SingularClip: Preventing Spectral Collapse to Maintain Plasticity in Continual and Reinforcement Learning

Neural networks trained on nonstationary tasks frequently lose the ability to fit new targets, a phenomenon referred to as loss of plasticity. We identify a novel source of plasticity loss due to the growing anisotropy of weight matrices' singular values during training, and analyze this phenomenon both empirically and theoretically. To mitigate this issue, we introduce SingularClip, a procedure that periodically clips the singular values of all weight matrices. We show that SingularClip performs strongly against baselines across a range of tasks in both continual supervised learning and deep reinforcement learning.

Is Grokking a Loss of Normal Hyperbolicity of the Interpolation Manifold?

A recent line of work recasts the post-memorization phase of grokking as constrained optimization: once a network interpolates the training set, weight decay drives a slow drift along the zero-loss manifold toward lower norm. In the language of dynamical systems, this is a fast-slow system in which the interpolation manifold plays the role of a slow manifold. We ask a question that this framing makes natural but the existing literature does not address: is the sharp generalization transition a loss of normal hyperbolicity of that manifold: a fold- or bifurcation-like event in which a normal restoring direction goes flat? Or does the manifold stay uniformly attracting while generalization happens by smooth drift? We propose a simple, optimizer-agnostic diagnostic: the smallest nonzero singular value $σ_{\min}^{+}(\mathbf J)$ of the residual Jacobian, which, for the squared loss, equals the slowest normal restoring rate of the manifold. On a two-layer ReLU network trained to grok modular addition under squared loss, $σ_{\min}^{+}(\mathbf J)$ does not collapse at the transition; it is near zero only before memorization and attains its largest values during the transition. The result holds across five seeds, and the six smallest singular values behave identically; there is no subspace-local collapse either. This is preliminary evidence against the bifurcation hypothesis and in favor of the smooth-contraction picture. We are explicit that a single-setting, gradual-transition experiment under Adam optimizer does not prove the absence of a bifurcation; it constrains where one could hide.