, data pipeline, and network performance tuning. Maintaining high efficiency throughout the training process (i.e., stability) is an important consideration in production given the long extent of LLM training jobs. Many hard stability issues only emerge at large scale, and in-depth observability is the key to address them. We develop a set of diagnosis tools to monitor system components and events deep in the stack, identify root causes, and derive effective techniques to achieve fault tolerance and mitigate stragglers. MegaScale achieves 55.2% Model FLOPs Utilization (MFU) when training a 175B LLM model on 12,288 GPUs, improving the MFU by 1.34x compared to Megatron-LM. We share our operational experience in identifying and fixing failures and stragglers. We hope by articulating the problems and sharing our experience from a systems perspective, this work can inspire future LLM systems research.

Domain adaptive detection aims to improve the generality of a detector, learned from the labeled source domain, on the unlabeled target domain. In this work, drawing inspiration from the concept of stability from the control theory that a robust system requires to remain consistent both externally and internally regardless of disturbances, we propose a novel framework that achieves unsupervised domain adaptive detection through stability analysis. In specific, we treat discrepancies between images and regions from different domains as disturbances, and introduce a novel simple but effective Network Stability Analysis (NSA) framework that considers various disturbances for domain adaptation. Particularly, we explore three types of perturbations including heavy and light image-level disturbances and instancelevel disturbance. For each type, NSA performs external consistency analysis on the outputs from raw and perturbed images and/or internal consistency analysis on their features, using teacher-student models. By integrating NSA into Faster R-CNN, we immediately achieve state-of-the-art results. In particular, we set a new record of 52.7% mAP on Cityscapes-to-FoggyCityscapes, showing the potential of NSA for domain adaptive detection. It is worth noticing, our NSA is designed for general purpose, and thus applicable to one-stage detection model (e.g., FCOS) besides the adopted one, as shown by experiments. https://github.com/tiankongzhang/NSA.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading generalization properties on clean data.

We demonstrate how collective memory emerges in decentralized multi-agent systems through the interplay between individual agent memory and environmental trace communication. Our agents maintain internal memory states while depositing persistent environmental traces, creating a spatially distributed collective memory without centralized control. Comprehensive validation across five environmental conditions (20x20 to 50x50 grids, 5-20 agents, 50 runs per configuration) reveals a critical asymmetry: individual memory alone provides 68.7% performance improvement over no-memory baselines (1563.87 vs 927.23, p < 0.001), while environmental traces without memory fail completely. This demonstrates that memory functions independently but traces require cognitive infrastructure for interpretation. Systematic density-sweep experiments (rho in [0.049, 0.300], up to 625 agents) validate our theoretical phase transition prediction. On realistic large grids (30x30, 50x50), stigmergic coordination dominates above rho ~ 0.20, with traces outperforming memory by 36-41% on composite metrics despite lower food efficiency. The experimental crossover confirms the predicted critical density rho_c = 0.230 within 13% error.

Fine-tuning over large pretrained language models (PLMs) has established many state-of-the-art results. Despite its superior performance, such fine-tuning can be unstable, resulting in significant variance in performance and potential risks for practical applications. Previous works have attributed such instability to the catastrophic forgetting problem in the top layers of PLMs, which indicates iteratively that fine-tuning layers in a top-down manner is a promising solution. In this paper, we first point out that this method does not always work out due to the different convergence speeds of different layers/modules. Inspired by this observation, we propose a simple component-wise gradient norm clipping method to adjust the convergence speed for different components. Experiment results demonstrate that our method achieves consistent improvements in terms of generalization performance, convergence speed, and training stability. The codebase can be found at https://github.com/yangalan123/FineTuningStability.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Accurate weather forecasts are important for disaster prevention, agricultural planning, etc. Traditional numerical weather prediction (NWP) methods offer physically interpretable high-accuracy predictions but are computationally expensive and fail to fully leverage rapidly growing historical data. In recent years, deep learning models have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and insufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework (OneForecast) based on graph neural networks. By combining a dynamic system perspective with multi-grid theory, we construct a multi-scale graph structure and densify the target region to capture local high-frequency features. We introduce an adaptive messaging mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event forecasting. For high-resolution regional forecasts, we propose a neural nested grid method to mitigate boundary information loss. Experimental results show that OneForecast performs excellently across global to regional scales and short-term to long-term forecasts, especially in extreme event predictions. Codes link https://github.com/YuanGao-YG/OneForecast.

Neural Radiance Fields (NeRFs) can be dramatically accelerated by spatial grid representations. However, they do not explicitly reason about scale and so introduce aliasing artifacts when reconstructing scenes captured at different camera distances. Mip-NeRF and its extensions propose scale-aware renderers that project volumetric frustums rather than point samples but such approaches rely on positional encodings that are not readily compatible with grid methods. We propose a simple modification to grid-based models by training model heads at different spatial grid resolutions. At render time, we simply use coarser grids to render samples that cover larger volumes. Our method can be easily applied to existing accelerated NeRF methods and significantly improves rendering quality (reducing error rates by 20-90% across synthetic and unbounded real-world scenes) while incurring minimal performance overhead (as each model head is quick to evaluate). Compared to Mip-NeRF, we reduce error rates by 20% while training over 60x faster.

