cs.LGMay 7, 2026

Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes

Authors: Liu Hanqing, Jianjun Cao, Yuanze Li, Zijian Zhou

Organizations: 1Tsinghua University · 2The University of Tokyo

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Deep neural networks exhibit periodic loss spikes during unregularized long-term training, a phenomenon known as the "Slingshot Mechanism." Existing work usually attributes this to intrinsic optimization dynamics, but its triggering mechanism remains unclear. This paper proves that this phenomenon is a result of floating-point arithmetic precision limits. As training enters a high-confidence stage, the difference between the correct-class logit and the other logits may exceed the absorption-error threshold. Then during backpropagation, the gradient of the correct class is rounded exactly to zero, while the gradients of the incorrect classes remain nonzero. This breaks the zero-sum constraint of gradients across classes and introduces a systematic drift in the parameter update of the classifier layer. We prove that this drift forms a positive feedback loop with the feature, causing the global classifier mean and the global feature mean to grow exponentially. We call this mechanism Numerical Feature Inflation (NFI). This mechanism explains the rapid norm growth before a Slingshot spike, the subsequent reappearance of gradients, and the resulting loss spike. We further show that NFI is not equivalent to an observed loss spike: in more practical tasks, partial absorption may not produce visible spikes, but it can still break the zero-sum constraint and drive rapid growth of parameter norms. Our results reinterpret Slingshot as a numerical dynamic of finite-precision training, and provide a testable explanation for abnormal parameter growth and logit divergence in late-stage training.

Explore similar work

CardsList
May 17, 2026cs.LG

Bug or Feature2^2: Weight Drift, Activation Sparsity and Spikes

The design of modern neural architectures has converged through incremental empirical choices, yet the mechanisms governing their training dynamics remain only partially understood. We identify and analyze a negative weight drift induced by the interaction between standard losses and positively biased activation functions. We prove that under MSE or cross-entropy loss, the gradient with respect to positive pre-activations is non-negative in expectation at initialization, driving downstream weights toward negative values during early training. The drift is intrinsic to optimization rather than data, and persists across architectures (MLP, ResNet, ViT, GPT-nano, MP-SENe) and asymmetric activation functions (ReLU, GELU, SiLU). Coupled with ReLU, weight drift produces activation sparsity reaching up to 90% in GPT-nano. We characterize the sparsity-accuracy tradeoff across 79 configurations and identify a sharp accuracy cliff above ∼\sim70% activation sparsity. While ReLU2^2 achieves a good sparsity--accuracy ratio in GPT-nano, it pathologically amplifies identified activation spikes in intermediate transformer layers. Clipping resolves this while preserving the representational benefits of squaring: clipped ReLU2^2 outperforms its unclipped version, and GELU2^2 achieves the lowest validation loss on GPT-nano. Code is available at https://github.com/On-Point-RND/BugOrFeature.
Egor Shvetsov, Aleksandr Serkov, Shokorov Viacheslav +3
Model WeightsNeural ArchitecturesBinary SpikesCross-Entropy LossesOpenaiBug
AskPDF
Jul 23, 2026cs.LG

Weight-norm Criticality: A Mechanism for Loss Spikes Induced by the Normalization and Weight Decay

Most explanations of training instability focus on \emph{learning-rate criticality}, typically characterized by the Edge of Stability, beyond which optimization becomes unstable. We argue that, in practical deep neural network training, there is an additional and often overlooked \emph{weight-norm criticality}. This criticality is induced by the interaction between normalization (which introduces scale-invariant components) and weight decay (which persistently shrinks parameter norms). As the weight decay coefficient increases, the norms of scale-invariant weights are progressively driven toward zero. Meanwhile, the sharpness of the loss landscape increases rapidly, destabilizing the optimization dynamics and resulting in abrupt loss spikes. This perspective provides a rationale for why weight penalties can improve generalization yet cannot be made arbitrarily strong: excessive decay drives scale-invariant weight norms past a critical boundary and destabilizes training. Our work provides a new mechanistic understanding of loss spikes through the lens of \emph{weight-norm criticality}. Moreover, \emph{weight-norm criticality} yields testable predictions that we validate empirically in networks with scale-invariant components, providing empirical support for the proposed mechanism.
Xiaolong Li, Zhangchen Zhou, Zhi-Qin John Xu
Loss LandscapeModel WeightsNormalization
AskPDF
Apr 18, 2026stat.ML

A Mechanism Study of Delayed Loss Spikes in Batch-Normalized Linear Models

Delayed loss spikes have been reported in neural-network training, but existing theory mainly explains earlier non-monotone behavior caused by overly large fixed learning rates. We study one stylized hypothesis: normalization can postpone instability by gradually increasing the effective learning rate during otherwise stable descent. To test this hypothesis at theorem level, we analyze batch-normalized linear models. Our flagship result concerns whitened square-loss linear regression, where we derive explicit no-rising-edge and delayed-onset conditions, bound the waiting time to directional onset, and show that the rising edge self-stabilizes within finitely many iterations. Combined with a square-loss decomposition, this yields a concrete delayed-spike mechanism in the whitened regime. For logistic regression, under highly restrictive active-margin assumptions, we prove only a supporting finite-horizon directional precursor in a knife-edge regime, with an optional appendix-only loss lower bound under an extra non-degeneracy condition. The paper should therefore be read as a stylized mechanism study rather than a general explanation of neural-network loss spikes. Within that scope, the results isolate one concrete delayed-instability pathway induced by batch normalization.
Peifeng Gao, Wenyi Fang, Yang Zheng +1
Batch NormalizationLearning RatesDescentInstability
AskPDF