Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks

Training Physics-Informed Neural Networks (PINNs) requires jointly optimizing physics residual and initial/boundary condition loss terms, which often induce conflicting gradients. Gradient surgery methods mitigate this issue by constructing directions from loss-specific gradients to reduce conflict before optimizer transformation. However, even when the constructed direction is conflict-free, this property may not be preserved after optimizer transformation. Let $a_t$ denote the direction constructed by gradient surgery, $u_t$ the optimizer proposal, and $\mathcal{C}_t$ the conflict-free cone induced by the loss-specific gradients. We show that modern optimizers can transform $a_t$ through mechanisms such as historical state, adaptive scaling, preconditioning, or decoupled weight decay, so $a_t \in \mathcal{C}_t$ does not generally imply $u_t \in \mathcal{C}_t$. We refer to this optimizer-induced discrepancy in conflict-freeness between $a_t$ and $u_t$ as Gradient-Update Mismatch (GUM). Accordingly, we propose Gradient-Update Alignment (GUA), which projects $u_t$ onto $\mathcal{C}_t$ to obtain the aligned update $p_t$ and applies $p_t$ to the parameters. When the optimizer maintains internal state, GUA further adjusts this state toward targets reconstructed from the applied update. We conduct extensive experiments and find that GUM is widespread across momentum, adaptive, and curvature-based optimizers, with conflict rates reaching up to 86.3%. Across all PINN settings, GUA achieves conflict-free applied updates and consistently improves various gradient surgery methods, reducing the relative $L_2$ error by up to 98.2% in individual settings. Data and code are available at https://github.com/JingXiao10/GUA.

CAT-GS: Balanced Multimodal Learning via Calibrated Gating and Fusion Surgery

End-to-end training of multimodal neural networks often exhibits unstable neural dynamics characterized by three coupled failure modes that degrade learning: (i) modality imbalance, where one branch dominates gradient-based optimization; (ii) unstable gating, where noisy confidence cues induce erratic modality selection; and (iii) fusion interference, where modality-specific gradients conflict at the shared fusion layer. We propose CAT-GS (Calibrated, Adaptive, Thresholded Gating with Fusion Surgery), a neural dynamics-based optimization controller for intelligent computing applications. CAT-GS operates during backpropagation without modifying model architectures, fusion modules, or task losses. Through calibration of teacher-derived reliability via temperature scaling and EMA smoothing, CAT-GS stabilizes neural dynamics using a margin-thresholded policy to switch between warm-up dropout, weak-modality prioritization, and weak-biased blending, stabilizes gradient magnitudes under aggressive gating via capped gradient-budget renormalization, and applies fusion-only PCGrad to reduce destructive cross-modal interference at the primary shared bottleneck. We evaluate CAT-GS on audio--visual multimodal pattern recognition benchmarks (CREMA-D, AV-MNIST, and VGGSound), a tri-modal setting (UR-FUNNY), controlled synthetic data (CG-MNIST), and additional cross-domain benchmarks (AVE and CMU-MOSI). CAT-GS improves or matches fused multimodal accuracy against strong imbalance-aware baselines (including OGM-GE, G$^2$D, and UMT) across settings, and yields smoother gating behavior with fewer conflicting fusion gradients.