Non-linear inhibitory responses enhance performance in collective decision-making

TL;DR

This work tackles how non-linear inhibitory signaling shapes decentralized binary decisions in a honeybee-inspired model. It introduces sigmoid-like cross-inhibition within the LES mean-field framework and complements analytic fixed-point analysis with stochastic simulations to quantify consensus quality and decision speed. The key finding is that non-linear cross-inhibition improves consensus strength and markedly reduces deliberation time, at the cost of reduced accuracy in selecting the best option, especially when options are similar; the effect is robust across system sizes and discovery noise and has potential applications in swarm robotics. The study provides a general mechanism for time-independent non-linear inhibition to enhance rapid, robust collective decisions and outlines a path for experimental validation in robotic swarms.

Abstract

The precise modulation of activity through inhibitory signals ensures that both insect colonies and neural circuits operate efficiently and adaptively, highlighting the fundamental importance of inhibition in biological systems. Modulatory signals are produced in various contexts and are known for subtly shifting the probability of receiver behaviors based on response thresholds. Here we propose a non-linear function to introduce inhibitory responsiveness in collective decision-making inspired by honeybee house-hunting. We show that, compared with usual linear functions, non-linear responses enhance final consensus and reduce deliberation time. This improvement comes at the cost of reduced accuracy in identifying the best option. Nonetheless, for value-based tasks, the benefits of faster consensus and enhanced decision-making might outweigh this drawback.

Figures (5)

• Figure 1: Non-linear inhibitory responses and their effects on collective decision-making.(a): Strength of the cross-inhibition non-linear responses as a function of the population fraction that is sending the inhibitory signals, $f_\beta$. Different lines represent responses that will be studied throughout the text, separated into two panels for clarity. On the left, a smooth sigmoid, $\sigma_1(f_\beta; x_0 = 0.333, a = 20)$ (light blue), and a sharp sigmoid $\sigma_1(f_\beta; x_0 = 0.3, a = 500)$ (dark blue), are depicted. On the right a smooth linearly bounded sigmoid, $\sigma_2(f_\beta; x_0 = 0.3, a = 10)$ (light red), and a sharp linearly bounded sigmoid $\sigma_2(f_\beta; x_0 = 0.3, a = 500)$ (dark red), are depicted. The parameter $x_0$ controls the ascent of the sigmoid and the parameter $a$ controls the smoothness of the ascent (see Eq. \ref{['definitive:eq:sigmas']} for more details). The black dotted line indicates a linear cross-inhibition response. (b): Bifurcation diagrams on increasing interdependence $\lambda$ for linear cross-inhibition (black circles), a sharp sigmoid cross-inhibition function $\sigma_1(f_\beta;x_0 = 0.3,a=500)$ (blue squares), and a smooth bounded sigmoid function $\sigma_2(f_\beta;x_0=0.3,a=10)$
• Figure 2: Comparison between linear and non-linear cross-inhibition responses in a binary-decision problem.(a): Occupation fraction for the best-quality site, $f_2^*$. (b): Probability of reaching the best option, $P(f_2^*)$. (c): Time to settle into the stationary state, $t_{ss}$. Other model parameters are $\pi_1 = \pi_2 = 0.1$, $q_1 = 9$, $q_2 = 10$, and $\lambda'=1$, for a system of size $N=1000$. Error bars indicate the standard error of the mean.
• Figure 3: Performance of non-linear cross-inhibition responses under varying interdependence. Performance ratio $\chi$ of non-linear cross-inhibitory responses on increasing interdependence $\lambda$, in a binary-choice scenario. Three quality pairs are represented in (a): $(q_1 = 8,q_2 = 10)$, (b): $(q_1 = 9,q_2 = 10)$ and (c): $(q_1 = 9.5,q_2 = 10)$. Other model parameters are $\pi_1 = \pi_2 = 0.1$, $\lambda'=1$ and system size $N = 1000$. Error bars indicate the propagated standard error of the mean.
• Figure 4: Performance of a non-linear cross-inhibition response with varying system size. Performance ratio $\chi$ of the sharp sigmoid non-linear cross-inhibition response $\sigma_1 (x_0 = 0.3, a = 500)$ on increasing interdependence $\lambda$ for different system sizes $N$. Other model parameters are $\pi_1 = \pi_2 = 0.1$, $\lambda'=1$, $q_2 = 10$, and $q_1 = 8$ (a) and $q_1 = 9.5$ (b), as indicated in each plot. Error bars indicate the propagated standard error of the mean. The inset in panel (a) shows the non-linear cross-inhibition function used, indicating the cross-inhibition strength $\sigma$ as a function of the inhibiting population $f_\beta$.
• Figure 5: Performance of non-linear cross-inhibition responses under varying options' discovery probabilities. Performance ratio $\chi$ of non-linear cross-inhibition responses as a function of spontaneous discovery probabilities $\pi_1 = \pi_2 \equiv \pi_{1,2}$, in a binary-decision choice. Other parameters are $q_1 = 9$, $q_2 = 10$, $\lambda = 0.6$, $\lambda'=1$ and $N = 1000$. Error bars indicate the propagated standard error of the mean.