What Makes a Bacterial Model a Good Reservoir Computer? Predicting Performance from Separability and Similarity
Authors: Laura Alonso Bartolomé, Jean-Loup Faulon, Xavier Hinaut
Organizations: MICALIS, Mnemosyne · University Paris Saclay, INRAE, AgroParisTech, MICALIS Institute, 78350 Jouy-en-Josas, France · Centre Inria de l’Universit´e de Bordeaux, France · Institut des Maladies Neurod´eg´en´eratives, Universit´e de Bordeaux, CNRS, UMR 5293 · LaBRI, Bordeaux INP, CNRS, UMR 5800, France · MICALIS · Mnemosyne
Abstract
Biological systems are promising substrates for computation because they naturally process environmental information through complex internal dynamics. In this study, we investigate whether bacterial metabolic models can act as physical reservoirs and whether their computational performance can be predicted from dynamical properties linked to separability and similarity. We simulated the growth dynamics of five bacterial species, one yeast species, and 29 Escherichia coli single-gene deletion mutants using dynamic flux balance analysis (dFBA), with glucose and xylose concentrations as inputs and growth curves as reservoir states. Computational performance was assessed on random nonlinear classification tasks using a linear readout, while reservoir properties linked to separability and similarity were characterised through kernel and generalisation ranks computed from growth-curve state matrices. Several microbial models achieved high classification accuracy, showing that bacterial metabolic dynamics can support nonlinear computation. Clear differences were observed between species, with some models converging more rapidly and others reaching higher maximum accuracy, revealing a trade-off between convergence speed and peak performance. In contrast, all E. coli mutants were dominated by the wild-type model, suggesting that gene deletions reduce the dynamical richness required for efficient computation. The difference between kernel and generalisation ranks was generally associated with improved accuracy, but deviations across models and sensitivity at low rank values limited its predictive power in practice. Overall, these results show that bacterial metabolic models constitute promising substrates for reservoir computing and provide a first step towards identifying microbial strains with favourable computational properties for future experimental implementations.
Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.
A fundamental challenge in microbial ecology is determining whether bacteria compete or cooperate in different environmental conditions. With recent advances in genome-scale metabolic models, we are now capable of simulating interactions between thousands of pairs of bacteria in thousands of different environmental settings at a scale infeasible experimentally. These approaches can generate tremendous amounts of data that can be exploited by state-of-the-art machine learning algorithms to uncover the mechanisms driving interactions. Here, we present Friend or Foe, a compendium of 64 tabular environmental datasets, consisting of more than 26M shared environments for more than 10K pairs of bacteria sampled from two of the largest collections of metabolic models. The Friend or Foe datasets are curated for a wide range of machine learning tasks -- supervised, unsupervised, and generative -- to address specific questions underlying bacterial interactions. We benchmarked a selection of the most recent models for each of these tasks and our results indicate that machine learning can be successful in this application to microbial ecology. Going beyond, analyses of the Friend or Foe compendium can shed light on the predictability of bacterial interactions and highlight novel research directions into how bacteria infer and navigate their relationships.
Oleksandr Cherednichenko, Josephine Solowiej-Wedderburn, Laura M. Carroll +1
We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers, focusing on how closely the model's nonlinearity should align with that of the data. By reducing minimal RCs to a single tunable nonlinearity parameter, we explore how the predictive performance varies with the degree of nonlinearity in the reservoir. To provide controlled testbeds, we generalize to the fractional Halvorsen system, a novel chaotic system with fractional exponents. Our experiments reveal that the prediction performance is maximized when the reservoir's nonlinearity matches the nonlinearity present in the data. In cases where multiple nonlinearities are present in the data, we find that the correlation dimension of the predicted signal is reconstructed correctly when the smallest nonlinearity is matched. We use this observation to propose a method for estimating the minimal nonlinearity in unknown time series by sweeping the reservoir exponent and identifying the transition to a successful reconstruction. Applying this method to both synthetic and real-world datasets, including financial time series, we demonstrate its practical viability. Finally, we transfer these insights to classical RC by augmenting traditional architectures with fractional, generalized reservoir states. This yields performance gains, particularly in resource-constrained scenarios such as physical reservoirs, where increasing reservoir size is impractical or economically unviable. Our work provides a principled route toward tailoring RCs to the intrinsic complexity of the systems they aim to model.