<transcript><audio_35>so we can clear the first square row and updates in the list and anytime we want to get a single proof we just need to extract the single proof here and</transcript><transcript><audio_36>apply those update requests in this new list and get the single proof so actually this amortized</transcript><transcript><audio_37>case can be improved to worst case and actually we can also set a parameter here to deal with the situation if the aggregation set is always very large or always very small</transcript><transcript><audio_38>so it's just a balance of it's just a trade-off between uh update all and and actually uh we go we can see the uh table from hyperproofs and</transcript><transcript><audio_39>many of our vector commitment schemes which has a login or unlocking square time to open oral can be applied to our compiler and we can get a new vector scheme</transcript><transcript><audio_40>and as long as it has a log and polylog time to open or and it has aggregation time so that's all for this</transcript><transcript><audio_41>compiler and actually if we just use this greater log assumption i kind of believe that if we can improve this uh</transcript><transcript><audio_42>i mean if we can improve this uh if we can improve this uh compiler we can actually improve the algorithm of fmt which means fft is something like this uh</transcript><transcript><audio_43>some something of convolution computation and the update part is actually uh arbitrarily updated some of the of one function and the get one single proof is</transcript> so we can clear the first square row and updates in the list and anytime we want to get a single proof we just need to extract the single proof here and apply those update requests in this new list and get the single proof so actually this amortized case can be improved to worst case and actually we can also set a parameter here to deal with the situation if the aggregation set is always very large or always very small so it's just a balance of it's just a trade-off between uh update all and and actually uh we go we can see the uh table from hyperproofs and many of our vector commitment schemes which has a login or unlocking square time to open oral can be applied to our compiler and we can get a new vector scheme and as long as it has a log and polylog time to open or and it has aggregation time so that's all for this compiler and actually if we just use this greater log assumption i kind of believe that if we can improve this uh i mean if we can improve this uh if we can improve this uh compiler we can actually improve the algorithm of fmt which means fft is something like this uh some something of convolution computation and the update part is actually uh arbitrarily updated some of the of one function and the get one single proof is
{"source": "grass-yt-cc-by.-rZTckp-Urw|shard_10005_10|create_multimodal_data.extract_yt_and_generate_transcripts.28|shard_10005|create_multimodal_data.generate_captions.28|shard_10005|create_multimodal_data.generate_captions.28", "params": {"id": "-rZTckp-Urw", "channel_id": "UCJvMzILpV3b4AWXTEeQjcng", "duration": 780, "view_count": 103, "age_limit": 0, "like_count": 1, "channel_follower_count": 8710, "license": "Creative Commons Attribution license (reuse allowed)", "uploader_id": "@ProtocolLabs", "yt_tar_file": "/leonardo_work/EUHPC_E03_068/audio/fixed_download/grass-yt-cc-by//shard_10005/-rZTckp-Urw.tar.gz"}}