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: "generalization of erm in stochastic convex optimization the dimension strikes back"
  Abstract: In stochastic convex optimization the goal is to minimize a convex function $F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set $\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each $f(\cdot)$ in the support of $D$ is convex over $\cal K$. The optimization is commonly based on i.i.d.~samples $f^1,f^2,\ldots,f^n$ from $D$. A standard approach to such problems is empirical risk minimization (ERM) that optimizes $F_S(x) \doteq \frac{1}{n}\sum_{i\leq n} f^i(x)$. Here we consider the question of how many samples are necessary for ERM to succeed and the closely related question of uniform convergence of $F_S$ to $F$ over $\cal K$. We demonstrate that in the standard $\ell_p/\ell_q$ setting of Lipschitz-bounded functions over a $\cal K$ of bounded radius, ERM requires sample size that scales linearly with the dimension $d$. This nearly matches standard upper bounds and improves on $\Omega(\log d)$ dependence proved for $\ell_2/\ell_2$ setting by Shalev-Shwartz et al. (2009). In stark contrast, these problems can be solved using dimension-independent number of samples for $\ell_2/\ell_2$ setting and $\log d$ dependence for $\ell_1/\ell_\infty$ setting using other approaches. We further show that our lower bound applies even if the functions in the support of $D$ are smooth and efficiently computable and even if an $\ell_1$ regularization term is added. Finally, we demonstrate that for a more general class of bounded-range (but not Lipschitz-bounded) stochastic convex programs an infinite gap appears already in dimension 2.

Connected through hyperedge HE-1 (induced by source paper "reasoning about generalization via conditional mutual information"):
  with members:
    - "robust generalization via α mutual information"
    - "in defense of uniform convergence generalization via derandomization with an application to interpolating predictors"
    - "strengthened information theoretic bounds on the generalization error"
    - "tightening mutual information based bounds on generalization error"
    - "high probability generalization bounds for uniformly stable algorithms with nearly optimal rate"
    - "a new analysis of differential privacy s generalization guarantees"
    - "pac learning with stable and private predictions"
    - "a direct sum result for the information complexity of learning"

Connected through hyperedge HE-2 (induced by source paper "can implicit bias explain generalization stochastic convex optimization as a case study"):
  with members:
    - "uniform convergence may be unable to explain generalization in deep learning"
    - "implicit regularization in deep matrix factorization"
    - "implicit bias of gradient descent on linear convolutional networks"
    - "implicit regularization in deep learning"
    - "geometry of optimization and implicit regularization in deep learning"
    - "generalization properties and implicit regularization for multiple passes sgm"
    - "understanding deep learning requires rethinking generalization"
    - "in search of the real inductive bias on the role of implicit regularization in deep learning"

Connected through hyperedge HE-3 (induced by source paper "does learning require memorization a short tale about a long tail"):
  with members:
    - "learning imbalanced datasets with label distribution aware margin loss"
    - "two models of double descent for weak features"
    - "harmless interpolation of noisy data in regression"
    - "high probability generalization bounds for uniformly stable algorithms with nearly optimal rate"
    - "large scale fine grained categorization and domain specific transfer learning"
    - "towards demystifying membership inference attacks"
    - "dnn or k nn that is the generalize vs memorize question"
    - "privacy preserving prediction"

Connected through hyperedge HE-4 (induced by source paper "high probability generalization bounds for uniformly stable algorithms with nearly optimal rate"):
  with members:
    - "hypothesis set stability and generalization"
    - "generalization bounds for uniformly stable algorithms"
    - "privacy preserving prediction"
    - "tight analyses for non smooth stochastic gradient descent"
    - "statistical optimality of stochastic gradient descent on hard learning problems through multiple passes"
    - "data dependent stability of stochastic gradient descent"
    - "subgaussian tail bounds via stability arguments"
    - "concentration bounds for high sensitivity functions through differential privacy"

Connected through hyperedge HE-5 (induced by source paper "private stochastic convex optimization with optimal rates"):
  with members:
    - "high probability generalization bounds for uniformly stable algorithms with nearly optimal rate"
    - "differentially private empirical risk minimization revisited faster and more general"
    - "bolt on differential privacy for scalable stochastic gradient descent based analytics"
    - "statistical query algorithms for mean vector estimation and stochastic convex optimization"
    - "train faster generalize better stability of stochastic gradient descent"
    - "algorithmic stability for adaptive data analysis"
    - "preserving statistical validity in adaptive data analysis"
    - "differentially private empirical risk minimization efficient algorithms and tight error bounds"

Connected through hyperedge HE-6 (induced by source paper "stochastic approximation of smooth and strongly convex functions beyond the o 1 t convergence rate"):
  with members:
    - "a hitting time analysis of stochastic gradient langevin dynamics"
    - "empirical risk minimization for stochastic convex optimization o 1 n and o 1 n 2 type of risk bounds"
    - "memory and communication efficient distributed stochastic optimization with minibatch prox"
    - "from exp concavity to variance control high probability o 1 n rates and high probability online to batch conversion"
    - "escaping from saddle points online stochastic gradient for tensor decomposition"
    - "passive learning with target risk"
    - "stochastic gradient descent for non smooth optimization convergence results and optimal averaging schemes"
    - "making gradient descent optimal for strongly convex stochastic optimization"

Connected through hyperedge HE-7 (induced by source paper "generalization bounds for uniformly stable algorithms"):
  with members:
    - "high probability generalization bounds for uniformly stable algorithms with nearly optimal rate"
    - "privacy preserving prediction"
    - "data dependent stability of stochastic gradient descent"
    - "subgaussian tail bounds via stability arguments"
    - "concentration bounds for high sensitivity functions through differential privacy"
    - "a pac bayesian analysis of randomized learning with application to stochastic gradient descent"
    - "bolt on differential privacy for scalable stochastic gradient descent based analytics"
    - "on the generalization properties of differential privacy"

Connected through hyperedge HE-8 (induced by source paper "empirical risk minimization for stochastic convex optimization o 1 n and o 1 n 2 type of risk bounds"):
  with members:
    - "from exp concavity to variance control high probability o 1 n rates and high probability online to batch conversion"
    - "average stability is invariant to data preconditioning implications to exp concave empirical risk minimization"
    - "making gradient descent optimal for strongly convex stochastic optimization"
    - "optimistic rates for learning with a smooth loss"

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)