arXiv:2605.24549v1 Announce Type: new Abstract: Efficiently updating Large Language Models (LLMs) with new or evolving factual knowledge remains a central challenge, as even parameter-efficient adaptation can erode previously acquired reasoning abilities. This tension reflects a plasticity-stability dilemma: models must incorporate new knowledge while preserving skill-critical representations. In this work, we study this trade-off through the spectral structure of multilayer perceptron weight matrices. We show, both theoretically and empirically, that information essential for reasoning is not localized only in dominant singular directions, but is instead distributed across the singular spectrum. Motivated by this observation, we introduce PALoRA, a two-stage framework for knowledge injection with reduced interference. PALoRA first trains a Singular Value Fine-Tuning (SVF) expert on a reasoning dataset and uses its learned singular scaling vector as a frozen geometric probe to identify components that are critical for the target skill. It then performs factual knowledge injection with Low-Rank Adaptation (LoRA) under a structural orthogonality constraint, ensuring that updates avoid the identified skill-relevant subspace. Across Llama 3.1 8B and Mistral 7B, and across mathematical, coding, and scientific reasoning benchmarks, PALoRA preserves on average 95% of the SVF expert's reasoning performance while maintaining competitive factual recall. It consistently improves skill retention over prior spectral Parameter-Efficient Fine-Tuning (PEFT) methods while adding less than 0.006% parameter overhead.

arXiv:2602.14078v1 Announce Type: cross Abstract: Despite their success, large pretrained vision models remain vulnerable to catastrophic forgetting when adapted to new tasks in class-incremental settings. Parameter-efficient fine-tuning (PEFT) alleviates this by restricting trainable parameters, yet most approaches still rely on cross-entropy (CE) loss, a surrogate for the 0-1 loss, to learn from new data. We revisit this choice and revive the true objective (0-1 loss) through a reinforcement learning perspective. By formulating classification as a one-step Markov Decision Process, we derive an Expected Policy Gradient (EPG) method that directly minimizes misclassification error with a low-variance gradient estimation. Our analysis shows that CE can be interpreted as EPG with an additional sample-weighting mechanism: CE encourages exploration by emphasizing low-confidence samples, while EPG prioritizes high-confidence ones. Building on this insight, we propose adaptive entropy annealing (aEPG), a training strategy that transitions from exploratory (CE-like) to exploitative (EPG-like) learning. aEPG-based methods outperform CE-based methods across diverse benchmarks and with various PEFT modules. More broadly, we evaluate various entropy regularization methods and demonstrate that lower entropy of the output prediction distribution enhances adaptation in pretrained vision models.