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arxiv: 1907.01856 · v1 · pith:VZADTCOHnew · submitted 2019-07-03 · 💻 cs.NE · cs.ET

A general representation of dynamical systems for reservoir computing

Sidney Pontes-Filho , Anis Yazidi , Jianhua Zhang , Hugo Hammer , Gustavo B. M. Mello , Ioanna Sandvig , Gunnar Tufte , Stefano Nichele This is my paper

Pith reviewed 2026-05-25 09:45 UTC · model grok-4.3

classification 💻 cs.NE cs.ET
keywords cellular automatareservoir computingartificial neural networksdynamical systemsupdate rulesdeep learning librariesevolutionary optimizationphysical computing
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The pith

Dynamical systems can be represented as artificial neural networks for reservoir computing by redefining connection weights and activation functions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how dynamical systems used in reservoir computing can be cast as artificial neural networks. It begins with the simplest case, cellular automata, by setting the network weights and activation function to reproduce a chosen cellular-automaton update rule while keeping the standard ANN mathematical structure. This representation lets the same systems run inside existing deep-learning libraries and makes it possible to evolve connectivity, update rules, and learning rules. The approach is presented as the first step toward a single framework that covers many kinds of dynamical systems and can be applied to both abstract computation and physical substrates.

Core claim

Any dynamical system can be expressed as an artificial neural network in which the connection weights and activation function are chosen to implement the system's state-update rule, demonstrated first by mapping cellular-automaton rules onto this form so that the network evolves exactly as the original automaton would.

What carries the argument

The reparameterized artificial neural network in which weights and activation function are set to encode a cellular-automaton update rule, thereby turning the network into a simulator of the dynamical system.

If this is right

  • Dynamical systems can be simulated directly inside optimized deep-learning libraries without custom code.
  • The same representation can be extended to other network types beyond cellular automata.
  • Cellular automata and other dynamical systems can be evolved by varying connectivity, update rules, and learning rules inside the neural-network form.
  • The evolved systems can be tuned specifically to improve performance in reservoir-computing applications.
  • Physical computing substrates can be modeled by treating their dynamics as instances of the same neural-network representation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The neural-network form may allow gradient-based methods to optimize the dynamical rules themselves when the activation is made differentiable.
  • Hybrid models could combine fixed cellular-automaton rules with trainable weights inside the same network structure.
  • The representation opens a route to compare abstract dynamical systems directly with physical substrates that perform computation.

Load-bearing premise

Mapping a cellular-automaton update rule onto neural-network weights and an activation function preserves the original dynamical behavior well enough for reservoir-computing tasks.

What would settle it

Compare the exact sequence of states produced by a standard cellular-automaton simulator and by the corresponding neural-network version when both start from the same initial grid and apply the same rule for many steps; any mismatch falsifies the representation.

Figures

Figures reproduced from arXiv: 1907.01856 by Anis Yazidi, Gunnar Tufte, Gustavo B. M. Mello, Hugo Hammer, Ioanna Sandvig, Jianhua Zhang, Sidney Pontes-Filho, Stefano Nichele.

Figure 1
Figure 1. Figure 1: Elementary cellular automaton with 16 cells and wrapped grid. (a) [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: 2D cellular automaton with 16 cells (4 × 4) and wrapped grid. (a) Example of the grid of cells with states. (b) Indices of the cells and von Neumann counting neighborhood of 2D CA where thick border means the current cell and thin border means the neighbors. (c) Generated adjacency matrix for this 2D CA. of the Python framework, EvoDynamic must have a general representation to all of them. Therefore we are… view at source ↗
Figure 3
Figure 3. Figure 3: States of Conway’s Game of Life in a 7x7 wrapped lattice alongside their PCA-transformed state transition diagrams of the two first principal [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Dynamical systems are capable of performing computation in a reservoir computing paradigm. This paper presents a general representation of these systems as an artificial neural network (ANN). Initially, we implement the simplest dynamical system, a cellular automaton. The mathematical fundamentals behind an ANN are maintained, but the weights of the connections and the activation function are adjusted to work as an update rule in the context of cellular automata. The advantages of such implementation are its usage on specialized and optimized deep learning libraries, the capabilities to generalize it to other types of networks and the possibility to evolve cellular automata and other dynamical systems in terms of connectivity, update and learning rules. Our implementation of cellular automata constitutes an initial step towards a general framework for dynamical systems. It aims to evolve such systems to optimize their usage in reservoir computing and to model physical computing substrates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a general representation of dynamical systems (beginning with cellular automata) as artificial neural networks for reservoir computing. It asserts that the mathematical fundamentals of ANNs are preserved while weights and activation functions are adjusted to implement CA update rules, enabling use of DL libraries, generalization to other networks, and evolutionary optimization of connectivity, updates, and learning rules for reservoir computing and physical substrate modeling.

Significance. If the mapping exactly reproduces the original discrete state transitions, fixed points, and transients, the approach could allow direct application of optimized deep-learning frameworks and evolutionary algorithms to reservoir computing with cellular automata and other dynamical systems. This would be a useful bridge between discrete physical computing models and continuous ANN toolchains.

major comments (2)
  1. [Abstract] Abstract: the claim that 'the mathematical fundamentals behind an ANN are maintained' while weights and activations are adjusted to serve as a CA update rule is unsupported; no equations, weight matrices, activation definitions, or verification that the resulting network produces identical state evolution to the original CA are supplied.
  2. No section demonstrates that the re-defined network exactly replicates the CA transition function (including for arbitrary neighborhoods) or that any continuous relaxation leaves information-processing capacity unchanged; this equivalence is load-bearing for the stated advantages in reservoir computing.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will make the indicated revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'the mathematical fundamentals behind an ANN are maintained' while weights and activations are adjusted to serve as a CA update rule is unsupported; no equations, weight matrices, activation definitions, or verification that the resulting network produces identical state evolution to the original CA are supplied.

    Authors: We accept the criticism that the abstract claim requires explicit support. The revised manuscript will add the weight matrices, activation-function definitions, and the corresponding equations that realize the CA update rule within the ANN formalism, together with direct verification that the resulting network reproduces the original CA state transitions. revision: yes

  2. Referee: [—] No section demonstrates that the re-defined network exactly replicates the CA transition function (including for arbitrary neighborhoods) or that any continuous relaxation leaves information-processing capacity unchanged; this equivalence is load-bearing for the stated advantages in reservoir computing.

    Authors: We agree that a formal demonstration of exact replication is necessary. The revision will include a dedicated subsection proving that the mapping reproduces the CA transition function for arbitrary neighborhoods. The manuscript does not claim that continuous relaxations preserve information-processing capacity; we will add an explicit statement clarifying that the primary construction is discrete and that any relaxation is outside the current scope. revision: yes

Circularity Check

0 steps flagged

No circularity: representational mapping is self-contained without reduction to inputs

full rationale

The paper describes a representational construction in which ANN weights and activation functions are adjusted to encode cellular-automaton update rules while claiming the mathematical fundamentals of ANNs are retained. No equations, derivations, or fitted parameters are exhibited that would reduce any claimed prediction or general result to the inputs by construction. No self-citations appear as load-bearing premises for uniqueness theorems, ansatzes, or external justification. The central step is therefore an explicit redefinition presented as an initial modeling choice rather than a derived claim forced by prior results or data fits, rendering the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the representation is described at the level of a conceptual adjustment to existing ANN components.

pith-pipeline@v0.9.0 · 5690 in / 1079 out tokens · 31564 ms · 2026-05-25T09:45:14.152797+00:00 · methodology

discussion (0)

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