Experiences with iterated traffic microsimulations in Dallas

Abstract
This paper reports experiences with iterated traffic microsimulations in the context of a Dallas study. ``Iterated microsimulations'' here means that the information generated by a microsimulation is fed back into the route planner so that the simulated individuals can adjust their routes to circumvent congestion. This paper gives an overview over what has been done in the Dallas context to better understand the relaxation process, and how to judge the robustness of the results.

arXiv:adap-org/9712001v1 10 Dec 1997
Experiences with iterated traﬃc microsimulations
in Dallas
Kai Nagel
Los Alamos National Laboratory, TSA-DO/SA Mail Stop M997,
Los Alamos NM 87544, USA, kai@lanl.gov
May 21, 2018
Abstract
This paper reports experiences with iterated traﬃc microsi mulations
in the context of a Dallas study. “Iterated microsimulation s” here means
that the information generated by a microsimulation is fed b ack into the
route planner so that the simulated individuals can adjust t heir routes to
circumvent congestion. This paper gives an overview over wh at has been
done in the Dallas context to better understand the relaxati on process,
and how to judge the robustness of the results.
1 Introduction
The advent of ever more powerful workstation computers makes large scale
transportation microsimulation projects feasible. At the same time , traditional
tools are having a hard time treating all the complexities of modern co ngested
transportation systems. As a result, there has been considerab le progress in
the area of transportation microsimulation in recent years, both in terms of
theoretical understanding of micro-models [1, 2, 3, 4] and in terms of practi-
cal implementations [5, 6, 7, 8, 9, 10, 11]. Yet, having good transpo rtation
microsimulations is only part of the problem. When running such a micro simu-
lation, one ﬁnds oneself confronted with the question of how to “dr ive” it: when
a driver in the microsimulation approaches an intersection, how does she know
which way to proceed?
The traditional answer to this question are turning percentages: for exam-
ple 50% of the vehicles go straight, 20% left, and 30% right. One is, th ough,
immediately faced with a data collection problem: It is improbable that o ne
knows the turn counts for all intersections of a regional area; an d if one does
not, one needs methods to “generate” the missing information [10]. Also, for
transportation planning purposes one recognizes quickly that these numbers are
not very useful because they change easily with infrastructure c hanges.

A somewhat better way is to use origin-destination matrices. Yet, t he prob-
lems are the same: The information is not available, especially for non- work
trips; and these matrices change with major infrastructure chan ges.
An answer to this is to start from demographics: It is improbable tha t peo-
ple’s income changes or that they move in a matter of weeks in respon se to trans-
portation infrastructure changes. From there, for a microsimulation project, the
ﬁrst step is to generate “synthetic” populations from the demogr aphic data [12].
The next task is to derive activities (sleep, work, shop, . . .) for each member of
a synthetic population, and then to derive the transportation dem and from this.
So far no project has succeeded in completely executing this progr am, i.e. to use
activities based on demographics to “drive” a transportation micro simulation.
There are considerable challenges “on the way”. For example, even when
given a time-dependent origin-destination matrix and a traﬃc netwo rk, how does
one allocate the trips to the network? Traditional assignment meth ods can be
shown to be dynamically inconsistent under heavily congested condit ions. One
of the major problems is that for links where demand is higher than ca pacity,
the link travel time depends on for how long the congested condition has been
in place and not just on demand only, and thus the traditional link tra vel time
functions are invalid.
A way out is to replace the traditional cost functions by a microsimula tions.
In short, one allocates traﬃc streams to the road network, runs the microsim-
ulation and collects link travel times, re-allocates some of the traﬃc streams,
re-runs the microsimulation, etc. This mimics “day-to-day” dynamic s, i.e. “over
night” some drivers decide to try a new route the next day. Obvious ly, one faces
considerable challenges, such as: Which fraction of the population s hould be re-
planned? How do we reach fast convergence of the process? Does the process
converge at all? Can we measure convergence? Is a real traﬃc sys tem con-
verged? This paper will report results related to these questions in the context
of a Dallas study. After providing the context (Sec. 2) and showing the ﬁrst re-
sults (Sec. 3), the paper will summarize systematic feedback stud ies (Sec. 4) and
possible “structural” convergence criterions (Sec. 5). After th at, this paper will
look at diﬀerent aspects of the “robustness” of results; ﬁrst un der the change
of a random seed (Sec. 6), then under the change of the complete microsimu-
lation (Sec. 7), then in comparison to reality (Sec. 8). Section 9 disc usses the
robustness question in somewhat more general, pointing out that o ne ﬁrst needs
to deﬁne the question that the simulation is supposed to answer. Th e paper is
concluded by a short summary (Sec. 10).
2 The context
The context of the results reported here is the Dallas/Fort Worth case study of
the TRANSIMS project. The goal of the case study was to demons trate that
the approach has the general capability of generating output tha t is useful for
stake-holder analysis and scenario evaluation [13]. The setting of th e study was
a 5 miles times 5 miles area (“study area”) around the busy freeway in tersection

