Toward Sentient Neurotechnology

Visual Object Unity May Be Structured by and Constrain Neural Interactions

Raymond Pavloski

Psychology Department, Indiana Univ. of PA, 15701, Indiana, PA, U.S.A.

Keywords: Hard Problem, Neurotechnology, Recurrent Neural Network, Sentience, Tolerance Space, Visual Object

Unity.

Abstract: Achieving an understanding of how qualities of experience arise in concert with the operation of neural

networks could produce a revolutionary advance in neurotechnology. The work reported here explores a

relationship between a visual quality and neural activity that has not previously been investigated: visual

object unity may emerge from and constrain neural interactions. Simulations were employed to determine if

a topological signature of a unified object develops as a recurrent neural network’s activity is modulated by

retinal input. Results show that differences in recurrent excitatory conductance values produced by adjacent

active neurons are negligibly small, and can be described by a tolerance relation. Tolerance open balls about

the vectors of conductance values produced by active neurons emerge in response to the retinal image of an

object and a connected open set consisting of intersecting open balls quickly develops. Such connected open

sets are invariant over fluctuations in participating neurons, demonstrate several characteristics of perception,

and are hypothesized to be objective signatures of perceived object unity. Dynamical network phenomena,

such as hysteresis, lead to empirical predictions that can be tested with human participants. Means of

identifying objective signatures in brain activity are considered.

1 INTRODUCTION

The domain of neurotechnology is limited by the

absence of an explanation for how the qualities of

experience arise in concert with the operation of

neural networks in the brain, often referred to as the

‘hard problem’ (Chalmers, 1996; Hut and Shepard,

1996). As a result of this limitation, we are unable to

construct a cortical prosthesis that when interfaced

with damaged visual cortex would make it possible

for a patient to regain aspects of visual experience that

have been lost through cortical lesions.

There is no doubt that significant progress has

been made in identifying objective signatures of

conscious access, the ability to report an experience

following presentation of a stimulus (Dehaene, 2014).

However, this achievement provides no information

regarding the neural mechanisms involved in the

appearance of a particular quality of experience

(Block, 2001; 2007). Nor does it provide any

information on how the processes that underlie any

specific quality of experience are involved in neural

dynamics. Without such information, it is difficult to

take seriously the claim that “there is now sufficient

evidence to consider the design and construction of a

conscious artifact (Edelman et al., 2011).”

It seems unlikely that a general solution to the

hard problem will be found in the absence of work

that relates specific aspects of experience to specific

aspects of neural activity. In order for experimental

and theoretical progress to be made, it is essential that

an aspect of experience can be described so that its

relation to neural activity is evident. This report puts

forward the appearance of visual object unity (Chen,

2005), modelled as a connected open set in a

tolerance space (Peters and Wasilewski, 2012), as

such an aspect of experience.

From a naïve viewpoint, it is easy to overlook the

fact that the experience of a unified entity, one aspect

of the full experience of a visual object, is an

achievement of the visual system. Of course, this is

obvious to those who believe that vision proceeds

from part to whole and from geometrically simple to

geometrically complex. From this perspective, it is

assumed that receptive field data show that an object

image is initially decomposed into patches of

contrast, and that processes in successively higher

cortical areas in some way bind successively more

complex geometric features into the visual object that

is experienced (e.g., Roelfsema and Houtkamp,

Pavloski, R..

Toward Sentient Neurotechnology - Visual Object Unity May Be Structured by and Constrain Neural Interactions.

In Proceedings of the 3rd International Congress on Neurotechnology, Electronics and Informatics (NEUROTECHNIX 2015), pages 81-90

ISBN: 978-989-758-161-8

2011). The topological approach to perceptual

organization that is advanced by Chen (2005; see also

Zhang, 2005) is in agreement with the conclusion that

visual object unity is an achievement of the visual

system. According to this approach, however, visual

unity is a topological visual primitive and is extracted

from the object image very early in visual processing.

Despite the volume of excellent experimental

work carried out by Chen and his colleagues in

support of the topological approach, the means by

which visual neural networks deal with topological

properties has remained a mystery (Minsky and

Papert, 1988; Pomerantz, 2003). As indicated by

Chen (2005), the topological approach can be made

compatible with the fundamentally discrete nature of

the visual system if it is assumed that vision is tolerant

to differences in the retinal image at various scales.

