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arxiv: 2606.23742 · v1 · pith:K5P2ABMAnew · submitted 2026-06-21 · 💻 cs.LG · cs.AI· cs.AR

Low-power analogue neural networks with trainable nonlinear connections for continuous control

Ian T. Vidamour , Fernando Aguirre , Thomas J. Hayward , Matthew O. A. Ellis , Charles Swindells , Alexander McDonnell , Martin Trefzer , Finley Robins
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Luca Manneschi Susan Stepney Tony Kenyon Oliver J. Sutton Jack C. Gartside Ivan Y. Tyukin Adnan Mehonic Eleni Vasilaki
This is my paper

Pith reviewed 2026-06-26 10:18 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.AR
keywords analogue neural networksKolmogorov-Arnold networkstrainable nonlinear connectionscontinuous controlfield-programmable analogue arraysrobotic kinematicslow-power hardwarephotovoltaic maximum power point tracking
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The pith

Placing trainable nonlinear functions on analogue connections lets networks represent smooth continuous targets with far fewer nodes than multilayer perceptrons.

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

The paper establishes that analogue neural networks inspired by Kolmogorov-Arnold networks, with trainable nonlinear band-pass filters placed on each connection rather than scalar weights, efficiently capture smooth continuously valued functions such as robotic joint trajectories and photovoltaic power-point tracking. This architecture yields a clear reduction in nodes and connections compared with standard multilayer perceptrons precisely when the target function is smooth, while showing no such advantage on tasks with sharp decision boundaries. Trained instances transfer to physical field-programmable analogue arrays across roughly 35,000 connections with measurable fidelity, and a projected dedicated CMOS version would run at approximately 30 microwatts. A memristive simulation reproduces the same efficiency pattern, confirming that the gain arises from the placement of nonlinearity on connections rather than from any specific device physics.

Core claim

Realising trainable nonlinear functions as analogue band-pass filters on field-programmable analogue arrays allows the networks to represent smooth, continuously valued targets, including robotic kinematics, continuous control, and photovoltaic maximum-power-point tracking, with far fewer nodes and connections than multilayer perceptrons, while offering no parameter-efficiency advantage on classification-like decision boundaries; the same behaviour appears in a memristive simulation, indicating the advantage stems from trainable nonlinearity on connections.

What carries the argument

Trainable nonlinear connections realised as analogue band-pass filters on field-programmable analogue arrays

If this is right

  • Networks achieve the same task performance on robotic kinematics and photovoltaic tracking using substantially fewer nodes and connections than multilayer perceptrons.
  • Trained networks map to physical hardware across approximately 35,000 connections with quantified fidelity.
  • A dedicated CMOS implementation is projected to operate at approximately 30 microwatts.
  • A memristive version reproduces the identical parameter-efficiency pattern, showing the gain is independent of any single device technology.

Where Pith is reading between the lines

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

  • The same connection-wise nonlinearity could be ported to other physical substrates whose native device responses already supply smooth nonlinearities, potentially extending the efficiency gain beyond field-programmable analogue arrays.
  • For sensor-driven continuous control loops that must remain always on, the projected microwatt power budget opens the possibility of embedding the entire controller inside the sensor package without external digital processors.
  • Because the advantage vanishes on non-smooth decision boundaries, hybrid systems could route smooth sub-tasks to the analogue nonlinear network and discrete sub-tasks to conventional digital layers.

Load-bearing premise

The computational benefit appears only for tasks whose targets are smooth and follows directly from the smoothness of the underlying physical basis.

What would settle it

A direct comparison on a smooth continuous-control benchmark in which the nonlinear-connection network requires equal or greater total parameters than a multilayer perceptron of comparable accuracy, or a hardware transfer whose output fidelity falls below the level needed for closed-loop stability.

Figures

Figures reproduced from arXiv: 2606.23742 by Adnan Mehonic, Alexander McDonnell, Charles Swindells, Eleni Vasilaki, Fernando Aguirre, Finley Robins, Ian T. Vidamour, Ivan Y. Tyukin, Jack C. Gartside, Luca Manneschi, Martin Trefzer, Matthew O. A. Ellis, Oliver J. Sutton, Susan Stepney, Thomas J. Hayward, Tony Kenyon.

