's hidden state by h Then we need to calculate the second part of Eq. Using the Bayes' theorem, we have: p In Section 4.3, we devise a Sigmoid function to adapt the γ during the supernet training, which is defined as: γ (t) = 1 Sigmoidnull ( t total epochs 2 1) b null, (19) Section 3.2 theoretically demonstrates the benefit of the proposed architecture complementation loss function,

In the standard MLE setting [see, e.g., Murphy, 2012, Ch. 9] we are interested in learning the These two definitions are, however, essentially equivalent. Eq. (15) is a smooth objective that can be optimized with a (stochastic) gradient descent procedure. This section contains the proofs of the results relative to the perturb and map section (Section 3.2) and The proposition now follows from arguments made in Papandreou and Y uille [2011] Its moment generating function has the form E[exp(tX)] = Γ(1 τt). As mentioned in Johnson and Balakrishnan [p. Parts of the proof are inspired by a post on stackexchange Xi'an [2016].Theorem 1.

We present Deep Region Competition (DRC), an algorithm designed to extract foreground objects from images in a fully unsupervised manner. Foreground extraction can be viewed as a special case of generic image segmentation that focuses on identifying and disentangling objects from the background. In this work, we rethink the foreground extraction by reconciling energy-based prior with generative image modeling in the form of Mixture of Experts (MoE), where we further introduce the learned pixel re-assignment as the essential inductive bias to capture the regularities of background regions. With this modeling, the foreground-background partition can be naturally found through Expectation-Maximization (EM). We show that the proposed method effectively exploits the interaction between the mixture components during the partitioning process, which closely connects to region competition [1], a seminal approach for generic image segmentation. Experiments demonstrate that DRC exhibits more competitive performances on complex real-world data and challenging multi-object scenes compared with prior methods. Moreover, we show empirically that DRC can potentially generalize to novel foreground objects even from categories unseen during training.

"E-step" (Steps 1 and 2 in Algorithm 1) and a weighted maximum likelihood estimation (MLE) "M-step" (Step 3; see [ ( t 1) (t 1) One may use these in a number of different ways. The following observation is due to Chebyshev's inequality. One can use Proposition S2.1 to construct a confidence interval on, for example, the expected squared Note that 1) the bound in Proposition S2.1 is CbAS naturally controls the importance weight variance. Design procedures that leverage a trust region can naturally bound the variance of the importance weights. We used CbAS as follows.

Currently there are several theories for how neural activity may represent probability distributions.