That's it! Antigonon leptopus. Thanks.

Thanks for all the help and suggestions. Their leaves and stem look more succulent than those of Lily of the Valley. I don't use mulch in this area but compost instead. And I noticed yesterday that the same kind of plant also grows near my compost pile which is in a shady area so it looks like they can grow in both sunny and shady areas. Another thing is they all bunch up together. Maybe I will just let them grow for a while and see if they will reveal themselves. Or I can post a more up-to-date photo later on. Please let me know if you think of other possibilities. Thanks again everyone.

Thank you very much for the ID's. The first one is near the spot where I saw the bad-looking P. mugo subsp. rotunda about which I asked an ID too. At first I though they were both the same species because they looked similar, but when I went too look closer then I could see the cones were definitely different. Funny part is that someone else suggested in that thread where I asked for an ID that it could be P. thunbergii. So I guess both trees are similar looking indeed. The second one I think comes from a hedge close-by that was (I think) never trimmed and therefore started producing cones. The third one is almost a miracle to me. Closest Abies koreana that I'm aware of is at least a few hundred meters away from where I found it. I'm very glad I dug it out too because A. koreana was also on my wanted list. :)

Ledebouria socialis--violet squill. I have a silver squill that looks just like yours but mine has tiny white flowers. This plant spreads fast and is SO easy to care for. Leona