between the LBJ freeway and the Dallas North Tollway north of Dallas down-
town. The problem was approached by starting out with a “focused network”
and a production-attraction (PA) matrix. The focused road netw ork contained
all streets inside the study area, but got considerably thinner with inc reasing
distance from the study area. A production-attraction matrix is e ssentially a 24-
hour origin-destination matrix with some land-use information include d (trips
from work to home are entered as trips from home to work, with the result that
the zones where trips originate in these matrices need to be residen tial zones).
The PA matrix for Dallas/Fort Worth contained approximately 10 million trips
during a 24-h period.
Since TRANSIMS is a microscopic approach, the ﬁrst thing that was d one
was to decompose the PA matrix into individual trips. This was done us ing a 24-
hour time use function, i.e. each trip had a starting time, and the dist ribution
of starting times reﬂected rush period traﬃc. Out of these trips, only the
trips starting between 5am and 10am were considered. These trips were routed
along the road network, and only the trips which went through the s tudy area
were retained (about 300 000 trips). This set of trips, sometimes c alled “initial
planset”, forms the basis of all studies presented here. See [13, 1 4] for further
details.
3 First results
Just using the routes from the initial planset and sending them thro ugh a traﬃc
simulation1 typically generates a result as in Fig. 1, where many streets are
occupied by jammed traﬃc. The problem behind this is, obviously, tha t the
route generation phase for the initial planset did not take into acco unt what
other people were going to do. Yet, predicting what everybody else will do in
a straightforward way is impossible; imagine yourself in a situation whe re you
wake up one morning in a city where you need to go to work, and the on ly two
pieces of information you have is a map of the transportation syste m and the
information that everybody else is in the same situation as you.
The way we solve this is by iterations between microsimulation and plann er.
A possible method is the following: the microsimulation is run, link travel times
are extracted from the microsimulation, a certain percentage of t he travelers
computes new routes based on these link travel times, the microsim ulation is run
again with these new plans, etc. New routes are computed using time -dependent
fastest path based on the starting time, starting location, destin ation, and link
travel times from the microsimulation. Other iteration schemes are possible,
see, e.g., [15].
An open question here is which percentage of the travelers should b e re-
planned. First, we started out with a fairly high percentage, 10%, a nd used
1Note that this remark implies that we are using microsimulat ions based on route plans ,
i.e. each driver knows before her trip starts exactly the seq uence of links she wishes to take
through the network.

Figure 1: Microsimulation run based on initial planset, snapshot at 9:3 0 am.
that until the results started oscillating, which was after the 7th it eration.2 In
iterations number 8–12, 5% of the trips were re-routed; in iteratio ns number
13–14, 2% of the trips. A typical result after 14 iterations can be s een in Figs. 2
and 3. Clearly, the traﬃc jams have cleared, and traﬃc is not only mo re evenly
distributed, but because the system is more eﬃcient, traﬃc does n ot back up.
Fig. 2 looks “plausible”, whereas Fig. 1 does not. Further informatio n can be
found in [14].
2The reason for the oscillation is easy to understand: Assume you have two route alterna-
tives, and one is slightly faster. If you re-route a certain p ercentage of people, than the other
alternative will be faster. Without additional measures, t his will be an undamped oscillation.

Figure 2: Microsimulation run based on the planset after 14 iteration s, snapshot
at 9:30 am. Compare to Fig. 1.
4 Systematic feedback studies
Using a relaxation scheme such as the above is not very practical (b ecause
it needs human supervision) and scientiﬁcally not very convincing: Qu estions
such as “Does the process converge? If so, can we quantify ‘dista nce’ from
the converged state? Is real traﬃc converged?” come up. One n ext step is
thus to more systematically test relaxation schemes and relaxation properties.
(Since we do not know if the process “converges” in the mathematic al sense, we
will talk about “relaxation” instead.) Rickert [5, 16] has run such tes ts in the
same Dallas/Fort Worth context, but with a diﬀerent microsimulation [6]. His
microsimulation is somewhat less realistic (most important points: no s ignal
plans, no turn pockets, no lane changing for turning behavior), bu t it currently

Figure 3: Microsimulation run based on the planset after 14 iteration s, snapshot
at 9:30 am, detail. Traﬃc lights are shown by their colors at the end of links.
Cars can be color coded according to speciﬁed criteria – in this speciﬁ c example,
cars that were not able to follow their intended plans because they c ould not
get into the desired lane are shown red.
runs more than 20 times faster than the microsimulation used in the la st section.
Some comparisons between the results obtained by both microsimula tions will
be shown below; we believe using a diﬀerent microsimulation will not have any
signiﬁcant impact on the general results that will be discussed in this section.
Fig. 4 shows the sum of all travel times as a function of the iteration number
for diﬀerent iteration schemes. For example, the full line (also mark ed by +)
is for the same relaxation scheme as described in the last section. Th e data
marked by the × symbol is for an iteration series where in each iteration only
1% of the travelers was re-planned. The dotted lines are for iterat ion series
where 5% of the travelers were re-planned; in one case these 5% we re selected
randomly, in the other case they were selected according to “age” : A traveler

1e+08
1.5e+08
2e+08
2.5e+08
3e+08
3.5e+08
4e+08
4.5e+08
20 40 60 80 100
sum travel time at 10:00 am [sec]
iteration
random, 3*20%, 3*10%, 3*5%, 2*2% (run 1)
random, 110*1%, RP2 (run 4)
linear age, 5% (run 11)
random, 5% (run 12)
Figure 4: Sum of all travel times as a function of the iteration. Clear ly, the sum
of all travel times decreases with the iterations because congest ion clears and
the eﬃciency of the whole system increases. Diﬀerent iteration sch emes result
in diﬀerent relaxation speeds. From [16].
who had not tried a new route for a long time was more prone to re-pla nning.
Several observations can be made from this plot:
• The simulations relax to a value of approx. 1 .1 ·108 seconds for the sum of
all travel times. Clearly, the iteration described by the full line and “ +”
is not yet there.
• The iterations marked by the × symbol are relaxing very slowly. The
reason for this is that 1% re-planning means that the probability of not
having been re-planned after 110 iterations is 0 .99110 ≈ 0.33, i.e. about one
third of all trips still follow their initial route which has been computed
without any feedback information.
• As the line for “age-dependent” re-planning shows, much faster r elaxation
schemes are possible even when they are non supervised.
For further information, see [5, 16].
5 Characteristics of fastest paths in relaxed vs.
unrelaxed traﬃc situations
The above quantity, sum of all travel times, has the disadvantage that as a
relaxation criterion it is only meaningful in the context of a relaxation series:
One can follow its behavior, and from that one can decide that the se ries is now
“relaxed” or not. This approach is not useful for answering the qu estion where
the “real” system is. Is it somewhere along such a relaxation line, but not quite
at the bottom? Is it totally diﬀerent? The sum of all trip times is a numb er
that cannot be compared across diﬀerent networks: That numbe r would, for
example, depend on the size of the region.

