Noise and the evolution of neural network modularity

Guiding Neuroevolution with Structural Objectives

The structure and performance of neural networks are intimately connected, and by use of evolutionary algorithms, neural network structures optimally adapted to a given task can be explored. Guiding such neuroevolution with additional objectives related to network structure has been shown to improve performance in some cases, especially when modular neural networks are beneficial. However, apart from objectives aiming to make networks more modular, such structural objectives have not been widely explored. We propose two new structural objectives and test their ability to guide evolving neural networks on two problems which can benefit from decomposition into subtasks. The first structural objective guides evolution to align neural networks with a user-recommended decomposition pattern. Intuitively, this should be a powerful guiding target for problems where human users can easily identify a structure. The second structural objective guides evolution towards a population with a high diversity in decomposition patterns. This results in exploration of many different ways to decompose a problem, allowing evolution to find good decompositions faster. Tests on our target problems reveal that both methods perform well on a problem with a very clear and decomposable structure. However, on a problem where the optimal decomposition is less obvious, the structural diversity objective is found to outcompete other structural objectives-and this technique can even increase performance on problems without any decomposable structure at all.

Can computational efficiency alone drive the evolution of modularity in neural networks?

Some biologists have abandoned the idea that computational efficiency in processing multipart tasks or input sets alone drives the evolution of modularity in biological networks. A recent study confirmed that small modular (neural) networks are relatively computationally-inefficient but large modular networks are slightly more efficient than non-modular ones. The present study determines whether these efficiency advantages with network size can drive the evolution of modularity in networks whose connective architecture can evolve. The answer is no, but the reason why is interesting. All simulations (run in a wide variety of parameter states) involving gradualistic connective evolution end in non-modular local attractors. Thus while a high performance modular attractor exists, such regions cannot be reached by gradualistic evolution. Non-gradualistic evolutionary simulations in which multi-modularity is obtained through duplication of existing architecture appear viable. Fundamentally, this study indicates that computational efficiency alone does not drive the evolution of modularity, even in large biological networks, but it may still be a viable mechanism when networks evolve by non-gradualistic means.

The relative efficiency of modular and non-modular networks of different size

Most biological networks are modular but previous work with small model networks has indicated that modularity does not necessarily lead to increased functional efficiency. Most biological networks are large, however, and here we examine the relative functional efficiency of modular and non-modular neural networks at a range of sizes. We conduct a detailed analysis of efficiency in networks of two size classes: ‘small’ and ‘large’, and a less detailed analysis across a range of network sizes. The former analysis reveals that while the modular network is less efficient than one of the two non-modular networks considered when networks are small, it is usually equally or more efficient than both non-modular networks when networks are large. The latter analysis shows that in networks of small to intermediate size, modular networks are much more efficient that non-modular networks of the same (low) connective density. If connective density must be kept low to reduce energy needs for example, this could promote modularity. We have shown how relative functionality/performance scales with network size, but the precise nature of evolutionary relationship between network size and prevalence of modularity will depend on the costs of connectivity.

Neural modularity helps organisms evolve to learn new skills without forgetting old skills

A long-standing goal in artificial intelligence is creating agents that can learn a variety of different skills for different problems. In the artificial intelligence subfield of neural networks, a barrier to that goal is that when agents learn a new skill they typically do so by losing previously acquired skills, a problem called catastrophic forgetting. That occurs because, to learn the new task, neural learning algorithms change connections that encode previously acquired skills. How networks are organized critically affects their learning dynamics. In this paper, we test whether catastrophic forgetting can be reduced by evolving modular neural networks. Modularity intuitively should reduce learning interference between tasks by separating functionality into physically distinct modules in which learning can be selectively turned on or off. Modularity can further improve learning by having a reinforcement learning module separate from sensory processing modules, allowing learning to happen only in response to a positive or negative reward. In this paper, learning takes place via neuromodulation, which allows agents to selectively change the rate of learning for each neural connection based on environmental stimuli (e.g. to alter learning in specific locations based on the task at hand). To produce modularity, we evolve neural networks with a cost for neural connections. We show that this connection cost technique causes modularity, confirming a previous result, and that such sparsely connected, modular networks have higher overall performance because they learn new skills faster while retaining old skills more and because they have a separate reinforcement learning module. Our results suggest (1) that encouraging modularity in neural networks may help us overcome the long-standing barrier of networks that cannot learn new skills without forgetting old ones, and (2) that one benefit of the modularity ubiquitous in the brains of natural animals might be to alleviate the problem of catastrophic forgetting.

A long-standing goal in artificial intelligence (AI) is creating computational brain models (neural networks) that learn what to do in new situations. An obstacle is that agents typically learn new skills only by losing previously acquired skills. Here we test whether such forgetting is reduced by evolving modular neural networks, meaning networks with many distinct subgroups of neurons. Modularity intuitively should help because learning can be selectively turned on only in the module learning the new task. We confirm this hypothesis: modular networks have higher overall performance because they learn new skills faster while retaining old skills more. Our results suggest that one benefit of modularity in natural animal brains may be allowing learning without forgetting.

Modular network evolution under selection for robustness to noise

Real networks often exhibit modularity, which is defined as the degree to which a network can be decomposed into several subnetworks. The question of how a modular network arises is still open to discussion. The leading hypothesis is that high modularity evolves under multiple goals, which are decomposable to subproblems, as well as under the evolutionary constraint that selection prefers sparse links in a network. In the present study, we investigate an alternative evolutionary constraint entailing increased robustness to noise. To examine this, we present noise-interfused network models involving an analytically solvable linear system and biologically inspired nonlinear systems. The models demonstrate that it is possible to evolve a modular network under both modularly changing goal orientations and enhancing robustness to noise, thereby reducing sensitivity to noise. By performing theoretical analyses of linear systems, it is shown that the evolutionary constraint enforces the establishment of well-balanced noise sensitivities of multiple noise sources and leads to a modular network underlying a modular structure in goals. Moreover, computer simulations confirm that the presented mechanisms of modular network evolution are robust to variations of nonlinearity in network functions. Our findings suggest a positive role for the presence of noise in network evolution.

Modularity-based graph partitioning using conditional expected models

Modularity-based partitioning methods divide networks into modules by comparing their structure against random networks conditioned to have the same number of nodes, edges, and degree distribution. We propose a novel way to measure modularity and divide graphs, based on conditional probabilities of the edge strength of random networks. We provide closed-form solutions for the expected strength of an edge when it is conditioned on the degrees of the two neighboring nodes, or alternatively on the degrees of all nodes comprising the network. We analytically compute the expected network under the assumptions of Gaussian and Bernoulli distributions. When the Gaussian distribution assumption is violated, we prove that our expression is the best linear unbiased estimator. Finally, we investigate the performance of our conditional expected model in partitioning simulated and real-world networks.