Asymmetric Coupling Anisotropy for Causal Information Filtering in Physical Reservoirs

Takashi Hikihara; Yuma Aoki

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Asymmetric Coupling Anisotropy for Causal Information Filtering in Physical Reservoirs

Takashi Hikihara, Yuma Aoki

arXiv:2608.26741v1Aug 27, 2026nlin.AOcs.NEphysics.class-ph

TL;DR

PRC reliability remains insufficiently addressed when systems face semantic drifts and environmental disturbances. This paper introduces asymmetric coupling in a network of Duffing oscillators to create causal information filtering and hardware-level self-diagnosis. The resulting architecture detects and isolates anomalies, supports autonomous recovery, and reduces MSE by approximately two orders of magnitude during re-learning.

Problem
Previous PRC research has emphasized computational performance while leaving physical-layer reliability against semantic drifts and environmental disturbances insufficiently discussed.
Method
The paper embeds asymmetrical bidirectional coupling among Duffing resonators to create directional anomaly propagation, hardware-level monitoring, and physical interlocks.
Results
The 50-node architecture localizes and isolates anomalies, detects deviations under traveling-wave inputs, and supports autonomous recovery before global computational failure.
Takeaways & Limitations
The results support using reservoir topology’s intrinsic causality and dissipative stability as a framework for autonomous reliability and fault-tolerant physical intelligence.

Abstract

from arXiv · show

We demonstrate a physical mechanism for causal information filtering in a physical reservoir computing (PRC) by exploiting asymmetric coupling anisotropy. Using a network of coupled Duffing oscillators, we show that the directionality of internal coupling induces a spatial gradient in the effective potential, establishing a deterministic upstream-to-downstream information flow. This anisotropy allows for the selective amplification of semantic drifts, triggering a macroscopic saddle-node bifurcation as a physical interlock before global computational failure. Through spatiotemporal analysis of a 50-node system under traveling wave inputs, we confirm that local phase transitions effectively purge anomalous information while preserving the computational integrity of the remaining nodes. The results suggest that the intrinsic causality of the reservoir's topology provides a robust framework for autonomous reliability and fault-tolerant physical intelligence.

1 Introduction

PRC offers hardware-efficient, low-power nonlinear information processing, but prior work has emphasized computational performance more than physical-layer reliability. The paper addresses this gap by using asymmetric coupling to support anomaly detection, recovery, and fault-tolerant operation.

PRC is a hardware-efficient learning framework for edge computing that exploits nonlinear physical dynamics for real-time information processing.The passage also associates PRC with remarkably low power consumption and applications including time-series prediction and pattern recognition.
Previous PRC research has primarily focused on maximizing computational performance rather than ensuring reliability against semantic drifts and environmental disturbances.The stated disturbances include infinitesimal statistical anomalies in input data and thermal drifts.
The paper formulates asymmetric coupling, simulates a 50-node PRC with distributed 3-node detection units, and evaluates anomaly detection and recovery.The system detects upstream anomalies, can recover after anomalies subside, and can exclude faulty blocks under persistent failures.
The proposed physical-intelligence design embeds physical laws into information processing to support quasi-real-time reliability and autonomous restoration of computational integrity.The paper presents this as a framework for fault-tolerant physical intelligence.

2 Physical Anisotropy and Causal Flow

The reservoir uses an asymmetrical ring of coupled Duffing resonators to create directional anomaly propagation and hardware-level monitoring. Forward coupling amplifies anomalies toward downstream stages, while reverse coupling counters common-mode drift; accumulated bias can eliminate the stable state at a critical threshold.

Internal Topology with Self-Diagnostic Functionality: The proposed topology gives internal coupling dual functionality: high-dimensional signal mixing and hardware-level anomaly detection without external digital monitoring circuits.A ring-shaped asymmetrical bidirectional coupling is embedded between nonlinear resonators.
Formulation of Asymmetric Ring Coupling: Each MEMS-based reservoir resonator follows nonlinear Duffing dynamics and receives an input signal plus a bias α_i representing statistical anomalies.The resonators are coupled in an asymmetrical ring configuration.
Causal Flow: When k_fwd ≫ k_rev, the forward path cumulatively propagates and amplifies anomalies toward subsequent stages until a saddle-node bifurcation acts as a physical interlock.The reverse path supplies a weak restoring force that synchronizes and cancels baseline shifts caused by common-mode noise.
Collapse of Effective Potential and Symmetry Breaking: The reservoir’s integrity is monitored through adjacent-node displacement deviations, Δx_i,j = |x_i − x_j|, with equilibria determined by extrema of an effective potential.This provides the basis for detecting local distortions in the coupled system.
Collapse of Effective Potential and Symmetry Breaking: When the cumulative bias B_eff = k_fwd x_i−1 + k_rev x_i+1 + α_i exceeds B_c ≈ 0.35 for β = 3.23 and k_fwd = 0.05, the stable solution vanishes and the system jumps.The resulting phase transition can halt operation before MSE diverges.

