Itiswellknownthatmultiple objectsinnatural scenes compete forneural resources and attentional guidance helps to resolve the ensuing competition [5]. Due to the limited information processing capacity ofthevisual system, neural activity isbiased infavorofthe attended location [6,7].

Transformer-based models [1] have achieved great success in the domains of natural language processing (NLP) [2,3] and computer vision [4-6].

Wepresent an orchestration of the computations such that theoutcome isaccompanied withaproofofcorrectness thatcanbeverifiedwith substantially less computational resources than it takes to run the computations fromscratch withstate-of-the-art algorithms. Specifically,weadopt analgebraic proof system developed incomputational complexity theory,inwhich theproof is represented by a polynomial; evaluating the polynomial at a random point amounts to a verification of the proof with probabilistic guarantees.

Tosupportthis, we compute the cosine similarity between representations from augmented and original samples, i.e., CS = Ex D,t T[sim(g f(t(x)),g f(x))]. For linear evaluation benchmarks, we randomly choose validation samples in the training split for each dataset when the validation split is not officially provided. Note that the pretraining setups are the same as they officiallyusedforImageNet pretraining described in[2,5,30]. When incorporating our AugSelf into the methods, we use λ=1.0andAAugSelf ={crop,color},unlessotherwisestated. Other hyperparameters are the same as the ImageNet100 setup describedinSectionF.1.

Furthermore, AugSelf can easily be incorporated into recent state-of-the-art representation learning methods with a negligible additional training cost.

The most well-known work in the reward shaping domain is the potential-based reward shaping (PBRS) method [12], which is the first to show that policy invariance can be guaranteed if the shaping reward function is in the form of the difference of potential values.