The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the atmosphere-ocean coupling. Thus, the proposed method should be viewed as potentially applicable to air-sea coupled flows in turbulent regime. The method consists of two key ingredients. The geometric averaging approach is used for efficient and stable decoupling of the problem, which would allow for the usage of preexisting codes for the air and sea domain separately, as "black boxes". This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.

We present the first general-relativistic resistive magnetohydrodynamics simulations of self-consistent, rotating neutron stars with mixed poloidal and toroidal magnetic fields. Specifically, we investigate the role of resistivity in the dynamical evolution of neutron stars over a period of up to 100 ms and its effects on their quasi-equilibrium configurations. Our results demonstrate that resistivity can significantly influence the development of magnetohydrodynamic instabilities, resulting in markedly different magnetic field geometries. Additionally, resistivity suppresses the growth of these instabilities, leading to a reduction in the amplitude of emitted gravitational waves. Despite the variations in magnetic field geometries, the ratio of poloidal to toroidal field energies remains consistently 9:1 throughout the simulations, for the models we investigated.

We describe MGARD, a software providing MultiGrid Adaptive Reduction for floating-point scientific data on structured and unstructured grids. With exceptional data compression capability and precise error control, MGARD addresses a wide range of requirements, including storage reduction, high-performance I/O, and in-situ data analysis. It features a unified application programming interface (API) that seamlessly operates across diverse computing architectures. MGARD has been optimized with highly-tuned GPU kernels and efficient memory and device management mechanisms, ensuring scalable and rapid operations.

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) Non-uniqueness: there are many different eigendecompositions of the same Laplacian, and (2) Instability: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a "hard partition" of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to "softly partition" eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.

Power electronic converters are becoming the main components of modern power systems due to the increasing integration of renewable energy sources. However, power converters may become unstable when interacting with the complex and time-varying power grid. In this paper, we propose an adaptive data-driven control method to stabilize power converters by using only online input-output data. Our contributions are threefold. First, we reformulate the output-feedback control problem as a state-feedback linear quadratic regulator (LQR) problem with a controllable non-minimal state, which can be constructed from past input-output signals. Second, we propose a data-enabled policy optimization (DeePO) method for this non-minimal realization to achieve efficient output-feedback adaptive control. Third, we use high-fidelity simulations to verify that the output-feedback DeePO can effectively stabilize grid-connected power converters and quickly adapt to the changes in the power grid.

Constructing an adaptive hexahedral tessellation to fit an input triangle boundary is a key challenge in grid-based methods. The conventional method first removes outside elements (RO) and then projects the axis-aligned boundary onto the input triangle boundary, which has no guarantee on improving the initial Intersection over Union (IoU) and Hausdorff distance ratio (HR, w.r.t bounding box diagonal). The proposed MCHex approach replaces RO with a Marching Cubes method MCHex. Given the same computational budget (benchmarked using an identical precomputed Signed Distance Field, which dominates the runtime), MCHex provides better boundary approximation (higher IoU and lower HR) while guaranteeing a lower, yet still positive, minimum scaled Jacobian (>0 vs. RO's >0.48).

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

DARTS is a popular algorithm for neural architecture search (NAS). Despite its great advantage in search efficiency, DARTS often suffers weak stability, which reflects in the large variation among individual trials as well as the sensitivity to the hyper-parameters of the search process. This paper owes such instability to an optimization gap between the super-network and its sub-networks, namely, improving the validation accuracy of the super-network does not necessarily lead to a higher expectation on the performance of the sampled sub-networks. Then, we point out that the gap is due to the inaccurate estimation of the architectural gradients, based on which we propose an amended estimation method. Mathematically, our method guarantees a bounded error from the true gradients while the original estimation does not. Our approach bridges the gap from two aspects, namely, amending the estimation on the architectural gradients, and unifying the hyper-parameter settings in the search and re-training stages. Experiments on CIFAR10 and ImageNet demonstrate that our approach largely improves search stability and, more importantly, enables DARTS-based approaches to explore much larger search spaces that have not been investigated before.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the field of continual learning to overcome this forgetting, we show that a set of common state-of-the-art methods still suffers from substantial forgetting upon starting to learn new tasks, except that this forgetting is temporary and followed by a phase of performance recovery. We refer to this intriguing but potentially problematic phenomenon as the stability gap. The stability gap had likely remained under the radar due to standard practice in the field of evaluating continual learning models only after each task. Instead, we establish a framework for continual evaluation that uses per-iteration evaluation and we define a new set of metrics to quantify worst-case performance. Empirically we show that experience replay, constraint-based replay, knowledge-distillation, and parameter regularization methods are all prone to the stability gap; and that the stability gap can be observed in class-, task-, and domain-incremental learning benchmarks. Additionally, a controlled experiment shows that the stability gap increases when tasks are more dissimilar. Finally, by disentangling gradients into plasticity and stability components, we propose a conceptual explanation for the stability gap.