Figure 1
Figure 1. Figure 1: Constructing trainable nonlinear connections from analogue filters. (a) Schematic of network components (PhyKAN). Inputs are encoded as frequencies at network nodes, which pass signals to network edges. Edges are univariate functions, and here edge ba￾sis functions resemble tuneable band-pass filters. These filters consist of high-pass, low-pass, and amplification stages. Multiple basis functions (band-pas… view at source ↗
Figure 2
Figure 2. Figure 2: Six-axis Robot Arm Kinematics with Analogue Electronic Networks. (a) Schematic diagram showing the joint configuration of the six-axis IRB120 commercial robotic ma￾nipulator modelled here. Rotational axes are shown in grey, where φi denotes the joint angle at each of the joints, and black arrows show the plane of rotation around each of the joints. The payload (end-effector) location is shown in black. (b)… view at source ↗
Figure 3
Figure 3. Figure 3: Continuous-Action CartPole Control with Analogue Electronic Networks. (a) Schematic diagram of the CartPole task. The actor provides a continuous output corresponding to a vector force applied to the cart, with the goal of keeping the pole displacement, x, and pole angle, θ close to zero. (b) and (c) compare the average duration for which the agent maintains the pole upright between analogue electronic net… view at source ↗
Figure 4
Figure 4. Figure 4: Maximum Power Point Tracking for Photovoltaic Cells Under Partial Shading Conditions (MPPT). (a) Schematic diagram of the MPPT task. Four arrays operate under variable irradiance. A state vector of current, voltage, power, and change in power is passed to a network, which outputs a voltage change to a voltage-booster circuit, and as a consequence changes the generated power and current across the arrays. (… view at source ↗
Figure 5
Figure 5. Figure 5: Memristor-based PhyKANs. (a) Circuit topology of the underlying nonlinear element, showing the input and reference voltages, operational amplifier, memristor (MR), and output load. (b-d) Performance comparison between MLPs (black) and MemKANs (red) for the (b) six-axis forward kinematics task, (c) CartPole task, and (d) photovoltaic-cell control task. Markers show mean performance and shaded regions show t… view at source ↗
read the original abstract

Physical neural networks promise low-power machine learning by computing directly with analogue device physics, but most architectures force nonlinear device responses to act as scalar weights. Inspired by Kolmogorov-Arnold networks, we place trainable nonlinear functions on the connections, making each physical connection a learnable computational element. Realising these functions as analogue band-pass filters on field-programmable analogue arrays, we find that the benefit is task-dependent and follows from the smoothness of the physical basis: the networks represent smooth, continuously valued targets, including robotic kinematics, continuous control, and photovoltaic maximum-power-point tracking, with far fewer nodes and connections than multilayer perceptrons, but offer no parameter-efficiency advantage on classification-like decision boundaries. Trained networks transfer to hardware across approximately 35,000 connections with quantified fidelity, and a dedicated CMOS implementation is projected to operate at approximately 30 microwatts. A memristive realisation reproduces the same behaviour in simulation, indicating that the advantage comes from placing trainable nonlinearity on connections, rather than from a particular device.

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

0 major / 2 minor

Summary. The manuscript introduces analogue neural networks that place trainable nonlinear functions (implemented as band-pass filters on field-programmable analogue arrays) on the connections rather than using scalar weights, drawing inspiration from Kolmogorov-Arnold networks. It claims that this yields parameter-efficiency gains specifically for smooth, continuously valued targets such as robotic kinematics, continuous control, and photovoltaic maximum-power-point tracking—using far fewer nodes and connections than multilayer perceptrons—while showing no such advantage on classification-like tasks. The work reports successful hardware transfer of trained networks across ~35,000 connections with quantified fidelity, projects ~30 µW operation for a dedicated CMOS implementation, and reproduces the behavior in memristor simulations to argue that the advantage arises from the placement of trainable nonlinearity on connections.

Significance. If the empirical hardware results and task-dependent comparisons hold, the architecture offers a concrete route to low-power physical neural networks for continuous-control domains by exploiting device physics directly for edge nonlinearities. The explicit hardware transfer across tens of thousands of connections and the memristive simulation check are strengths that distinguish the contribution from purely theoretical proposals.

minor comments (2)
  1. [Abstract] Abstract: the central empirical claims (hardware transfer fidelity, node/connection counts versus MLPs, task-dependent advantage, power projection) are stated without accompanying metrics, baselines, error bars, or experimental protocol summaries, which reduces verifiability of the headline results even though the full manuscript presumably contains these details.
  2. The manuscript should clarify whether the reported node/connection savings are measured at equivalent task performance (e.g., same mean-squared error or tracking accuracy) or at a fixed architecture size; this distinction is load-bearing for the parameter-efficiency claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on analogue neural networks with trainable nonlinear connections and for recommending minor revision. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claims rest on empirical hardware transfer experiments across ~35,000 connections and separate memristor simulations, with performance advantages presented as observed, task-dependent outcomes for smooth continuous targets rather than derived necessities. No equations, fitted parameters, or self-citations are invoked in a load-bearing way that reduces predictions to inputs by construction; the Kolmogorov-Arnold inspiration is external and the advantage is explicitly attributed to the placement of nonlinearity on connections, not to any internal self-referential step.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the domain assumption that band-pass filter smoothness matches continuous task requirements and that training transfers reliably to hardware; no ad-hoc fitted constants or new entities are introduced beyond standard training parameters.

free parameters (1)
  • band-pass filter parameters
    Trainable parameters of the nonlinear connection functions are learned to match target tasks.
axioms (1)
  • domain assumption The analogue band-pass filters provide a smooth physical basis suitable for continuous valued targets
    Invoked to explain task-dependent performance advantage over MLPs.

pith-pipeline@v0.9.1-grok · 5773 in / 1163 out tokens · 52656 ms · 2026-06-26T10:18:31.243033+00:00 · methodology

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