The OED I have suggests that 'up to date' be without hyphens when it is used as an adverb, but be 'up-to-date' with hyphens when used as an adjective. Also 'up-dately', 'up-to-datish', 'up-to-dateness' and 'up-to-datism'.
Hope it heps
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I myself would follow your example in both cases:
1. 'Up-to-date information' – used as an adjective before a noun: hyphenated.
2. 'Stay up to date!' – elsewhere: not hyphenated.
Others may differ.