3 Numerical Simulation

The simulations evaluate asymmetric ring coupling for drift-robust anomaly detection, physical interlocking, and autonomous recovery in Duffing-oscillator reservoirs. Differential monitoring suppresses common-mode drift, while bifurcation-based detection precedes computational failure and re-learning restores accuracy.

Simulation setup: A 10:1 forward-to-reverse coupling ratio forms a three-node asymmetric ring that ensures information recurrence.The simulation uses N = 5 Duffing oscillators and introduces the ring among three nodes.
Drift robustness: AUC ≈0.90 demonstrates high discrimination accuracy for the asymmetric ring under high-noise environmental conditions.The ring is compared with a conventional unidirectional ladder topology that is susceptible to drift.
Drift robustness: Differential monitoring physically cancels in-phase environmental drift, isolating injected statistical anomalies more clearly than absolute monitoring in a ladder.The differential signal is defined as ∆x12 = |x1 − x2|.
Physical interlock: The differential interlock signal rises before the explosive MSE increase caused by data unsoundness, enabling computation to halt before erroneous outputs.The low linear correlation reflects nonlinear loss of computational capability at a critical potential distortion.
Autonomous self-repair: After anomaly cessation, the dissipative physical layer returns to equilibrium and triggers readout-weight re-learning for accuracy recovery.This recovery uses the stable-equilibrium return as the trigger for updating readout weights.
Autonomous self-repair: W = 100 samples reduces MSE by approximately two orders of magnitude, from 10−1 to 10−3, compared with no re-learning.The reduction is reported as the effect of training-window size on prediction accuracy.

4 Spatiotemporal Dynamics and Scalability in Large-Scale Systems

A 50-node asymmetric chain with embedded three-node monitors tests how localized anomalies propagate and are intercepted during traveling-wave computation. The topology confines deviations, identifies downstream failures, and maintains reservoir integrity under dynamic backgrounds.

Large-scale configuration: The 50-node configuration investigates how localized physical anomalies propagate through and are intercepted within a spatially extended computational medium.Distributed monitoring units are used to evaluate scalability and spatial reliability.
Causal topology: Strong forward bias kfwd ≫ krev establishes deterministic upstream-to-downstream causal flow and sequential traveling-wave propagation.The chain connects reservoir nodes outside the embedded monitor units.
Distributed monitoring: Embedded three-node ring monitors intercept information flow while preserving computational throughput in the chain segments.The monitors localize and amplify semantic drifts as diagnostic interfaces.
Distributed anomaly detection: Only the monitor immediately downstream of an anomaly at Node 23, Nodes 25–27, captures a significant differential signal while the displacement offset remains localized.Other distributed monitors, including Nodes 10–12 and 40–42, do not capture the comparable deviation.
Traveling-wave reliability: Under traveling-wave inputs, monitoring units distinguish normal propagation from anomalous deviations with high SNR despite an oscillating spatiotemporal background.The macroscopic saddle-node bifurcation remains a reliable failure indicator in these dynamic computational states.
Traveling-wave reliability: The physical layer traps semantic drift and isolates the identified faulty block, protecting global MSE and the remaining reservoir computation.This isolation maintains overall reservoir integrity during traveling-wave processing.

5 Autonomous Self-healing and Functional Recovery

Persistent anomalies are managed by isolating contaminated blocks, while stable physical recovery triggers re-learning that restores computational accuracy.

5.1 Block-wise Isolation under Persistent Failure: Monitor units identify failure coordinates so the readout layer can exclude contaminated nodal states from global computation.This block-wise isolation protocol addresses sustained failures.
5.1 Block-wise Isolation under Persistent Failure: Physical masking prevents the MSE from escalating further and maintains baseline operational continuity under adverse conditions.
5.2 Full Recovery by Autonomous Re-learning: After the physical layer returns to stable equilibrium, a re-learning cycle updates Wout to accommodate post-anomaly reservoir dynamics.Recovery can follow disturbance removal or structural stabilization.
5.2 Full Recovery by Autonomous Re-learning: The MSE decreases by approximately two orders of magnitude, from 10^-3 to 10^-5, after autonomous re-learning.

6 Conclusion

Asymmetric coupling anisotropy establishes directional information flow and hardware-level anomaly filtering in a physical reservoir. A 50-node analysis further supports fault localization, block-wise isolation, and autonomous recovery for fault-tolerant operation.

6 Conclusion: Asymmetric coupling anisotropy establishes deterministic causal information filtering and autonomous reliability in a coupled Duffing-oscillator reservoir.
6 Conclusion: Breaking spatial symmetry induces directional information flow that selectively amplifies semantic drifts.
6 Conclusion: A macroscopic saddle-node bifurcation acts as a deterministic interlock that purges anomalous information before global computational failure.
6 Conclusion: A 50-node spatiotemporal analysis confirms robust fault localization under dynamic traveling wave inputs.
6 Conclusion: Block-wise isolation physically masks contaminated nodal states to maintain operational continuity during persistent failures.
6 Conclusion: Return to stable equilibrium triggers self-healing re-learning that reduces mean squared error by approximately two orders of magnitude.