For example, visual unity can readily be perceived in

a collection of image elements that are spatially

separated by sufficiently small distances. This is

expressed formally by stating that a pair of image

elements belongs to a tolerance relation τ if the

distance between them is less than some criterion.

Like equality, tolerance τ is a relation that is reflexive

(for an element a, the pair (a,a) belongs to τ) and

symmetric (if (a,b) belongs to τ, then (b,a) belongs to

τ). Unlike equality, however, tolerance is not

transitive: (a,b) belongs to τ and (b,c) belongs to τ do

not imply that (a,c) belongs to τ. Work in

computational vision shows that it is possible to apply

a tolerance relation to the elements of an image and

thereby to identify topological properties of the image

(Huang et al., 2010). How the brain might accomplish

this task is not known. More importantly, even having

a neural network that computes topological properties

might not tell us how the experience of visual unity

arises within that network, how we see visual unity.

An alternative approach is to study the sources

and consequences of a tolerance relation within the

recurrent neural interactions of richly interconnected

networks of the visual system. Introducing a bit of

tolerance space terminology is very helpful in seeing

how this might be done (Peters and Wasilewski,

2012). If we use accepted terminology, then the set of

elements x such that (a,x) belongs to τ is called an

open ball about a, or OB(a). For example, we might

have OB(a) = {a,b}, OB (b) = {a,b,c}, and OB(c) =

{b,c}. A set that contains the open balls about each of

its elements is called an open set, so {a,b,c} is open.

Finally, an open set is said to be connected if it cannot

be separated into two disjoint open sets, both not

empty. Using this definition, we can readily see that

{a,b, c} is a connected open set (COS). The definition

of a COS indicates that it is a reasonable model of

visual object unity, given that the elements with

which we are working must be discrete.

Figure 1: A schematic of the central idea motivating the

present work is shown. See text for details.

The work reported here is based on the idea that

recurrent neural network inputs are structured by

retinal image input, the network’s synaptic

architecture, the dynamics of synaptic events, and a

tolerance relation τ into a COS, and thereby “make

sense” as visual object unity. It is assumed that

recurrent inputs from two network neurons belong to

τ if they are sufficiently similar as to have

indistinguishable effects on network neurons.

Figure 1 is a schematic illustration of recurrent

inputs arising from the N neurons in a network. In a

fully-connected network, each neuron contributes N

such inputs that are modelled as an N-dimensional

vector. These vectors can be projected on basis

vectors for the 3D space in which the neurons are

located. The top left graphic in Figure 1 demonstrates

the result for a network with N = 1089 in which the

neurons receive inputs from the image of a square.

Neurons that receive little input from the image

produce very small vectors of recurrent inputs that

project to the origin of the coordinate system being

used. More active neurons have larger projections,

but these provide no information regarding the

presence of a unified object.

The bottom right graphic shows projections of the

same vectors of recurrent input on a dimension that

reflects the rapid decay of recurrent input synaptic

conductance with time, and on two dimensions that

reflect the decay of recurrent input synaptic

NEUROTECHNIX 2015 - International Congress on Neurotechnology, Electronics and Informatics

conductance with distance between source and target

neurons. Large projections on the temporal decay

dimension are produced by neurons that receive

retinotopic input from the square image and have

recently fired action potentials (APs), and pairs of

projections that are joined by line segments form a

COS that models visual object unity. It is proposed

that, rather than computing topological properties,

such a network creates the perceived unity of a visual

object.

The remainder of this paper shows how this idea

can be realized in a simple recurrent neural network

(RNN). Section 2 provides a description of the

network model. Previous work employing singular

value decomposition (SVD) of a matrix of recurrent

excitatory conductance values G(t) showed that a

small number of basis vectors span the row space of

G(t) and allow a portrayal of stable structures that

form in response to an input image (Pavloski, 2011).

Section 2.1 shows that the row space basis vectors

arise from the distribution of synaptic weights and the

decay of conductance values over time. In Section

2.2, evidence for a tolerance relation containing pairs

of similar vectors of recurrent conductance values is

presented. Simulations show that this tolerance

relation permits a COS of the vectors of sodium

conductance values produced by active RNN neurons

to emerge from the retinal image of an object. Results

showing that COSs demonstrate several

characteristics of vision are described in Section 2.3.

These include just noticeable differences, the Gestalt

phenomenon of grouping by proximity, similarities to

V1 fMRI data for real motion and apparent motion,

and object constancy over rotation and changes of

size and orientation of an image. The issue of

determining whether a COS is an emergent entity is

considered briefly in Section 3. Two approaches to

testing the hypothesis that a COS is an objective

signature of a unified visual object are described in

Section 4, and conclusions are stated in Section 5.

2 A RNN THAT PRODUCES

CONNECTED OPEN SETS OF

CONDUCTANCE VECTORS

Simulated grayscale images were presented to a

simulated retina consisting of a 33 x 33 lattice of

model neurons. The inputs from the simulated image

to these model neurons were arranged so that each

receptive field was concentric, with a small diameter

ON center within which illumination excites the cell,

and a larger diameter OFF surround within which

illumination inhibits the cell. This was done in the

following way for each retinal neuron. The membrane

potential (E

) was set to 2.5 times the sum of the

illumination at each point in the image multiplied by

the value of a normal pdf (mean μ = 0 and standard

deviation σ = 1) at the Euclidean distance between the

image point and the location of the neuron, minus .6

times the sum of the illumination at each point in the

image multiplied by the value of a normal pdf (μ = 0

and σ = 4) at the Euclidean distance between the

image point and the location of the neuron. Using this

method, E

is affected by light in the simulated

images as shown in the top left panel of Figure 2. The

probability of an AP increased monotonically with E

above a threshold.

Figure 2: ON-center, OFF-surround neurons and RNN

neurons are depicted in the top and middle panels. A retinal

response to a 15 x 15 pixel image and a snapshot of RNN

excitatory neuron action potentials (APs) are shown in the

bottom panel.

Retinal neuron APs map retinotopically to

excitatory synapses on excitatory single compartment

model RNN neurons, which are also arranged in a 33

x 33 lattice and shown in Figure 2 as dots. An AP

produced by any retinal neuron is assigned the value

1 (present) or 0 (absent), and the effect on any

excitatory RNN neuron is given by this value

multiplied by a synaptic weight, which is .01 times

the value of a normal pdf (μ = 0 and σ = .03) at the

Toward Sentient Neurotechnology - Visual Object Unity May Be Structured by and Constrain Neural Interactions

Euclidean distance between the 2-dimensional

location of the retinal neuron and the 2-dimensional

location of the excitatory RNN neuron. The summed

effects of all retinal inputs on each neuron affected

excitatory sodium conductance according to an alpha

function (Sterratt et al., 2011); specifically, the value

of the conductance on each iteration of the network

was set to 0.7 times the summed weighted inputs plus

0.3 times the current value of the conductance.

Each excitatory RNN neuron sends output to all

excitatory neurons and also to inhibitory neurons

(shown in Figure 2 as circles) that are interspersed

among the excitatory neurons in an 11 x 11 lattice.

The inhibitory neurons, in turn, send outputs to all

excitatory neurons. All synaptic weights decrease

exponentially with distance (plus a random

component) between the source and target neurons,

with inhibition following off less rapidly than

excitation. The exponential functions were chosen to

promote very stable network dynamics. Excitatory

weights vary from a minimum of 0.15 to a maximum

of 0.23, and inhibitory weights vary from a minimum

of 0.34 to a maximum of 0.37 over the range of

distances in the lattice of neurons (distances range

from 0. to (2x32

)

1/2

Conductance based equations for the point

neurons follow standard sources (Sterratt et al.,

2011), and parameter values are taken from O’Reilly

and Munakata (2000). Both excitatory (sodium) and

inhibitory (chloride) conductance values produced by

RNN neuron APs were calculated in the same fashion

as the excitatory conductance values produced by

retinal neurons. The value of E

of each neuron was

determined by treating the membrane as an RC circuit

with time constant .2 and each synapse as a variable

conductance in series with the appropriate

equilibrium potential. All synapses were in parallel

with each other and with the resting E

and leak

conductance. Values were scaled so that E

varied

between 0 and 1. An AP was produced with a low

probability (.01) if E

is less than a threshold value =

.25, and the probability of an AP increased

monotonically for E

> .25. Updating was

synchronous, with every value in the RNN updated

on each iteration of the simulation using values of

current inputs and values of network variables from

the previous iteration. Retinal neuron membrane

potentials and APs produced by RNN excitatory

neurons on one iteration in response to a 15x15 pixel

image are shown in the bottom panel of Figure 2.

2.1 Singular Value Decomposition of

the Recurrent Excitatory

Conductance Matrix

After approximately 11 iterations, the RNN achieves

a stable response to an image. As indicated in Section

1, previous work demonstrated that a small number of

dimensions describe the row space of G(t). The entry

in the i

row and j

column of this matrix is the

conductance value g

produced in excitatory neuron j

by excitatory neuron i. Thus, row i is vector g

conductance values in all RNN excitatory neurons

produced by neuron i. SVD of G(t) reveals that the

first three singular vectors serve as basis vectors for

the row space of G(t), accounting for over 99% of the

variance in the entries of the matrix. The top panel of

Figure 3 shows row projections on the basis vectors

for a COS that results from an 11 x 11 pixel input

image on one iteration of the simulation.

The log of the projections of conductance vectors

on the first basis vector are linearly dependent on the

time of the most recent AP (r

> 0.99). This is

expected because each conductance falls off

exponentially over time following the most recent

AP. The projections of each conductance vector on

the second and third singular vectors are linearly

related to the relative row and column position of the

neuron giving rise to that conductance vector. It is not

possible to quantify the goodness of fit with a single

correlation coefficient because the slope of the best-

fit line is much smaller for smaller conductance

values that are produced by APs occurring in the past.

This is illustrated by the middle and bottom panels of

Figure 3, which show projections of conductance

vectors plotted as functions of each neuron’s row

position in the lattice shown in Figure 2. For

simplicity, axes of all subsequent plots of COSs will

continue to be labelled as Row Basis Vectors.

2.2 Connected Open Sets of Vectors of

Conductances Result from

Tolerance to Small Differences in

Recurrent Inputs

It is easy to recognize a natural source of tolerance in

the RNN. Adjacent excitatory neurons are very likely

to receive virtually identical inputs from retinal

neurons and from other RNN neurons. They are

therefore likely to fire very similar trains of APs and

thus to produce very similar vectors of conductance

values. This is confirmed by simulations. For

example, closely positioned neurons that recently

fired an AP in response to a 7 x 7 image yield a mean

difference between conductance vector magnitudes

NEUROTECHNIX 2015 - International Congress on Neurotechnology, Electronics and Informatics

equal to 5.05 x 10

-6

(se = 2.23 x 10

-7

)

and a mean

difference in angular orientations of .03 rad (se = 4.46

x 10

-4

). Such small differences in conductance vector

magnitudes and orientations are of no consequence

with respect to their impact on the temporal evolution

of conductance vectors.

Figure 3: Plot of COS conductance vector projections on

three dominant singular vectors (top). Vectors within a

tolerance are joined by lines. The projection of each

conductance vector on the second singular vector is linearly

related to the rotated row position of the neuron giving rise

to that conductance vector with a slope determined by the

time of the most recent AP (middle, bottom). See Sections

2.1 and 2.2 for details.

Frequency histograms of vector magnitude

differences and orientation differences imply that a

magnitude difference less than 10

-4

and an orientation

difference less than .03 rad are appropriate criteria for

a pair of vectors to belong to the tolerance relation.

Figure 4: A COS occurs on iterations 11-20 in response to

an 11 x 11 input image presented on iterations 6-15 (top).

Projections of conductance vectors on the second and third

basis vectors for the rows of conductance matrix G(t) are

shown as a function of iteration number. Conductance

vectors on successive iterations that are within a tolerance

are joined by light gray line segments. No lines are drawn

between vectors within a tolerance on a given iteration for

this and subsequent figures. The solid curve in the bottom

graph plots the function r

for iteration i= 11 of the

simulation, the dashed curve plots results for i=12, and the

dotted curve plots results for i=13. Lag = t

– t

The top panel of Figure 4 plots the COSs that arise

from an 11 x 11 pixel input image. The image was

shown on iterations 6-15, and COSs appear on

iterations 11-20. In this figure, the iteration number is

used as the x-axis, and the second and third singular

vectors are used for y and z as they were in Figure 3.

Conductance vectors on successive iterations that

meet tolerance criteria are joined by gray line

segments. The spatiotemporal consistency in COS

composition occurs jointly with large fluctuations in

neurons giving rise to vectors in the COS. This is

Toward Sentient Neurotechnology - Visual Object Unity May Be Structured by and Constrain Neural Interactions

demonstrated by the bottom panel, which plots the

simple correlation function

= (N

- N

) / D

(1)

where N

is the number of distinct pairs of neurons

giving rise to conductance vectors within a tolerance

(tolerance pairs) at times t

and t

, N

is the number of

tolerance pairs that are present at time t

but not at

time t

, N

is the number of tolerance pairs that are

present at time t

but not at time t

, and D

is the total

number of distinct tolerance pairs present at time t

at time t

. The majority of tolerance pairs occurred

only once or twice over the 10 iterations of the

network for which the correlation function is plotted

in Figure 4. Thus, similar conductance vectors are

produced on sequential iterations by different pairs of

neurons.

2.3 COS Phenomena Mimic Visual

Phenomena

COSs demonstrate just noticeable differences (jnd’s)

and grouping by proximity. These phenomena are

demonstrated by simulation results depicted in Figure

5. The COSs are shown after the RNN has stabilized

(i.e., beginning on iteration 12).

It has been shown that fMRI data from human

primary visual cortex (V1) show a moving pattern of

activation during perception of real motion and

apparent motion (Larsen et al., 2006). It is of interest

that the COSs that emerge from the smooth motion of

an image and from simulation of the conditions for

apparent motion behave very similarly to V1 fMRI

data. The COSs that result from these two conditions

over 20 iterations are shown in the top and bottom

panels of Figure 6.

In a similar fashion, COSs track the change of

orientation of the image of a rectangle, a change of

size of a square, and rotation of a rectangle, as shown

in Figure 7. The behaviour of the COSs mimics object

constancy over similar changes in object images.

3 IS A COS IN RECURRENT

NETWORK INPUTS A MODEL

OF LARGE-SCALE ORDER?

Results presented in Section 2.2 demonstrate that

similar pairs of conductance vectors that are elements

of a COS are produced by different pairs of neurons

on sequential iterations of the simulated RNN.

Figure 5: Two COSs emerge in response to two, 3x3 pixel

images that are separated by three pixels diagonally (top).

One COS emerges when the diagonal separation is reduced

to one pixel (middle). Grouping by proximity results in one

COS to an image of 16 one-pixel elements with one-pixel

spacings (bottom).

This finding suggests the possibility that a COS

models emergent large-scale order that is invariant

over participating neurons. COS phenomena that

mimic visual phenomena (Section 2.3) are consistent

with this possibility. For example, a single COS

persists over time even as size and orientation of an

image change, and a COS persists under the

conditions of apparent motion, which involve brief

elimination of the image of an object.

NEUROTECHNIX 2015 - International Congress on Neurotechnology, Electronics and Informatics

Figure 6: The COSs in the top panel on iterations 11-30

result from an 11 x 11 image shown in one corner for 10

iterations, then shown displaced by 5 pixels horizontally

and vertically for 5 iterations repeatedly until finishing at

the diagonally opposite corner for 5 iterations. The COSs in

the bottom panel shown on iterations 11-30 result from a 5

x 7 image shown in one position for 20 iterations, then not

shown for 2 iterations. Each point is then displaced

vertically by 9 pixels and shown for 10 iterations.

These results should be replicated using a much

larger scale simulation that would include

arrangements of a retina and RNN with receptive

fields that overlap like those in mammalian visual

systems. This would permit the use of more realistic

images of multiple objects and should also enhance

the similarities in recurrent inputs between adjacent

neurons. In addition, asynchronous updating using

very small time steps would more closely

approximate biological vision and should enhance the

temporal persistence of COSs.

Figure 7: COSs smoothly track step changes in orientation

(top) and in size (middle), and a step rotation (bottom). The

top image of each pair was shown for 15 iterations and

replaced by the bottom image for 15 iterations, and the

COSs are plotted from iterations 16-30.

Toward Sentient Neurotechnology - Visual Object Unity May Be Structured by and Constrain Neural Interactions

A network with these characteristics should make

it possible to analyse the projections of G(t) on row

basis vectors for the presence of topological

properties such as the number of connected objects

and the number of holes. Such work would provide

an approach that would complement the direct

introduction of a tolerance relation, as done here.

Two strategies might be then be followed in

testing the hypothesis that large-scale topological

objects emerge within recurrent interactions. The first

is to use simulations in order to determine if a COS

possesses typically-observed properties of such large-

scale order. We expect to find a control parameter that

can be varied to modulate the shape of a potential that

is a function of an order parameter, such as the density

of a COS (e.g., number of conductance vectors per

unit volume). Using data gathered from human

participants (see Section 4), we will attempt to find a

potential function empirically, and to incorporate this

in simulations in order to make predictions that can

then be tested with human participants.

A second strategy involves implementing a RNN

in an electronic circuit. In principle, it should be

possible to interface an analog electronic RNN with a

biological visual system so that they cooperate to

produce one or more COSs. Such an arrangement

could serve both as a critical test of ideas that underlie

the approach to the hard problem that is advocated,

and as a prototype for a prosthetic device. There is no

question that many difficult obstacles must be

overcome for this strategy to become feasible. Poon

and Zhou (2011) provide a fairly recent overview of

the challenges and opportunites presented by

neuromorphic silicon neurons and large scale neural

networks, and a wide-ranging and thorough review of

such circuits is provided by Indiveri et al., (2011).

4 IS A COS IN RECURRENT

NETWORK INPUTS AN

OBJECTIVE SIGNATURE OF

PERCEIVED OBJECT UNITY?

The results presented above are consistent with the

hypothesis that a COS of recurrent vectors of sodium

ion conductance is an objective signature of perceived

object unity. Empirical tests using data collected from

human participants and from non-human species are

required to test this hypothesis.

Two approaches to devising such tests are

considered in this section. The first approach is based

on comparisons of dynamical phenomena exhibited

by COSs in neural network simulations with

dynamical phenomena in human visual perception.

This approach has a strong existing basis in the

perception literature, particularly in work based on

Haken’s (1996) Synergetics. The second approach is

much more direct, as it is based on a search for

evidence of a COS in recordings of brain activity.

4.1 Do Perceived Object Unity and

COSs Exhibit the Same Dynamical

Phenomena?

In addition to the visual phenomena that are

mimicked by COSs as presented above, dynamical

effects of sequential presentations of stimuli are well

documented in perception. For example, categorical

perception of speech sounds has been shown to

exhibit both enhanced contrast and hysteresis (Tuller

et al., 1994). Enhanced contrast occurs when a

perception changes from one category to another at

one parameter value as values are initially increased

and at a higher parameter value as values are

subsequently decreased. In hysteresis, the change

occurs at a higher parameter value for initial increases

than for subsequent decreases. Tuller et al., (1994)

showed that the data collected from human

participants fit an underlying model for which

hysteresis dominates during early trials, and enhanced

contrast dominates as experience with the task brings

certain cognitive factors into play. The simple RNN

has no capacity for such cognitive functions, and is

therefore expected to display hysteresis.

The phenomenon of grouping by proximity was

used to test this hypothesis. The images used consist

of 140 one-pixel spots. One hundred of the spots are

repositioned randomly within the 33 x 33 pixel image

area on each iteration. The remaining 40 spots are

positioned randomly within a square window the

sides of which are reduced from a length of 33 pixels

to a length of seven over the first 31 iterations; the

sides increase over the remaining 30 iterations to the

original length of 33. The inset in the top panel of

Figure 8 shows images from iterations 1, 10, 20 (top

row), 30, 31, 32 (middle row), and 42, 52, and 61

(bottom row). The portion of the

graph with forward

arrows (→)

plots the size of the emergent COS as the

sides of the window containing the critical 40 dots is

initially decreased, and the portion of the graph with

backward arrows (←) plots COS size as window size

is subsequently decreased. It is clear that hysteresis is

present. We are currently testing human participants

with a version of the grouping by proximity task that

has been modified to make it appropriate for the

human visual system. The procedure used by Tuller

et al., (1994) for categorical perception of speech

NEUROTECHNIX 2015 - International Congress on Neurotechnology, Electronics and Informatics

sounds was changed slightly in order to apply it to

perception of object unity. In this task, 1600 dots are

displayed on each trial. Of these, 1500 are randomly

positioned within a 10 x 10 square on each trial. An

additional 100 dots are randomly positioned within a

square window that grows or shrinks over trials. Dot

diameter is 0.2 percent of the width of the 10 x 10

square. The bottom panel of Figure 8 illustrates

results from five pilot subjects. On each of two blocks

of trials, the length of the sides of the square

containing the additional 100 dots was reduced from

10 to 1.5 over the first 100 trials and then increased

over the remaining 100 trials to the original length of

10. Hysteresis is present in the total number of reports

of a unified object (out of 10 maximum).

Figure 8: The top panel shows hysteresis in the number of

conductance vectors that are elements of a COS. The inset

shows simulated retinal images for nine iterations of one

simulation, as described in the text. The graph with forward

arrows (→) plots the number of conductance vectors in the

resulting COS on iterations 1-31, and the graph with

backward arrows (←) plots the size of the COS on iterations

32-61. This graph clearly demonstrates hysteresis. The

bottom panel shows hysteresis in perception of a unified

object for five participants.

4.2 Can the Presence of a COS Be

Inferred from Recordings of Brain

Activity?

A direct test of the hypothesis that a COS of

excitatory recurrent conductance vectors is indicative

of the experience of visual object unity would be

possible if extracranial or intracranial recordings

could be used to detect a COS. It is possible that large-

scale brain simulations and visualizations (e.g., Jones

et al., 2013) could answer this question.

Such large-scale simulations have been shown to

model successfully network dynamics of primary

visual cortex at multiple scales (e.g., Rangan et al.,

2009), and the network model appears to account for

V1 activity associated with the line-motion illusion

(Rangan et al., 2005). It is important to replicate the

strategy used by previous researchers in order to

determine if the presence of a COS produces a

signature in simulations of recorded activity that

include single unit, population, and

electroencephalogram recordings and optical imaging

with voltage-sensitive dyes. Some of these studies

would employ non-invasive methods and can be

performed with human participants. Others are

clearly invasive and would have to be performed with

non-human species.

5 CONCLUSIONS

Progress in the development of neurotechnologies is

necessarily limited by our current understanding of

the specific ways in which neural network activities

are involved with particular aspects or qualities of

conscious experience. The central problem that we

face is theoretical. It is precisely the famous ‘hard

problem’ (Chalmers, 1996; Hut and Shepard, 1996).

The introduction of a formal model of an aspect

of experience makes it possible to state a testable

hypothesis that bears directly on the hard problem:

the unified aspect of a visual object arises as a COS

of vectors of recurrent excitatory conductance values

emerges from cooperative network activity. Results

using a small RNN driven by simulated activity of

retinal neurons with a concentric receptive field

organization are very promising. These results

demonstrate a natural source of tolerance that

underlies the formation of a COS, and visual

phenomena that include just noticeable differences,

grouping by proximity, similarities to V1 fMRI

activity patterns in response to real and apparent

motion, and visual object constancy with changes in

size, shape and rotation are all reproduced by COSs.

Toward Sentient Neurotechnology - Visual Object Unity May Be Structured by and Constrain Neural Interactions

The COS is also subject to the nonlinear phenomenon

of hysteresis that characterizes multistability in

perception.

It is important to use a variety of strategies to test

two hypotheses that arise from the work reported

here: (1) a COS of excitatory recurrent conductance

vectors is a model of large-scale order within

recurrent network interactions; and (2) such a COS is

an objective signature of the unity or oneness aspect

of a visual object.

ACKNOWLEDGEMENTS

The author wishes to thank Dr. Charles Lamb of the

IUP Department of Mathematics for the many

positive contributions that he has made to the work

reported here in our numerous discussions. The

author also thanks Mr. Ian Bright who collected the

pilot data reported in Section 4.1 and who contributed

in all aspects of that work. Two anonymous reviewers

are also thanked for their thoughtful and useful

comments.

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