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To adapt to real-world data streams, continual learning (CL) systems must rapidly learn new concepts while preserving and utilizing prior knowledge. When it comes to adding new information to continually-trained deep neural networks (DNNs), classifier weights for newly encountered categories are typically initialized randomly, leading to high initial training loss (spikes) and instability. Consequently, achieving optimal convergence and accuracy requires prolonged training, increasing computational costs. Inspired by Neural Collapse (NC), we propose a weight initialization strategy to improve learning efficiency in CL. In DNNs trained with mean-squared-error, NC gives rise to a Least-Square (LS) classifier in the last layer, whose weights can be analytically derived from learned features. We leverage this LS formulation to initialize classifier weights in a data-driven manner, aligning them with the feature distribution rather than using random initialization. Our method mitigates initial loss spikes and accelerates adaptation to new tasks. We evaluate our approach in large-scale CL settings, demonstrating faster adaptation and improved CL performance. 

Generative large language models (LLMs) exhibit impressive capabilities, which can be further augmented by integrating a pre-trained vision model into the original LLM to create a multimodal LLM (MLLM). However, this integration often significantly decreases performance on natural language understanding and generation tasks, compared to the original LLM. This study investigates this issue using the LLaVA MLLM, treating the integration as a continual learning problem. We evaluate five continual learning methods to mitigate forgetting and identify a technique that enhances visual understanding while minimizing linguistic performance loss. Our approach reduces linguistic performance degradation by up to 15% over the LLaVA recipe, while maintaining high multimodal accuracy. We also demonstrate the robustness of our method through continual learning on a sequence of vision-language tasks, effectively preserving linguistic skills while acquiring new multimodal capabilities. 

Out-of-distribution (OOD) detection and OOD generalization are widely studied in Deep Neural Networks (DNNs), yet their relationship remains poorly understood. We empirically show that the degree of Neural Collapse (NC) in a network layer is inversely related with these objectives: stronger NC improves OOD detection but degrades generalization, while weaker NC enhances generalization at the cost of detection. This trade-off suggests that a single feature space cannot simultaneously achieve both tasks. To address this, we develop a theoretical framework linking NC to OOD detection and generalization. We show that entropy regularization mitigates NC to improve generalization, while a fixed Simplex ETF projector enforces NC for better detection. Based on these insights, we propose a method to control NC at different DNN layers. In experiments, our method excels at both tasks across OOD datasets and DNN architectures.