The evolutionary origins of hierarchy

Hierarchical organization -- the recursive composition of sub-modules -- is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force--the cost of connections--promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.Comment: 32 page

Hi-Val: Iterative Learning of Hierarchical Value Functions for Policy Generation

Task decomposition is effective in manifold applications where the global complexity of a problem makes planning and decision-making too demanding. This is true, for example, in high-dimensional robotics domains, where (1) unpredictabilities and modeling limitations typically prevent the manual specification of robust behaviors, and (2) learning an action policy is challenging due to the curse of dimensionality. In this work, we borrow the concept of Hierarchical Task Networks (HTNs) to decompose the learning procedure, and we exploit Upper Confidence Tree (UCT) search to introduce HOP, a novel iterative algorithm for hierarchical optimistic planning with learned value functions. To obtain better generalization and generate policies, HOP simultaneously learns and uses action values. These are used to formalize constraints within the search space and to reduce the dimensionality of the problem. We evaluate our algorithm both on a fetching task using a simulated 7-DOF KUKA light weight arm and, on a pick and delivery task with a Pioneer robot

Hierarchical Multi-resolution Mesh Networks for Brain Decoding

We propose a new framework, called Hierarchical Multi-resolution Mesh Networks (HMMNs), which establishes a set of brain networks at multiple time resolutions of fMRI signal to represent the underlying cognitive process. The suggested framework, first, decomposes the fMRI signal into various frequency subbands using wavelet transforms. Then, a brain network, called mesh network, is formed at each subband by ensembling a set of local meshes. The locality around each anatomic region is defined with respect to a neighborhood system based on functional connectivity. The arc weights of a mesh are estimated by ridge regression formed among the average region time series. In the final step, the adjacency matrices of mesh networks obtained at different subbands are ensembled for brain decoding under a hierarchical learning architecture, called, fuzzy stacked generalization (FSG). Our results on Human Connectome Project task-fMRI dataset reflect that the suggested HMMN model can successfully discriminate tasks by extracting complementary information obtained from mesh arc weights of multiple subbands. We study the topological properties of the mesh networks at different resolutions using the network measures, namely, node degree, node strength, betweenness centrality and global efficiency; and investigate the connectivity of anatomic regions, during a cognitive task. We observe significant variations among the network topologies obtained for different subbands. We, also, analyze the diversity properties of classifier ensemble, trained by the mesh networks in multiple subbands and observe that the classifiers in the ensemble collaborate with each other to fuse the complementary information freed at each subband. We conclude that the fMRI data, recorded during a cognitive task, embed diverse information across the anatomic regions at each resolution.Comment: 18 page

Quantifying the vanishing gradient and long distance dependency problem in recursive neural networks and recursive LSTMs

Recursive neural networks (RNN) and their recently proposed extension recursive long short term memory networks (RLSTM) are models that compute representations for sentences, by recursively combining word embeddings according to an externally provided parse tree. Both models thus, unlike recurrent networks, explicitly make use of the hierarchical structure of a sentence. In this paper, we demonstrate that RNNs nevertheless suffer from the vanishing gradient and long distance dependency problem, and that RLSTMs greatly improve over RNN's on these problems. We present an artificial learning task that allows us to quantify the severity of these problems for both models. We further show that a ratio of gradients (at the root node and a focal leaf node) is highly indicative of the success of backpropagation at optimizing the relevant weights low in the tree. This paper thus provides an explanation for existing, superior results of RLSTMs on tasks such as sentiment analysis, and suggests that the benefits of including hierarchical structure and of including LSTM-style gating are complementary