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: "constrained deep networks lagrangian optimization via log barrier extensions"
  Abstract: This study investigates imposing inequality constraints on the outputs of CNNs, with application to weakly supervised segmentation. In the context of deep networks, constraints are commonly handled with penalties for their simplicity, and despite their well-known limitations. Lagrangian-dual optimization has been largely avoided, mainly due to the computational complexity and stability/convergence issues caused by alternating explicit dual updates/projections and stochastic optimization. Several studies showed that, for deep CNNs, the theoretical and practical advantages of Lagrangian optimization over penalties do not materialize in practice. We propose log-barrier extensions, which approximate Lagrangian optimization of constrained-CNN problems with a sequence of unconstrained losses. Unlike standard interior-point and log-barrier methods, our formulation does not need an initial feasible solution. Furthermore, we provide a new technical result, which shows that the proposed extensions yield an upper bound on the duality gap. This generalizes the duality-gap result of standard log-barriers, yielding sub-optimality certificates for feasible solutions. While sub-optimality is not guaranteed for non-convex problems, our result shows that log-barrier extensions are a principled way to approximate Lagrangian optimization for constrained CNNs via implicit dual variables. We report comprehensive constrained-CNN experiments, showing that our formulation outperforms several penalty-based methods, in terms of accuracy and training stability.

Connected through hyperedge HE-1 (induced by source paper "non parametric uni modality constraints for deep ordinal classification"):
  with members:
    - "ordinal distribution regression for gait based age estimation"
    - "constrained cnn losses for weakly supervised segmentation"
    - "min max entropy for weakly supervised pointwise localization"
    - "deep weakly supervised learning methods for classification and localization in histology images a survey"
    - "imposing hard constraints on deep networks promises and limitations"
    - "deep label distribution learning with label ambiguity"
    - "constrained deep weak supervision for histopathology image segmentation"
    - "learning to play in a day faster deep reinforcement learning by optimality tightening"

Connected through hyperedge HE-2 (induced by source paper "deep ordinal classification with inequality constraints"):
  with members:
    - "ordinal distribution regression for gait based age estimation"
    - "min max entropy for weakly supervised pointwise localization"
    - "imposing hard constraints on deep networks promises and limitations"
    - "deep label distribution learning with label ambiguity"
    - "constrained deep weak supervision for histopathology image segmentation"
    - "learning to play in a day faster deep reinforcement learning by optimality tightening"
    - "deep residual learning for image recognition"
    - "constrained convolutional neural networks for weakly supervised segmentation"

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.CV(Computer Vision and Pattern Recognition)