We employ unsupervised machine learning to enhance the accuracy of our
recently presented scaling method for wave confinement analysis [1]. We employ
the standard k-means++ algorithm as well as our own model-based algorithm. We
investigate cluster validity indices as a means to find the correct number of
confinement dimensionalities to be used as an input to the clustering
algorithms. Subsequently, we analyze the performance of the two clustering
algorithms when compared to the direct application of the scaling method
without clustering. We find that the clustering approach provides more
physically meaningful results, but may struggle with identifying the correct
set of confinement dimensionalities. We conclude that the most accurate outcome
is obtained by first applying the direct scaling to find the correct set of
confinement dimensionalities and subsequently employing clustering to refine
the results. Moreover, our model-based algorithm outperforms the standard
k-means++ clustering.

使用无监督机器学习方法优化了一种用于波束约束分析的扩展方法，通过聚类算法精确定位合适的约束维度，实验中发现模型算法表现更佳。

无监督机器学习分类周期超结构中波的约束

Unsupervised Machine Learning to Classify the Confinement of Waves in  Periodic Superstructures

We present a combined scaling method - named BASIC - that achieves 85.7%
top-1 accuracy on the ImageNet ILSVRC-2012 validation set without learning from
any labeled ImageNet example. This accuracy surpasses best published similar
models - CLIP and ALIGN - by 9.3%. Our BASIC model also shows significant
improvements in robustness benchmarks. For instance, on 5 test sets with
natural distribution shifts such as ImageNet-{A,R,V2,Sketch} and ObjectNet, our
model achieves 84.3% top-1 average accuracy, only a small drop from its
original ImageNet accuracy. To achieve these results, we scale up the
contrastive learning framework of CLIP and ALIGN in three dimensions: data
size, model size, and batch size. Our dataset has 6.6B noisy image-text pairs,
which is 4x larger than ALIGN, and 16x larger than CLIP. Our largest model has
3B weights, which is 3.75x larger in parameters and 8x larger in FLOPs than
ALIGN and CLIP. Finally, our batch size is 65536 which is 2x more than CLIP and
4x more than ALIGN. We encountered two main challenges with the scaling rules
of BASIC. First, the main challenge with implementing the combined scaling
rules of BASIC is the limited memory of accelerators, such as GPUs and TPUs. To
overcome the memory limit, we propose two simple methods which make use of
gradient checkpointing and model parallelism. Second, while increasing the
dataset size and the model size has been the defacto method to improve the
performance of deep learning models like BASIC, the effect of a large
contrastive batch size on such contrastive-trained image-text models is not
well-understood. To shed light on the benefits of large contrastive batch
sizes, we develop a theoretical framework which shows that larger contrastive
batch sizes lead to smaller generalization gaps for image-text models such as
BASIC.

研究使用 BASIC 方法将对比学习框架在三个方面进行扩展：数据规模、模型规模和批次大小，并取得了对比学习模型的极高准确性和健壮性。