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Recent research endeavors have shown that combining neural radiance fields (NeRFs) with pre-trained diffusion models holds great potential for text-to-3D generation. However, a hurdle is that they often encounter guidance collapse when rendering multi-object scenes with relatively long sentences. Specifically, text-to-image diffusion models are inherently unconstrained, making them less competent to accurately associate object semantics with 3D structures. To address it, we propose a novel framework, dubbed CompoNeRF, to explicitly incorporates an editable 3D scene layout to provide effective guidance at the object (i.e., local) and scene (i.e., global) levels. Firstly, we interpret the multi-object text as an editable 3D scene layout containing multiple local NeRFs associated with the object-specific 3D boxes and text prompt. Then, we introduce a composition module to calibrate the latent features from local NeRFs, which surprisingly improves the view consistency across different local NeRFs. Lastly, we apply text guidance on global and local levels through their corresponding views to avoid guidance ambiguity. Additionally, NeRFs can be decomposed and cached for composing other scenes with fine-tuning. This way, our CompoNeRF allows for flexible scene editing and re-composition of trained local NeRFs into a new scene by manipulating the 3D layout or text prompt. Leveraging the open-source Stable Diffusion model, our CompoNeRF can generate faithful and editable text-to-3D results while opening a potential direction for text-guided multi-object composition via the editable 3D scene layout. Notably, our CompoNeRF can achieve at most 54% performance gain based on the CLIP score metric. Code is available at //.

Current physics-informed (standard or operator) neural networks still rely on accurately learning the initial conditions of the system they are solving. In contrast, standard numerical methods evolve such initial conditions without needing to learn these. In this study, we propose to improve current physics-informed deep learning strategies such that initial conditions do not need to be learned and are represented exactly in the predicted solution. Moreover, this method guarantees that when a DeepONet is applied multiple times to time step a solution, the resulting function is continuous.

This paper targets a novel trade-off problem in generalizable prompt learning for vision-language models (VLM), i.e., improving the performance on unseen classes while maintaining the performance on seen classes. Comparing with existing generalizable methods that neglect the seen classes degradation, the setting of this problem is more strict and fits more closely with practical applications. To solve this problem, we start from the optimization perspective, and leverage the relationship between loss landscape geometry and model generalization ability. By analyzing the loss landscape of the state-of-the-art method and the widely-used Sharpness-aware Minimization (SAM), we conclude that the trade-off performance correlates to both loss value and loss sharpness, while each of them are indispensable. However, we find the optimizing gradient of existing methods cannot always maintain high consistency with both loss value and loss sharpness during the whole optimization procedure. To this end, we propose an novel SAM-based method for prompt learning, denoted as Gradient Constrained Sharpness-aware Context Optimization (GCSCoOp), to dynamically constrains the optimizing gradient, thus achieving above two-fold optimization objective simultaneously. Extensive experiments verify the effectiveness of GCSCoOp in the trade-off problem.

Gaussian elimination with partial pivoting (GEPP) is a widely used method to solve dense linear systems. Each GEPP step uses a row transposition pivot movement if needed to ensure the leading pivot entry is maximal in magnitude for the leading column of the remaining untriangularized subsystem. We will use theoretical and numerical approaches to study how often this pivot movement is needed. We provide full distributional descriptions for the number of pivot movements needed using GEPP using particular Haar random ensembles, as well as compare these models to other common transformations from randomized numerical linear algebra. Additionally, we introduce new random ensembles with fixed pivot movement counts and fixed sparsity, $\alpha$. Experiments estimating the empirical spectral density (ESD) of these random ensembles leads to a new conjecture on a universality class of random matrices with fixed sparsity whose scaled ESD converges to a measure on the complex unit disk that depends on $\alpha$ and is an interpolation of the uniform measure on the unit disk and the Dirac measure at the origin.

This study examines the efficacy of various neural network (NN) models in interpreting mental constructs via electroencephalogram (EEG) signals. Through the assessment of 16 prevalent NN models and their variants across four brain-computer interface (BCI) paradigms, we gauged their information representation capability. Rooted in comprehensive literature review findings, we proposed EEGNeX, a novel, purely ConvNet-based architecture. We pitted it against both existing cutting-edge strategies and the Mother of All BCI Benchmarks (MOABB) involving 11 distinct EEG motor imagination (MI) classification tasks and revealed that EEGNeX surpasses other state-of-the-art methods. Notably, it shows up to 2.1%-8.5% improvement in the classification accuracy in different scenarios with statistical significance (p < 0.05) compared to its competitors. This study not only provides deeper insights into designing efficient NN models for EEG data but also lays groundwork for future explorations into the relationship between bioelectric brain signals and NN architectures. For the benefit of broader scientific collaboration, we have made all benchmark models, including EEGNeX, publicly available at (//github.com/chenxiachan/EEGNeX).