For answering such a question, one needs a more “structural” app roach, one
that looks “directly” at the properties that supposedly relax. The property
that relaxes in the above approach is the “incentive to deviate”. Ou r behav-
ioral assumption is that people, given the starting time and location a nd the
destination, will switch routes until they ﬁnd a reasonably fast rou te. To a
certain extent, this follows the traditional assumption both for th e Wardropian
equilibrium in transportation and for a Nash equilibrium in game theory in that
rational players choose their best strategy (= fastest route), based on the as-
sumption that everybody else is rational. Yet, in reality people do not search for
the fastest route at all costs; also, the above relaxation scheme when inspected
closer reveals that in it people do not select the route with the faste st expected
travel time, even not in the average.
So the question becomes if we can measure a quantity which reﬂects the
incentive to deviate; and if so, if this quantity decreased with the ite ration
numbers. A diﬀerent way to formulate the question is: How much add itional
time would you need for your second-best route? One of the proble ms here is
that “second-best” route is not well-deﬁned; simply computing k–shortest paths
in an algorithmic way will generate many solutions that most people will n ot
consider alternatives; such as leaving a freeway at an oﬀ-ramp, cr ossing the
intersection, and getting on again at the other side of the intersec tion. Yet,
other approaches based on “reasonableness” cannot be conside red satisfying for
the present question [17].
In order to have a quantitatively sound criterion, we used k–fastest paths but
then calculated the “diﬀerence to the fastest path”. By this, one can distinguish
between routes which diﬀer only little from the fastest path and rou tes which
diﬀer a lot. We then plot that quantity as a function of, say, addition al travel
time. The information provided thus is (Fig. 5a): Given I accept x seconds
more travel time, how diﬀerent are my possible routes from my fast est route?
One can now calculate this information for many diﬀerent origin-dest ination
pairs. Averaging the resulting information for given amounts of add itional travel
time results in Fig. 5b, i.e. the ﬁgure provides an answer to the quest ion: How
diﬀerent will my route be in the average from the fastest route if I accept
x seconds of additional travel time?
Now, note that the two curves in Fig. 5b have been computed with tw o
diﬀerent link travel time sets: (i) “unrelaxed congested” uses link t ravel times
obtained from an “unrelaxed” simulation (i.e. based on the “initial plan set”)
at a congested time of the day; (ii) “relaxed congested” uses link tr avel times
obtained from a “relaxed” simulation (i.e. after many iterations) at t he same
congested time of the day. Clearly, when accepting a certain amoun t of ad-
ditional travel time, the options one has under relaxed conditions a re in the
average much more diverse than under unrelaxed conditions. In ot her words,
many diﬀerent routes will provide near-optimum performance for t he individual
driver; the optimum becomes “ﬂat”. This means that the system ar ranges itself
in a way that the “incentive to deviate” is fairly small, because even if y ou do
not use the optimal route, the gains from switching are fairly small. F or further
information, see [18].

0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 20 40 60 80 100 120
similarity to fastest path
additional travel time [sec]
OD pair #
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0 20 40 60 80 100 120
similarity to fastest path
additional travel time [sec]
average similarity to fastest path for given additional travel time
unrelaxed congested
relaxed congested
Figure 5: Plotting “similarity to fastest path” as a function of “addit ional travel
time”. Top: Example. One observes that, if one allows more and more addi-
tional travel time, one obtains more and more options that are ver y diﬀerent
from the fastest option. Bottom: Average over 955 origin destination pairs. One
sees that, for given additional travel time, one has more diverse o ptions in the
relaxed congested case. From [18].
6 Random ﬂuctuations
Our microsimulations are stochastic, i.e. they use random numbers d uring the
computation of their dynamics. That means that a simple change of a random
seed can change the entire dynamic trajectory of the simulation. F ig. 6 is an
example how dramatically the situationcan change with only the chang e of a
random seed shown (compare to Fig. 2). Clearly, using stochastic d ynamics
makes formal deﬁnitions, analytical proofs, and computational p roofs of conver-
gence much harder. Yet, we believe that it is a necessary feature o f reality; also,
it makes the computational search process more robust against g etting “stuck”
in implausible situations.
A result of stochasticity is that transportation simulation project s can, for
any given question, at best return a “distribution” of possible answ ers, i.e.
deterministic answers are not possible. Note that, if the distributio n is not

Figure 6: Demonstration of random ﬂuctuations. Microsimulation ru n based on
planset after 14 iterations, snapshot at 9:30 am. Compare to Fig. 2 , the only
diﬀerence between the runs is a changed random seed.
Gaussian, then using the arithmetic mean as a replacement for the d eterministic
answer can be misleading, for example in the case of a bi-modal distrib ution.
This indicates that more systematic studies of the eﬀects of stoch astic dy-
namics need to be done.
7 Diﬀerent microsimulations
At the current stage, it is unclear in how far transportation simulat ion projects
will be able to provide “robust” answers to questions that are relev ant to society.
As a minimum requirement, one should be able to extract “similar” answ ers from
diﬀerent codes. Fig. 7 shows an example of using a diﬀerent microsimu lation

