Quantifying the biomimicry gap in biohybrid systems

Biohybrid systems in which robotic lures interact with animals have become compelling tools for probing and identifying the mechanisms underlying collective animal behavior. One key challenge lies in the transfer of social interaction models from simulations to reality, using robotics to validate the modeling hypotheses. This challenge arises in bridging what we term the "biomimicry gap", which is caused by imperfect robotic replicas, communication cues and physics constrains not incorporated in the simulations that may elicit unrealistic behavioral responses in animals. In this work, we used a biomimetic lure of a rummy-nose tetra fish (Hemigrammus rhodostomus) and a neural network (NN) model for generating biomimetic social interactions. Through experiments with a biohybrid pair comprising a fish and the robotic lure, a pair of real fish, and simulations of pairs of fish, we demonstrate that our biohybrid system generates high-fidelity social interactions mirroring those of genuine fish pairs. Our analyses highlight that: 1) the lure and NN maintain minimal deviation in real-world interactions compared to simulations and fish-only experiments, 2) our NN controls the robot efficiently in real-time, and 3) a comprehensive validation is crucial to bridge the biomimicry gap, ensuring realistic biohybrid systems.

Predicting long-term collective animal behavior with deep learning

Deciphering the social interactions that govern collective behavior in animal societies has greatly benefited from advancements in modern computing. Computational models diverge into two kinds of approaches: analytical models and machine learning models. This work introduces a deep learning model for social interactions in the fish species Hemigrammus rhodostomus, and compares its results to experiments and to the results of a state-of-the-art analytical model. To that end, we propose a systematic methodology to assess the faithfulness of a model, based on the introduction of a set of stringent observables. We demonstrate that machine learning models of social interactions can directly compete against their analytical counterparts. Moreover, this work demonstrates the need for consistent validation across different timescales and highlights which design aspects critically enables our deep learning approach to capture both short- and long-term dynamics. We also show that this approach is scalable to other fish species.

Parameter-free Statistically Consistent Interpolation: Dimension-independent Convergence Rates for Hilbert kernel regression

Previously, statistical textbook wisdom has held that interpolating noisy data will generalize poorly, but recent work has shown that data interpolation schemes can generalize well. This could explain why overparameterized deep nets do not necessarily overfit. Optimal data interpolation schemes have been exhibited that achieve theoretical lower bounds for excess risk in any dimension for large data (Statistically Consistent Interpolation). These are non-parametric Nadaraya-Watson estimators with singular kernels. The recently proposed weighted interpolating nearest neighbors method (wiNN) is in this class, as is the previously studied Hilbert kernel interpolation scheme, in which the estimator has the form $\hat{f}(x)=\sum_i y_i w_i(x)$, where $w_i(x)= \|x-x_i\|^{-d}/\sum_j \|x-x_j\|^{-d}$. This estimator is unique in being completely parameter-free. While statistical consistency was previously proven, convergence rates were not established. Here, we comprehensively study the finite sample properties of Hilbert kernel regression. We prove that the excess risk is asymptotically equivalent pointwise to $\sigma^2(x)/\ln(n)$ where $\sigma^2(x)$ is the noise variance. We show that the excess risk of the plugin classifier is less than $2|f(x)-1/2|^{1-\alpha}\,(1+\varepsilon)^\alpha \sigma^\alpha(x)(\ln(n))^{-\frac{\alpha}{2}}$, for any $0<\alpha<1$, where $f$ is the regression function $x\mapsto\mathbb{E}[y|x]$. We derive asymptotic equivalents of the moments of the weight functions $w_i(x)$ for large $n$, for instance for $\beta>1$, $\mathbb{E}[w_i^{\beta}(x)]\sim_{n\rightarrow \infty}((\beta-1)n\ln(n))^{-1}$. We derive an asymptotic equivalent for the Lagrange function and exhibit the nontrivial extrapolation properties of this estimator. We present heuristic arguments for a universal $w^{-2}$ power-law behavior of the probability density of the weights in the large $n$ limit.