This study focuses on the use of model and data fusion for improving the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions of separated flows. In particular, our goal is to develop of models that not-only assimilate sparse experimental data to improve performance in computational models, but also generalize to unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the Ensemble Kalman Filtering approach (EnKF), to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via a parameterization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected velocity profiles, skin friction, and pressure coefficients for separated flows. Despite using of observational data from a single flow condition around a backward-facing step (BFS), the recalibrated SA model demonstrates generalization to other separated flows, including cases such as the 2D-bump and modified BFS. Significant improvement is observed in the quantities of interest, i.e., skin friction coefficient ($C_f$) and pressure coefficient ($C_p$) for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for external, unseparated flows, such as flow around a NACA-0012 airfoil without any danger of extrapolation, and that the individually calibrated terms in the SA model are targeted towards specific flow-physics wherein the calibrated production term improves the re-circulation zone while destruction improves the recovery zone.

A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy management, stealth, or implicit coordination. We formulate the problem of planning under uncertainty when the robot's observations are intermittent but their timing is known via a pre-declared schedule. After having established the appropriate notion of an optimal policy for such settings, we tackle the problem of joint optimization of the cumulative execution cost and the number of state observations, both in expectation under discounts. To approach this multi-objective optimization problem, we introduce an algorithm that can identify the Pareto front for a class of schedules that are advantageous in the discounted setting. The algorithm proceeds in an accumulative fashion, prepending additions to a working set of schedules and then computing incremental changes to the value functions. Because full exhaustive construction becomes computationally prohibitive for moderate-sized problems, we propose a filtering approach to prune the working set. Empirical results demonstrate that this filtering is effective at reducing computation while incurring only negligible reduction in quality. In summarizing our findings, we provide a characterization of the run-time vs quality trade-off involved.

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric nonlinear Hamiltonian systems is challenged by several factors: (i) the geometric structure encoding the physical properties of the dynamics; (ii) the slowly decaying Kolmogorov n-width of conservative dynamics; (iii) the gradient structure of the nonlinear flow velocity; (iv) high variations in the numerical rank of the state as a function of time and parameters. We propose to address these aspects via a structure-preserving adaptive approach that combines symplectic dynamical low-rank approximation with adaptive gradient-preserving hyper-reduction and parameters sampling. Additionally, we propose to vary in time the dimensions of both the reduced basis space and the hyper-reduction space by monitoring the quality of the reduced solution via an error indicator related to the projection error of the Hamiltonian vector field. The resulting adaptive hyper-reduced models preserve the geometric structure of the Hamiltonian flow, do not rely on prior information on the dynamics, and can be solved at a cost that is linear in the dimension of the full order model and linear in the number of test parameters. Numerical experiments demonstrate the improved performances of the fully adaptive models compared to the original and reduced models.

This paper surveys vision-language pre-training (VLP) methods for multimodal intelligence that have been developed in the last few years. We group these approaches into three categories: ($i$) VLP for image-text tasks, such as image captioning, image-text retrieval, visual question answering, and visual grounding; ($ii$) VLP for core computer vision tasks, such as (open-set) image classification, object detection, and segmentation; and ($iii$) VLP for video-text tasks, such as video captioning, video-text retrieval, and video question answering. For each category, we present a comprehensive review of state-of-the-art methods, and discuss the progress that has been made and challenges still being faced, using specific systems and models as case studies. In addition, for each category, we discuss advanced topics being actively explored in the research community, such as big foundation models, unified modeling, in-context few-shot learning, knowledge, robustness, and computer vision in the wild, to name a few.

Recent work pre-training Transformers with self-supervised objectives on large text corpora has shown great success when fine-tuned on downstream NLP tasks including text summarization. However, pre-training objectives tailored for abstractive text summarization have not been explored. Furthermore there is a lack of systematic evaluation across diverse domains. In this work, we propose pre-training large Transformer-based encoder-decoder models on massive text corpora with a new self-supervised objective. In PEGASUS, important sentences are removed/masked from an input document and are generated together as one output sequence from the remaining sentences, similar to an extractive summary. We evaluated our best PEGASUS model on 12 downstream summarization tasks spanning news, science, stories, instructions, emails, patents, and legislative bills. Experiments demonstrate it achieves state-of-the-art performance on all 12 downstream datasets measured by ROUGE scores. Our model also shows surprising performance on low-resource summarization, surpassing previous state-of-the-art results on 6 datasets with only 1000 examples. Finally we validated our results using human evaluation and show that our model summaries achieve human performance on multiple datasets.