1. An apparatus, comprising: a plurality of processor cores, each comprising a computation unit and a memory; and an interconnection network to transmit data among the processor cores; with one or more of the memories each configured as a cache for storing cached data from memory external to the processor cores, and one or more of the processor cores configured to transmit a message over the interconnection network to access a cache of another processor core; and with at least some of the processor cores configured to operate in a first mode in which valid data from a given external memory address are stored in at most one of the caches, and a second mode in which valid data from a given external memory address are coherently updated in a plurality of the caches; and in the first mode, a set of multiple memory pages are cached in caches of multiple processor cores, with each memory page stored in a cache of at most one home processor core of the multiple processor cores, and a first home processor core that stores a first memory page is configured to access a cache line of the first memory page from its own cache, and processor cores other than the first home processor core are configured to access a cache line of the first memory page by transmitting a message over the interconnection network to access the cache of the first home processor core.