Figure 7: Using a diﬀerent microsimulation in the same study context. Compare
to Figs. 2 and 6. Unfortunately, a plot showing individual vehicles as in the other
plots was not available; but to a certian extent, a comparison is poss ible. Gray
means link density (occupancy) below 10%, green means below 30% (w hich
corresponds roughly to capacity), yellow means below 50%, red mea ns below
70%, and purple means above 70%. From [16].
in the same context; in fact, the microsimulation is the same as the on e used
for the results described in Sec. 4. The ﬁgure should be compared w ith Figs. 2
and 6. Clearly, there are similarities. Traﬃc on the eastern part of t he east-west
freeway is in general heavy whereas most of the other simulation ar ea turns out
to be outside the congested regime. In some sense, Fig. 7 is in betwe en Figs. 2
and 6, which only diﬀer by the initial random seed. Beyond these some what
general observations, comparison between diﬀerent microsimulat ions is not very
well deﬁned problem; see Sec. 9 for a further discussion of this sub ject and [19]
for more information.

8 Comparison to reality
In the context of the Dallas study, we had some turn counts from s elected
intersections available. Before turning to the results, some details about the
comparison have to be noted, which are a consequence of the fact that the
north-south freeway in the study area did not exist in its full length before
1990:
• The main inputs for our microsimulations are the network and the trip
tables (PA matrices).
• The trip table that we use is from before 1990, i.e. before the northern
part of the north-south freeway existed .
• The network that we use is from after 1990, i.e. after the northern part of
the north-south freeway was opened.
• The reality counts are from 1996, i.e. from a time where the network was
similar to the one in the simulation, but the trips had adjusted to the
existence of a much faster way to travel north-south in the nort hern part
of the study area.
In consequence, we would expect that our studies underestimate north-south
traﬃc in our study area compared to the 1996 counts.
When looking at Fig. 8, this is clearly the case. But this is not the only
feature. One also notices that in fairly general our simulation over- estimates
traﬃc on minor roads and through turns; this is most probably a con sequence
of the way the re-planner works because it only looks at travel times and not,
for example, at inconveniences caused by sharp turns or by stop s igns. These
results reﬂect work in progress; further results will be published e lsewhere [19].
9 Robustness of (micro-)simulation results
The previous two sections ask the question of how to compare diﬀer ent mi-
crosimulations or of how to compare microsimulations with reality. In p rinciple,
this should be easy: microsimulations generate microscopic observa bles, and so
we simply extract the same information from the microsimulations and from
reality and we compare them. Yet, it is unclear which information to exactly
to extract: Which is the most meaningful information? For example, does the
fact that microsimulation XYZ has 20% too many right turns on a cert ain in-
tersection really matter? Or what is more important: 100 vehicles mo re at the
end of an already large traﬃc jam, or 100 vehicles more on unconges ted roads?
One needs to relate this problem to the question one attempts to an swer
with a speciﬁc simulation project. The level of ﬁdelity of a simulation pr oject
will always depend on the level of eﬀort spent; and it seems reasona ble to us to
adjust the level of eﬀort to what is really necessary for a given que stion. Also,
with a given question at hand, the problem of comparing simulations be comes

Figure 8: Comparison with reality between 8:30am and 8:45am. At most in-
tersections, there are three principal bars, one for right turns , one for traﬃc
going straight, and one for left turns. For each of these principal bars, the
middle (black/white) bar shows the observed value, the outside (gr ay) bar the
value from the simulation. For example, for the intersection in the rig ht up-
per corner, the simulation is underestimating both southbound and northbound
through traﬃc. – When interpreting this ﬁgure, one needs to know that the
rightmost north-south road and the topmost east-west roads a re major arteri-
als, the dark grey roads are freeways, roads immediately parallel t o the freeways
are frontage roads, and all other roads are minor. Only then it bec omes clear
that we are overestimating traﬃc that goes through “inconvenien t” routes, i.e.
through sharp turns and over minor roads. Also, we underestimat e north-south
traﬃc in general due to the data inconsistency described in the tex t. Note
that we have made no attempt to “calibrate” the simulation to these values.
From [19].

5 6 7 8 9 10 11 12
median speed [m/sec]
simulation time [h]
PAMINA (run 11, it 58/59/60)
TRANSIMS
Figure 9: Comparison of median “geographical” speeds between two simula-
tions. What we mean by geographical speed is “geographical distan ce” divided
by “travel time”, i.e. not the average driving speed. This measures accessability
of an area; in this case accessabiliby of the interior of the simulation a rea when
coming from the outside. From [19].
better deﬁned: One does not need any more to decide if two simulatio ns are
“equal”, but only if two diﬀerent simulations give the same answer to t he spec-
iﬁed questions. This latter approach is much better accessible to th e statistical
tools at hand; admittedly, it is not very satisfying because it means t hat for any
new question one needs, in some sense, to start over.
Fig. 9 presents one such possible result. Plotted is the average spe ed for
reaching the center of the simulation area when coming from the out side. The
speed here is calculated by “geographical distance divided by trip tim e”, i.e. it
does not reﬂect driving speed but is a measure of “accessibility”: Low speeds
reﬂect that the destination is diﬃcult to reach. Our plot is a simpliﬁed v ersion
of a type of questions that are really important in the context of “s take-holder
analysis”. For example, does the introduction of a light rail make tra vel to the
downtown area faster for people who do not own a car? (Probably y es.) Does it
make the same travel faster for people who own a car? (Probably n ot, at least
not during uncongested conditions.)
Now note that Fig. 9 only gives part of the full answer. We certainly s ee
that in both simulations, accessibility of the center of the simulated a rea drops
during the morning rush period. We also see that the drop in accessib ility is
diﬀerent between both microsimulations. Yet, if the question were f or example
to ﬁnd the time of worst accessibility during the morning rush period, both
simulations would give the same answer.
Last, but not least, note that this paper deliberately side-steps t he ques-
tion of the trustworthiness of the microsimulation itself. In this pap er, we have
concentrated on “macroscopic” aspects, such as large scale ﬂuc tuations and the
interplay between route planner and microsimulation. Yet, it is also us eful to
test and document microscopic aspects of traﬃc models. The discu ssion of what
to measure here and how is ongoing; but there seems to be some slow ly growing

