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Without such control, activations and gradients may vanish, explode, or enter unstable regimes that make optimization fail. Modern architectures often mitigate this problem through Batch Normalization, residual connections, or other normalization layers, which repeatedly re-scale or bypass intermediate representations. However, these mechanisms are not always appropriate. In Physics-Informed Neural Networks (PINNs), the network represents a continuous physical field and its input derivatives define the training objective, making batch-dependent normalization problematic because it can introduce non-local dependencies into the predicted field and its derivatives. We propose StableGrad, an optimizer-level scale-control mechanism that corrects layer-wise weight-gradient imbalances without modifying the forward model. Because the normalizati","title":"StableGrad: Backward Scale Control without Batch Normalization","url":"https://arxiv.org/abs/2605.19856","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.19856v1 Announce Type: cross \nAbstract: Training very deep neural networks requires controlling the propagation of magnitudes across depth. Without such control, activations and gradients may vanish, explode, or enter unstable regimes that make optimization fail. Modern architectures often mitigate this problem through Batch Normalization, residual connections, or other normalization layers, which repeatedly re-scale or bypass intermediate representations. However, these mechanisms are not always appropriate. In Physics-Informed Neural Networks (PINNs), the network represents a continuous physical field and its input derivatives define the training objective, making batch-dependent normalization problematic because it can introduce non-local dependencies into the predicted field and its derivatives. We propose StableGrad, an optimizer-level scale-control mechanism that corrects layer-wise weight-gradient imbalances without modifying the forward model. 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