This is a general question.
Is there a general file type associated with AI projects?
Photoshop = .psd Excel = csv Artificial Intelligence = ?
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No, there is no file type associated with AI projects in general.
Your examples of Photoshop and Excel are specific corporate branded products. These store bespoke data that only works with those products (plus maybe a few converters that can read the files for competitor products).
Even more general examples such as
.jpg for images or
.txt for text documents are not a good match to AI in general. AI is such a broad field, it is next to impossible to define a standard set of components of an "AI project" in order to build a single file format that could handle the contents of all AI projects.
That said, practical work in AI is likely to include use of specific file formats and extensions, depending on what you do. For instance if you work with Python and TensorFlow you are likely to use
.py files for your source code,
.ckpt for neural network training checkpoints,
.pb for saved models. The last two extensions - ckpt and pb - are only semi-formal naming conventions though.
This lack of a single file extension, and use of maybe a dozen ones that you would be familiar with on a project, is true of most coding and software development work. If you work with an integrated devlopment environment (IDE), then you might have a single "master" file that allows you to load up all the resources in the project to work on them. That is entirely optional though, and may have any of a number of extensions depending on which IDE you use.
As a quick example, the Transformers project on github is a popular resource for natural language processing, a topic often considered as part of AI. A quick look at that project shows:
.or with various extensions -
.pyfiles for Python source code
.shextension or with extension removed for convenience of using on command line
.ipynbfiles used for Jupyter notebooks - a format that bundles documentation, Python scripts and their output for sharing work.