Class (philosophy)

About: Class (philosophy) is a research topic. Over the lifetime, 821 publications have been published within this topic receiving 28000 citations.

Conformal surface embeddings and extremal length

Abstract: Given two Riemann surfaces with boundary and a homotopy class of topological embeddings between them, there is a conformal embedding in the homotopy class if and only if the extremal length of every simple multi-curve is decreased under the embedding. Furthermore, the homotopy class has a conformal embedding that misses an open disk if and only if extremal lengths are decreased by a definite ratio. This ratio remains bounded away from one under covers.

Horn versus full first-order

Abstract: We study techniques for deciding the computational complexity of infinite-domain constraint satisfaction problems. For certain basic algebraic structures Δ, we prove definability theorems of the following form: for every first-order expansion Γ of Δ, either Γ has a quantifier-free Horn definition in Δ, or there is an element d of Γ such that all non-empty relations in Γ contain a tuple of the form (d,₀,d), or all relations with a first-order definition in Δ have a primitive positive definition in Γ. The results imply that several families of constraint satisfaction problems exhibit a complexity dichotomy: the problems are either polynomial-time solvable or NP-hard depending on the choice of the allowed relations. As concrete examples, we investigate fundamental algebraic constraint satisfaction problems. The first class consists of all relational structures with a first-order definition in (ℚ; +) that contain the relation {(x, y, z) ∈ ℚ3 | x + y = z}. The second class is the affine variant of the first class. In both cases, we obtain full dichotomies by utilizing our general methods.

Learning to Classify With Incremental New Class.

Abstract: New class detection and effective model expansion are of great importance in incremental data mining. In open incremental data environments, data often come with novel classes, e.g., the emergence of new classes in image classification or new topics in opinion monitoring, and is denoted as class-incremental learning (C-IL) in literature. There are two main challenges in C-IL: how to conduct novelty detection and how to update the model with few novel class instances. Most previous methods pay much attention to the former challenge while ignoring the problem of efficiently updating models. To solve this problem, we propose a novel framework to handle the incremental new class, named learning to classify with incremental new class (LC-INC), which can process these two challenges automatically in one unified framework. In detail, LC-INC utilizes a novel structure network to consider the prototype information between class centers of known classes and newly incoming instances, which can dynamically combine the prediction information with structure information to detect novel class instances efficiently. On the other hand, the proposed structure network can also act as a meta-network, which can learn to expand the model much faster and more efficiently with inadequate novel class instances. Experiments on synthetic and real-world datasets successfully validate the effectiveness of our proposed method.

Meta-Learning-Based Incremental Few-Shot Object Detection

Abstract: Recent years have witnessed meaningful progress in the task of few-shot object detection. However, most of the existing models are not capable of incremental learning with a few samples, i.e., the detector can’t detect novel-class objects by using only a few samples of novel classes (without revisiting the original training samples) while maintaining the performances on base classes. This is largely because of catastrophic forgetting, which is a general phenomenon in few-shot learning that the incorporation of the unseen information (e.g., novel-class objects) will lead to a serious loss of the knowledge learnt before (e.g., base-class objects). In this paper, a new model is proposed for incremental few-shot object detection, which takes CenterNet as the fundamental framework and redesigns it by introducing a novel meta-learning method to make the model adapted to unseen knowledge while overcoming forgetting to a great extent. Specifically, a meta-learner is trained with the base-class samples, providing the object locator of the proposed model with a good weight initialization, and thus the proposed model can be fine-tuned easily with few novel-class samples. On the other hand, the filters correlated to base classes are preserved when fine-tuning the proposed model with the few samples of novel classes, which is a simple but effective solution to mitigate the problem of forgetting. The experiments on the benchmark MS COCO and PASCAL VOC datasets demonstrate that the proposed model outperforms the state-of-the-art methods by a large margin in the detection performances on base classes and all classes while achieving best performances when detecting novel-class objects in most cases. The project page can be found in https://mic.tongji.edu.cn/e6/d5/c9778a190165/page.htm.