consensus that certain building blocks of the ﬂow characteristics, such as ﬂow
through a stop sign as function of the traﬃc on the major road, un realistic as
these examples may be, should be part of these systematic tests. The devel-
opment of more complex test suites would certainly be desirable. For further
information on this in the context of TRANSIMS, see [20].
10 Summary
Iterated transportation microsimulations provide a very powerfu l addition to
the tools of transportation planning. Their power lies both in the cap ability
to represent time-dependent scenarios in their “true” time-depe ndent dynam-
ics and in the possibility to access individual, microscopic quantities dire ctly.
Yet, one needs to note that research in this area is at its beginning; no con-
sistent theory is available to help and even the building of intuition is in its
initial stages. This paper provides a summary of what has been done in the
context of a TRANSIMS study of the Dallas area in order to provide e xactly
some of this intuition. These results can be summarized as follows: (i) Iter-
ations between router and microsimulation adjust routes in a way th at traﬃc
becomes “plausible”. (ii) The number of iterations that are necessa ry until the
process is plausibly “relaxed” can be signiﬁcantly reduced by using “in telligent”
relaxation schemes. (iii) It seems possible to distinguish “unrelaxed” from “re-
laxed” conditions by looking at fastest paths in both situations. The result is
interpretable in the sense that in relaxed transportation systems , there is not
much diﬀerence in travel time between the strictly fastest path an d very dif-
ferent routes. (iv) In stochastic microsimulations, simply changing the random
seed can generate large ﬂuctuations. (v) Using a diﬀerent microsim ulation in
the same scenario produces results that look similar, but that are d iﬃcult to
compare in general. (vi) Comparing to reality has the same caveats, plus the
problem of data consistency. Nevertheless, the comparison prov ides useful in-
sights. (vii) In general, comparison between microsimulations need t o be geared
to speciﬁc questions. An example of such a question is provided.
Acknowledgments
Los Alamos National Laboratory is operated by the University of Ca lifornia for
the U.S. Department of Energy under contract W-7405-ENG-36. This article is
work performed under the auspices of the U.S. Department of Ene rgy.
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Sentient Networks

Sentient Networks

Abstract
In this paper we consider the question whether a distributed network of sensors and data processors can form "perceptions" based on the sensory data. Because sensory data can have exponentially many explanations, the use of a central data processor to analyze the outputs from a large ensemble of sensors will in general introduce unacceptable latencies for responding to dangerous situations. A better idea is to use a distributed "Helmholtz machine" architecture in which the collective state of the network as a whole provides an explanation for the sensory data.

adap-org/9712004 13 Dec 1997
Sentient Networks
George Chapline
Lawrence Livermore National Laboratory
chapline1@llnl.gov
Abstract
The engineering problems of constructing autonomous networks of
sensors and data processors that can provide alerts for dangerous situations
provide a new context for debating the question whether man-made systems
can emulate the cognitive capabilities of the mammalian brain. In this paper we
consider the question whether a distributed network of sensors and data
processors can form “perceptions” based on sensory data. Because sensory
data can have exponentially many explanations, the use of a central data
processor to analyze the outputs from a large ensemble of sensors will in
general introduce unacceptable latencies for responding to dangerous
situations. A better idea is to use a distributed “Helmholtz machine” architecture
in which the sensors are connected to a network of simple processors, and the
collective state of the network as a whole provides an explanation for the
sensory data. In general communication within such a network will require time
division multiplexing, which opens the door to the possibility that with certain
refinements to the Helmholtz machine architecture it may be possible to build
sensor networks that exhibit a form of artificial consciousness.
1. Introduction
During the next few decades autonomous networks of sensors and data
processors are going to come into widespread use for industrial process
monitoring and detection of threats to populations and infrastructures. If the
individual sensors have sufficient sensitivity and the environmental data are
unambiguous, then these sensor networks can be operated as robots; which
means the sensory data can be used to directly activate responses. Obviously
automatic warning systems that can quickly respond to malfunctions in an
industrial process or hostile acts which threaten populations or essential
infrastructures would have many practical applications. Unfortunately, in
practice it may be very difficult on the basis of outputs from sensors to decide in
a timely way that something untoward is happening. For example, it might be
that state of the art sensors do not have sufficient sensitivity or discrimination to
provide unambiguos signals regarding malfunctions or hostile acts. Even in
networks where the individual detectors are very sensitive it may be necessary
to correlate the outputs from sensors in different locations and also possibly
from different kinds of sensors in order to determine whether a dangerous

