Learning withQ-state clock neurons

Gerl, Franz; Bauer, Karin; Krey, U.

doi:10.1007/bf01470923

Cited by 18 publications

(10 citation statements)

References 19 publications

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“…Comparing with other three-state neuron perceptron models we recall that for κ = 0 and uniform patterns the Q = 3 Ising perceptron can maximally reach an optimal capacity equal to 1.5, depending on the separation between the plateaus of the gain function (see [14], [15]) for the precise details) and the Q = 3 clock and Potts model both reach an optimal capacity of 2.40 [12], [21] while the value for the BEG perceptron found here is 2.24. Here we have to recall that the Q = 3 Ising perceptron and the BEG perceptron have the same topology structure in the neurons, whereas the Q = 3 clock and Potts models have a different topology.…”

Section: Replica Symmetric Analysismentioning

confidence: 85%

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Optimal capacity of the Blume-Emery-Griffiths perceptron

2003

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Section: Replica Symmetric Analysismentioning

confidence: 85%

“…This may allow for a possible geometrical interpretation of the Gardner optimal capacity in the space of local fields as it has been suggested for the Q-state clock model in [21].…”

Section: Replica Symmetric Analysismentioning

confidence: 90%

Optimal capacity of the Blume-Emery-Griffiths perceptron

2003

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“…By analogy with a network of phase oscillators, it may then be required that k assumes a value larger than a certain critical value k c . Finally, it is well known that the storage capacity of an oscillator network constructed by using the Hebbian rule is given by α c = P/N = 0.0377 [15][16][17]. Therefore, using the generalized Hebbian rule, we expect that our models work well when α < α c .…”

mentioning

confidence: 88%

Network of Neural Oscillators for Retrieving Phase Information

Aoyagi

1995

Phys. Rev. Lett.

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We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and the strength of the neuronal spikes, respectively. Using the amplitudes for encoding, we enable the network to realize not only oscillatory states but also non-firing states. In addition, it is shown that under suitable conditions the system has a Lyapunov function ensuring a stable retrieval process. Finally, the associative memory capability of the network is demonstrated numerically.

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“…This class of models was inspired by the Potts glass model in solid-state physics. Another model with multilevel neurons is the so-called “complex Hopfield network” (20, 35–42). Here, the model neurons are discretized phasors, and, as a result, the states of the model are complex vectors whose components have unity norm, and phase angles chosen from a finite, equidistant set.…”

Section: Introductionmentioning

confidence: 99%

Robust computation with rhythmic spike patterns

Frady

Sommer

2019

Proc. Natl. Acad. Sci. U.S.A.

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Information coding by precise timing of spikes can be faster and more energy efficient than traditional rate coding. However, spike-timing codes are often brittle, which has limited their use in theoretical neuroscience and computing applications. Here, we propose a type of attractor neural network in complex state space and show how it can be leveraged to construct spiking neural networks with robust computational properties through a phase-to-timing mapping. Building on Hebbian neural associative memories, like Hopfield networks, we first propose threshold phasor associative memory (TPAM) networks. Complex phasor patterns whose components can assume continuous-valued phase angles and binary magnitudes can be stored and retrieved as stable fixed points in the network dynamics. TPAM achieves high memory capacity when storing sparse phasor patterns, and we derive the energy function that governs its fixed-point attractor dynamics. Second, we construct 2 spiking neural networks to approximate the complex algebraic computations in TPAM, a reductionist model with resonate-and-fire neurons and a biologically plausible network of integrate-and-fire neurons with synaptic delays and recurrently connected inhibitory interneurons. The fixed points of TPAM correspond to stable periodic states of precisely timed spiking activity that are robust to perturbation. The link established between rhythmic firing patterns and complex attractor dynamics has implications for the interpretation of spike patterns seen in neuroscience and can serve as a framework for computation in emerging neuromorphic devices.

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Learning withQ-state clock neurons

Cited by 18 publications

References 19 publications

Optimal capacity of the Blume-Emery-Griffiths perceptron

Optimal capacity of the Blume-Emery-Griffiths perceptron

Network of Neural Oscillators for Retrieving Phase Information

Robust computation with rhythmic spike patterns

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