Omnidirectional (or 360-degree) images are increasingly being used for 3D applications since they allow the rendering of an entire scene with a single image. Existing works based on neural radiance fields demonstrate successful 3D reconstruction quality on egocentric videos, yet they suffer from long training and rendering times. Recently, 3D Gaussian splatting has gained attention for its fast optimization and real-time rendering.

This section provides the detailed proof for Theorem 1 and the lower bounds of the precision and recall. We derive such theorems with the concentration inequalities in probabilistic theory. In this section, we frequently use the spectral norm. U = I when U is an orthogonal matrix). A.2 Proof of Theorem 1 We deal with some require lemmas which are used for the proof of Theorem 1. Lemma 1.

Modern deep neural networks (DNNs) become weak when the datasets contain noisy (incorrect) class labels. Robust techniques in the presence of noisy labels can be categorized into two types: developing noise-robust functions or using noisecleansing methods by detecting the noisy data. Recently, noise-cleansing methods have been considered as the most competitive noisy-label learning algorithms. Despite their success, their noisy label detectors are often based on heuristics more than a theory, requiring a robust classifier to predict the noisy data with loss values. In this paper, we propose a novel detector for filtering label noise. Unlike most existing methods, we focus on each data point's latent representation dynamics and measure the alignment between the latent distribution and each representation using the eigen decomposition of the data gram matrix. Our framework, coined as filtering noisy instances via their eigenvectors (FINE), provides a robust detector using derivative-free simple methods with theoretical guarantees. Under our framework, we propose three applications of the FINE: sample-selection approach, semi-supervised learning (SSL) approach, and collaboration with noiserobust loss functions.

Keypoint detector and descriptor are two main components of point cloud registration. Previous learning-based keypoint detectors rely on saliency estimation for each point or farthest point sample (FPS) for candidate points selection, which are inefficient and not applicable in large scale scenes. This paper proposes Random Sample-based Keypoint Detector and Descriptor Network (RSKDD-Net) for large scale point cloud registration. The key idea is using random sampling to efficiently select candidate points and using a learning-based method to jointly generate keypoints and descriptors. To tackle the information loss of random sampling, we exploit a novel random dilation cluster strategy to enlarge the receptive field of each sampled point and an attention mechanism to aggregate the positions and features of neighbor points. Furthermore, we propose a matching loss to train the descriptor in a weakly supervised manner. Extensive experiments on two large scale outdoor LiDAR datasets show that the proposed RSKDD-Net achieves state-of-the-art performance with more than 15 times faster than existing methods.

Transformers are central in modern natural language processing and computer vision applications. Despite recent works devoted to reducing the quadratic cost of such models with respect to sequence length, dealing with ultra long sequences (e.g., >16K tokens) remains challenging. Applications such as answering questions based on a book or summarizing a scientific article are inefficient or infeasible. Here, we propose to significantly improve the efficiency of Transformers for ultra long sequences, by compressing the sequence into a much smaller representation at each layer. Specifically, by exploiting the fact that in many tasks, only a small subset of special tokens, which we call VIP-tokens, are most relevant to the final prediction, we propose a VIP-token centric compression (VCC) scheme which selectively compresses the sequence based on their impact on approximating the representation of the VIP-tokens. Compared with competitive baselines, our algorithm is not only efficient (achieving more than 3 compute efficiency gain compared to baselines on 4K and 16K lengths), but also offers competitive/better performance on a large number of tasks. Further, we show that our algorithm scales to 128K tokens (or more) while consistently offering accuracy improvement. Code is available at https://github.com/mlpen/VCC.

Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine learning and spatial statistics. Parametric and nonparametric inference methods have been proposed in the finite case, i.e. when the point patterns live in a finite ground set. In the continuous case, only parametric methods have been investigated, while nonparametric maximum likelihood for DPPs - an optimization problem over trace-class operators - has remained an open question. In this paper, we show that a restricted version of this maximum likelihood (MLE) problem falls within the scope of a recent representer theorem for nonnegative functions in an RKHS. This leads to a finite-dimensional problem, with strong statistical ties to the original MLE. Moreover, we propose, analyze, and demonstrate a fixed point algorithm to solve this finite-dimensional problem. Finally, we also provide a controlled estimate of the correlation kernel of the DPP, thus providing more interpretability.

The machine learning community has witnessed impressive advancements since large language models (LLMs) first appeared. Yet, their massive memory consumption has become a significant roadblock to large-scale training. For instance, a 7B model typically requires at least 60 GB of GPU memory with full parameter training, which presents challenges for researchers without access to high-resource environments. Parameter efficient fine-tuning techniques such as Low-Rank Adaptation (LoRA) have been proposed to alleviate this problem. However, in most large-scale fine-tuning settings, their performance does not reach the level of full parameter training because they confine the parameter search to a low-rank subspace. Attempting to complement this deficiency, we investigate the layerwise properties of LoRA on fine-tuning tasks and observe an unexpected but consistent skewness of weight norms across different layers. Utilizing this key observation, a surprisingly simple training strategy is discovered, which outperforms both LoRA and full parameter training in a wide range of settings with memory costs as low as LoRA. We name it Layerwise Importance Sampled AdamW (LISA), a promising alternative for LoRA, which applies the idea of importance sampling to different layers in LLMs and randomly freeze most middle layers during optimization. Experimental results show that with similar or less GPU memory consumption, LISA surpasses LoRA or even full parameter tuning in downstream fine-tuning tasks, where LISA consistently outperforms LoRA by over 10%-35% in terms of MT-Bench score while achieving on-par or better performance in MMLU, AGIEval and WinoGrande.