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: We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers.   After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.

Output: We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning.


Input: Consider Input: Plan recognition aims to look for target plans to best explain the observed actions based on plan libraries and/or domain models. Despite the success of previous approaches on plan recognition, they mostly rely on correct action observations. 
 Recent advances in visual activity recognition have the potential of enabling applications such as automated video surveillance. Effective approaches for such problems would require the ability to recognize the plans of agents from video information. Traditional plan recognition algorithms rely on access to detailed planning domain models. One recent promising direction involves learning approximate (or shallow) domain models directly from the observed activity sequences. Such plan recognition approaches expect observed action sequences as inputs. However, visual inference results are often noisy and uncertain, typically represented as a distribution over possible actions. In this work, we develop a visual plan recognition framework that recognizes plans with an approximate domain model learned from uncertain visual data.

Output: Handling Uncertainty in Visual Perception for Plan Recognition


Input: Consider Input: We study the robust one-bit compressed sensing problem whose goal is to design an algorithm that faithfully recovers any sparse target vector
 $\theta_0\in\mathbb{R}^d$ \emph{uniformly} from $m$ quantized noisy measurements. Under the assumption that the measurements are sub-Gaussian,  to recover any $k$-sparse $\theta_0$ ($k\ll d$) \emph{uniformly} up to an error $\varepsilon$ with high probability, the best known computationally tractable algorithm requires\footnote{Here, an algorithm is ``computationally tractable'' if it has provable convergence guarantees. The notation $\tilde{\mathcal{O}}(\cdot)$ omits a logarithm factor of $\varepsilon^{-1}$. } $m\geq\tilde{\mathcal{O}}(k\log d/\varepsilon^4)$. In this paper, we consider a new framework for the one-bit sensing problem where the sparsity is implicitly enforced via mapping a low dimensional representation $x_0$ through a known $n$-layer ReLU generative network $G:\mathbb{R}^k\rightarrow\mathbb{R}^d$. Such a framework poses low-dimensional priors on $\theta_0$ without a known basis. We propose to recover the target $G(x_0)$ via an unconstrained empirical risk minimization (ERM) problem under a much weaker \emph{sub-exponential  measurement assumption}.  For such a problem, we establish a joint statistical and computational analysis . In particular, we prove that the ERM estimator in this new framework achieves an improved statistical rate of $m=\tilde{\mathcal{O}} (kn\log d /\epsilon^2)$ recovering any $G(x_0)$ uniformly up to an error $\varepsilon$. Moreover, from the lens of computation, we prove that under proper conditions on the ReLU weights, our proposed empirical risk, despite non-convexity, has no stationary point outside of small neighborhoods around the true representation $x_0$ and its negative multiple. Furthermore, we show that the global minimizer of the empirical risk stays within the neighborhood around $x_0$ rather than its negative multiple. Our analysis sheds some light on the possibility of inverting a deep generative model under partial and quantized measurements, complementing the recent success of using deep generative models for inverse problems.


Output: We provide statistical and computational analysis of one-bit compressed sensing problem with a generative prior.