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: "lifted proximal operator machines"
  Abstract: We propose a new optimization method for training feed-forward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feed-forward neural network by adding the proximal operators to the objective function as penalties, hence we call the lifted proximal operator machine (LPOM). LPOM is block multi-convex in all layer-wise weights and activations. This allows us to use block coordinate descent to update the layer-wise weights and activations in parallel. Most notably, we only use the mapping of the activation function itself, rather than its derivatives, thus avoiding the gradient vanishing or blow-up issues in gradient based training methods. So our method is applicable to various non-decreasing Lipschitz continuous activation functions, which can be saturating and non-differentiable. LPOM does not require more auxiliary variables than the layer-wise activations, thus using roughly the same amount of memory as stochastic gradient descent (SGD) does. We further prove the convergence of updating the layer-wise weights and activations. Experiments on MNIST and CIFAR-10 datasets testify to the advantages of LPOM.

Connected through hyperedge HE-1 (induced by source paper "differentiable linearized admm"):
  with members:
    - "k meansnet when k means meets differentiable programming"
    - "optimization algorithm inspired deep neural network structure design"
    - "theoretical linear convergence of unfolded ista and its practical weights and thresholds"
    - "deep image prior"
    - "trainable nonlinear reaction diffusion a flexible framework for fast and effective image restoration"
    - "learning deep cnn denoiser prior for image restoration"
    - "unrolled optimization with deep priors"
    - "densely connected convolutional networks"

Connected through hyperedge HE-2 (induced by source paper "implicit deep learning"):
  with members:
    - "satnet bridging deep learning and logical reasoning using a differentiable satisfiability solver"
    - "deep equilibrium models"
    - "differentiable mpc for end to end planning and control"
    - "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"

Connected through hyperedge HE-3 (induced by source paper "contrastive learning for lifted networks"):
  with members:
    - "fenchel lifted networks a lagrange relaxation of neural network training"
    - "lifted neural networks"
    - "proximal backpropagation"
    - "fashion mnist a novel image dataset for benchmarking machine learning algorithms"
    - "training neural networks without gradients a scalable admm approach"
    - "equilibrium propagation bridging the gap between energy based models and backpropagation"
    - "trusting svm for piecewise linear cnns"
    - "efficient training of very deep neural networks for supervised hashing"

Connected through hyperedge HE-4 (induced by source paper "fenchel lifted networks a lagrange relaxation of neural network training"):
  with members:
    - "lifted neural networks"
    - "parmac distributed optimisation of nested functions with application to binary autoencoders"
    - "entropy sgd biasing gradient descent into wide valleys"
    - "training neural networks without gradients a scalable admm approach"
    - "efficient training of very deep neural networks for supervised hashing"
    - "batch normalization accelerating deep network training by reducing internal covariate shift"
    - "adam a method for stochastic optimization"
    - "identifying and attacking the saddle point problem in high dimensional non convex 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)