Notice is required contractually in some cases, and should be respected in the case that you are contractualy obligated to do so. You would have signed this agreement prior to employment if it is a pending agreement. In some cases employment contracts refer to other documents such as employee manuals, or employee policies which are not provided at the time of signing the contract. In this case signing that you recieved these documents may amend your employment contract after the fact.
In the case where notice is not contractualy an obligation because you signed an employment agreement with this provision, or local law does not demand notice you are pretty much on your own to decide. In general, companies do have another way to set policy on notice periods by their established procedures.
In some states if a company does not accept notice periods without ceasing to compensate the employee for it's endurance they may have no ability to legaly claim you gave no notice. In my state there is precedent in court for an employee suing, and winning damages for their former employer stating that the employee gave no notice when the company had some history of immediate dismissal upon recieveing notice.
I consider notice is established as required only when reasonably percieved to be something which is accepted by the employer. Accepting notice means you are paid, and your ending date is considered to be the date specified in your resignation letter. This would include for calculating benefits, vestings, training reimbursement period expirations, scheduled pay increases, etc. Beyond that, wait until you are vested, benefits are earned, training reimbursement periods are passed, and you get that last pay raise so you can claim it as your highest pay rate before you give notice.