The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a multiwavelet-based neural operator learning scheme that compresses the associated operator's kernel using fine-grained wavelets. By explicitly embedding the inverse multiwavelet filters, we learn the projection of the kernel onto fixed multiwavelet polynomial bases. The projected kernel is trained at multiple scales derived from using repeated computation of multiwavelet transform. This allows learning the complex dependencies at various scales and results in a resolution-independent scheme.

The current trend in computer vision is to utilize one universal model to address all various tasks. Achieving such a universal model inevitably requires incorporating multi-domain data for joint training to learn across multiple problem scenarios. In point cloud based 3D object detection, however, such multi-domain joint training is highly challenging, because large domain gaps among point clouds from different datasets lead to the severe domain-interference problem. In this paper, we propose OneDet3D, a universal one-for-all model that addresses 3D detection across different domains, including diverse indoor and outdoor scenes, within the same framework and only one set of parameters. We propose the domain-aware partitioning in scatter and context, guided by a routing mechanism, to address the data interference issue, and further incorporate the text modality for a language-guided classification to unify the multi-dataset label spaces and mitigate the category interference issue. The fully sparse structure and anchor-free head further accommodate point clouds with significant scale disparities. Extensive experiments demonstrate the strong universal ability of OneDet3D to utilize only one trained model for addressing almost all 3D object detection tasks (Figure 1).

In this section, we discuss the unique characteristics of CATE estimation in more detail. As outlined in section 2, we consider three characteristics most important: 1. The need to rely on untestable assumptions. To infer causal effects from observational data, one needs to make strong untestable assumptions which ensure identifiability of a treatment effect and should be assessed by a domain expert in practice.

We present L4GM, the first 4D Large Reconstruction Model that produces animated objects from a single-view video input - in a single feed-forward pass that takes only a second. Key to our success is a novel dataset of multiview videos containing curated, rendered animated objects from Objaverse. This dataset depicts 44K diverse objects with 110K animations rendered in 48 viewpoints, resulting in 12M videos with a total of 300M frames. We keep our L4GM simple for scalability and build directly on top of LGM [49], a pretrained 3D Large Reconstruction Model that outputs 3D Gaussian ellipsoids from multiview image input. L4GM outputs a per-frame 3D Gaussian Splatting representation from video frames sampled at a low fps and then upsamples the representation to a higher fps to achieve temporal smoothness. We add temporal self-attention layers to the base LGM to help it learn consistency across time, and utilize a per-timestep multiview rendering loss to train the model. The representation is upsampled to a higher framerate by training an interpolation model which produces intermediate 3D Gaussian representations. We showcase that L4GM that is only trained on synthetic data generalizes well on in-the-wild videos, producing high quality animated 3D assets.

Definition 4. Given a metric space (X, d), a mapping T: X X is called contractive if there exist a constant c [0, 1) and a metric d such that following holds: d(T (x

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

We thank all the reviewers for their time and insightful feedback about our work. Many of the recent few-shot learning works focus on computer vision compared to NLU tasks. We leverage self-training with several advances to bridge this gap. R1 (Q1) raises an important point with respect to developing a sound annotation scheme. Similar baselines reported for active learning [Gal et al., 2017] and preference learning [Houlsby et al., UDA [Xie et al., 2019] and self-training with noisy student [Xie et al., 2020] show these techniques to work best with Additionally, for IMDB longer sequence length plays a big role.

TSP and CVRP experiments in this paper are following the setup where node locations are randomly sampled from the unit square, i.e., x (0, 1) and y (0, 1). All transformations for the 8 instance augmentation used in the experiments preserve the range of x and y, and therefore the new problem instances generated by these transformations are still valid. For the sake of improving the inference result, however, there is no need to stick to "valid" problem instances that comply to the setup rule, as long as the (near-) optimal ordering of node sequence can be generated. Take, for example, rotation by 10 degrees with the center of rotation at (0.5, 0.5). The new problem instance generated by this transformation may (or may not!) contain nodes that are outside the unit square, but this is okay.