human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "satnet bridging deep learning and logical reasoning using a differentiable satisfiability solver"
  Abstract: Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. We demonstrate that by integrating this solver into end-to-end learning systems, we can learn the logical structure of challenging problems in a minimally supervised fashion. In particular, we show that we can learn the parity function using single-bit supervision (a traditionally hard task for deep networks) and learn how to play 9x9 Sudoku solely from examples. We also solve a "visual Sudok" problem that maps images of Sudoku puzzles to their associated logical solutions by combining our MAXSAT solver with a traditional convolutional architecture. Our approach thus shows promise in integrating logical structures within deep learning.

Connected through hyperedge HE-1 (induced by source paper "it s not what machines can learn it s what we cannot teach"):
  with members:
    - "mipaal mixed integer program as a layer"
    - "generating difficult sat instances by preventing triangles"
    - "hidden stratification causes clinically meaningful failures in machine learning for medical imaging"
    - "guiding high performance sat solvers with unsat core predictions"
    - "a survey on bias and fairness in machine learning"
    - "deep learning for symbolic mathematics"
    - "the use of deep learning for symbolic integration a review of lample and charton 2019"
    - "mixmatch a holistic approach to semi supervised learning"

Connected through hyperedge HE-2 (induced by source paper "solving np hard problems on graphs with extended alphago zero"):
  with members:
    - "universal invariant and equivariant graph neural networks"
    - "on the universality of invariant networks"
    - "provably powerful graph networks"
    - "elf opengo an analysis and open reimplementation of alphazero"
    - "combinatorial optimization with graph convolutional networks and guided tree search"
    - "neural message passing for quantum chemistry"
    - "learning combinatorial optimization algorithms over graphs"
    - "semi supervised classification with graph convolutional networks"

Connected through hyperedge HE-3 (induced by source paper "differentiable fixed point iteration layer"):
  with members:
    - "differentiable convex optimization layers"
    - "anderson acceleration for geometry optimization and physics simulation"
    - "acquisition of localization confidence for accurate object detection"
    - "deep value networks learn to evaluate and iteratively refine structured outputs"
    - "optnet differentiable optimization as a layer in neural networks"
    - "input convex neural networks"
    - "structured prediction energy networks"
    - "flownet learning optical flow with convolutional networks"

Connected through hyperedge HE-4 (induced by source paper "deep equilibrium models"):
  with members:
    - "equilibrated recurrent neural network neuronal time delayed self feedback improves accuracy and stability"
    - "implicit deep learning"
    - "transformer xl attentive language models beyond a fixed length context"
    - "generating long sequences with sparse transformers"
    - "pytorch an imperative style high performance deep learning library"
    - "recurrent stacking of layers for compact neural machine translation models"
    - "trellis networks for sequence modeling"
    - "relational recurrent neural networks"

Connected through hyperedge HE-5 (induced by source paper "powerset convolutional neural networks"):
  with members:
    - "on the limitations of representing functions on sets"
    - "learning a sat solver from single bit supervision"
    - "graphvae towards generation of small graphs using variational autoencoders"
    - "deep sets"
    - "simplicial closure and higher order link prediction"
    - "janossy pooling learning deep permutation invariant functions for variable size inputs"
    - "neural message passing for quantum chemistry"
    - "robust spatial filtering with graph convolutional neural networks"

Connected through hyperedge HE-6 (induced by source paper "differentiation of blackbox combinatorial solvers"):
  with members:
    - "mipaal mixed integer program as a layer"
    - "exact combinatorial optimization with graph convolutional neural networks"
    - "guiding high performance sat solvers with unsat core predictions"
    - "raynet learning volumetric 3d reconstruction with ray potentials"
    - "smart predict and optimize for hard combinatorial optimization problems"
    - "end to end learning and optimization on graphs"
    - "learning a sat solver from single bit supervision"
    - "direct optimization through arg max for discrete variational auto encoder"

Connected through hyperedge HE-7 (induced by source paper "mipaal mixed integer program as a layer"):
  with members:
    - "decision focused learning of adversary behavior in security games"
    - "melding the data decisions pipeline decision focused learning for combinatorial optimization"
    - "machine learning for combinatorial optimization a methodological tour d horizon"
    - "deep reinforcement learning for green security games with real time information"
    - "what game are we playing end to end learning in normal and extensive form games"
    - "optnet differentiable optimization as a layer in neural networks"
    - "learning combinatorial optimization algorithms over graphs"
    - "position indexed formulations for kidney exchange"

Connected through hyperedge HE-8 (induced by source paper "implicit deep learning"):
  with members:
    - "deep equilibrium models"
    - "differentiable mpc for end to end planning and control"
    - "lifted proximal operator machines"
    - "neural ordinary differential equations"
    - "fenchel lifted networks a lagrange relaxation of neural network training"
    - "lifted neural networks"
    - "optnet differentiable optimization as a layer in neural networks"
    - "task based end to end model learning in stochastic optimization"

Question: Please tell me which class the center node 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)