Recent studies show that Large Language Models (LLMs) with safety alignment can be jail-broken by fine-tuning on a dataset mixed with harmful data. First time in the literature, we show that the jail-broken effect can be mitigated by separating states in the finetuning stage to optimize the alignment and user datasets. Unfortunately, our subsequent study shows that this simple Bi-State Optimization (BSO) solution experiences convergence instability when steps invested in its alignment state is too small, leading to downgraded alignment performance. By statistical analysis, we show that the excess drift towards consensus could be a probable reason for the instability. To remedy this issue, we propose Lazy(i) safety alignment (Lisa), which introduces a proximal term to constraint the drift of each state. Theoretically, the benefit of the proximal term is supported by the convergence analysis, wherein we show that a sufficient large proximal factor is necessary to guarantee Lisa's convergence. Empirically, our results on four downstream finetuning tasks show that Lisa with a proximal term can significantly increase alignment performance while maintaining the LLM's accuracy on the user tasks. Code is available at https://github.com/git-disl/Lisa.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

Deep ResNet architectures have achieved state of the art performance on many tasks. While they solve the problem of gradient vanishing, they might suffer from gradient exploding as the depth becomes large (Yang et al. 2017). Moreover, recent results have shown that ResNet might lose expressivity as the depth goes to infinity (Yang et al. 2017, Hayou et al. 2019). To resolve these issues, we introduce a new class of ResNet architectures, called Stable ResNet, that have the property of stabilizing the gradient while ensuring expressivity in the infinite depth limit.

The creation of photorealistic virtual worlds requires the accurate modeling of 3D surface geometry for a wide range of objects. For this, meshes are appealing since they 1) enable fast physics-based rendering with realistic material and lighting, 2) support physical simulation, and 3) are memory-efficient for modern graphics pipelines. Recent work on reconstructing and statistically modeling 3D shape, however, has critiqued meshes as being topologically inflexible. To capture a wide range of object shapes, any 3D representation must be able to model solid, watertight, shapes as well as thin, open, surfaces. Recent work has focused on the former, and methods for reconstructing open surfaces do not support fast reconstruction with material and lighting or unconditional generative modelling. Inspired by the observation that open surfaces can be seen as islands floating on watertight surfaces, we parameterize open surfaces by defining a manifold signed distance field on watertight templates. With this parameterization, we further develop a grid-based and differentiable representation that parameterizes both watertight and non-watertight meshes of arbitrary topology. Our new representation, called Ghost-on-the-Shell (G-Shell), enables two important applications: differentiable rasterization-based reconstruction from multiview images and generative modelling of non-watertight meshes. We empirically demonstrate that G-Shell achieves state-of-the-art performance on non-watertight mesh reconstruction and generation tasks, while also performing effectively for watertight meshes.

Although deep learning (DL) has received much attention in accelerated magnetic resonance imaging (MRI), recent studies show that tiny input perturbations may lead to instabilities of DL-based MRI reconstruction models. However, the approaches of robustifying these models are underdeveloped. Compared to image classification, it could be much more challenging to achieve a robust MRI image reconstruction network considering its regression-based learning objective, limited amount of training data, and lack of efficient robustness metrics. To circumvent the above limitations, our work revisits the problem of DL-based image reconstruction through the lens of robust machine learning. We find a new instability source of MRI image reconstruction, i.e., the lack of reconstruction robustness against spatial transformations of an input, e.g., rotation and cutout. Inspired by this new robustness metric, we develop a robustness-aware image reconstruction method that can defend against both pixel-wise adversarial perturbations as well as spatial transformations. Extensive experiments are also conducted to demonstrate the effectiveness of our proposed approaches.

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

The solar wind is a medium characterized by strong turbulence and significant field fluctuations on various scales. Recent observations have revealed that magnetic turbulence exhibits a self-similar behavior. Similarly, high-resolution measurements of the proton density have shown comparable characteristics, prompting several studies into the multifractal properties of these density fluctuations. In this work, we show that low-resolution observations of the solar wind proton density over time, recorded by various spacecraft at Lagrange point L1, also exhibit non-linear and multifractal structures. The novelty of our study lies in the fact that this is the first systematic analysis of solar wind proton density using low-resolution (hourly) data collected by multiple spacecraft at the L1 Lagrange point over a span of 17 years. Furthermore, we interpret our results within the framework of non-extensive statistical mechanics, which appears to be consistent with the observed nonlinear behavior. Based on the data, we successfully validate the q-triplet predicted by non-extensive statistical theory. To the best of our knowledge, this represents the most rigorous and systematic validation to date of the q-triplet in the solar wind.

