Implementation of Linear Differential Equations Using Pulse-Coupled Oscillators With an Ultra-Low Power Neuromorphic Realization
Bibliographic record
Abstract
Pulse-coupled oscillators (PCOs) are used as models for oscillatory systems in diverse fields such as biology, physics, and engineering. When correctly coupled, PCOs can display sophisticated emergent dynamics for a large number of oscillators. Here, we propose an algorithm and hardware implementation of PCOs to emulate arbitrary systems of linear differential equations (DEs) with inputs, which are similar to the equations used in feedback control laws or linearizations of nonlinear systems. We show that m populations of oscillators can solve a set of m-dimensional linear DEs with simple coupling schemes, and crucially, without the matrix multiplications required in Euler integration. The emergence of linear dynamical systems in networks of PCOs occurs when the number of oscillators within a population becomes large, as demonstrated through an analytically exact mean-field derivation. In addition, a hardware architecture of PCOs for digital implementation is proposed and realized on an ultra-low power FPGA as a proof of concept. These results show that there are simple coupling schemes for pulse-coupled oscillator networks that collectively compute complex dynamical systems. These PCO networks also have an immediate implementation as low power neuromorphic edge devices.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".