DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data distribution by incrementally injecting noise into the data. To numerically simulate the sampling process, a discretisation schedule from the reference back towards clean data must be chosen. An appropriate discretisation schedule is crucial to obtain high quality samples. However, beyond hand crafted heuristics, a general method for choosing this schedule remains elusive. This paper presents a novel algorithm for adaptively selecting an optimal discretisation schedule with respect to a cost that we derive. Our cost measures the work done by the simulation procedure to transport samples from one point in the diffusion path to the next. Our method does not require hyperparameter tuning and adapts to the dynamics and geometry of the diffusion path. Our algorithm only involves the evaluation of the estimated Stein score, making it scalable to existing pre-trained models at inference time and online during training. We find that our learned schedule recovers performant schedules previously only discovered through manual search and obtains competitive FID scores on image datasets.

Heterogeneity, e.g., due to different types of layers or multiple sub-models, poses key challenges in analyzing the generalization behavior of several modern architectures. For instance, descriptors based on Persistent Homology (PH) are being increasingly integrated into Graph Neural Networks (GNNs) to augment them with rich topological features; however, the generalization of such PH schemes remains unexplored. We introduce a novel PAC-Bayes framework that provides a general recipe to analyze a broad spectrum of models including those with heterogeneous layers. Specifically, we provide the first data-dependent generalization bounds for a widely adopted PH vectorization scheme (that subsumes persistence landscapes, images, and silhouettes) as well as PH-augmented GNNs. Using our framework, we also obtain bounds for GNNs and neural nets with ease. Our bounds also inform the design of novel regularizers. Empirical evaluations on several standard real-world datasets demonstrate that our theoretical bounds highly correlate with empirical generalization performance, leading to improved classifier design via our regularizers.

Over the past years, we have observed an abundance of approaches for modeling dynamic 3D scenes using Gaussian Splatting (GS). These solutions use GS to represent the scene's structure and the neural network to model dynamics. Such approaches allow fast rendering and extracting each element of such a dynamic scene. However, modifying such objects over time is challenging. SC-GS (Sparse Controlled Gaussian Splatting) enhanced with Deformed Control Points partially solves this issue. However, this approach necessitates selecting elements that need to be kept fixed, as well as centroids that should be adjusted throughout editing.

This paper questions the effectiveness of a modern predictive uncertainty quantification approach, called (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their perceived strong empirical performance on downstream tasks, a line of recent studies by Bengs et al. identify limitations of the existing methods to conclude their learned epistemic uncertainties are unreliable, e.g., in that they are non-vanishing even with infinite data. Building on and sharpening such analysis, we 1) provide a sharper understanding of the asymptotic behavior of a wide class of EDL methods by unifying various objective functions; 2) reveal that the EDL methods can be better interpreted as an out-of-distribution detection algorithm based on energy-based-models; and 3) conduct extensive ablation studies to better assess their empirical effectiveness with real-world datasets. Through all these analyses, we conclude that even when EDL methods are empirically effective on downstream tasks, this occurs despite their poor uncertainty quantification capabilities. Our investigation suggests that incorporating model uncertainty can help EDL methods faithfully quantify uncertainties and further improve performance on representative downstream tasks, albeit at the cost of additional computational complexity.

Fine-grained understanding of objects, attributes, and relationships between objects is crucial for visual-language models (VLMs). To evaluate VLMs' fine-grained understanding, existing benchmarks primarily focus on evaluating VLMs' capability to distinguish between two very similar captions given an image. In this paper, our focus is on evaluating VLMs' capability to distinguish between two very similar images given a caption. To this end, we introduce a new, challenging benchmark termed Visual Minimal-Change Understanding (VisMin), which requires models to predict the correct image-caption match given two images and two captions. Importantly, the image pair (as well as the caption pair) contains minimal changes, i.e., between the two images (as well as between the two captions), only one aspect changes at a time from among the following possible types of changes: object, attribute, count, and spatial relation.

