FIRE通过数学优化平衡模型稳定性与适应性，避免遗忘旧知识又提升新任务学习能力。
FIRE: Frobenius-Isometry Reinitialization for Balancing the Stability-Plasticity Tradeoff
- 基于弗罗贝尼乌斯误差与权重等距性设计重初始化策略
- 在三个不同任务中均显著优于传统方法，稳定性和适应性双提升
- 适合需要持续学习的场景，如在线训练或增量学习
在非平稳数据上训练的深度神经网络需平衡稳定性（保留旧知识）与可塑性（适应新任务）。现有重初始化方法难以调优：保守方法无法恢复可塑性，激进方法则会遗忘有用知识。本文提出FIRE，一种基于理论的重初始化方法，显式平衡稳定性-可塑性权衡。FIRE用平方弗罗贝尼乌斯误差（SFE）度量与历史权重的距离，用偏离等距性（DfI）反映权重各向同性，通过约束优化求解最小化SFE且DfI为零的重初始化点，该问题由牛顿-舒尔茨迭代高效近似求解。FIRE在持续视觉学习（CIFAR-10，ResNet-18）、语言建模（OpenWebText，GPT-0.1B）和强化学习（HumanoidBench，SAC；Atari游戏，DQN）上评估，结果一致优于无干预训练和标准重初始化方法，证明其能有效平衡稳定性与可塑性。
原文摘要 · Abstract (English)
Deep neural networks trained on nonstationary data must balance stability (i.e., retaining prior knowledge) and plasticity (i.e., adapting to new tasks). Standard reinitialization methods, which reinitialize weights toward their original values, are widely used but difficult to tune: conservative reinitializations fail to restore plasticity, while aggressive ones erase useful knowledge. We propose FIRE, a principled reinitialization method that explicitly balances the stability-plasticity tradeoff. FIRE quantifies stability through Squared Frobenius Error (SFE), measuring proximity to past weights, and plasticity through Deviation from Isometry (DfI), reflecting weight isotropy. The reinitialization point is obtained by solving a constrained optimization problem, minimizing SFE subject to DfI being zero, which is efficiently approximated by Newton-Schulz iteration. FIRE is evaluated on continual visual learning (CIFAR-10 with ResNet-18), language modeling (OpenWebText with GPT-0.1B), and reinforcement learning (HumanoidBench with SAC and Atari games with DQN). Across all domains, FIRE consistently outperforms both naive training without intervention and standard reinitialization methods, demonstrating effective balancing of the stability-plasticity tradeoff.
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