If you value social authentication more than the regular approach, it's better to have social log in logos as CTAs (buttons instead of only logos; e.g. Airbnb), and at the top.
Also, studies has shown that labels for input fields perform the best at the top of its respective field. I'd prefer having placeholders to save space.
I would also suggest you to separate log in and sign up from each other, as it may easily confuse your users having two submit buttons. Best-practice for this can be either Tab approach like in SoundCloud authentication:
PS: I advise you to try to keep consistency with your copy. For example, you have both "LOG IN" and "Login". And, take how and where to display error messages, for example in case of a failed log in or invalid email address etc...