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.

Transformers excel through content-addressable retrieval and the ability to exploit contexts of, in principle, unbounded length. We recast associative memory at the level of probability measures, treating a context as a distribution over tokens and viewing attention as an integral operator on measures. Concretely, for mixture contexts $ν= I^{-1} \sum_{i=1}^I μ^{(i^*)}$ and a query $x_{\mathrm{q}}(i^*)$, the task decomposes into (i) recall of the relevant component $μ^{(i^*)}$ and (ii) prediction from $(μ_{i^*},x_\mathrm{q})$. We study learned softmax attention (not a frozen kernel) trained by empirical risk minimization and show that a shallow measure-theoretic Transformer composed with an MLP learns the recall-and-predict map under a spectral assumption on the input densities. We further establish a matching minimax lower bound with the same rate exponent (up to multiplicative constants), proving sharpness of the convergence order. The framework offers a principled recipe for designing and analyzing Transformers that recall from arbitrarily long, distributional contexts with provable generalization guarantees.