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 except at extreme levels. 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 (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 different network architectures, but the quantitative relationships depends on the architecture type. 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 intelligent systems in situations of real-world complexity. 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.
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