situation has arisen. Another frequent problem that occurs with the
interpretation of real world sensor data is that signal to noise ratios for the
signatures of interest are not sufficiently large to provide unambiguous signals.
These problems are similar to those faced by many species of animals in the
natural world. Actually almost all animals can respond to dangers. However, in
all invertebrates (with the possible exception of cephalopods) this response is
always a pre-conditioned automatic response. For example in order to navigate
around obstacles the brains of flying insects must almost instantaneously
recognize how these obstacles are moving relative to the insect, and then
immediately send appropriate signals to the muscles controling its flight. It is the
goal of most current robotics research projects to duplicate this kind of
automatic response in various kinds of man-made electromechanical devices.
In vertebrates, on the other hand, there is a new anatomical feature - the
cerebral cortex - which provides an additional channel for responding to
sensory inputs. As a consequence vertebrates can respond to dangers either by
making use of a rapid midbrain response system similar to that in invertebrates
or in a somewhat slower fashion by making use of their cerebral cortex. In the
cerebral cortex of vertebrates sensory data is processed in a much more
sophisticated way than in the brains of invertebrates. Not only is the extraction
of features from the sensory data more elaborate, but studies in both humans
and animals of the functions of the cerebral cortex suggest that the processing
of sensory data in the cerebral cortex is primarily concerned with the formation
of explanations for the sensory data; i.e. "perceptions" [1].
One of the obvious evolutionary advantages of being able to take into account
various possible explanations for sensory data is that this greatly enhances an
animal's capability to cope with stealthy predators. A vivid example of the
necessity of having such a capability is provided by the dilemma faced by a
zebra on the African savanah. A lion sitting in plain view is very likely not to be
an immediate threat, whereas recognizing that one is being stalked by a lion
will often require making that determination on the basis of manifestly
ambiguous data - for example, a slight movement of the grass or the state of
agitation of birds or other animals. It is clear that faced with ambiguous
information an animal may or may not want to respond. Indeed it is tempting to
speculate that vertebrates employ some kind of statistical inference engine in
order to determine whether in ambiguius situations there is a danger that
requires flight or some other prompt respone. In fact there is strong
circumstancial evidence [2] that humans in effect make use of a statistical
inference system in order to make decisions. Although initially it might seem
implausible that humans - not to mention animals with no obvious capabilities
for understanding abstract concepts - could utilize probabilistic reasoning, it is
perhaps logically inescapable [3] that the vertebrate cerebral cortex must be
capable of inferring and somehow encoding estimates of the posterior
probabilities for the occurrence of various situations or events that are important
for survival. Historically it was suggested more than a century ago by Helmholtz
that the main function of the human perceptual system is to infer probable
causes for sensory inputs.

In the following section 2 we briefly review the well known statistical basis for
the assertion that it is the availability of posterior probabilities that makes it
possible for a network of sensors and processors to provide explanations for
sensory data. Unfortunately it is unknown exactly how the vertebrate cerebral
cortex evaluates and records posterior probabilites. Nevertheless some parallel
computation architectures have appeared in the literature which, at least in
principle, should make it possible to use posterior probabilities to provide
explanations for sensory data. Although parallel computation architectures for
the interpretation of sensor outputs have not yet come into widespread use in
engineering systems, there are reasons for expecting that this type of
architecture will find widespread use in the future when real time responses are
desired. For example, even in the case of robotic feedback control systems
where the use of parallel computation architectures may not be mandatory the
significant speed advantages of parallel analog circuits will make the use of
VLSI parallel analog circuits [4] increasingly attractive for the real time
interpretation of sensor data [5]. In the case of distributed networks of sensors
rapid interpretation of the sensory data will almost certainly require new
computational paradigms. In particular, when the sensory data are ambiguous,
the use of parallel computation is almost manditory because in general there
can be exponentially many explanations for a particular set of sensor outputs.
The rationale for parallel computation in those cases where one is faced with an
exponential proliferation of possible explanations for the sensor outputs is that
the required computational task of finding the most likely explanation is
intractible for a single sequential data processor. This will be especially true
when finding an explanation for sensor data involves using Markov chain Monte
Carlo methods to “invert” a stochastic model for the world. On the other hand, as
noted by Hopfield and Tank in a celebrated paper [6], parallel computation
using a “neural network” architecture provides a remarkable capability for
finding good solutions to computationally intractible problems. Consequently
although various kinds of computational schemes, e.g. rule based expert
systems, might be employed in special cases to rapidly explain sensory data,
artificial neural networks do provide a natural universal computational
framework to use in an autonomous system seeking an explanation for sensor
data precisely because of their ability to provide good solutions to
computationally difficult problems. Furthermore although there are various
parallel computation architectures that might be adopted to the problem of
explaining sensor data we would like to focus in the following on the fact that
physical systems of interacting 2-state units, viz. “spins”, in thermal equilibrium
with a heat bath can duplicate the behaivor of artificial neural networks like
those introduced by Hopfield, and in fact have certain advantages over
completely deterministic neural networks (this is the basic idea behind
simulated annealing [7]).
The main point we would like to make in this paper is that in a distributed
network of autonomous sensors and data processors alternative interpretations
of sensor inputs can be represented by the collective state of physically
separated binary units, each of which has activation level 0 or 1. In other words

