Projecting Gaussian Ellipsoids While Avoiding Affine Projection Approximation

Recently, 3D Gaussian Splatting has dominated novel-view synthesis with its real-time rendering speed and state-of-the-art rendering quality. However, during the rendering process, the use of the Jacobian of the affine approximation of the projection transformation leads to inevitable errors, resulting in blurriness, artifacts and a lack of scene consistency in the final rendered images. To address this issue, we introduce an ellipsoid-based projection method to calculate the projection of Gaussian ellipsoid onto the image plane, which is the primitive of 3D Gaussian Splatting. As our proposed ellipsoid-based projection method cannot handle Gaussian ellipsoids with camera origins inside them or parts lying below $z=0$ plane in the camera space, we designed a pre-filtering strategy. Experiments over multiple widely adopted benchmark datasets show that our ellipsoid-based projection method can enhance the rendering quality of 3D Gaussian Splatting and its extensions.

Control-oriented Clustering of Visual Latent Representation

We initiate a study of the geometry of the visual representation space -- the information channel from the vision encoder to the action decoder -- in an image-based control pipeline learned from behavior cloning. Inspired by the phenomenon of neural collapse (NC) in image classification, we investigate whether a similar law of clustering emerges in the visual representation space. Since image-based control is a regression task without explicitly defined classes, the central piece of the puzzle lies in determining according to what implicit classes the visual features cluster, if such a law exists. Focusing on image-based planar pushing, we posit the most important role of the visual representation in a control task is to convey a goal to the action decoder. We then classify training samples of expert demonstrations into eight "control-oriented" classes based on (a) the relative pose between the object and the target in the input or (b) the relative pose of the object induced by expert actions in the output, where one class corresponds to one relative pose orthant (REPO). Across four different instantiations of architecture, we report the prevalent emergence of control-oriented clustering in the visual representation space according to the eight REPOs. Beyond empirical observation, we show such a law of clustering can be leveraged as an algorithmic tool to improve test-time performance when training a policy with limited expert demonstrations. Particularly, we pretrain the vision encoder using NC as a regularization to encourage control-oriented clustering of the visual features. Surprisingly, such an NC-pretrained vision encoder, when finetuned end-to-end with the action decoder, boosts the test-time performance by 10% to 35% in the low-data regime. Real-world vision-based planar pushing experiments confirmed the surprising advantage of control-oriented visual representation pretraining.

DMSD-CDFSAR: Distillation from Mixed-Source Domain for Cross-Domain Few-shot Action Recognition

Few-shot action recognition is an emerging field in computer vision, primarily focused on meta-learning within the same domain. However, challenges arise in real-world scenario deployment, as gathering extensive labeled data within a specific domain is laborious and time-intensive. Thus, attention shifts towards cross-domain few-shot action recognition, requiring the model to generalize across domains with significant deviations. Therefore, we propose a novel approach, ``Distillation from Mixed-Source Domain", tailored to address this conundrum. Our method strategically integrates insights from both labeled data of the source domain and unlabeled data of the target domain during the training. The ResNet18 is used as the backbone to extract spatial features from the source and target domains. We design two branches for meta-training: the original-source and the mixed-source branches. In the first branch, a Domain Temporal Encoder is employed to capture temporal features for both the source and target domains. Additionally, a Domain Temporal Decoder is employed to reconstruct all extracted features. In the other branch, a Domain Mixed Encoder is used to handle labeled source domain data and unlabeled target domain data, generating mixed-source domain features. We incorporate a pre-training stage before meta-training, featuring a network architecture similar to that of the first branch. Lastly, we introduce a dual distillation mechanism to refine the classification probabilities of source domain features, aligning them with those of mixed-source domain features. This iterative process enriches the insights of the original-source branch with knowledge from the mixed-source branch, thereby enhancing the model's generalization capabilities. Our code is available at URL: \url{https://xxxx/xxxx/xxxx.git}

