The following lemma is standard in the literature, see e.g.

We study low-rank tensor-product B-spline (TPBS) models for regression tasks and investigate Dirichlet energy as a measure of smoothness. We show that TPBS models admit a closed-form expression for the Dirichlet energy, and reveal scenarios where perfect interpolation is possible with exponentially small Dirichlet energy. This renders global Dirichlet energy-based regularization ineffective. To address this limitation, we propose a novel regularization strategy based on local Dirichlet energies defined on small hypercubes centered at the training points. Leveraging pretrained TPBS models, we also introduce two estimators for inference from incomplete samples. Comparative experiments with neural networks demonstrate that TPBS models outperform neural networks in the overfitting regime for most datasets, and maintain competitive performance otherwise. Overall, TPBS models exhibit greater robustness to overfitting and consistently benefit from regularization, while neural networks are more sensitive to overfitting and less effective in leveraging regularization.

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We present a novel introspective variational autoencoder (IntroV AE) model for synthesizing high-resolution photographic images. IntroV AE is capable of self-evaluating the quality of its generated samples and improving itself accordingly. Its inference and generator models are jointly trained in an introspective way.

We thank the reviewers for their constructive feedback on our paper. Below we provide point-by-point response.

Previous work has investigated this problem under either full-information loss feedback with unknown transitions (Zhao et al., 2024), or bandit

Inter-GPU communication has become a major bottleneck for modern AI workloads as models scale and improvements in hardware compute throughput outpace improvements in interconnect bandwidth. Existing systems mitigate this through compute-communication overlap but often fail to meet theoretical peak performance across heterogeneous workloads and new accelerators. Instead of operator-specific techniques, we ask whether a small set of simple, reusable principles can systematically guide the design of optimal multi-GPU kernels. We present ParallelKittens (PK), a minimal CUDA framework that drastically simplifies the development of overlapped multi-GPU kernels. PK extends the ThunderKittens framework and embodies the principles of multi-GPU kernel design through eight core primitives and a unified programming template, derived from a comprehensive analysis of the factors that govern multi-GPU performance$\unicode{x2014}$data-transfer mechanisms, resource scheduling, and design overheads. We validate PK on both Hopper and Blackwell architectures. With fewer than 50 lines of device code, PK achieves up to $2.33 \times$ speedup for data- and tensor-parallel workloads, $4.08 \times$ for sequence-parallel workloads, and $1.22 \times$ for expert-parallel workloads.