an autonomous network of sensors and data processors can be conceived of as
the hardware embodiment of an abstract statistical system of interacting spins
functioning as a neural network. In section 4 we describe one particular way,
which we call the Helmholtz machine after the corresponding abstract neural
network architecture, in which a hardware network of sensors and data
processors might be made to emulate a spin system functioning as a statistical
inference engine . In section 5 we briefly discuss how a hardware Helmholtz
machine might be built using existing data processing and communication
technologies. In particular we compare and contrast the intelligent agents
required for a Helmholtz machine with the TCP/IP interfaces used in Ethernet
networks. In section 6 we address the question whether a distributed network of
sensors and simple data processors could behave as though it were
“conscious”.
2. Statistical theory of pattern recognition
It has been understood for some time that pattern recognition systems
are in essence machines that utilize either preconceived probability
distributions or empirically determined posterior probabilities to classify
patterns. In the ideal case where the a priori probability distribution p(α ) for the
occurence of various classes α of feature vectors and probability densities p(x|
α ) for the distribution of data sets x within each class are known, then the best
possible classification procedure would be to simply choose the class α for
which the posterior probability
P x p p x
p p x( | ) ( ) ( | )
( ) ( | )α α α
β β
β
=
∑
(1)
is largest. Unfortunately in the real world one is typically faced with the situation
that neither the class probabilities p(α ) nor class densities p(x|α) are precisely
known, so that one must rely on empirical information to estimate the
conditional probabilities P(α | x) needed to classify data sets. In practice this
means that one must adopt a parametric model for the class probabilities and
densities, and then use empirical data to fix the parameters θ of the probability
model. Once values for the model parameters have been fixed, then sensory
data can be classified by simply substituting values for the model probabilities
p(α; θ ) and p(x|α; θ ) into equation (1).
Unfortunately determining values for the model parameters from
empirical data is itself a computationally intractible problem. This means that in
practice one is usually limited to using models of relatively modest complexity,
and consequently one is always faced with the issue of choosing the best
possible values for the model patameters. One popular way of measuring how
good a paticular set of model parameters is at reproducing the observed data,

known as the maximum likelihood (ML) estimator, can be motivated by noting
that the formula for the posterior probability given in equation (1) can be
formally interpreted as the canonical Boltzmann distribution for the population
of energy levels of a physical system in equilibrium with a heat bath. In
particular if one defines the "energy" of a classification α to be
E p p xα α α= − log ( ) ( | ) , (2)
then the posterior probability introduced in (1) can be formally expressed in the
form
P x e
e
E
E( | )α
α
α
α
=
−
−
∑
, (3)
where the energies are those defined in equation (2). If we suppose that the
energy levels Eα defined in equation (2) define a physical system whose energy
levels are populated according to a canonical distribution of the form (3), then
the thermodynamic free energy of this system will be given by
F (x) = { ( ) ( ( )log ( ))}E P P Pα
α
α α α∑ − − , (4)
where we have used P( )α as shorthand notation for the canonical distribution
(3). If instead of the true probability distributions p(α ) and p(x|α) one uses
model probabilities p(α; θ ) and p(x|α; θ) to calculate a probability
distribution Pθ α( ) for different classifications of a data set x, then equation (3) will
no longer necessarily be satisfied and the free energy calculated from eqation
(4) will in general differ from the true free energy. In particular we would have
that
F (x) = F (x, θ) − P P Pθ θ
α
α α α( )log[ ( ) / ( )]∑ (5)
where F (x, θ ) is the free energy calculated using the distribution Pθ α( ) .The
quantity P P Pθ θ
α
α α α( )log[ ( ) / ( )]∑ in the second term in equation (5) is always
positive and measures of the difference in bits between the model
distribution Pθ α( ) and the true distribution P( )α . This distance measure, known
as the Kullback- Leibler divergence, is the basis for the ML estimator that is
widely used by statisticians to measure how well a given set of model
probabilities reproduces the empirical data [8 ]. Minimization of the Kullback-
Leibler distribution with respect to the model parameters θ is one way of
choosing the best possible values for these parameters. It should also be noted

that the estimated free energy F (x, θ ) is always greater than the equilibrium
free energy F (x) , so that the best possible probability distribution to use for
classifications is that which minmizes the estimated free energy. This analogy
between pattern recognition and statistical physics opens the door to using
insights from theoretical physics to solve pattern recognition problems.
An ingenious physics model in which the posterior probabilities P( α| x; θ)
are naturally represented in the canonical Boltzmann distribution form (3) was
introduced in 1985 by Ackley, Hinton, and Sejnowski [9 ]. In this model, known
as the Boltzmann machine, data sets and their “explanations” are represented
by configurations of binary units with activation levels ai= 0 or 1.The energy
function for the assembly of binary units is assumed to have a form similar to
that used by physicists to describe a system of interacting spins in a magnet:
E(a) = −
≠
∑
2 w a aij
i j
i j
+ θi
i
ia∑ , (6)
where a ={ ai} denotes the set of activation levels, theθi are biases, and the
weights wij describes the interaction strength between binary units i and j In the
work of Ackley et. al. these interactions are assumed to be symmetric; i.e. wij =
wji. If the system of binary units is assumed to be in contact with a heat bath at
some fxed temperature the probabilty distribution for the activation levels will
approach a stationary equilibrium whose form is just the Boltzmann distribution
(3) corresponding to the energy function (6). In the case of the Boltzmann
machine the probability distribution Pθ α( ) will be the probability distribution for
the activation levels in a certain subset, referred to as the hidden units, of all
binary units. The remaining binary units, referred to as the visible units,
represent the environmental data x. The model parameters θ for the Boltzmann
machine are the connection strengths wij and biases θi for the binary units.
These parameters are determined by minimizing the Kullbach-Leibler
divergence between the probability distribution Pθ α( ) with the visible unit
activation levels fixed and the probability distribution for classifications with the
activation levels of the visible units allowed to vary freely. Used as a pattern
recognition device the Boltzmann machine has the virtue that non-trivial
correlations between different instances of environmental data are
automatically represented, and used in the classification of data sets. This
means that the classifications provided by the Boltzmann machine take into
account more information than just the relationship between a class and its
feature vectors. Unfortunately Boltzmann machines have not found many
practical applications because determination of the connection strengths and
biases for realistic data sets is very slow using even the fastest supercomputers.
Moreover even when the connection strengths and biases are known the
classification of data sets is slow because of the necessity for repetitive

