Why do networks have inhibitory/negative connections?
This provides a foundational theoretical explanation for a core aspect of neural network design, relevant to both machine learning and neuroscience.
The paper tackles the problem of why neural networks and brains require inhibitory or negative connections, concluding that negative weights are essential for universal approximation, as networks with only non-negative weights and non-decreasing activations cannot represent all functions.
Why do brains have inhibitory connections? Why do deep networks have negative weights? We propose an answer from the perspective of representation capacity. We believe representing functions is the primary role of both (i) the brain in natural intelligence, and (ii) deep networks in artificial intelligence. Our answer to why there are inhibitory/negative weights is: to learn more functions. We prove that, in the absence of negative weights, neural networks with non-decreasing activation functions are not universal approximators. While this may be an intuitive result to some, to the best of our knowledge, there is no formal theory, in either machine learning or neuroscience, that demonstrates why negative weights are crucial in the context of representation capacity. Further, we provide insights on the geometric properties of the representation space that non-negative deep networks cannot represent. We expect these insights will yield a deeper understanding of more sophisticated inductive priors imposed on the distribution of weights that lead to more efficient biological and machine learning.