human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "inference in deep networks in high dimensions"):
  Abstract: Deep generative networks provide a powerful tool for modeling complex data in a wide range of applications. In inverse problems that use these networks as generative priors on data, one must often perform inference of the inputs of the networks from the outputs. Inference is also required for sampling during stochastic training on these generative models. This paper considers inference in a deep stochastic neural network where the parameters (e.g., weights, biases and activation functions) are known and the problem is to estimate the values of the input and hidden units from the output. While several approximate algorithms have been proposed for this task, there are few analytic tools that can provide rigorous guarantees in the reconstruction error. This work presents a novel and computationally tractable output-to-input inference method called Multi-Layer Vector Approximate Message Passing (ML-VAMP). The proposed algorithm, derived from expectation propagation, extends earlier AMP methods that are known to achieve the replica predictions for optimality in simple linear inverse problems. Our main contribution shows that the mean-squared error (MSE) of ML-VAMP can be exactly predicted in a certain large system limit (LSL) where the numbers of layers is fixed and weight matrices are random and orthogonally-invariant with dimensions that grow to infinity. ML-VAMP is thus a principled method for output-to-input inference in deep networks with a rigorous and precise performance achievability result in high dimensions.

Includes members:
  Member "multi layer generalized linear estimation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "deep s 3 pr simultaneous source separation and phase retrieval using deep generative models")
  Member "hybrid approximate message passing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "bilinear recovery using adaptive vector amp")
  Member "generalized expectation consistent signal recovery for nonlinear measurements":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "inference in multi layer networks with matrix valued unknowns")
  Member "the replica symmetric prediction for compressed sensing with gaussian matrices is exact":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "unsourced multiuser sparse regression codes achieve the symmetric mac capacity")
  Member "learning and free energies for vector approximate message passing":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "inference with deep generative priors in high dimensions")
  Member "the mutual information in random linear estimation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "bilinear recovery using adaptive vector amp")
  Member "inferring sparsity compressed sensing using generalized restricted boltzmann machines":
    also connected through other hyperedges:
      (none)
  Member "vector approximate message passing for the generalized linear model":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "capacity bounds for communication systems with quantization and spectral constraints")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.LG(Machine Learning)