I guess that depends on what "general description" means. Take Stellar Wind for example, as briefings were limited to the Gang of Eight. [1] I would like to know what the "general description" of that program was and what other members were informed of.
[1]: https://www.lawfaremedia.org/article/brief-history-programma...
The former is likely true. However, the lack of the latter, (which I assure you, is the case as SCI (Secret Compartmentalized Information) was developed specifically for that reason), sets an upper bound on the effective capabilities of anyone tasked with the job of oversight. You must be 10% smarter than that which you oversee to really do it effectively.
If you've ever chased down a memory leak, you'll understand what I mean. Senator Wyden cannot oversee the super secret Soylent Green program until somebody slips up enough to someone for word of a program that converts people to food to make it back to him to ask about.
They couldn't ask the question if they'd already signed the appropriate contracts on which access to SCI or other classified info is underpinned, If they had, asking the question would amount to a tacit disclosure.
Other Senators who have signed those documents have confirmed as much. Once the IC gets burned by you, even if they don't press charges due to political impossibility, you don't get invited to those parties anymore.