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The PDM Digital Neural Network System

Outlook of the PDM Digital Neural Network System

Basic Functions of the System

1. PDM is the acronym of Pulse Density Modulation. Analog output from each neuron is transmitted neither by analog voltage nor by binary digital data, but by a pulse stream whose frequency is proportinal to the output as our real neurons do. The system is designed with fully digital circuits and benefits from the state-of-the-art semiconductor technologies.
2. The behavior of each neuron obeys the following nonlinear first-order differential equation:
   
   
   
   (LaTeX-like expression:
   \mu_{i} \frac{d y^{*}_{i}(t)}{dt} = -y^{*}_{i}(t) + \sum_{j=1}^{N} w_{ij} y_{j}(t) + I_{i}(t) + y^{*}_{i}(0) .....(1)
y_{i}(t) = \varphi( y^{*}_{i}(t) )
\varphi(a) = a if a > 0, 0 oterwise. )
   where
   • \mu_{i}: Time constant of the i-th neuron.
   • y^{*}_{i}(t): Internal potential of the i-th neuron at time t.
   • w_{ij}: Synaptic weight from the j-th neuron to the i-th neuron.
   • y_{j}(t): Output from the j-th neuron at time t.
   • I_{i}(t): External input to the i-th neuron at time t.
   • y^{*}_{i}(0): Initial value of the internal potential of the i-th neuron.
   • \varphi(a): Analog threshold output function.
3. The number of neurons in this system is N=1,008. Each neuron has 1,020 synapses including 12 synapses receiving a set of external inputs. The total number of synapses is, therefore, 1,028,160.
4. The precision of internal potential is 12-bit, output is 11-bit and synaptic weight is 7-bit.
5. The precision of these parameters should be taken into account carefully when you implement your neural networks in this system. Since the precision of synaptic weight is very limited, scaling the magnitude of input and each weight is especially important.
6. More details may be found in Hirai97(PS file 3.8MB)
   Hirai, Y.: "A 1,000-Neuron System with One Million 7-bit Physical Interconnections." In Jordan, M.I., Kearns, M.J. and Solla, S.A. eds. Advances in Neural Information Processing Systems 10, A Bradford Book, The MIT Press, Cambridge, Massachusetts, pp.705-711, 1998.
   
7. Some response characteristic data can be found in Hirai98(PDF file 108KB)
   Toda, H. and Hirai, Y.: "Summation characteristics of PDM digital neural network system." Proceedings of the Fifth International Conference on Neural Information Processing. pp.574-577, 1998.
   

Specifications of the PDM System

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