Graph Feedback Bandits with Similar Arms

In this paper, we study the stochastic multi-armed bandit problem with graph feedback. Motivated by the clinical trials and recommendation problem, we assume that two arms are connected if and only if they are similar (i.e., their means are close enough). We establish a regret lower bound for this novel feedback structure and introduce two UCB-based algorithms: D-UCB with problem-independent regret upper bounds and C-UCB with problem-dependent upper bounds. Leveraging the similarity structure, we also consider the scenario where the number of arms increases over time. Practical applications related to this scenario include Q\&A platforms (Reddit, Stack Overflow, Quora) and product reviews in Amazon and Flipkart. Answers (product reviews) continually appear on the website, and the goal is to display the best answers (product reviews) at the top. When the means of arms are independently generated from some distribution, we provide regret upper bounds for both algorithms and discuss the sub-linearity of bounds in relation to the distribution of means. Finally, we conduct experiments to validate the theoretical results.

CLOSURE: Fast Quantification of Pose Uncertainty Sets

We investigate uncertainty quantification of 6D pose estimation from keypoint measurements. Assuming unknown-but-bounded measurement noises, a pose uncertainty set (PURSE) is a subset of SE(3) that contains all possible 6D poses compatible with the measurements. Despite being simple to formulate and its ability to embed uncertainty, the PURSE is difficult to manipulate and interpret due to the many abstract nonconvex polynomial constraints. An appealing simplification of PURSE is to find its minimum enclosing geodesic ball (MEGB), i.e., a point pose estimation with minimum worst-case error bound. We contribute (i) a dynamical system perspective, and (ii) a fast algorithm to inner approximate the MEGB. Particularly, we show the PURSE corresponds to the feasible set of a constrained dynamical system, and this perspective allows us to design an algorithm to densely sample the boundary of the PURSE through strategic random walks. We then use the miniball algorithm to compute the MEGB of PURSE samples, leading to an inner approximation. Our algorithm is named CLOSURE (enClosing baLl frOm purSe boUndaRy samplEs) and it enables computing a certificate of approximation tightness by calculating the relative size ratio between the inner approximation and the outer approximation. Running on a single RTX 3090 GPU, CLOSURE achieves the relative ratio of 92.8% on the LM-O object pose estimation dataset and 91.4% on the 3DMatch point cloud registration dataset with the average runtime less than 0.2 second. Obtaining comparable worst-case error bound but 398x and 833x faster than the outer approximation GRCC, CLOSURE enables uncertainty quantification of 6D pose estimation to be implemented in real-time robot perception applications.

Multi-view Distillation based on Multi-modal Fusion for Few-shot Action Recognition

In recent years, few-shot action recognition has attracted increasing attention. It generally adopts the paradigm of meta-learning. In this field, overcoming the overlapping distribution of classes and outliers is still a challenging problem based on limited samples. We believe the combination of Multi-modal and Multi-view can improve this issue depending on information complementarity. Therefore, we propose a method of Multi-view Distillation based on Multi-modal Fusion. Firstly, a Probability Prompt Selector for the query is constructed to generate probability prompt embedding based on the comparison score between the prompt embeddings of the support and the visual embedding of the query. Secondly, we establish a Multi-view. In each view, we fuse the prompt embedding as consistent information with visual and the global or local temporal context to overcome the overlapping distribution of classes and outliers. Thirdly, we perform the distance fusion for the Multi-view and the mutual distillation of matching ability from one to another, enabling the model to be more robust to the distribution bias. Our code is available at the URL: \url{https://github.com/cofly2014/MDMF}.

Forced Exploration in Bandit Problems

The multi-armed bandit(MAB) is a classical sequential decision problem. Most work requires assumptions about the reward distribution (e.g., bounded), while practitioners may have difficulty obtaining information about these distributions to design models for their problems, especially in non-stationary MAB problems. This paper aims to design a multi-armed bandit algorithm that can be implemented without using information about the reward distribution while still achieving substantial regret upper bounds. To this end, we propose a novel algorithm alternating between greedy rule and forced exploration. Our method can be applied to Gaussian, Bernoulli and other subgaussian distributions, and its implementation does not require additional information. We employ a unified analysis method for different forced exploration strategies and provide problem-dependent regret upper bounds for stationary and piecewise-stationary settings. Furthermore, we compare our algorithm with popular bandit algorithms on different reward distributions.

