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You can train a custom extraction model in Azure AI Document Intelligence without setting your container access level to public. To securely provide access, you can use a Shared Access Signature (SAS) token. A SAS token allows you to grant temporary, limited access to your private storage container by appending it to the storage URL. Alternatively, if your Document Intelligence resource is in the same Azure subscription, you can assign it the Storage Blob Data Reader role via Managed Identity, enabling secure access without exposing credentials. This ensures compliance with security policies while allowing the training process to proceed.
Please refer: Create SAS tokens for storage containers.
I hope this helps. Thank you.