GPU Accelerated Computation of VR Barcodes in Evaluating Deep Learning Models

Explore GPU-accelerated computation of Vietoris-Rips barcodes and their applications in evaluating deep learning models in this 56-minute conference talk. Delve into the challenges of GPU acceleration after Moore's Law's end, its necessity in deep learning, and the development of Ripser++, a GPU-accelerated software for computing VR barcodes. Discover how Ripser++ has been applied to measure shifts between generated and real data distributions under the manifold hypothesis. Learn about the simplex-wise flag filtration, persistent homology, and efficient persistent pair hashmaps. Investigate the use of topology in deep learning model evaluation, including MTop-Divergence properties and experiments. Examine computational aspects, distribution shift detection, and the application of VR barcodes to attention graphs in BERT models. Gain insights into cutting-edge techniques bridging topological data analysis and machine learning.

Intro
GPU Acceleration after the End of Moore
Challenges to achieve GPU acceleration
GPUs in Deep Learning
The Simplex-wise Flag Filtration
Persistent homology: Birth and Death for of the C. elegans Dataset
Design Goals for High Performance
Efficient Persistent Pair Hashmap
Filtration Construction with Clearing is jus Filtering and Sorting Problem
Why do we need Ripser++
What is a Generative Adversarial Network
Deep learning model evaluation: using topology
MTop-Divergence Properties
Computational aspect of MTopDiv
Experiments with MTopDiv
Detecting distribution shifts
Computational considerations
Conclusion
VR barcodes of attention graphs as feature • Pretrained or finetuned BERT model with pretrained Key, Query Weight matrices. For each head compute the matrix of pairwise self attention