Runaway electron current generated during the Current Quench phase of tokamak disruptions could result in severe damage to future high performance devices. To control and mitigate such runaway electron current, it is important to accurately describe the runaway electron current dominated equilibrium, based on which further stability analysis could be carried out. In this paper, we derive a Grad-Shafranov-like equation solving for the axisymmetric drift surfaces of the runaway electrons for the simple case that all runaway electron share the same parallel momentum. This new equilibrium equation is then numerically solved with simple rectangular wall with ITER-like and MAST-like geometry parameters. The deviation between the drift surfaces and the flux surfaces is readily obtained, and runaway electrons is found to be well confined even in regions with open field lines. The change of the runaway electron parallel momentum is found to result in a horizontal current center displacement without any changes in the total current or the external field. The runaway current density profile is found to affect the susceptibility of such displacement, with flatter profiles result in more displacement by the same momentum change. With up-down asymmetry in the external poloidal field, such displacement is accompanied by a vertical displacement of runaway electron current. It is found that this effect is more pronounced in smaller, compact device and weaker poloidal field cases. The above results demonstrate the dynamics of current center displacement caused by the momentum space change in the runaway electrons, and pave way for future, more sophisticated runaway current equilibrium theory with more realistic consideration on the runaway electron momentum distribution. This new equilibrium theory also provides foundation for future stability analysis of the runaway electron current.

Large Language Models (LLMs) can significantly improve their reasoning capabilities by interacting with external tools, a paradigm known as Tool-Integrated Reasoning (TIR). However, extending TIR to multi-turn scenarios using Reinforcement Learning (RL) is often hindered by training instability and performance collapse. We identify that such instability is primarily caused by a distributional drift from external tool feedback, leading to the generation of low-probability tokens. This issue compounds over successive turns, causing catastrophic gradient norm explosions that derail the training process. To address this challenge, we introduce SimpleTIR , a plug-and-play algorithm that stabilizes multi-turn TIR training. Its core strategy is to identify and filter out trajectories containing void turns, i.e., turns that yield neither a code block nor a final answer. By removing these problematic trajectories from the policy update, SimpleTIR effectively blocks the harmful, high-magnitude gradients, thus stabilizing the learning dynamics. Extensive experiments show that SimpleTIR achieves state-of-the-art performance on challenging math reasoning benchmarks, notably elevating the AIME24 score from a text-only baseline of 22.1 to 50.5 when starting from the Qwen2.5-7B base model. Furthermore, by avoiding the constraints of supervised fine-tuning, SimpleTIR encourages the model to discover diverse and sophisticated reasoning patterns, such as self-correction and cross-validation.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Neural Radiance Field training can be accelerated through the use of grid-based representations in NeRF's learned mapping from spatial coordinates to colors and volumetric density. However, these grid-based approaches lack an explicit understanding of scale and therefore often introduce aliasing, usually in the form of jaggies or missing scene content. Anti-aliasing has previously been addressed by mip-NeRF 360, which reasons about sub-volumes along a cone rather than points along a ray, but this approach is not natively compatible with current grid-based techniques. We show how ideas from rendering and signal processing can be used to construct a technique that combines mip-NeRF 360 and grid-based models such as Instant NGP to yield error rates that are 8% - 77% lower than either prior technique, and that trains 24x faster than mip-NeRF 360.

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in n-dimensional space, calculating the value of a sampled point requires interpolating the values of its 2^n neighboring vertices. The exponential scaling with dimension leads to significant computational overheads. To address this issue, we propose a simplex-based approach for encoding graphics primitives. The number of vertices in a simplex-based structure increases linearly with dimension, making it a more efficient and generalizable alternative to grid-based representations. Using the non-axis-aligned simplicial structure property, we derive and prove a coordinate transformation, simplicial subdivision, and barycentric interpolation scheme for efficient sampling, which resembles transformation procedures in the simplex noise algorithm. Finally, we use hash tables to store multiresolution features of all interest points in the simplicial grid, which are passed into a tiny fully connected neural network to parameterize graphics primitives. We implemented a detailed simplex-based structure encoding algorithm in C++ and CUDA using the methods outlined in our approach. In the 2D image fitting task, the proposed method is capable of fitting a giga-pixel image with 9.4% less time compared to the baseline method proposed by instant-ngp, while maintaining the same quality and compression rate. In the volumetric rendering setup, we observe a maximum 41.2% speedup when the samples are dense enough.

Generative Artificial Intelligence image models have achieved outstanding performance in text-to-image generation and other tasks, such as inpainting that completes images with missing fragments. The performance of inpainting can be accurately measured by taking an image, removing some fragments, performing the inpainting to restore them, and comparing the results with the original image. Interestingly, inpainting can also be applied recursively, starting from an image, removing some parts, applying inpainting to reconstruct the image, and then starting the inpainting process again on the reconstructed image, and so forth. This process of recursively applying inpainting can lead to an image that is similar or completely different from the original one, depending on the fragments that are removed and the ability of the model to reconstruct them. Intuitively, stability, understood as the capability to recover an image that is similar to the original one even after many recursive inpainting operations, is a desirable feature and can be used as an additional performance metric for inpainting. The concept of stability is also being studied in the context of recursive training of generative AI models with their own data. Recursive inpainting is an inference-only recursive process whose understanding may complement ongoing efforts to study the behavior of generative AI models under training recursion. In this paper, the impact of recursive inpainting is studied for one of the most widely used image models: Stable Diffusion. The results show that recursive inpainting can lead to image collapse, so ending with a nonmeaningful image, and that the outcome depends on several factors such as the type of image, the size of the inpainting masks, and the number of iterations.

