# Feature Transformation-Based Few-Shot Class-Incremental Learning
## 1 Introduction
Their method maintains the relative topological structure among class prototypes, enabling the model to retain old knowledge while adapting to new classes in a few-shot incremental setting. In contrast, [PERSON] et al. [10] proposed a decoupled approach where the feature extractor remains fixed and only the classifier is continually updated. They employed a graph attention network to capture semantic relationships between old and new class prototypes, resulting in an evolving KNN-based classifier that effectively balances stability and plasticity throughout the incremental learning process. Recent modular and attention-based designs have also shown promise in improving representation robustness in multi-domain settings. For instance, [PERSON] et al. [11] proposed a hybrid KAN-BiLSTM Transformer, which leverages dynamic attention and architectural modularity to effectively process structurally diverse inputs. These strategies offer valuable insights for FSCIL under few-shot constraints, where feature distribution alignment is critical yet data is limited. Lightweight adaptation techniques such as LoRA [12] and Adapters [13] have been proposed to efficiently fine-tune large pre-trained models by injecting small trainable modules into frozen backbones. These methods have demonstrated strong performance in few-shot and incremental learning scenarios, highlighting the potential benefits of low-rank or bottleneck-based parameter adaptation. However, these methods still struggle to avoid the phenomenon of neural collapse in few-shot class-incremental learning [14]. Neural collapse refers to a special convergence behavior and feature space degeneration observed when training neural networks with a limited number of samples in an incremental setting. Specifically, the weights of the final classification layer are disrupted by the newly added data, rendering the original classifier ineffective. This phenomenon highlights that a well-performing classifier requires its final-layer weights to be aligned with the class prototypes, and that the class centers should be as well-separated as possible [15]. Mathematically, the neural collapse phenomenon is characterized by several distinct properties: (1) classifier weights and class means become aligned, forming a simplex equiangular tight frame (ETF) where the angle (or cosine similarity) between any pair of class prototypes is equal; (2) within-class variability collapses, meaning features from the same class concentrate around the class mean; and (3) all class prototypes lie on a sphere and are maximally separated in angular space. These characteristics can be quantitatively assessed via pairwise inner products or angular deviations between normalized class means. A common strategy to mitigate this issue is feature transformation, which aims to map features from the current space to a more desirable feature space where the effects of neural collapse are minimized. Traditionally, feature transformation is a technique used in transfer learning to reduce distributional shifts between the source and target domains [16]. Based on whether the distance metric is explicitly defined, feature transformation methods can be categorized into statistical and geometric approaches [17]. Statistical feature transformation explicitly specifies a distance measure, whereas geometric methods rely on an implicit metric derived from the geometric properties of the data. The core idea of both approaches is to minimize the distributional discrepancy between the source and target domains under a certain metric. For statistical methods, one of the most widely used metrics is Maximum Mean Discrepancy (MMD). For example, Transfer Component Analysis (TCA) [18] assumes that the conditional distributions across domains are identical, while the marginal distributions differ. By minimizing the MMD between the source and target domain marginals, TCA aligns the joint distributions of the two domains.