Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 134 tok/s
Gemini 2.5 Pro 41 tok/s Pro
GPT-5 Medium 23 tok/s Pro
GPT-5 High 29 tok/s Pro
GPT-4o 79 tok/s Pro
Kimi K2 188 tok/s Pro
GPT OSS 120B 434 tok/s Pro
Claude Sonnet 4.5 37 tok/s Pro
2000 character limit reached

Topological Measurement of Deep Neural Networks Using Persistent Homology (2106.03016v1)

Published 6 Jun 2021 in cs.LG and cs.AI

Abstract: The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training process, and interpret their outputs. In this paper, we propose a novel approach to investigate the inner representation of DNNs through topological data analysis (TDA). Persistent homology (PH), one of the outstanding methods in TDA, was employed for investigating the complexities of trained DNNs. We constructed clique complexes on trained DNNs and calculated the one-dimensional PH of DNNs. The PH reveals the combinational effects of multiple neurons in DNNs at different resolutions, which is difficult to be captured without using PH. Evaluations were conducted using fully connected networks (FCNs) and networks combining FCNs and convolutional neural networks (CNNs) trained on the MNIST and CIFAR-10 data sets. Evaluation results demonstrate that the PH of DNNs reflects both the excess of neurons and problem difficulty, making PH one of the prominent methods for investigating the inner representation of DNNs.

Citations (13)

Summary

We haven't generated a summary for this paper yet.

Dice Question Streamline Icon: https://streamlinehq.com

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube