Each of these subsystems illuminates various aspects of the relationship between VLSI analogs and their neurobiological counterparts. The relationship between neuml systems and VLSI is rooted in the shared limitations imposed by computers in similar physical media.
List of Tables
Chapter 1
Introduction
Overview
- The Silicon Retina
I designed an interchip communication protocol that takes advantage of the representation of the visual world created by the silicon retina. The nodes of the analog circuit mimic the response of the large difference cell types observed in the macaque monkey's primary visual cortex.
Chapter 2
The Silicon Retina
Vertebrate Retina
The OPL and IPL are the site of interaction between the different cell types of the retina. The horizontal cells provide two forms of lateral inhibition, one through feedback inhibition on the cones, the other through feedforward inhibition of the bipolar cells.
Silicon Retina
This view highlights the lateral spread of the resistive network, corresponding to the horizontal cell layer. The voltage at each point in the network represents a spatially weighted average of photoreceptor inputs.
- Accessing the Array
- Data-An Electrode's Eye View
- Time Response
- Adaptation
- Form and Function: Encoding Information with a Phys- ical System
- Wiring
H is a measure of the extent to which changes in grid voltage affect the photoreceptor output. As described in the photoreceptor section, Wn is proportional to the logarithm of the light intensity.
2 .6 Summary
Chapter 3
The Silicon Optic Nerve
Introduction
Summary of Existing Techniques
Each time slot is assigned to a specific node and the receiving device must be synchronized with the sending device to preserve the identity of the transmitting node. The choice of multiplexing technique depends on how the neural elements in the system encode information. Some systems use analog-valued outputs, which encode multiple bits of information on a single wire.
More importantly, the variations in the parameters of fabrication on different wafers mean that different chips will have different interpretations of analog voltages. Asynchronous serial digital communication Inetods in which the duration of the digital pulse encodes several bits of information have been used [3, 20J. In the voltage-controlled-oscillator encoder used by Murray and co-workers [20, 3], the duration of the pulse is inversely proportional to the analog value of the output.
Instead of using a global frequency llllcchanisllll to divide specific time slots into separate nodes, the identity of the scnciillg neuron is determined by its position in the pulse stream.
The Address- Event Representation
Another major advantage of the address-event communication framework is that it minimizes time aliasing by transmitting events as they occur. Because the address-event communication protocol specifically synchronizes data transmission with data timing, the details of timing performance cannot be analyzed without a model of the data being transmitted. However, it is possible to perform an analysis of the average behavior of the system by assuming that elements in the array initiate data transfer requests independently of each other, each at a specified rate.
When implementing the address-event communication framework described in this chapter, the data transfer time, Tp, scales logarithmically with the number of neurons. This model is oversimplified in several respects. One aspect is that the data is unlikely to be evenly distributed across all elements in the system. In the latter case, the specification of the mapping between input and output can be controlled by a digital host computer.
It is certainly the case in the nervous system that the ground potential is not uniform in different areas of the brain.
Data Transfer In One Dimension
Because the real system has many levels of delay lumped together in this diagram in the inverting amplifiers, the circuit cannot hang in a state where PP is just balanced by NA. The "axon hillock" circuit was prevented from sticking by positive feedback through a coupling capacitor between the initiation node and the acknowledgment node). The temporal progression of the acknowledgment signal is a digital amplitude pulse whose onset is triggered by the trigger node crossing the threshold of the inverter. The successful transfer of an address is the culmination of the forward phase of the data transfer cycle.
In a one-dimensional system, the Acknowledge only needs to reset the initiation node of the neuron from which the data was transferred. In this implementation, the acknowledgment signal returns to the transmitter and all initiation nodes are reset. When the Request signal is withdrawn, the state of the entire Arbiter is initialized.
The current through QR is similar to the delayed rectifier potassium current of the biological neuron.
Data Transfer In Two Dimensions
The AND of address coordinates in two dimensions is a direct extension of the decoding process described in the one-dimensional system. The generalization of the data transfer protocol is more difficult for a two-dimensional sender. The selection of the pixel that will transmit its address must be consistent in both dimensions.
In the second phase of the initiation cycle, the horizontal arbitrator selects an initiating pixel on the row just selected by the vertical arbitrator and activates the appropriate column selection line. As in the one-dimensional case, the state of the selected pixel is reset, this time by the AND of a row and column selection signal. The address flow would be interrupted by resetting the horizontal Arbiter, which would switch the request to the receiver chip.
The selected vertical Arbiter initiation node could be reset by the acknowledgment signal, which would also reset all horizontal Arbiter initiation nodes.
Image Transfer
The first step in image transfer is the creation of the image on the retina. The integration time of the pixel was changed by changing the bias voltages on the tau and delta controls. Values of the refractory transistor gate voltage are shown next to each pair of responses.
The magnitude of the reset current set by the voltage across capacitor CR decays at a rate set by the refractory control. Action potential gain is generated in biological neurons by positive feeding. The sodium phase of the action potential is generated by the on-chip digital circuitry.
The size of the step in light intensity is encoded by the number of peaks generated.
Future System D e velopment
The origin of the addresses is in the upper left corner of the image. The voltages at the nodes of the receiver are sequentially scanned for display on the video monitor. The origin of the addresses is in the lower left corner of the image.
Consequently, the activity pattern at the receiver is mirrored around the horizontal axis from that of the sender in Figure 3.24. The address bits are set by the Arbiter element at the appropriate tree level. The number of wires in the address event representation can be further reduced by multiplexing the address bits.
This method reduces the temporal resolution of the address event encoding to the synchronous clock period.
Chapter 4
Stereopsis
The Problem of Stereo correspondence
The feature in the image projects through the node of the eye along a line of sight. That line of sight is imaged through the node of the other eye to the corresponding cpipolar line. Corresponding epipolar lines in the two images result in the intersection of the plane defined by the nodes of the two eyes and the target, with the image planes.
All the epipolar lines intersect at the point defined by the intersection of the line joining the nodal points of the eyes and the (infinitely extended) image plane [lOJ. Once the stereo correspondence of the targets is determined, the disparity can be calculated. The epipolar lines intersect at the intersection between the line joining the nodal points of the eyes and the image plane.
Otherwise, the geometric horopter exists only in the horizontal plane that intersects the nodes of the eye and is perpendicular to the image plane.
Overview
The locus of points in space that stimulate the same coordinates on the two retinas is called the horopter and is the zero-disparity fixation surface. The horopter only exists over a fully two-dimensional image when the optical axes of the eyes are parallel. The simplest interpretation of the one-dimensional stereocorresponciencc ch.ip is that it calculates correspondence on the epipolar line of this circle.
All the image features corresponding to targets in the plane of the Vieth-Muller circle have the same retinal y-coordinate. However, some of the neurophysiological characteristics of the neurons thought to participate in the computation have been elucidated. He lists five main categories of cell: the tuned excitatory cell, which is only strongly stimulated by binocular stimuli close to zero disparity; the tuned inhibitory cell, which is typically strongly stimulated by monocular targets presented to one of the two eyes and always inhibited by binocular stimuli at zero disparity; the tuned-near/tuned-far cells and the near/far cells, which are driven by stimuli of greater crossed or uncrossed disparity; and the disparity flat cells stimulated by targets presented by either eye alone, or by binocular targets at any disparity.
Cooperative algorithms typically involve arrays of units that are narrowly tuned for dissonance, similar to tuned null neurons.
A nonlocal interaction that gathers evidence to guide this decision
- The Chip
- Input
- Analog Psychophysics
- Interpolation from Unambiguous Endpoints
The resistors connecting the analog units are pulled with fuses controlled by the output of the monocular units. The response of the analog-valued array and the inhibitory array is monitored on an oscilloscope. . rope --9. The heart of the chip is the correlator array, analogous to the tuned excitatory cells.
The disparity adjustment curve for the voltage on the common line of the WTA circuit is shown in Figure 4.16. This tuning curve is analogous to the disparity tuning curve of a flat disparity cell. Analog units combine activity in the correlator matrix along the same cyclopean angle lines for analog estimation of image disparity.
The magnitude of the retinal input to the monocular cell relative to that in the correlation array is set by controlling the input gain. As in the correlation set, the magnitude of the positive feedback varies with the magnitude of the retinal input. Adding units with analog values allows the interpolation to occur in a more natural form.