Watermark has been widely deployed by industry to detect AI-generated images. A recent watermarking framework called Stable Signature (proposed by Meta) roots watermark into the parameters of a diffusion model's decoder such that its generated images are inherently watermarked. Stable Signature makes it possible to watermark images generated by open-source diffusion models and was claimed to be robust against removal attacks. In this work, we propose a new attack to remove the watermark from a diffusion model by fine-tuning it. Our results show that our attack can effectively remove the watermark from a diffusion model such that its generated images are non-watermarked, while maintaining the visual quality of the generated images. Our results highlight that Stable Signature is not as stable as previously thought.

We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as the Hessian-Riemannian and natural gradient descent methods. More specifically, we incorporate these preconditioned gradient descent algorithms in the recently introduced Adaptive Energy Gradient Descent (AEGD) framework. In particular, we discuss theoretical results on the unconditional energy-stability and convergence rates across three classes of objective functions. Furthermore, our numerical results demonstrate excellent performance of the proposed method on several test bed optimization problems.

Crystalline materials are a fundamental component in next-generation technologies, yet modeling their distribution presents unique computational challenges. Of the plausible arrangements of atoms in a periodic lattice only a vanishingly small percentage are thermodynamically stable, which is a key indicator of the materials that can be experimentally realized. Two fundamental tasks in this area are to (a) predict the stable crystal structure of a known composition of elements and (b) propose novel compositions along with their stable structures. We present FlowMM, a pair of generative models that achieve state-of-the-art performance on both tasks while being more efficient and more flexible than competing methods. We generalize Riemannian Flow Matching to suit the symmetries inherent to crystals: translation, rotation, permutation, and periodic boundary conditions. Our framework enables the freedom to choose the flow base distributions, drastically simplifying the problem of learning crystal structures compared with diffusion models. In addition to standard benchmarks, we validate FlowMM's generated structures with quantum chemistry calculations, demonstrating that it is about 3x more efficient, in terms of integration steps, at finding stable materials compared to previous open methods.

Point-based image editing has attracted remarkable attention since the emergence of DragGAN. Recently, DragDiffusion further pushes forward the generative quality via adapting this dragging technique to diffusion models. Despite these great success, this dragging scheme exhibits two major drawbacks, namely inaccurate point tracking and incomplete motion supervision, which may result in unsatisfactory dragging outcomes. To tackle these issues, we build a stable and precise drag-based editing framework, coined as StableDrag, by designing a discirminative point tracking method and a confidence-based latent enhancement strategy for motion supervision. The former allows us to precisely locate the updated handle points, thereby boosting the stability of long-range manipulation, while the latter is responsible for guaranteeing the optimized latent as high-quality as possible across all the manipulation steps. Thanks to these unique designs, we instantiate two types of image editing models including StableDrag-GAN and StableDrag-Diff, which attains more stable dragging performance, through extensive qualitative experiments and quantitative assessment on DragBench.

Stars on the AGB can exhibit acoustic pulsation modes of different radial orders, along with non-radial modes. These pulsations are essential to the mass-loss process and influence the evolutionary pathways of AGB stars. P-L relations serve as a valuable diagnostic for understanding stellar evolution along the AGB. 3D RHD simulations provide a powerful tool for investigating pulsation phenomena driven by convective processes and their non-linear coupling with stellar oscillations. We investigate multi-mode pulsations in AGB stars using advanced 3D 'star-in-a-box' simulations with the CO5BOLD code. Signatures of these multi-mode pulsations were weak in our previous 3D models. Our focus is on identifying and characterising the various pulsation modes, examining their persistence and transitions, and comparing the results with 1D model predictions and observational data where applicable. We produced a new model grid comprising AGB stars with current masses of 0.7, 0.8, and 1,M_{odot}. Fourier analysis was applied to dynamic, time-dependent quantities to extract dominant pulsation modes and their corresponding periods. Additionally, wavelet transforms were employed to identify mode-switching behaviour over time. The models successfully reproduce the P-L sequences found in AGB stars. Mode-switching phenomena are found in both the models and wavelet analyses of observational data, allowing us to infer similarities in the underlying pulsation dynamics. These 3D simulations highlight the natural emergence of multi-mode pulsations, including both radial and non-radial modes, driven by the self-consistent interplay of convection and oscillations. Our findings underscore the value of 3D RHD models in capturing the non-linear behaviour of AGB pulsations, providing insights into mode switching, envelope structures, and potential links to episodic mass-loss events.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time on long video sequences. To address this issue, we (1) introduce a diagnostic tool which produces input sequences optimized to trigger instabilities and that can be interpreted as visualizations of temporal receptive fields, and (2) propose two approaches to enforce the stability of a model during training: constraining the spectral norm or constraining the stable rank of its convolutional layers. We then introduce Stable Rank Normalization for Convolutional layers (SRN-C), a new algorithm that enforces these constraints. Our experimental results suggest that SRN-C successfully enforces stability in recurrent video processing models without a significant performance loss.

