Semidefinite programs (SDPs) and their solvers are powerful tools with many
applications in machine learning and data science. Designing scalable SDP
solvers is challenging because by standard the positive semidefinite decision
variable is an $n \times n$ dense matrix, even though the input is often an $n
\times n$ sparse matrix. However, the information in the solution may not
correspond to a full-rank dense matrix as shown by Bavinok and Pataki. Two
decades ago, Burer and Monterio developed an SDP solver $\texttt{SDPLR}$ that
optimizes over a low-rank factorization instead of the full matrix. This
greatly decreases the storage cost and works well for many problems. The
original solver $\texttt{SDPLR}$ tracks only the primal infeasibility of the
solution, limiting the technique's flexibility to produce moderate accuracy
solutions. We use a suboptimality bound for trace-bounded SDP problems that
enables us to track the progress better and perform early termination. We then
develop $\texttt{SDPLR+}$, which starts the optimization with an extremely
low-rank factorization and dynamically updates the rank based on the primal
infeasibility and suboptimality. This further speeds up the computation and
saves the storage cost. Numerical experiments on Max Cut, Minimum Bisection,
Cut Norm, and Lov\'{a}sz Theta problems with many recent memory-efficient
scalable SDP solvers demonstrate its scalability up to problems with
million-by-million decision variables and it is often the fastest solver to a
moderate accuracy of $10^{-2}$.

通过低秩分解和子优度界限优化，加速计算并节省存储成本，实现可扩展的半正定规划求解器。

追踪有界 SDP 的非最优界限为 SDPLR + 提供了更快和可扩展的低秩 SDP 求解器

Suboptimality bounds for trace-bounded SDPs enable a faster and scalable  low-rank SDP solver SDPLR+

3D Gaussian Splatting is a new method for modeling and rendering 3D radiance
fields that achieves much faster learning and rendering time compared to SOTA
NeRF methods. However, it comes with a drawback in the much larger storage
demand compared to NeRF methods since it needs to store the parameters for
several 3D Gaussians. We notice that many Gaussians may share similar
parameters, so we introduce a simple vector quantization method based on
\kmeans algorithm to quantize the Gaussian parameters. Then, we store the small
codebook along with the index of the code for each Gaussian. Moreover, we
compress the indices further by sorting them and using a method similar to
run-length encoding. We do extensive experiments on standard benchmarks as well
as a new benchmark which is an order of magnitude larger than the standard
benchmarks. We show that our simple yet effective method can reduce the storage
cost for the original 3D Gaussian Splatting method by a factor of almost
$20\times$ with a very small drop in the quality of rendered images.

用基于 k-means 算法的简单向量量化方法和类似于游程编码的方法来减少 3D 高斯雨滴方法的存储成本，并在质量下降很小的情况下减少存储成本近 20 倍。

Compact3D: 压缩高斯散射辐射场模型与矢量量化

Compact3D: Compressing Gaussian Splat Radiance Field Models with Vector  Quantization

Video streams tremendously occupied the highest portion of online traffic.
Multiple versions of a video are created to fit the user's device
specifications. In cloud storage, Keeping all versions of frequently accessed
video streams in the repository for the long term imposes a significant cost
paid by video streaming providers. Generally, the popularity of a video changes
each period of time, which means the number of views received by a video could
be dropped, thus, the video must be deleted from the repository. Therefore, in
this paper, we develop a method that predicts the popularity of each video
stream in the repository in the next period. On the other hand, we propose an
algorithm that utilizes the predicted popularity of a video to compute the
storage cost, and then it decides whether the video will be kept or deleted
from the cloud repository. The experiment results show a cost reduction of the
cloud services by 15% compared to keeping all video streams.

提出算法对云存储仓库中不同视频流的受欢迎程度进行预测，根据预测结果决定是否从云存储中删除某些视频以降低存储成本，结果表明与保存所有视频流相比，云服务的成本降低了 15%。