  It has long been believed that the brain is highly modular both in terms of
structure and function, although recent evidence has led some to question the
extent of both types of modularity. We used artificial neural networks to test
the hypothesis that structural modularity is sufficient to guarantee functional
specialization, and find that in general, this doesn't necessarily hold. We
then systematically tested which features of the environment and network do
lead to the emergence of specialization. We used a simple toy environment, task
and network, allowing us precise control, and show that in this setup, several
distinct measures of specialization give qualitatively similar results. We
further find that in this setup (1) specialization can only emerge in
environments where features of that environment are meaningfully separable, (2)
specialization preferentially emerges when the network is strongly
resource-constrained, and (3) these findings are qualitatively similar across
the different variations of network architectures that we tested, but that the
quantitative relationships depend on the precise architecture. Finally, we show
that functional specialization varies dynamically across time, and demonstrate
that these dynamics depend on both the timing and bandwidth of information flow
in the network. We conclude that a static notion of specialization, based on
structural modularity, is likely too simple a framework for understanding
intelligence in situations of real-world complexity, from biology to
brain-inspired neuromorphic systems. We propose that thoroughly stress testing
candidate definitions of functional modularity in simplified scenarios before
extending to more complex data, network models and electrophysiological
recordings is likely to be a fruitful approach.
