Inference Suppose S: X R is a continuous set function w.r.t Hausdorff distance dH(,). ε > 0, foranyfunctionf andanyinvertiblemapP: X Rn, functionhandg,suchthatfor anyX X: |S(X) g(P

Theorem 2. The Instances in the bag are represented by random variables Θ1,Θ2,...,Θn, the information entropy of the bag under the correlation assumption can be expressed as H(Θ1,Θ2,...,Θn), and the information entropy of the bag under the i.i.d. Therefore, it is proved that the information source under the correlation assumption has smaller information entropy. In other words, correlation assumption reduces the uncertainty and brings more useful information. Given a set of bags {X1,X2,...,Xb}, and each bag Xi contains multiple instances {xi,1,xi,2,...,xi,n} and a corresponding label Yi. Obviously, the key to Transformer based MIL is how to design the mapping of X T. However, there are many difficulties to directly apply Transformer in WSI classification, including the large number of instances in each bag and the large variation in the number of instances in different bags (e.g., ranging from hundreds to thousands).