We study signal propagation at initialization in transformers through the averaged partial Jacobian norm (APJN), a measure of gradient amplification across layers. We extend APJN analysis to transformers with bidirectional attention and permutation-symmetric input token configurations by deriving recurrence relations for activation statistics and APJNs across layers. Our theory predicts how attention modifies the asymptotic behavior of the APJN at large depth and matches APJNs measured in deep vision transformers. The criticality picture known from residual networks carries over to transformers: the pre-LayerNorm architecture exhibits power-law APJN growth, whereas transformers with LayerNorm replaced by elementwise $\tanh$-like nonlinearities have stretched-exponential APJN growth, indicating that the latter are subcritical. Applied to Dynamic Tanh (DyT) and Dynamic erf (Derf) transformers, the theory explains why these architectures can be more sensitive to initialization and optimization choices and require careful tuning for stable training.

Meanwhile, its"parallel" computation allowsforthesimultaneous explorationofdifferent reasoning paths andbenefits more robust and efficient execution of operations that are mutually independent (e.g. when counting individual colors for the query:"determine the maximum occurring color amongst all t-shirts"). We design IPRM as a lightweight and fully-differentiable neural module thatcanbeconveniently applied toboth transformer and non-transformer vision-language backbones.

First, a student model is trained to recover the classifier'spredictions andtomatch theexplanations givenbytheexplainer.

DePT induces a cone-shaped spatial-temporal attention prior,which injects theinformation propagation and aggregation principles and enables a global view. With physical constraint inductive bias baked into its design, our DePT is ready to plug and play for a broad class of multi-agent systems. The experimental results on one of the most challenging CPS - network-scale traffic signal control system in the open world - show that our model outperformed the state-of-the-art expert methods on synthetic and real-world datasets.

Totackle with arange of noise levels, the training images are corrupted by Gaussian noisewithσ randomly chosefrom[0,50]. Swin transformer: Hierarchical vision transformer using shifted windows.