Offline-to-online reinforcement learning (RL) has emerged as a practical paradigm that leverages offline datasets for pretraining and online interactions for fine-tuning. However, its empirical behavior is highly inconsistent: design choices of online-fine tuning that work well in one setting can fail completely in another. We propose a stability--plasticity principle that can explain this inconsistency: we should preserve the knowledge of pretrained policy or offline dataset during online fine-tuning, whichever is better, while maintaining sufficient plasticity. This perspective identifies three regimes of online fine-tuning, each requiring distinct stability properties. We validate this framework through a large-scale empirical study, finding that the results strongly align with its predictions in 45 of 63 cases. This work provides a principled framework for guiding design choices in offline-to-online RL based on the relative performance of the offline dataset and the pretrained policy.

Winograd convolution is the standard algorithm for efficient inference, reducing arithmetic complexity by 2.25x for 3x3 kernels. However, it faces a critical barrier in the modern era of low precision computing: numerical instability. As tiles scale to maximize efficiency (e.g., F(6,3), F(8,3)), the condition numbers of standard integer based transforms explode, reaching kappa = 2 x 10^5 for F(8,3), rendering them unusable in FP16 or Int8. We introduce NOVA (Numerical Optimization of Vandermonde Arithmetic), a discovery framework that breaks the decades old convention of integer interpolation. Treating Winograd point selection as a continuous optimization problem, NOVA searches the manifold R^n-1 via Evolution Strategy, snaps candidates to simple rationals, and guarantees correctness via symbolic verification. This process uncovers a hidden landscape of stable, fractional configurations such as {+-5/6, +-7/6, +-3/5} that defy traditional vocabulary constraints. The impact is transformative: NOVA improves the conditioning of F(8,3) by 415x in 1D, which squares to a 172,484x improvement for 2D convolution. In real world FP16 ImageNet inference, where standard transforms collapse to random chance (e.g., 4.7 percent accuracy on VGG16), NOVA's points restore full accuracy (75 to 78 percent), recovering over 70 percentage points without retraining, calibration, or learned parameters. These discovered transforms act as drop in replacements, effectively unlocking the efficiency of large tile Winograd convolution for next generation hardware.

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue near the maximum value which allows convergence (edge of stability). These phenomena are intrinsically non-linear and do not happen for models in the constant Neural Tangent Kernel (NTK) regime, for which the predictive function is approximately linear in the parameters. As such, we consider the next simplest class of predictive models, namely those that are quadratic in the parameters, which we call second-order regression models. For quadratic objectives in two dimensions, we prove that this second-order regression model exhibits progressive sharpening of the NTK eigenvalue towards a value that differs slightly from the edge of stability, which we explicitly compute. In higher dimensions, the model generically shows similar behavior, even without the specific structure of a neural network, suggesting that progressive sharpening and edge-of-stability behavior aren't unique features of neural networks, and could be a more general property of discrete learning algorithms in high-dimensional non-linear models.

Text-to-image diffusion models, e.g. Stable Diffusion (SD), lately have shown remarkable ability in high-quality content generation, and become one of the representatives for the recent wave of transformative AI. Nevertheless, such advance comes with an intensifying concern about the misuse of this generative technology, especially for producing copyrighted or NSFW (i.e. not safe for work) images. Although efforts have been made to filter inappropriate images/prompts or remove undesirable concepts/styles via model fine-tuning, the reliability of these safety mechanisms against diversified problematic prompts remains largely unexplored. In this work, we propose Prompting4Debugging (P4D) as a debugging and red-teaming tool that automatically finds problematic prompts for diffusion models to test the reliability of a deployed safety mechanism. We demonstrate the efficacy of our P4D tool in uncovering new vulnerabilities of SD models with safety mechanisms. Particularly, our result shows that around half of prompts in existing safe prompting benchmarks which were originally considered "safe" can actually be manipulated to bypass many deployed safety mechanisms, including concept removal, negative prompt, and safety guidance. Our findings suggest that, without comprehensive testing, the evaluations on limited safe prompting benchmarks can lead to a false sense of safety for text-to-image models.

The ionosphere is a critical component of near-Earth space, shaping GNSS accuracy, high-frequency communications, and aviation operations. For these reasons, accurate forecasting and modeling of ionospheric variability has become increasingly relevant. To address this gap, we present IonCast, a suite of deep learning models that include a GraphCast-inspired model tailored for ionospheric dynamics. IonCast leverages spatiotemporal learning to forecast global Total Electron Content (TEC), integrating diverse physical drivers and observational datasets. Validating on held-out storm-time and quiet conditions highlights improved skill compared to persistence. By unifying heterogeneous data with scalable graph-based spatiotemporal learning, IonCast demonstrates how machine learning can augment physical understanding of ionospheric variability and advance operational space weather resilience.

