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.

[Q]: We propose a solution for evaluation of mathematical expression. However, instead of designing a single end-to-end model we propose a Lego bricks style architecture. In this architecture instead of training a complex end-to-end neural network, many small networks can be trained independently each accomplishing one specific operation and acting a single lego brick. More difficult or complex task can then be solved using a combination of these smaller network. In this work we first identify 8 fundamental operations that are commonly used to solve arithmetic operations (such as 1 digit multiplication, addition, subtraction, sign calculator etc). These fundamental operations are then learned using simple feed forward neural networks. We then shows that different operations can be designed simply by reusing these smaller networks. As an example we reuse these smaller networks to develop larger and a more complex network to solve n-digit multiplication, n-digit division, and cross product. This bottom-up strategy not only introduces reusability, we also show that it allows to generalize for computations involving n-digits and we show results for up to 7 digit numbers. Unlike existing methods, our solution also generalizes for both positive as well as negative numbers.
[A]: We train many small networks each for a specific operation, these are then combined to perform complex operations


[Q]: We present Value Propagation (VProp), a set of parameter-efficient differentiable planning modules built on Value Iteration which can successfully be trained using reinforcement learning to solve unseen tasks, has the capability to generalize to larger map sizes, and can learn to navigate in dynamic environments. We show that the modules enable learning to plan when the environment also includes stochastic elements, providing a cost-efficient learning system to build low-level size-invariant planners for a variety of interactive navigation problems. We evaluate on static and dynamic configurations of MazeBase grid-worlds, with randomly generated environments of several different sizes, and on a StarCraft navigation scenario, with more complex dynamics, and pixels as input.
[A]: We present planners based on convnets that are sample-efficient and that generalize to larger instances of navigation and pathfinding problems.


[Q]: Are neural networks biased toward simple functions?
 Does depth always help learn more complex features?
 Is training the last layer of a network as good as training all layers?
 These questions seem unrelated at face value, but in this work we give all of them a common treatment from the spectral perspective.
 We will study the spectra of the *Conjugate Kernel, CK,* (also called the *Neural Network-Gaussian Process Kernel*), and the *Neural Tangent Kernel, NTK*.
 Roughly, the CK and the NTK tell us respectively ``"what a network looks like at initialization" and "``what a network looks like during and after training."
 Their spectra then encode valuable information about the initial distribution and the training and generalization properties of neural networks.
 By analyzing the eigenvalues, we lend novel insights into the questions put forth at the beginning, and we verify these insights by extensive experiments of neural networks.
 We believe the computational tools we develop here for analyzing the spectra of CK and NTK serve as a solid foundation for future studies of deep neural networks.
 We have open-sourced the code for it and for generating the plots in this paper at github.com/jxVmnLgedVwv6mNcGCBy/NNspectra.
[A]:
Eigenvalues of Conjugate (aka NNGP) and Neural Tangent Kernel can be computed in closed form over the Boolean cube and reveal the effects of hyperparameters on neural network inductive bias, training, and generalization.