Stochastic compositional optimization (SCO) problem constitutes a class of optimization problems characterized by the objective function with a compositional form, including the tasks with known derivatives, such as AUC maximization, and the derivative-free tasks exemplified by black-box vertical federated learning (VFL). From the learning theory perspective, the learning guarantees of SCO algorithms with known derivatives have been studied in the literature. However, the potential impacts of the derivative-free setting on the learning guarantees of SCO remains unclear and merits further investigation. This paper aims to reveal the impacts by developing a theoretical analysis for two derivative-free algorithms, black-box SCGD and SCSC. Specifically, we first provide the sharper generalization upper bounds of convex SCGD and SCSC based on a new stability analysis framework more effective than prior work under some milder conditions, which is further developed to the non-convex case using the almost co-coercivity property of smooth function. Then, we derive the learning guarantees of three black-box variants of non-convex SCGD and SCSC with additional optimization analysis. Comparing these results, we theoretically uncover the impacts that a better gradient estimation brings a tighter learning guarantee and a larger proportion of unknown gradients may lead to a stronger dependence on the gradient estimation quality. Finally, our analysis is applied to two SCO algorithms, FOO-based vertical VFL and VFL-CZOFO, to build the first learning guarantees for VFL that align with the findings of SCGD and SCSC.

Data science and engineering workflows often span multiple stages, from warehousing to orchestration, using tools like BigQuery, dbt, and Airbyte.

Variance exploding (VE) based diffusion models, an important class of diffusion models, have shown state-of-the-art (SOTA) performance. However, only a few theoretical works analyze VE-based models, and those works suffer from a worse forward convergence rate $1/\text{poly}(T)$ than the $\exp{(-T)}$ of variance preserving (VP) based models, where $T$ is the forward diffusion time and the rate measures the distance between forward marginal distribution $q_T$ and pure Gaussian noise. The slow rate is due to the Brownian Motion without a drift term. In this work, we design a new drifted VESDE forward process, which allows a faster $\exp{(-T)}$ forward convergence rate. With this process, we achieve the first efficient polynomial sample complexity for a series of VE-based models with reverse SDE under the manifold hypothesis. Furthermore, unlike previous works, we allow the diffusion coefficient to be unbounded instead of a constant, which is closer to the SOTA models. Besides the reverse SDE, the other common reverse process is the probability flow ODE (PFODE) process, which is deterministic and enjoys faster sample speed. To deepen the understanding of VE-based models, we consider a more general setting considering reverse SDE and PFODE simultaneously, propose a unified tangent-based analysis framework, and prove the first quantitative convergence guarantee for SOTA VE-based models with reverse PFODE.We also show that the drifted VESDE can balance different error terms and improve generated samples without training through synthetic and real-world experiments.

Visual relationship understanding has been studied separately in human-object interaction(HOI) detection, scene graph generation(SGG), and referring relationships(RR) tasks. Given the complexity and interconnectedness of these tasks, it is crucial to have a flexible framework that can effectively address these tasks in a cohesive manner.In this work, we propose FleVRS, a single model that seamlessly integrates the above three aspects in standard and promptable visual relationship segmentation, and further possesses the capability for open-vocabulary segmentation to adapt to novel scenarios. FleVRS leverages the synergy between text and image modalities, to ground various types of relationships from images and use textual features from vision-language models to visual conceptual understanding.Empirical validation across various datasets demonstrates that our framework outperforms existing models in standard, promptable, and open-vocabulary tasks, e.g., +1.9 $mAP$ on HICO-DET, +11.4 $Acc$ on VRD, +4.7 $mAP$ on unseen HICO-DET.Our FleVRS represents a significant step towards a more intuitive, comprehensive, and scalable understanding of visual relationships.

Spatio-temporal (ST) prediction has garnered a De facto attention in earth sciences, such as meteorological prediction, human mobility perception. However, the scarcity of data coupled with the high expenses involved in sensor deployment results in notable data imbalances. Furthermore, models that are excessively customized and devoid of causal connections further undermine the generalizability and interpretability. To this end, we establish a causal framework for ST predictions, termed CaPaint, which targets to identify causal regions in data and endow model with causal reasoning ability in a two-stage process. Going beyond this process, we utilize the back-door adjustment to specifically address the sub-regions identified as non-causal in the upstream phase.