The mathematical structure of innovation

Innovation is the driving force of human progress. Recent urn models reproduce well the dynamics through which the discovery of a novelty may trigger further ones, in an expanding space of opportunities, but neglect the effects of social interactions. Here we focus on the mechanisms of collective exploration and we propose a model in which many urns, representing different explorers, are coupled through the links of a social network and exploit opportunities coming from their...

Technology is essential to innovation and economic prosperity. Understanding technological changes can guide innovators to find new directions of design innovation and thus make breakthroughs. In this work, we construct a technology fitness landscape via deep neural embeddings of patent data. The landscape consists of 1,757 technology domains and their respective improvement rates. In the landscape, we found a high hill related to information and communication technologies (I...

We reconstruct the innovation dynamics of about two hundred thousand companies by following their patenting activity for about ten years. We define the technological portfolios of these companies as the set of the technological sectors present in the patents they submit. By assuming that companies move more frequently towards related sectors, we leverage on their past activity to build network-based and machine learning algorithms to forecast the future submission of patents ...

Different technological domains have significantly different rates of performance improvement. Prior theory indicates that such differing rates should influence the relative speed of diffusion of the products embodying the different technologies since improvement in performance during the diffusion process increases the desirability of the product diffusing. However, there has not been a broad empirical attempt to examine this effect and to clarify the underlying cause. There...

Empirical research has shown performance improvement of many different technological domains occurs exponentially but with widely varying improvement rates. What causes some technologies to improve faster than others do? Previous quantitative modeling research has identified artifact interactions, where a design change in one component influences others, as an important determinant of improvement rates. The models predict that improvement rate for a domain is proportional to ...

In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a non-linear system. We refer to the theory of complex networks and introduce the notion of sensitive networks. Sensitive networks are networks in which the introduction or the removal of a node/vertex dramatically changes the dynamic structu...

We study the empirical relationship between green technologies and industrial production at very fine-grained levels by employing Economic Complexity techniques. Firstly, we use patent data on green technology domains as a proxy for competitive green innovation and data on exported products as a proxy for competitive industrial production. Secondly, with the aim of observing how green technological development trickles down into industrial production, we build a bipartite dir...

We study a model of innovation with a large number of firms that create new technologies by combining several discrete ideas. These ideas are created via private investment and spread between firms. Firms face a choice between secrecy, which protects existing intellectual property, and openness, which facilitates learning from others. Their decisions determine interaction rates between firms, and these interaction rates enter our model as link probabilities in a learning netw...

Advanced economies exhibit a high degree of sophistication in the creation of various products. While critical to such sophistication, the nature and underlying structure of the interactions taking place inside production processes remain opaque when studying large systems such as industries or entire economies. Using partial information decomposition, we quantify the nature of these interactions, allowing us to infer how much innovation stems form specific input interactions...

The purpose of this study is to investigate the structure and evolution of knowledge spillovers across technological domains. Specifically, dynamic patterns of knowledge flow among 29 technological domains, measured by patent citations for eight distinct periods, are identified and link prediction is tested for capability for forecasting the evolution in these cross-domain patent networks. The overall success of the predictions using the Katz metric implies that there is a te...