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Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for the completeness proof are highly non-constructive. The question of completeness of GLP w.r.t. natural scattered topologies on ordinals is dependent on large cardinal axioms of set theory and is still open. So far, we are lacking a useable class of models for which GLP is complete. In this paper we define a natural class of countable general topological frames on ordinals for which GLP is sound and complete. The associated topologies are the same as the ordinal topologies introduced by Thomas Icard. However, the key point is to specify a suitable algebra of subsets of an ordinal closed under the boolean and topological derivative operations. The algebras we define are based on the notion of a periodic set of ordinals generalizing that of an ultimately periodic binary omega-word., Comment: 32 pages

The use of synthetic data in indoor 3D object detection offers the potential of greatly reducing the manual labor involved in 3D annotations and training effective zero-shot detectors. However, the complicated domain shifts across syn-to-real indoor datasets remains underexplored. In this paper, we propose a novel Object-wise Hierarchical Domain Alignment (OHDA) framework for syn-to-real unsupervised domain adaptation in indoor 3D object detection. Our approach includes an object-aware augmentation strategy to effectively diversify the source domain data, and we introduce a two-branch adaptation framework consisting of an adversarial training branch and a pseudo labeling branch, in order to simultaneously reach holistic-level and class-level domain alignment. The pseudo labeling is further refined through two proposed schemes specifically designed for indoor UDA. Our adaptation results from synthetic dataset 3D-FRONT to real-world datasets ScanNetV2 and SUN RGB-D demonstrate remarkable mAP25 improvements of 9.7% and 9.1% over Source-Only baselines, respectively, and consistently outperform the methods adapted from 2D and 3D outdoor scenarios. The code will be publicly available upon paper acceptance.

The field of self-supervised 3D representation learning has emerged as a promising solution to alleviate the challenge presented by the scarcity of extensive, well-annotated datasets. However, it continues to be hindered by the lack of diverse, large-scale, real-world 3D scene datasets for source data. To address this shortfall, we propose Generalizable Representation Learning (GRL), where we devise a generative Bayesian network to produce diverse synthetic scenes with real-world patterns, and conduct pre-training with a joint objective. By jointly learning a coarse-to-fine contrastive learning task and an occlusion-aware reconstruction task, the model is primed with transferable, geometry-informed representations. Post pre-training on synthetic data, the acquired knowledge of the model can be seamlessly transferred to two principal downstream tasks associated with 3D scene understanding, namely 3D object detection and 3D semantic segmentation, using real-world benchmark datasets. A thorough series of experiments robustly display our method's consistent superiority over existing state-of-the-art pre-training approaches.

Although 3D Gaussian Splatting has been widely studied because of its realistic and efficient novel-view synthesis, it is still challenging to extract a high-quality surface from the point-based representation. Previous works improve the surface by incorporating geometric priors from the off-the-shelf normal estimator. However, there are two main limitations: 1) Supervising normals rendered from 3D Gaussians effectively updates the rotation parameter but is less effective for other geometric parameters; 2) The inconsistency of predicted normal maps across multiple views may lead to severe reconstruction artifacts. In this paper, we propose a Depth-Normal regularizer that directly couples normal with other geometric parameters, leading to full updates of the geometric parameters from normal regularization. We further propose a confidence term to mitigate inconsistencies of normal predictions across multiple views. Moreover, we also introduce a densification and splitting strategy to regularize the size and distribution of 3D Gaussians for more accurate surface modeling. Compared with Gaussian-based baselines, experiments show that our approach obtains better reconstruction quality and maintains competitive appearance quality at faster training speed and 100+ FPS rendering., Comment: Project page: https://hlinchen.github.io/projects/VCR-GauS/

