SeqLoRA: Bilevel Orthogonal Adaptation for Continual Multi-Concept Generation

Parameter-efficient fine-tuning enables fast personalization of text-to-image diffusion models, but composing multiple custom concepts remains challenging due to representation interference. Existing modular methods either rely on expensive post-hoc fusion or freeze adaptation subspaces, which limit expressiveness and concept fidelity. To address this trade-off, we propose Sequential regularized LoRA (SeqLoRA), a constrained continual learning framework that jointly optimizes both LoRA factors via bilevel optimization. Theoretically, we establish strong convergence guarantees for our algorithm and model the residual layer activations as a matrix sub-Gaussian process to derive high-probability bounds on catastrophic forgetting. We further prove that learning the LoRA basis from data minimizes residual interference energy more effectively than frozen-basis methods. Experiments on multi-concept image generation demonstrate that SeqLoRA improves identity preservation and scalability across up to 101 concepts, while avoiding costly fusion and reducing attribute interference in composed generations.

An $H_2$-norm approach to performance analysis of networked control systems under multiplicative routing transformations

This paper investigates the performance of networked control systems subject to multiplicative routing transformations that alter measurement pathways without directly injecting signals. Such transformations, arising from faults or adversarial actions, modify the feedback structure and can degrade performance while remaining stealthy. An $H_2$-norm framework is proposed to quantify the impact of these transformations by evaluating the ratio between the steady-state energies of performance and residual outputs. Equivalent linear matrix inequality (LMI) formulations are derived for computational assessment, and analytical upper bounds are established to estimate the worst-case degradation. The results provide structural insight into how routing manipulations influence closed-loop behavior and reveal conditions for stealthy multiplicative attacks.