Neural networks are developed to model the behavior of the brain. One crucial question in this field pertains to when and how a neural network can memorize a given set of patterns. There are two mechanisms to store information: associative memory and sequential pattern recognition. In the case of associative memory, the neural network operates with dynamical attractors that are point attractors, each corresponding to one of the patterns to be stored within the network. In contrast, sequential pattern recognition involves the network memorizing a set of patterns and subsequently retrieving them in a specific order over time. From a dynamical perspective, this corresponds to the presence of a continuous attractor or a cyclic attractor composed of the sequence of patterns stored within the network in a given order. Evidence suggests that the brain is capable of simultaneously performing both associative memory and sequential pattern recognition. Therefore, these types of attractors coexist within the neural network, signifying that some patterns are stored as point attractors, while others are stored as continuous or cyclic attractors. This article investigates the coexistence of cyclic attractors and continuous or point attractors in certain nonlinear neural networks, enabling the simultaneous emergence of various memory mechanisms. By selectively grouping neurons, conditions are established for the existence of cyclic attractors, continuous attractors, and point attractors, respectively. Furthermore, each attractor is explicitly represented, and a competitive dynamic emerges among these coexisting attractors, primarily regulated by adjustments to external inputs.

Most existing works solving Room-to-Room VLN problem only utilize RGB images and do not consider local context around candidate views, which lack sufficient visual cues about surrounding environment. Moreover, natural language contains complex semantic information thus its correlations with visual inputs are hard to model merely with cross attention. In this paper, we propose GeoVLN, which learns Geometry-enhanced visual representation based on slot attention for robust Visual-and-Language Navigation. The RGB images are compensated with the corresponding depth maps and normal maps predicted by Omnidata as visual inputs. Technically, we introduce a two-stage module that combine local slot attention and CLIP model to produce geometry-enhanced representation from such input. We employ V&L BERT to learn a cross-modal representation that incorporate both language and vision informations. Additionally, a novel multiway attention module is designed, encouraging different phrases of input instruction to exploit the most related features from visual input. Extensive experiments demonstrate the effectiveness of our newly designed modules and show the compelling performance of the proposed method.

Despite the impressive results achieved by deep learning based 3D reconstruction, the techniques of directly learning to model 4D human captures with detailed geometry have been less studied. This work presents a novel neural compositional representation for Human 4D Modeling with transformER (H4MER). Specifically, our H4MER is a compact and compositional representation for dynamic human by exploiting the human body prior from the widely used SMPL parametric model. Thus, H4MER can represent a dynamic 3D human over a temporal span with the codes of shape, initial pose, motion and auxiliaries. A simple yet effective linear motion model is proposed to provide a rough and regularized motion estimation, followed by per-frame compensation for pose and geometry details with the residual encoded in the auxiliary codes. We present a novel Transformer-based feature extractor and conditional GRU decoder to facilitate learning and improve the representation capability. Extensive experiments demonstrate our method is not only effective in recovering dynamic human with accurate motion and detailed geometry, but also amenable to various 4D human related tasks, including monocular video fitting, motion retargeting, 4D completion, and future prediction.