Consistency Prototype Module and Motion Compensation for Few-Shot Action Recognition (CLIP-CP$\mathbf{M^2}$C)

Recently, few-shot action recognition has significantly progressed by learning the feature discriminability and designing suitable comparison methods. Still, there are the following restrictions. (a) Previous works are mainly based on visual mono-modal. Although some multi-modal works use labels as supplementary to construct prototypes of support videos, they can not use this information for query videos. The labels are not used efficiently. (b) Most of the works ignore the motion feature of video, although the motion features are essential for distinguishing. We proposed a Consistency Prototype and Motion Compensation Network(CLIP-CP$M^2$C) to address these issues. Firstly, we use the CLIP for multi-modal few-shot action recognition with the text-image comparison for domain adaption. Secondly, in order to make the amount of information between the prototype and the query more similar, we propose a novel method to compensate for the text(prompt) information of query videos when text(prompt) does not exist, which depends on a Consistency Loss. Thirdly, we use the differential features of the adjacent frames in two directions as the motion features, which explicitly embeds the network with motion dynamics. We also apply the Consistency Loss to the motion features. Extensive experiments on standard benchmark datasets demonstrate that the proposed method can compete with state-of-the-art results. Our code is available at the URL: https://github.com/xxx/xxx.git.

Latent Conservative Objective Models for Data-Driven Crystal Structure Prediction

In computational chemistry, crystal structure prediction (CSP) is an optimization problem that involves discovering the lowest energy stable crystal structure for a given chemical formula. This problem is challenging as it requires discovering globally optimal designs with the lowest energies on complex manifolds. One approach to tackle this problem involves building simulators based on density functional theory (DFT) followed by running search in simulation, but these simulators are painfully slow. In this paper, we study present and study an alternate, data-driven approach to crystal structure prediction: instead of directly searching for the most stable structures in simulation, we train a surrogate model of the crystal formation energy from a database of existing crystal structures, and then optimize this model with respect to the parameters of the crystal structure. This surrogate model is trained to be conservative so as to prevent exploitation of its errors by the optimizer. To handle optimization in the non-Euclidean space of crystal structures, we first utilize a state-of-the-art graph diffusion auto-encoder (CD-VAE) to convert a crystal structure into a vector-based search space and then optimize a conservative surrogate model of the crystal energy, trained on top of this vector representation. We show that our approach, dubbed LCOMs (latent conservative objective models), performs comparably to the best current approaches in terms of success rate of structure prediction, while also drastically reducing computational cost.

K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsets

Although deep learning (DL) methods are powerful for solving inverse problems, their reliance on high-quality training data is a major hurdle. This is significant in high-dimensional (dynamic/volumetric) magnetic resonance imaging (MRI), where acquisition of high-resolution fully sampled k-space data is impractical. We introduce a novel mathematical framework, dubbed k-band, that enables training DL models using only partial, limited-resolution k-space data. Specifically, we introduce training with stochastic gradient descent (SGD) over k-space subsets. In each training iteration, rather than using the fully sampled k-space for computing gradients, we use only a small k-space portion. This concept is compatible with different sampling strategies; here we demonstrate the method for k-space "bands", which have limited resolution in one dimension and can hence be acquired rapidly. We prove analytically that our method stochastically approximates the gradients computed in a fully-supervised setup, when two simple conditions are met: (i) the limited-resolution axis is chosen randomly-uniformly for every new scan, hence k-space is fully covered across the entire training set, and (ii) the loss function is weighed with a mask, derived here analytically, which facilitates accurate reconstruction of high-resolution details. Numerical experiments with raw MRI data indicate that k-band outperforms two other methods trained on limited-resolution data and performs comparably to state-of-the-art (SoTA) methods trained on high-resolution data. k-band hence obtains SoTA performance, with the advantage of training using only limited-resolution data. This work hence introduces a practical, easy-to-implement, self-supervised training framework, which involves fast acquisition and self-supervised reconstruction and offers theoretical guarantees.