The original CLUTRR data generation framework made sure that each testproof is not in the training set in order to test whether a model is able to generalize to unseen proofs. Initial results on the original CLUTRR test sets resulted in strong model performance ( 99%) on levels seen during training (2, 4, 6) but no generalization at all ( 0%) to other levels. The models are given as input " [story] [query] " and asked to generate the proof and answer. Models are trained on levels2,4,6only. In our case, the entity names are important to evaluate systematic generalization.

We first prove case (a).

Does the dataset contain all possible instancesorisitasample(notnecessarilyrandom) of instances from a larger set? If the dataset is a sample, then what is the larger set? Is the sample representative of the larger set (e.g., geographic coverage)? If so, please describe how this representativeness was validated/verified.

We first prove the direction Z T SI(Z;T) = 0, which is equivalent to prove I(Z;T) = 0 SI(Z;T) = 0. We prove the contrapositive, i.e. rather than show LHS = RHS, we show that RHS = LHS. Now assume that supwi,vj ρ(w i Z i,v j T j) > ϵ for some i,j. Then by setting those elements in w,v unrelated to Z i,T j to zero, and those related to Z i,T j exactlythesameaswi,vj,weknowthatsupw,vρ(w Z,v T) > ϵ. All neural networks are trained by Adam with its default settings and a learning rate η = 0.001. Early stopping is an useful technique for avoiding overfitting, however it needs to be carefully considered when applied to adversarial methods.

With respect to experiments, our contributions are twofold.

Tothebestofourknowledge, ourenhanced latent space blind model, optimization scheme, NFAEandFM2A havenot been reported in the previous literature.

The relative performance gain for Fig.1 c) is In Tab. 6, we show FPS(F) FPS(E) of various feature fusion models with the varied set sizeN. Notethatmethodswithout intra-set relationships, PFE [11] and CFAN [3], are computationally very fast and require little memory. Incontrast, the maximum set sizeN for RSA [7] is384 because the intra-set attention with the feature map is a memory-intensivemodule. In other words, it is the mean of the row-wise entropy of the normalized assignment map. Lower entropy value tells you that the cluster features are deviating from a simple average of all samples.

However, the number of learned group tokens in GroupViT is a hyper-parameter and there is no constraint on it. The textembeddings is used inacontrastiveloss tomatch with the global visual representations. Figure 1: Comparison results of recall for all 25 classes between HAN [2] and the proposed MGN in terms of event-level audio, visual and audio-visual metrics,i.e.,Event_A,Event_V,and Event_AV.

We use the open-source mimic-cxr repository4 to extract impression and findings for each report. Following [9], we pick out sequences of alphanumeric characters and drop all other characters and symbols for all reports, and remove reports which contain less than3 tokens. Following common practice in ViT [5], we split the radiograph with patch size16 16,which results in 196 visual tokens for each image. The instance-level projection layer is a two-layer MultiLayer Perceptron (MLP) with Batch Normalization [10] and ReLU activation function. Additionally, we use a frozen Batch Normalization layer after the MLP toobtain instance-levelembeddings.

We perform finetuning with image-textcontrastiveand image-textmatching losses. During inference, VLMO is first used as a dual encoder to obtain top-k candidates, then the model is used as a fusionencoder torerankthecandidates. For the text-only pre-training data, we use English Wikipedia and BookCorpus [5]. Table 1: Ablation study of the shared self-attention module used in Multiway Transformer.