Adversarial robustness is essential for security and reliability of machine learning systems. However, adversarial robustness enhanced by defense algorithms is easily erased as the neural network's weights update to learn new tasks. To address this vulnerability, it is essential to improve the capability of neural networks in terms of robust continual learning. Specially, we propose a novel gradient projection technique that effectively stabilizes sample gradients from previous data by orthogonally projecting back-propagation gradients onto a crucial subspace before using them for weight updates. This technique can maintaining robustness by collaborating with a class of defense algorithms through sample gradient smoothing. The experimental results on four benchmarks including Split-CIFAR100 and Split-miniImageNet, demonstrate that the superiority of the proposed approach in mitigating rapidly degradation of robustness during continual learning even when facing strong adversarial attacks.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

The core of Transferable Utility (T.U.) games is a well-known solution concept from cooperative game theory yielding a cost allocation among n agents (called players) forming a coalition that is stable (i.e. no subset of players has an interest to deviate). In this paper, inspired by a practical application in the context of a decision support system for collaborative transportation in a Short Food Supply Chain (SFSC), we mainly focus on Traveling Salesman Games (TSGs), where the objective is to allocate the cost of a Traveling Salesman Problem (TSP) with n locations and 1 depot to n players, each linked to exactly one of the locations. Given the computational complexity of computing an element of the core and the cost of a TSP, we study semicore allocations: a relaxation of the core that only requires that the subsets of size n -1 and of size 1 do not wish to deviate from the coalition. In the literature, instances of TSGs with empty cores and semicores are found. Hence, this paper first surveys the methods to approximate stability whenever the core is empty, such as the cost of stability (computing the minimum amount of money to subsidize the coalition with to attain stability) and the ε-core (which is a set of allocations that allow subsets of players to exceed their actual cost, but at most of a value of ε). We prove that these two solution

We introduce controlgym, a library of thirty-six safety-critical industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.

Satellite-to-street view synthesis aims at generating a realistic street-view image from its corresponding satellite-view image. Although stable diffusion models have exhibit remarkable performance in a variety of image generation applications, their reliance on similar-view inputs to control the generated structure or texture restricts their application to the challenging cross-view synthesis task. In this work, we propose CrossViewDiff, a cross-view diffusion model for satellite-to-street view synthesis. To address the challenges posed by the large discrepancy across views, we design the satellite scene structure estimation and cross-view texture mapping modules to construct the structural and textural controls for street-view image synthesis. We further design a cross-view control guided denoising process that incorporates the above controls via an enhanced cross-view attention module. To achieve a more comprehensive evaluation of the synthesis results, we additionally design a GPT-based scoring method as a supplement to standard evaluation metrics. We also explore the effect of different data sources (e.g., text, maps, building heights, and multi-temporal satellite imagery) on this task. Results on three public cross-view datasets show that CrossViewDiff outperforms current state-of-the-art on both standard and GPT-based evaluation metrics, generating high-quality street-view panoramas with more realistic structures and textures across rural, suburban, and urban scenes. The code and models of this work will be released at https://opendatalab.github.io/CrossViewDiff/.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our https://github.com/mikemccabe210/stabilizing_neural_operators{code} for reproducibility.

We present X^3 (pronounced XCube), a novel generative model for high-resolution sparse 3D voxel grids with arbitrary attributes. Our model can generate millions of voxels with a finest effective resolution of up to 1024^3 in a feed-forward fashion without time-consuming test-time optimization. To achieve this, we employ a hierarchical voxel latent diffusion model which generates progressively higher resolution grids in a coarse-to-fine manner using a custom framework built on the highly efficient VDB data structure. Apart from generating high-resolution objects, we demonstrate the effectiveness of XCube on large outdoor scenes at scales of 100mtimes100m with a voxel size as small as 10cm. We observe clear qualitative and quantitative improvements over past approaches. In addition to unconditional generation, we show that our model can be used to solve a variety of tasks such as user-guided editing, scene completion from a single scan, and text-to-3D. More results and details can be found at https://research.nvidia.com/labs/toronto-ai/xcube/.

Matbench Discovery simulates the deployment of machine learning (ML) energy models in a high-throughput search for stable inorganic crystals. We address the disconnect between (i) thermodynamic stability and formation energy and (ii) in-domain vs out-of-distribution performance. Alongside this paper, we publish a Python package to aid with future model submissions and a growing online leaderboard with further insights into trade-offs between various performance metrics. To answer the question which ML methodology performs best at materials discovery, our initial release explores a variety of models including random forests, graph neural networks (GNN), one-shot predictors, iterative Bayesian optimizers and universal interatomic potentials (UIP). Ranked best-to-worst by their test set F1 score on thermodynamic stability prediction, we find CHGNet > M3GNet > MACE > ALIGNN > MEGNet > CGCNN > CGCNN+P > Wrenformer > BOWSR > Voronoi tessellation fingerprints with random forest. The top 3 models are UIPs, the winning methodology for ML-guided materials discovery, achieving F1 scores of ~0.6 for crystal stability classification and discovery acceleration factors (DAF) of up to 5x on the first 10k most stable predictions compared to dummy selection from our test set. We also highlight a sharp disconnect between commonly used global regression metrics and more task-relevant classification metrics. Accurate regressors are susceptible to unexpectedly high false-positive rates if those accurate predictions lie close to the decision boundary at 0 eV/atom above the convex hull where most materials are. Our results highlight the need to focus on classification metrics that actually correlate with improved stability hit rate.