Empowering 3D Gaussian Splatting with generalization ability is appealing. However, existing generalizable 3D Gaussian Splatting methods are largely confined to narrow-range interpolation between stereo images due to their heavy backbones, thus lacking the ability to accurately localize 3D Gaussian and support free-view synthesis across wide view range. In this paper, we present a novel framework FreeSplat that is capable of reconstructing geometrically consistent 3D scenes from long sequence input towards free-view synthesis.Specifically, we firstly introduce Low-cost Cross-View Aggregation achieved by constructing adaptive cost volumes among nearby views and aggregating features using a multi-scale structure. Subsequently, we present the Pixel-wise Triplet Fusion to eliminate redundancy of 3D Gaussians in overlapping view regions and to aggregate features observed across multiple views. Additionally, we propose a simple but effective free-view training strategy that ensures robust view synthesis across broader view range regardless of the number of views. Our empirical results demonstrate state-of-the-art novel view synthesis peformances in both novel view rendered color maps quality and depth maps accuracy across different numbers of input views. We also show that FreeSplat performs inference more efficiently and can effectively reduce redundant Gaussians, offering the possibility of feed-forward large scene reconstruction without depth priors.

Recent advancements in vision-language foundation models have significantly enhanced open-vocabulary 3D scene understanding. However, the generalizability of existing methods is constrained due to their framework designs and their reliance on 3D data. We address this limitation by introducing Generalizable Open-Vocabulary Neural Semantic Fields (GOV-NeSF), a novel approach offering a generalizable implicit representation of 3D scenes with open-vocabulary semantics. We aggregate the geometry-aware features using a cost volume, and propose a Multi-view Joint Fusion module to aggregate multi-view features through a cross-view attention mechanism, which effectively predicts view-specific blending weights for both colors and open-vocabulary features. Remarkably, our GOV-NeSF exhibits state-of-the-art performance in both 2D and 3D open-vocabulary semantic segmentation, eliminating the need for ground truth semantic labels or depth priors, and effectively generalize across scenes and datasets without fine-tuning.

Many artificial intelligence (AI) devices have been developed to accelerate the training and inference of neural networks models. The most common ones are the Graphics Processing Unit (GPU) and Tensor Processing Unit (TPU). They are highly optimized for dense data representations. However, sparse representations such as graphs are prevalent in many domains, including science. It is therefore important to characterize the performance of available AI accelerators on sparse data. This work analyzes and compares the GPU and TPU performance training a Graph Neural Network (GNN) developed to solve a real-life pattern recognition problem. Characterizing the new class of models acting on sparse data may prove helpful in optimizing the design of deep learning libraries and future AI accelerators., Comment: 8 pages, 6 figures

This paper aims to give an epistemic interpretation to the tensor disjunction in dependence logic, through a rather surprising connection to the so-called weak disjunction in Medvedev's early work on intermediate logic under the Brouwer-Heyting-Kolmogorov (BHK)-interpretation. We expose this connection in the setting of inquisitive logic with tensor disjunction discussed by Ciardelli and Barbero (2019}, but from an epistemic perspective. More specifically, we translate the propositional formulae of inquisitive logic with tensor into modal formulae in a powerful epistemic language of "knowing how" following the proposal by Wang (2021). We give a complete axiomatization of the logic of our full language based on Fine's axiomatization of S5 modal logic with propositional quantifiers. Finally, we generalize the tensor operator with parameters $k$ and $n$, which intuitively captures the epistemic situation that one knows $n$ potential answers to $n$ questions and is sure $k$ answers of them must be correct. The original tensor disjunction is the special case when $k=1$ and $n=2$. We show that the generalized tensor operators do not increase the expressive power of our logic, the inquisitive logic, and propositional dependence logic, though most of these generalized tensors are not uniformly definable in these logics, except in our dynamic epistemic logic of knowing how., Comment: 20 pages, under submission

