In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
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Question: A BN20 network is a two level belief net in which parent interactions are modeled using the noisy-or interaction model. In this paper we discuss application of the SPI local expression language [1] to effi cient inference in large BN20 networks. In particular, we show that there is sig nificant structure which can be exploited to improve over the Quickscore result. We further describe how symbolic tech niques can provide information which can significantly reduce the computation required for computing all cause poste rior marginals. Finally, we present a novel approximation technique with pre liminary experimental results.

Answer: Symbolic Probabilistic Inference in large BN20 networks

Question: We study a subclass of POMDPs, called Deterministic POMDPs, that is characterized by deterministic actions and observations. These models do not provide the same generality of POMDPs yet they capture a number of interesting and challenging problems, and permit more efficient algorithms. Indeed, some of the recent work in planning is built around such assumptions mainly by the quest of amenable models more expressive than the classical deterministic models. We provide results about the fundamental properties of Deterministic POMDPs, their relation with AND/OR search problems and algorithms, and their computational complexity.

Answer: Deterministic POMDPs Revisited

Question: We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. [2016]: Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecturealgorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: a gradient based method appears to be first climbing uphill and then falling downhill between two points; whereas, in fact, they lie in the same basin.

Answer:
Empirical Analysis of the Hessian of Over-Parametrized Neural Networks