Score Distillation Sampling (SDS) leverages pretrained 2D diffusion models to advance text-to-3D generation but neglects multi-view correlations, being prone to geometric inconsistencies and multi-face artifacts in the generated 3D content. In this work, we propose Coupled Score Distillation (CSD), a framework that couples multi-view joint distribution priors to ensure geometrically consistent 3D generation while enabling the stable and direct optimization of 3D Gaussian Splatting. Specifically, by reformulating the optimization as a multi-view joint optimization problem, we derive an effective optimization rule that effectively couples multi-view priors to guide optimization across different viewpoints while preserving the diversity of generated 3D assets. Additionally, we propose a framework that directly optimizes 3D Gaussian Splatting (3D-GS) with random initialization to generate geometrically consistent 3D content. We further employ a deformable tetrahedral grid, initialized from 3D-GS and refined through CSD, to produce high-quality, refined meshes. Quantitative and qualitative experimental results demonstrate the efficiency and competitive quality of our approach.

In diffusion models, UNet is the most popular network backbone, since its long skip connects (LSCs) to connect distant network blocks can aggregate long-distant information and alleviate vanishing gradient. Unfortunately, UNet often suffers from unstable training in diffusion models which can be alleviated by scaling its LSC coefficients smaller. However, theoretical understandings of the instability of UNet in diffusion models and also the performance improvement of LSC scaling remain absent yet. To solve this issue, we theoretically show that the coefficients of LSCs in UNet have big effects on the stableness of the forward and backward propagation and robustness of UNet. Specifically, the hidden feature and gradient of UNet at any layer can oscillate and their oscillation ranges are actually large which explains the instability of UNet training. Moreover, UNet is also provably sensitive to perturbed input, and predicts an output distant from the desired output, yielding oscillatory loss and thus oscillatory gradient. Besides, we also observe the theoretical benefits of the LSC coefficient scaling of UNet in the stableness of hidden features and gradient and also robustness. Finally, inspired by our theory, we propose an effective coefficient scaling framework ScaleLong that scales the coefficients of LSC in UNet and better improves the training stability of UNet. Experimental results on four famous datasets show that our methods are superior to stabilize training and yield about 1.5x training acceleration on different diffusion models with UNet or UViT backbones. Code: https://github.com/sail-sg/ScaleLong

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Watermarking images is critical for tracking image provenance and claiming ownership. With the advent of generative models, such as stable diffusion, able to create fake but realistic images, watermarking has become particularly important, e.g., to make generated images reliably identifiable. Unfortunately, the very same stable diffusion technology can remove watermarks injected using existing methods. To address this problem, we present a ZoDiac, which uses a pre-trained stable diffusion model to inject a watermark into the trainable latent space, resulting in watermarks that can be reliably detected in the latent vector, even when attacked. We evaluate ZoDiac on three benchmarks, MS-COCO, DiffusionDB, and WikiArt, and find that ZoDiac is robust against state-of-the-art watermark attacks, with a watermark detection rate over 98% and a false positive rate below 6.4%, outperforming state-of-the-art watermarking methods. Our research demonstrates that stable diffusion is a promising approach to robust watermarking, able to withstand even stable-diffusion-based attacks.

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data, especially when the learned dynamics are governed by neural networks. We propose a novel methodology to learn neural contractive dynamical systems, where our neural architecture ensures contraction, and hence, global stability. To efficiently scale the method to high-dimensional dynamical systems, we develop a variant of the variational autoencoder that learns dynamics in a low-dimensional latent representation space while retaining contractive stability after decoding. We further extend our approach to learning contractive systems on the Lie group of rotations to account for full-pose end-effector dynamic motions. The result is the first highly flexible learning architecture that provides contractive stability guarantees with capability to perform obstacle avoidance. Empirically, we demonstrate that our approach encodes the desired dynamics more accurately than the current state-of-the-art, which provides less strong stability guarantees.

3D Gaussian Splatting (3DGS) has recently emerged as a powerful paradigm for photorealistic view synthesis, representing scenes with spatially distributed Gaussian primitives. While highly effective for rendering, achieving accurate and complete surface reconstruction remains challenging due to the unstructured nature of the representation and the absence of explicit geometric supervision. In this work, we propose DiGS, a unified framework that embeds Signed Distance Field (SDF) learning directly into the 3DGS pipeline, thereby enforcing strong and interpretable surface priors. By associating each Gaussian with a learnable SDF value, DiGS explicitly aligns primitives with underlying geometry and improves cross-view consistency. To further ensure dense and coherent coverage, we design a geometry-guided grid growth strategy that adaptively distributes Gaussians along geometry-consistent regions under a multi-scale hierarchy. Extensive experiments on standard benchmarks, including DTU, Mip-NeRF 360, and Tanks& Temples, demonstrate that DiGS consistently improves reconstruction accuracy and completeness while retaining high rendering fidelity.