TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: The tasks that an agent will need to solve often aren’t known during training. However, if the agent knows which properties of the environment we consider im- portant, then after learning how its actions affect those properties the agent may be able to use this knowledge to solve complex tasks without training specifi- cally for them. Towards this end, we consider a setup in which an environment is augmented with a set of user defined attributes that parameterize the features of interest. We propose a model that learns a policy for transitioning between “nearby” sets of attributes, and maintains a graph of possible transitions. Given a task at test time that can be expressed in terms of a target set of attributes, and a current state, our model infers the attributes of the current state and searches over paths through attribute space to get a high level plan, and then uses its low level policy to execute the plan. We show in grid-world games and 3D block stacking that our model is able to generalize to longer, more complex tasks at test time even when it only sees short, simple tasks at train time.


SOLUTION: Compositional attribute-based planning that generalizes to long test tasks, despite being trained on short & simple tasks.

PROBLEM: It is well-known that deeper neural networks are harder to train than shallower ones. In this short paper, we use the (full) eigenvalue spectrum of the Hessian to explore how the loss landscape changes as the network gets deeper, and as residual connections are added to the architecture. Computing a series of quantitative measures on the Hessian spectrum, we show that the Hessian eigenvalue distribution in deeper networks has substantially heavier tails (equivalently, more outlier eigenvalues), which makes the network harder to optimize with first-order methods. We show that adding residual connections mitigates this effect substantially, suggesting a mechanism by which residual connections improve training.

SOLUTION: Network depth increases outlier eigenvalues in the Hessian. Residual connections mitigate this.

PROBLEM: For many applications, in particular in natural science, the task is to
 determine hidden system parameters from a set of measurements. Often,
 the forward process from parameter- to measurement-space is well-defined,
 whereas the inverse problem is ambiguous: multiple parameter sets can
 result in the same measurement. To fully characterize this ambiguity, the full
 posterior parameter distribution, conditioned on an observed measurement,
 has to be determined. We argue that a particular class of neural networks
 is well suited for this task – so-called Invertible Neural Networks (INNs).
 Unlike classical neural networks, which attempt to solve the ambiguous
 inverse problem directly, INNs focus on learning the forward process, using
 additional latent output variables to capture the information otherwise
 lost. Due to invertibility, a model of the corresponding inverse process is
 learned implicitly. Given a specific measurement and the distribution of
 the latent variables, the inverse pass of the INN provides the full posterior
 over parameter space. We prove theoretically and verify experimentally, on
 artificial data and real-world problems from medicine and astrophysics, that
 INNs are a powerful analysis tool to find multi-modalities in parameter space,
 uncover parameter correlations, and identify unrecoverable parameters.

SOLUTION:
To analyze inverse problems with Invertible Neural Networks