Even though Non-rigid Structure-from-Motion (NRSfM) has been extensively studied and great progress has been made, there are still key challenges that hinder their broad real-world applications: 1) the inherent motion/rotation ambiguity requires either explicit camera motion recovery with extra constraint or complex Procrustean Alignment; 2) existing low-rank modeling of the global shape can over-penalize drastic deformations in the 3D shape sequence. This paper proposes to resolve the above issues from a spatial-temporal modeling perspective. First, we propose a novel Temporally-smooth Procrustean Alignment module that estimates 3D deforming shapes and adjusts the camera motion by aligning the 3D shape sequence consecutively. Our new alignment module remedies the requirement of complex reference 3D shape during alignment, which is more conductive to non-isotropic deformation modeling. Second, we propose a spatial-weighted approach to enforce the low-rank constraint adaptively at different locations to accommodate drastic spatially-variant deformation reconstruction better. Our modeling outperform existing low-rank based methods, and extensive experiments across different datasets validate the effectiveness of our method.

Linear attention mechanisms have gained prominence in causal language models due to their linear computational complexity and enhanced speed. However, the inherent decay mechanism in linear attention presents challenges when applied to multi-dimensional sequence modeling tasks, such as image processing and multi-modal learning. In these scenarios, the utilization of sequential scanning to establish a global receptive field necessitates multiple scans for multi-dimensional data, thereby leading to inefficiencies. This paper identifies the inefficiency caused by a "multiplicative" linear recurrence and proposes an efficient alternative "additive" linear recurrence to avoid the issue, as it can handle multi-dimensional data within a single scan. We further develop an efficient multi-dimensional sequential modeling framework called LightNet based on the new recurrence. Moreover, we present two new multi-dimensional linear relative positional encoding methods, MD-TPE and MD-LRPE to enhance the model's ability to discern positional information in multi-dimensional scenarios. Our empirical evaluations across various tasks, including image classification, image generation, bidirectional language modeling, and autoregressive language modeling, demonstrate the efficacy of LightNet, showcasing its potential as a versatile and efficient solution for multi-dimensional sequential modeling.

Most of the previous 3D human pose estimation work relied on the powerful memory capability of the network to obtain suitable 2D-3D mappings from the training data. Few works have studied the modeling of human posture deformation in motion. In this paper, we propose a new modeling method for human pose deformations and design an accompanying diffusion-based motion prior. Inspired by the field of non-rigid structure-from-motion, we divide the task of reconstructing 3D human skeletons in motion into the estimation of a 3D reference skeleton, and a frame-by-frame skeleton deformation. A mixed spatial-temporal NRSfMformer is used to simultaneously estimate the 3D reference skeleton and the skeleton deformation of each frame from 2D observations sequence, and then sum them to obtain the pose of each frame. Subsequently, a loss term based on the diffusion model is used to ensure that the pipeline learns the correct prior motion knowledge. Finally, we have evaluated our proposed method on mainstream datasets and obtained superior results outperforming the state-of-the-art.

Relative positional encoding is widely used in vanilla and linear transformers to represent positional information. However, existing encoding methods of a vanilla transformer are not always directly applicable to a linear transformer, because the latter requires a decomposition of the query and key representations into separate kernel functions. Nevertheless, principles for designing encoding methods suitable for linear transformers remain understudied. In this work, we put together a variety of existing linear relative positional encoding approaches under a canonical form and further propose a family of linear relative positional encoding algorithms via unitary transformation. Our formulation leads to a principled framework that can be used to develop new relative positional encoding methods that preserve linear space-time complexity. Equipped with different models, the proposed linearized relative positional encoding (LRPE) family derives effective encoding for various applications. Experiments show that compared with existing methods, LRPE achieves state-of-the-art performance in language modeling, text classification, and image classification. Meanwhile, it emphasizes a general paradigm for designing broadly more relative positional encoding methods that are applicable to linear transformers. The code is available at https://github.com/OpenNLPLab/Lrpe.

Sequence modeling has important applications in natural language processing and computer vision. Recently, the transformer-based models have shown strong performance on various sequence modeling tasks, which rely on attention to capture pairwise token relations, and position embedding to inject positional information. While showing good performance, the transformer models are inefficient to scale to long input sequences, mainly due to the quadratic space-time complexity of attention. To overcome this inefficiency, we propose to model sequences with a relative position encoded Toeplitz matrix and use a Toeplitz matrix-vector production trick to reduce the space-time complexity of the sequence modeling to log linear. A lightweight sub-network called relative position encoder is proposed to generate relative position coefficients with a fixed budget of parameters, enabling the proposed Toeplitz neural network to deal with varying sequence lengths. In addition, despite being trained on 512-token sequences, our model can extrapolate input sequence length up to 14K tokens in inference with consistent performance. Extensive experiments on autoregressive and bidirectional language modeling, image modeling, and the challenging Long-Range Arena benchmark show that our method achieves better performance than its competitors in most downstream tasks while being significantly faster. The code is available at https://github.com/OpenNLPLab/Tnn. Figure 1: The left figure shows the training speed (x-axis), performances (y-axis), and GPU memory footprints (circle sizes) of the TNN and competing methods on Long-Range Arena benchmark.

This paper discusses the results for the second edition of the Monocular Depth Estimation Challenge (MDEC). This edition was open to methods using any form of supervision, including fully-supervised, self-supervised, multi-task or proxy depth. The challenge was based around the SYNS-Patches dataset, which features a wide diversity of environments with high-quality dense ground-truth. This includes complex natural environments, e.g. forests or fields, which are greatly underrepresented in current benchmarks. The challenge received eight unique submissions that outperformed the provided SotA baseline on any of the pointcloud- or image-based metrics. The top supervised submission improved relative F-Score by 27.62%, while the top self-supervised improved it by 16.61%. Supervised submissions generally leveraged large collections of datasets to improve data diversity. Self-supervised submissions instead updated the network architecture and pretrained backbones. These results represent a significant progress in the field, while highlighting avenues for future research, such as reducing interpolation artifacts at depth boundaries, improving self-supervised indoor performance and overall natural image accuracy.