Jingyi Feng

Long Tian, Jingyi Feng, Wenchao Chen et al.

Transductive Few-Shot Learning (TFSL) has recently attracted increasing attention since it typically outperforms its inductive peer by leveraging statistics of query samples. However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called {\textbf P}rototypes-oriented {\textbf U}nbiased {\textbf T}ransfer {\textbf M}odel (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization.

Jingyi Feng, Chenming Zhang

Comprehending how the brain interacts with the external world through generated neural data is crucial for determining its working mechanism, treating brain diseases, and understanding intelligence. Although many theoretical models have been proposed, they have thus far been difficult to integrate and develop. In this study, we were inspired in part by grid cells in creating a more general and robust grid module and constructing an interactive and self-reinforcing cognitive system together with Bayesian reasoning, an approach called space-division and exploration-exploitation with grid-feedback (Grid-SD2E). Here, a grid module can be used as an interaction medium between the outside world and a system, as well as a self-reinforcement medium within the system. The space-division and exploration-exploitation (SD2E) receives the 0/1 signals of a grid through its space-division (SD) module. The system described in this paper is also a theoretical model derived from experiments conducted by other researchers and our experience on neural decoding. Herein, we analyse the rationality of the system based on the existing theories in both neuroscience and cognitive science, and attempt to propose special and general rules to explain the different interactions between people and between people and the external world. What's more, based on this framework, the smallest computing unit is extracted, which is analogous to a single neuron in the brain.

Xiao Liu, Jingyi Feng, Xinchao Liu

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition (POD) computes the optimal basis modes that represent the data, and a ROM can be constructed in the low-dimensional vector subspace spanned by the POD basis. For parametric governing equations, a potential challenge arises when there is a need to update the POD basis to adapt ROM that accurately capture the variation of a system's behavior over its parameter space (in design, control, uncertainty quantification, digital twins applications, etc.). In this paper, we propose a Projected Gaussian Process (pGP) and formulate the problem of adapting the POD basis as a supervised statistical learning problem, for which the goal is to learn a mapping from the parameter space to the Grassmann manifold that contains the optimal subspaces. A mapping is firstly established between the Euclidean space and the horizontal space of an orthogonal matrix that spans a reference subspace in the Grassmann manifold. A second mapping from the horizontal space to the Grassmann manifold is established through the Exponential/Logarithm maps between the manifold and its tangent space. Finally, given a new parameter, the conditional distribution of a vector can be found in the Euclidean space using the Gaussian Process (GP) regression, and such a distribution is then projected to the Grassmann manifold that enables us to predict the optimal subspace for the new parameter. As a statistical learning approach, the proposed pGP allows us to optimally estimate (or tune) the model parameters from data and quantify the statistical uncertainty associated with the prediction. The advantages of the proposed pGP are demonstrated by numerical experiments.

Jingyi Feng, Kai Yang

Understanding the mechanisms of neural encoding and decoding has always been a highly interesting research topic in fields such as neuroscience and cognitive intelligence. In prior studies, some researchers identified a symmetry in neural data decoded by unsupervised methods in motor scenarios and constructed a cognitive learning system based on this pattern (i.e., symmetry). Nevertheless, the distribution state of the data flow that significantly influences neural decoding positions still remains a mystery within the system, which further restricts the enhancement of the system's interpretability. Based on this, this paper mainly explores changes in the distribution state within the system from the machine learning and mathematical statistics perspectives. In the experiment, we assessed the correctness of this symmetry using various tools and indicators commonly utilized in mathematics and statistics. According to the experimental results, the normal distribution (or Gaussian distribution) plays a crucial role in the decoding of prediction positions within the system. Eventually, an algorithm board similar to the Galton board was built to serve as the mathematical foundation of the discovered symmetry.

Jingyi Feng, Yong Luo, Shuang Song

Neural decoding plays a vital role in the interaction between the brain and the outside world. In this paper, we directly decode the movement track of a finger based on the neural signals of a macaque. Supervised regression methods may overfit to actual labels containing noise, and require a high labeling cost, while unsupervised approaches often have unsatisfactory accuracy. Besides, the spatial and temporal information is often ignored or not well exploited by those methods. This motivates us to propose a robust weakly-supervised method, called ViF-SD2E, for neural decoding. In particular, it consists of a space-division (SD) module and a exploration--exploitation (2E) strategy, to effectively exploit both the spatial information of the outside world and the temporal information of neural activity, where the SD2E output is analogized with the weak 0/1 vision-feedback (ViF) label for training. It is worth noting that the designed ViF-SD2E is based on a symmetric phenomenon between the unsupervised decoding trajectory and the real trajectory in previous observations, then a cognitive pattern of fuzzy (robust) interaction in the nervous system may be discovered by us. Extensive experiments demonstrate the effectiveness of our method, which can be sometimes comparable to supervised counterparts.