Receptron Explained

The receptron (short for "reservoir perceptron") is a neuromorphic data processing model — specifically neuromorphic computing — that generalizes the traditional perceptron, by incorporating non-linear interactions between inputs.^[1] ^[2] Unlike classical perceptron, which rely on linearly independent weights, the receptron leverages complexity in physical substrates,^[3] such as the electric conduction properties of nanostructured materials or optical speckle fields, to perform classification tasks.^[4] ^[5] The receptron bridges unconventional computing and neural network principles,^[6] enabling solutions that do not require the training approaches typical of artificial neural networks based on the perceptron model.^[7]

Algorithm

The receptron is an algorithm for supervised learning of binary classifiers, so a classification algorithm that makes its predictions based on a predictor function, combining a set of weights with the feature vector.^[8] The mathematical model is based on the sum of inputs with non-linear interactions:

	n
\sum
	k=1

x_j\widetilde{w}_j(\vec{x})|S\inR

(1)

where

j\in[1,n]

and

\widetilde{w}_j

are non-linear weight functions depending on the inputs,

\vec{x}

. Nonlinearity will typically make the system extremely complex, and allowing for the solution of problems not solvable through the simpler rules of a linear system, such as the perceptron or McCulloch Pitts neurons, which is based on the sum of linearly independent weights:

	n
\sum
	k=1

x_j

	p
w
	j

(2)

where

w_j

are constant real values. A consequence of this simplicity is the limitation to linearly separable functions, which necessitates multi-layer architectures and training algorithms like backpropagation^[9]

As in the perceptron case,^[10] the summation in Eq. 1 origins the activation of the receptron output through the thresholding process,

Y(x_1,...,x_n)=\begin{cases}1&ifS>th\ 0&ifS\leqth\end{cases}

(3)

where th is a constant threshold parameter. Equation 3 can be written by using the Heaviside step function.

The weight functions

\widetilde{w}(\vec{x})

can be written with a finite number of parameters

w
	j_1...j_n

, simplifying the model representation. One can Taylor-expand

\widetilde{w}(\vec{x})

and use the idempotency of Boolean variables

	q
(x
	j)

=x_j\forallq\geq1

such that

S'=b+

	n
\sum
	k=1

x_j\widetilde{w}_j(\vec{x})

can be written as

S'(\vec{x})=b+\sum_jw_jx_j+\sum_j<kw_jkx_jx_k+\sum_j<k<lw_jklx_jx_kx_l+...

(4)

where

w
	j_1...j_n

are independent parameters that can be seen as the components of a tensor

(“weight tensor”) of rank

and type

(n,0)

The sum in Eq. [3] reduces to the perceptron case when off-diagonal terms of

vanish. If one considers

n=2

, one gets:

S'(\vec{x})=b+x₁w₁₁+x₂w₂₂+x₁x₂w₁₂

(5)

in the perceptron case, the vanishing of

w₁₂

implies linearity

S(1,1)=S(0,1)+S(1,0)

. In the receptron case

S(1,1) ≠ S(0,1)+S(1,0)

, meaning that the superposition principle is no longer valid, the latter terms being responsible of the more complex non-linear interaction between the inputs.

Design and implementations

1. Electrical Receptron

Substrate: Nanostructured and nanocomposite films (Au, Pt, Zr Au/Zr). These films form disordered networks of nanoparticles with resistive switching and non-linear electrical conduction.

2. Optical Receptron

Substrate: Optical speckle fields generated by random interference of light emerging from a disordered medium illuminated by a laser or coherent radiation.^[11]

Key features

Physical Substrate Computing: The receptron does not require digital training; instead, it exploits the natural complexity of materials (e.g., nanowire networks, diffractive media) to perform computations.

Non-Linear Separability: Unlike traditional perceptrons, which fail on problems like the XOR function, the receptron can solve such tasks due to its inherent non-linearity.

Training-Free Operation: Classification is achieved through the physical system's response rather than iterative weight adjustments, reducing computational overhead.

Notes and References

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Stieg . Adam Z. . Avizienis . Audrius V. . Sillin . Henry O. . Martin-Olmos . Cristina . Aono . Masakazu . Gimzewski . James K. . 2012-01-10 . Emergent Criticality in Complex Turing B-Type Atomic Switch Networks . Advanced Materials . en . 24 . 2 . 286–293 . 10.1002/adma.201103053 . 22329003 . 2012AdM....24..286S . 0935-9648. subscription .
Paroli . B. . Martini . G. . Potenza . M. A. C. . Siano . M. . Mirigliano . M. . Milani . P. . 2023-09-01 . Solving classification tasks by a receptron based on nonlinear optical speckle fields . Neural Networks . 166 . 634–644 . 10.1016/j.neunet.2023.08.001 . 37604074 . 0893-6080 . 2024-04-18 . 2025-09-03 . https://web.archive.org/web/20240418205454/https://www.sciencedirect.com/science/article/pii/S0893608023004203 . live . 2434/1026912 . free .
Iyer . Prasad P. . Bhatt . Gaurang R. . Desai . Saaketh . Fuller . Elliot J. . Teeter . Corinne M. . Léonard . François . Vineyard . Craig M. . 2025-08-08 . Is Computing with Light All You Need? A Perspective on Codesign for Optical Artificial Intelligence and Scientific Computing . Advanced Intelligent Systems . 2500371 . en . 10.1002/aisy.202500371 . 2640-4567. free .
Frenkel . Charlotte . Bol . David . Indiveri . Giacomo . June 2023 . Bottom-Up and Top-Down Approaches for the Design of Neuromorphic Processing Systems: Tradeoffs and Synergies Between Natural and Artificial Intelligence . Proceedings of the IEEE . 111 . 6 . 623–652 . 10.1109/JPROC.2023.3273520 . 0018-9219.
Barrows . Frank . Lin . Jonathan . Caravelli . Francesco . Chialvo . Dante R. . July 2025 . Uncontrolled Learning: Codesign of Neuromorphic Hardware Topology for Neuromorphic Algorithms . Advanced Intelligent Systems . en . 7 . 7 . 2400739 . 10.1002/aisy.202400739 . 2640-4567. free .
Widrow . B. . Lehr . M.A. . September 1990 . 30 years of adaptive neural networks: perceptron, Madaline, and backpropagation . Proceedings of the IEEE . 78 . 9 . 1415–1442 . 10.1109/5.58323 . 1990IEEEP..78.1415W .
Goh . A.T.C. . January 1995 . Back-propagation neural networks for modeling complex systems . Artificial Intelligence in Engineering . en . 9 . 3 . 143–151 . 10.1016/0954-1810(94)00011-S. subscription .
Block . H. D. . 1962-01-01 . The Perceptron: A Model for Brain Functioning. I . Reviews of Modern Physics . en . 34 . 1 . 123–135 . 10.1103/RevModPhys.34.123 . 1962RvMP...34..123B . 0034-6861. subscription .
Paroli . Bruno . Malfer . Alessandro . Potenza . Marco A.C. . Siano . Mirko . Milani . Paolo . 2025-08-21 . Binary Pattern Classification with a Photonic Neuromorphic Device Based on Optical Receptrons . Laser & Photonics Reviews . e00970 . en . 10.1002/lpor.202500970 . 1863-8880. free . 2434/1208162 . free .