We propose that a tree-like hierarchical structure represents a simple and effective way to model the emergent behaviour of financial markets, especially markets where there exists a pronounced intersection between social media influences and investor behaviour. To explore this hypothesis, we introduce an agent-based model of financial markets, where trading agents are embedded in a hierarchical network of communities, and communities influence the strategies and opinions of traders. Empirical analysis of the model shows that its behaviour conforms to several stylized facts observed in real financial markets; and the model is able to realistically simulate the effects that social media-driven phenomena, such as echo chambers and pump-and-dump schemes, have on financial markets.

Structural modularity is a pervasive feature of biological neural networks, which have been linked to several functional and computational advantages. Yet, the use of modular architectures in artificial neural networks has been relatively limited despite early successes. Here, we explore the performance and functional dynamics of a modular network trained on a memory task via an iterative growth curriculum. We find that for a given classical, non-modular recurrent neural network (RNN), an equivalent modular network will perform better across multiple metrics, including training time, generalizability, and robustness to some perturbations. We further examine how different aspects of a modular network's connectivity contribute to its computational capability. We then demonstrate that the inductive bias introduced by the modular topology is strong enough for the network to perform well even when the connectivity within modules is fixed and only the connections between modules are trained. Our findings suggest that gradual modular growth of RNNs could provide advantages for learning increasingly complex tasks on evolutionary timescales, and help build more scalable and compressible artificial networks.

Manufacturing energy consumption data contains important process signatures required for operational visibility and diagnostics. These signatures may be of different temporal scales, ranging from monthly to sub-second resolutions. We introduce a hierarchical machine learning approach to identify automotive process signatures from paint shop electricity consumption data at varying temporal scales (weekly and daily). A Multi-Layer Perceptron (MLP), a Convolutional Neural Network (CNN), and Principal Component Analysis (PCA) combined with Logistic Regression (LR) are used for the analysis. We validate the utility of the developed algorithms with subject matter experts for (i) better operational visibility, and (ii) identifying energy saving opportunities.

This paper presents an approach for constructing multifidelity surrogate models to simultaneously represent, and learn representations of, multiple information sources. The approach formulates a network of surrogate models whose relationships are defined via localized scalings and shifts. The network can have general structure, and can represent a significantly greater variety of modeling relationships than the hierarchical/recursive networks used in the current state of the art. We show empirically that this flexibility achieves greatest gains in the low-data regime, where the network structure must more efficiently leverage the connections between data sources to yield accurate predictions. We demonstrate our approach on four examples ranging from synthetic to physics-based simulation models. For the numerical test cases adopted here, we obtained an order-of-magnitude reduction in errors compared to multifidelity hierarchical and single-fidelity approaches.

The information contained in hierarchical topology, intrinsic to many networks, is currently underutilised. A novel architecture is explored which exploits this information through a multiscale decomposition. A dendrogram is produced by a Girvan-Newman hierarchical clustering algorithm. It is segmented and fed through graph convolutional layers, allowing the architecture to learn multiple scale latent space representations of the network, from fine to coarse grained. The architecture is tested on a benchmark citation network, demonstrating competitive performance. Given the abundance of hierarchical networks, possible applications include quantum molecular property prediction, protein interface prediction and multiscale computational substrates for partial differential equations.

This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and non-linear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and we give explicit proofs of how the resulting representation allows for scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.

Matrix Factorization (MF) is a common method for generating recommendations, where the proximity of entities like users or items in the embedded space indicates their similarity to one another. Though almost all applications implicitly use a Euclidean embedding space to represent two entity types, recent work has suggested that a hyperbolic Poincar\'e ball may be more well suited to representing multiple entity types, and in particular, hierarchies. We describe a novel method to embed a hierarchy of related music entities in hyperbolic space. We also describe how a parametric empirical Bayes approach can be used to estimate link reliability between entities in the hierarchy. Applying these methods together to build personalized playlists for users in a digital music service yielded a large and statistically significant increase in performance during an A/B test, as compared to the Euclidean model.

Filter banks are a popular tool for the analysis of piecewise smooth signals such as natural images. Motivated by the empirically observed properties of scale and detail coefficients of images in the wavelet domain, we propose a hierarchical deep generative model of piecewise smooth signals that is a recursion across scales: the low pass scale coefficients at one layer are obtained by filtering the scale coefficients at the next layer, and adding a high pass detail innovation obtained by filtering a sparse vector. This recursion describes a linear dynamic system that is a non-Gaussian Markov process across scales and is closely related to multilayer-convolutional sparse coding (ML-CSC) generative model for deep networks, except that our model allows for deeper architectures, and combines sparse and non-sparse signal representations. We propose an alternating minimization algorithm for learning the filters in this hierarchical model given observations at layer zero, e.g., natural images. The algorithm alternates between a coefficient-estimation step and a filter update step. The coefficient update step performs sparse (detail) and smooth (scale) coding and, when unfolded, leads to a deep neural network. We use MNIST to demonstrate the representation capabilities of the model, and its derived features (coefficients) for classification.