"An important question is then whether in the modification the normalization should stand in front of the deformed exponential function, or whether it should be included as " Throughout our paper, we use the definition of [10, 25], equivalent to the maxent problem (27). Since each slice of a paraboloid is an ellipsoid, we can apply Cavalieri's principle to obtain the volume of a paraboloid N (t; 0, 1) = 1 2 null erf null v 2 null erf null u 2 nullnull v N (v; 0, 1) + uN ( u; 0, 1), (50) from which the expectation (49) can be computed directly. We start with the following lemma:Lemma 1. Applying Fubini's theorem, we fix The training and test sets are perfectly balanced: 12.5K negative and The documents have 280 words on average. Figure 4 illustrates the difficulties that continuous attention models may face when trying to focus on objects that are too far from each other or that seem to have different relative importance to answer the question. Batch size 64 Word embeddings size 300 Input image features size 2048 Input question features size 512 Fused multimodal features size 1024 Multi-head attention hidden size 512 Number of MCA layers 6 Number of attention heads 8 Dropout rate 0.1 MLP size in flatten layers 512 Optimizer Adam Base learning rate at epoch t starting from 1 min(2.

Exponential families are widely used in machine learning; they include many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions in each of these families have fixed support. In contrast, for finite domains, there has been recent work on sparse alternatives to softmax (e.g. sparsemax and alpha-entmax), which have varying support, being able to assign zero probability to irrelevant categories. This paper expands that work in two directions: first, we extend alpha-entmax to continuous domains, revealing a link with Tsallis statistics and deformed exponential families. Second, we introduce continuous-domain attention mechanisms, deriving efficient gradient backpropagation algorithms for alpha in {1,2}. Experiments on attention-based text classification, machine translation, and visual question answering illustrate the use of continuous attention in 1D and 2D, showing that it allows attending to time intervals and compact regions.