In this paper, we present an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how. In our setting, an inquisitive logic formula $\alpha$ being supported by a state is formalized as "knowing how to resolve $\alpha$" (more colloquially, "knowing how $\alpha$ is true") holds on the S5 epistemic model corresponding to the state. Based on this epistemic interpretation, we use a dynamic epistemic logic with both know-how and know-that operators to capture the epistemic information behind the innocent-looking connectives in inquisitive logic. We show that the set of valid know-how formulas corresponds precisely to the inquisitive logic. The main result is a complete axiomatization with intuitive axioms using the full dynamic epistemic language. Moreover, we show that the know-how operator and the dynamic operator can both be eliminated without changing the expressivity over models, which is consistent with the modal translation of inquisitive logic existing in the literature. We hope our framework can give an intuitive alternative interpretation of various concepts and technical results in inquisitive logic, and also provide a powerful and flexible tool to do inquisitive reasoning in an epistemic context., Comment: draft, 28 pages, to appear in Annals of Pure and Applied Logic

In this paper, we propose an instance similarity learning (ISL) method for unsupervised feature representation. Conventional methods assign close instance pairs in the feature space with high similarity, which usually leads to wrong pairwise relationship for large neighborhoods because the Euclidean distance fails to depict the true semantic similarity on the feature manifold. On the contrary, our method mines the feature manifold in an unsupervised manner, through which the semantic similarity among instances is learned in order to obtain discriminative representations. Specifically, we employ the Generative Adversarial Networks (GAN) to mine the underlying feature manifold, where the generated features are applied as the proxies to progressively explore the feature manifold so that the semantic similarity among instances is acquired as reliable pseudo supervision. Extensive experiments on image classification demonstrate the superiority of our method compared with the state-of-the-art methods. The code is available at https://github.com/ZiweiWangTHU/ISL.git., Comment: Accepted to ICCV 2021

Programming for a diverse set of compute accelerators in addition to the CPU is a challenge. Maintaining separate source code for each architecture would require lots of effort, and development of new algorithms would be daunting if it had to be repeated many times. Fortunately there are several portability technologies on the market such as Alpaka, Kokkos, and SYCL. These technologies aim to improve the developer productivity by making it possible to use the same source code for many different architectures. In this paper we use heterogeneous pixel reconstruction code from the CMS experiment at the CERNL LHC as a realistic use case of a GPU-targeting HEP reconstruction software, and report experience from prototyping a portable version of it using Kokkos. The development was done in a standalone program that attempts to model many of the complexities of a HEP data processing framework such as CMSSW. We also compare the achieved event processing throughput to the original CUDA code and a CPU version of it., Comment: Submitted to 25th International Conference on Computing in High-Energy and Nuclear Physics (vCHEP 2021)

This paper presents a practical methodology for collecting performance data necessary to conduct hierarchical Roofline analysis on NVIDIA GPUs. It discusses the extension of the Empirical Roofline Toolkit for broader support of a range of data precisions and Tensor Core support and introduces a Nsight Compute based method to accurately collect application performance information. This methodology allows for automated machine characterization and application characterization for Roofline analysis across the entire memory hierarchy on NVIDIA GPUs, and it is validated by a complex deep learning application used for climate image segmentation. We use two versions of the code, in TensorFlow and PyTorch respectively, to demonstrate the use and effectiveness of this methodology. We highlight how the application utilizes the compute and memory capabilities on the GPU and how the implementation and performance differ in two deep learning frameworks., Comment: 9 pages

Deep learning applications are usually very compute-intensive and require a long run time for training and inference. This has been tackled by researchers from both hardware and software sides, and in this paper, we propose a Roofline-based approach to performance analysis to facilitate the optimization of these applications. This approach is an extension of the Roofline model widely used in traditional high-performance computing applications, and it incorporates both compute/bandwidth complexity and run time in its formulae to provide insights into deep learning-specific characteristics. We take two sets of representative kernels, 2D convolution and long short-term memory, to validate and demonstrate the use of this new approach, and investigate how arithmetic intensity, cache locality, auto-tuning, kernel launch overhead, and Tensor Core usage can affect performance. Compared to the common ad-hoc approach, this study helps form a more systematic way to analyze code performance and identify optimization opportunities for deep learning applications., Comment: 9 pages