Final answer:
The sense of smell, or olfactory information, bypasses the thalamus and connects directly to the cerebrum.
Step-by-step explanation:
The type of sensory information that is NOT routed through the thalamus on its way to the cerebrum is olfactory information. The olfactory system, associated with the sense of smell, has a direct connection to the cerebrum without the intermediation of the thalamus. This exception is rooted in evolutionary biology, as the cerebrum in early vertebrates primarily processes chemical information from the environment, which is akin to the sense of smell.