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.

Input: Consider Input: The goal of compressed sensing is to learn a structured signal $x$
from a limited number of noisy linear measurements $y pprox Ax$. In
traditional compressed sensing, ''structure'' is represented by
sparsity in some known basis. Inspired by the success of deep
learning in modeling images, recent work starting with~\cite{BDJP17}
has instead considered structure to come from a generative model
$G: \R^k o \R^n$. We present two results establishing the
difficulty of this latter task, showing that existing bounds are
tight.

First, we provide a lower bound matching the~\cite{BDJP17} upper
bound for compressed sensing from $L$-Lipschitz generative models
$G$. In particular, there exists such a function that requires
roughly $\Omega(k \log L)$ linear measurements for sparse recovery
to be possible. This holds even for the more relaxed goal of
\emph{nonuniform} recovery.

Second, we show that generative models generalize sparsity as a
representation of structure. In particular, we construct a
ReLU-based neural network $G: \R^{2k} o \R^n$ with $O(1)$ layers
and $O(kn)$ activations per layer, such that the range of $G$
contains all $k$-sparse vectors.

Output: Lower bound for compressed sensing w/ generative models that matches known upper bounds

Input: Consider Input: Extracting relevant information, causally inferring and predicting the future states with high accuracy is a crucial task for modeling complex systems. The endeavor to address these tasks is made even more challenging when we have to deal with high-dimensional heterogeneous data streams. Such data streams often have higher-order inter-dependencies across spatial and temporal dimensions. We propose to perform a soft-clustering of the data and learn its dynamics to produce a compact dynamical model while still ensuring the original objectives of causal inference and accurate predictions. To efficiently and rigorously process the dynamics of soft-clustering, we advocate for an information theory inspired approach that incorporates stochastic calculus and seeks to determine a trade-off between the predictive accuracy and compactness of the mathematical representation. We cast the model construction as a maximization of the compression of the state variables such that the predictive ability and causal interdependence (relatedness) constraints between the original data streams and the compact model are closely bounded. We provide theoretical guarantees concerning the convergence of the proposed learning algorithm. To further test the proposed framework, we consider a high-dimensional Gaussian case study and describe an iterative scheme for updating the new model parameters. Using numerical experiments, we demonstrate the benefits on compression and prediction accuracy for a class of dynamical systems. Finally, we apply the proposed algorithm to the real-world dataset of multimodal sentiment intensity and show improvements in prediction with reduced dimensions.

Output: Compact perception of dynamical process

Input: Consider Input: Prefrontal cortex (PFC) is a part of the brain which is responsible for behavior repertoire. Inspired by PFC functionality and connectivity, as well as human behavior formation process, we propose a novel modular architecture of neural networks with a Behavioral Module (BM) and corresponding end-to-end training strategy. This approach allows the efficient learning of behaviors and preferences representation. This property is particularly useful for user modeling (as for dialog agents) and recommendation tasks, as allows learning personalized representations of different user states. In the experiment with video games playing, the resultsshow that the proposed method allows separation of main task's objectives andbehaviors between different BMs. The experiments also show network extendability through independent learning of new behavior patterns. Moreover, we demonstrate a strategy for an efficient transfer of newly learned BMs to unseen tasks.
Output: Extendable Modular Architecture is proposed for developing of variety of Agent Behaviors in DQN.