Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Toward a new AI winter? How diffusion of technological innovation on networks leads to chaotic boom-bust cycles

Sabin Roman, Francesco Bertolotti

TL;DR

The paper develops three dynamical models to explain techno-structural evolution and potential AI-related downturns: (1) a network diffusion model with logistic-like growth and diffusion-driven carrying capacity, (2) a three-variable business-cycle model, and (3) a networked market that couples diffusion and investment across technologies. Through analysis on homogeneous networks (e.g., random-regular graphs) and Lyapunov diagnostics, it demonstrates that high diffusion or investment can trigger transient chaotic boom-bust cycles and reproduces patterns observed in NFT markets and AI progress trajectories. A key finding is that these mechanisms can yield an AI winter-like regime even without external shocks, highlighting the fragility of hype-driven growth. The work also discusses policy implications—such as open standards, interoperability, and counter-cyclical funding—to stabilize diffusion and mitigate systemic risk in fast-evolving AI ecosystems.

Abstract

Technological developments and the impact of artificial intelligence (AI) are omnipresent themes and concerns of the present day. Much has been written on these topics but applications of quantitative models to understand the techno-social landscape have been much more limited. We propose a mathematical model that can help understand in a unified manner the patterns underlying technological development and also identify the different regimes in which the technological landscape evolves. First, we develop a model of innovation diffusion between different technologies, the growth of each reinforcing the development of the others. The model has a variable that quantifies the level of development (or innovation, discovery) potential for a given technology. The potential, or market capacity, increases via diffusion from related technologies, reflecting the fact that a technology does not develop in isolation. Hence, the growth of each technology is influenced by how developed its neighboring (related) technologies are. This allows us to reproduce long-term trends seen in computing technology and large language models (LLMs). We then present a three-dimensional system of supply, demand, and investment which shows oscillations (business cycles) emerging if investment is too high into a given technology, product, or market. We finally combine the two models through a common variable and show that if investment or diffusion is too high in the network context, chaotic boom-bust cycles can emerge. These quantitative considerations allow us to reproduce the boom-bust patterns seen in non-fungible token (NFT) transaction data and also have deep implications for the development of AI which we highlight, such as the arrival of a new AI winter.

Toward a new AI winter? How diffusion of technological innovation on networks leads to chaotic boom-bust cycles

TL;DR

The paper develops three dynamical models to explain techno-structural evolution and potential AI-related downturns: (1) a network diffusion model with logistic-like growth and diffusion-driven carrying capacity, (2) a three-variable business-cycle model, and (3) a networked market that couples diffusion and investment across technologies. Through analysis on homogeneous networks (e.g., random-regular graphs) and Lyapunov diagnostics, it demonstrates that high diffusion or investment can trigger transient chaotic boom-bust cycles and reproduces patterns observed in NFT markets and AI progress trajectories. A key finding is that these mechanisms can yield an AI winter-like regime even without external shocks, highlighting the fragility of hype-driven growth. The work also discusses policy implications—such as open standards, interoperability, and counter-cyclical funding—to stabilize diffusion and mitigate systemic risk in fast-evolving AI ecosystems.

Abstract

Technological developments and the impact of artificial intelligence (AI) are omnipresent themes and concerns of the present day. Much has been written on these topics but applications of quantitative models to understand the techno-social landscape have been much more limited. We propose a mathematical model that can help understand in a unified manner the patterns underlying technological development and also identify the different regimes in which the technological landscape evolves. First, we develop a model of innovation diffusion between different technologies, the growth of each reinforcing the development of the others. The model has a variable that quantifies the level of development (or innovation, discovery) potential for a given technology. The potential, or market capacity, increases via diffusion from related technologies, reflecting the fact that a technology does not develop in isolation. Hence, the growth of each technology is influenced by how developed its neighboring (related) technologies are. This allows us to reproduce long-term trends seen in computing technology and large language models (LLMs). We then present a three-dimensional system of supply, demand, and investment which shows oscillations (business cycles) emerging if investment is too high into a given technology, product, or market. We finally combine the two models through a common variable and show that if investment or diffusion is too high in the network context, chaotic boom-bust cycles can emerge. These quantitative considerations allow us to reproduce the boom-bust patterns seen in non-fungible token (NFT) transaction data and also have deep implications for the development of AI which we highlight, such as the arrival of a new AI winter.
Paper Structure (7 sections, 4 equations, 4 figures, 1 table)

This paper contains 7 sections, 4 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature review
  3. Model overview
  4. Experimental design
  5. Results
  6. Discussion
  7. Conclusion

Figures (4)

  • Figure 1: Evolution of (a) hardware performance in computing technologies rupp2021microprocessor. The figure is generated independently from the original data collected in 2010 by M. Horowitz, F. Labonte, O. Shacham, K. Olukotun, L. Hammond, and C. Batten, showing long-term trends in transistor counts, performance, frequency, power, and cores, and (b) software-driven progress in LLMs villalobos2024willwerunoutofdata, illustrating the rapid acceleration of AI capabilities. Technological growth through innovation diffusion in conditions of (c) high growth rates and low diffusion and inversely, low growth rates and high diffusion, and (d) a single stock with higher growth rate.
  • Figure 2: The dynamical behavior exhibited by the business cycle model \ref{['eq:2']}: (a) reaches a fixed point (steady state) when $\alpha < \alpha_{c}$, (b) sustained oscillation when $\alpha > \alpha_{c}$. (c) Stable limit cycle and trajectory in phase space. (d) Bifurcation diagram (black dots) and equilibrium values for the demand (solid green).
  • Figure 3: Market model \ref{['eq:3']} dynamics: (a) convergence to a steady state for $\alpha = \alpha_{0} = 10^{-3}$ and $\sigma = 10^{-3}$, (b) chaotic boom-bust cycles for $\alpha = 10^{-3}$ and $\sigma = 5\times 10^{-3}$, (c) steady-state regime (white) and chaotic boom-bust cycle (black). Qualitatively identical regime maps are obtained for quasi-regular and hub-dominated (scale-free-like) topologies; only the boundary shifts (lower in hub-dominated networks). (d) NFTs transactions data where the number of transactions serves as a proxy for demand.
  • Figure 4: (a) Plot of demand averages with different initial conditions, which differ by $10^{-2}$. (b) Computation of Lyapunov exponent with a positive value of $10^{-3}$, showing an exponentially growing distance between the trajectories. This indicates a chaotic regime for $\alpha = 10^{-3}$ and $\sigma = 5\times 10^{-3}$.