Ultralight Bicycle Touring
Touring ultralight on a bicycle makes sense for mixed terrain touring since lots of climbing is usual. Unlike flat land touring which is often fully loaded, every pound carried in the alpine environment comes with a penalty.

Ultralight touring is wholistic. Not only a bike's weight considered, paring the entire load is essential. The entire load or traveling system consists of bicycle, rider and gear.

Bicycle
Bicycles are a balance between weight reduction and durability. A mixed terrain all-rounder bike needs to be durable, but must also be fairly light. Production touring bikes are often around 27-29 lbs. These bikes are great for fully loaded touring and with a few modifications can be used for mixed terrain touring. But they are heavy for ultralight touring. Today's mountain bikes with suspension also tend to be in this same weight range.

A bike specifically designed for ultralight mixed terrain touring can be durable enough yet weight around 21-25 lbs. Much lighter with today's technology and the bike will not be durable enough. To get within this weight range one must start with a fairly light frame (3.5-4.5 lbs). Lightweight wheels under 4 lbs for the set help. So does going tubeless. But choose tires carefully, there's a big difference in tire weights. A well considered tire/wheel system can shave a couple pounds off a bike. Which is a bid deal considering saving rotational weight (spinning on the outside of a tire/wheel) has about a 2 to 1 advantage over other weight.

Checking each part's weight and exploring options can help find weight savings in surprising ways. But the biggest savings probably comes from keeping the bike simple. Don't add a front rack and use the simplest, lightest rear rack available since the gear carried for ultralight touring will be minimal anyway.

Rider
Perhaps the biggest place to shave weight is from the rider. Of course this includes clothes and shoes. But body weight is the most important. Shedding excess body weight not only saves on weight hauled, but also increases the rider's performance.

With clothing and shoes, its best to choose a system that covers any likely weather situation with the least amount of items. Layering is important. Considering item weights is also imperative since there's a lot of variability.

Consider not using SPD or another clipless pedal system. Not only can you find substantially lighter platform pedals (with clips or power straps) but you don't need specialized shoes. You definitely need a good pair of shoes in case of hiking, so specialized bike shoes would require carrying 2 pairs.

Gear
Ultralight bicycle tourers try to keep their gear load down to around 20 lbs. Of course this takes considerable planning of gear and route.