深度持续学习中的谱坍缩导致塑性丧失
Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning
AI总结：
研究深度神经网络在持续学习中塑性丧失的原因，发现新任务初始化时的Hessian谱坍缩是主要因素，并提出基于Kronecker分解的两种正则化方法以保持塑性。
摘要：
我们研究为什么深度神经网络在持续学习中会丧失塑性，从而在不重新初始化参数的情况下无法学习新任务。我们表明，这种失败之前在新任务初始化时会出现Hessian谱坍缩，其中有意义的曲率方向消失，梯度下降变得无效。通过分析线性化ReLU网络，我们推导出成功训练的显式$ε$-秩条件，并证明损失加权Gram矩阵在谱上与广义高斯-牛顿近似等价，从而将NTK动力学与Hessian曲率联系起来。直接针对谱坍缩，我们讨论了Hessian的Kronecker因子近似，这激发了两种正则化增强：保持高有效特征秩和应用L2惩罚。在持续监督学习和强化学习任务上的实验证实，结合这两种正则化器可以有效保持塑性。
英文摘要：
We investigate why deep neural networks suffer from loss of plasticity in continual learning, and thus fail to learn new tasks without reinitializing parameters. We show that this failure is preceded by Hessian spectral collapse at new-task initialization, where meaningful curvature directions vanish and gradient descent becomes ineffective. Analyzing a linearized ReLU network, we derive explicit $ε$-rank conditions for successful training and prove that the loss-weighted Gram matrix is spectrally equivalent to the Generalized Gauss-Newton approximation, thereby relating NTK dynamics to Hessian curvature. Targeting spectral collapse directly, we then discuss the Kronecker factored approximation of the Hessian, which motivates two regularization enhancements: maintaining high effective feature rank and applying L2 penalties. Experiments on continual supervised and reinforcement learning tasks confirm that combining these two regularizers effectively preserves plasticity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