sampling of a joint probability distribution for the activation levels of the hidden
units.
3. Belief networks
As noted in the introduction vertebrates are often faced with the problem
of finding an explanation for sensory data whose interpretation is not
immediately obvious. This is a rather more subtle problem than the more
familiar problem of classifying static patterns because finding an explanation for
sensory data will in general involve taking into account structural relationships
that are inherent in the entire ensemble of environmental input data. One of the
main goals of artificial intelligence research is the development of algorithms
which can recognize and manipulate the structural relationships inherent in
data sets. Almost effortlessly the human brain is able to capture the essence of
these structural relationships by the use of hierarchical knowledge trees or
“ontologies”. At the present time there is a great deal of interest within the
artificial intelligence community in developing algorithmic tools for contructing
and utilizing ontologies for applications such as medical diagnosis and
battlefield management [10]. It remains unclear though whether these purely
algorithmic approaches to artificial intelligence will lead to systems that can
deal with the ambiguities and complexities of real world sensor data.
In existing computerized decision systems which use probabilistic
reasoning the knowledge base is represented by a description of the
dependencies between the variables of the system [11]. In a belief network
these dependencies are represented by a probability distribution for the states
of the nodes in a layered network which is a product of conditional probabilities
for each unit given the values of the units which proceed it in some ordering.
Many types of belief networks are possible, but typically belief networks have a
tree-like structure and the conditional probabilities have the Markov property;
i.e. the random variables at nodes not connected by a branch are conditionally
independent given those variables which are so connected. In addition belief
networks often incorporate unobserved latent variables known as hidden
variables. Software implementations of Markov belief networks with hidden
variables have been successfully used for some quite difficult real world pattern
recognition problems such as speech recognition [12], and represent a
promising general approach to the interpretation of complex data sets. Indeed
the success of hidden variable Markov models for speech recognition should
certainly be kept in mind when designing networks of sensors and data
processors to interpret environmental data, and is also perhaps a significant
clue as to how the cerebral cortex of vertebrates forms perceptions .
Models for the cerebral cortex which might function as belief networks
were first introduced by Little, Shaw, and Vasudevan [13], and indeed these
models were among the first artificial neural networks. The nodes of these
networks can be represented by binary units with activation level
ai =0 or 1, and

it has been pointed out [13 ] i that if the Markov transition probability for the
activation level of a single node in these models have the sigmoidal form
p(ai(n+1) | a (n)) = σ[β(1-2 ai(n+1)) w aij
j
j∑ ], (7)
where σ(x) = 1/[1+exp(-x)] then these models resemble Boltzmann machines.
The vector a(n) = { ai(n)} in equation (7) denotes the set of activation levels at
layer n of the network. In the original work of Little, Shaw, and Vasudevan the
way activation levels vary from layer to layer was thought of as describing the
time evolution of the whole network; whereas in their use as belief networks the
number n will generally be taken to represent actual physical layers of the
network. A little algebra shows that the Markov transition probability for the
ensemble of activation levels in a layer can be written in the form
P[a (n+1) | a(n)] = e
e
a n X n
a n X n
a n
β
β
( ) ( )
( ) ( )
( )
+ •
+ •
+
∑
, (8)
where Xi(n) = w a nij
j
j∑ ( ) -θi ia and we have used vector multiplication notation in
the exponents. If the interactions between units are symmetric, then the
transition matrix (8) will eventually become independent of n, and the
probability distribution for activation levels will have the canonical Boltzmann
form; if activation levels in the first layer are fixed we recover equation (3). If the
connection strengths between units are asymmetric, i.e. wij ≠ wji, then the
activation levels will vary from layer to layer and depend on the activities in the
first layer. The activation levels in the initial layer represent the environmental
data, while the activation levels in later layers can be thought of as representing
the explanation of the the environmental data [15]. It should be noted in this
connection that 2-dimensional arrays of binary units within each layer provide a
convenien way of representing and classifying feature vectors using redundant
population codes [16]. Thus Boltzmann machines with asymmetric weights
provide an attractive way to realize fault tolerent belief networks.
One of the main practical problems with using conventional belief
networks to explain sensor data is that given a set of conditional probabilities
and associated decision tree which constitutes a model for the world, finding
explanations for input data will in typically involve using Markov chain Monte
Carlo methods to invert the world model. Because of the need for repetitive
sampling, this cannot in general be done in real time. Another practical problem
with belief networks is that determining the network parameters from the
environmental data is very difficult if there are too many parameters. Fortunately
a descendent of the the Boltzmann machine form of belief networks, the
Helmholtz machine, has recently emerged that offers the promise of alleviating
these problems.

4. Helmholtz machine networks
The Helmholtz machine architecture introduced by Hinton et.al. [17] is a
stochastic neural network that resembles the Boltzmann machine in that the
nodes of the network consist of units whose activation levels are quantized to
be either 0 or 1. Another similarity between the Helmholtz and Boltzmann
machines is that some of the binary units represent environmental input data,
while the remaining "hidden units" represent possible explanations for the input
data. All information concerning conditional probabilities is contained in the
values of the connection strengths wij between nodes; indeed it is possible that
these weights play much the same role in the Helmholtz machine as the
synaptic connection in the cerebral cortex. The activation of the ith hidden unit
in the network is chosen stochastically in accordance with the probability p xj( ) =
p( ai(n+1) | a (n)) that with a particular set x of sensory inputs the ith hidden unit
in the nth layer has activation 1. The probabilities p xj( ) are calculated from the
weights for the connection between the ith unit and the activities of the units in
the previous layer using the sigmoidal formula (7). Thus the activities of units
are determined in a quasi-deterministic way similar to that in a feed-forward
neural network. If one assumes that the activities of the binary units within a
given layer are independent, then the probability of a particular explanation α
={a(n), n>1} will be given by the product :
Q(α) =
n>
∏
[ ( ] [ ( )]p a p aj
j
a
j
aj j
∏ −
−
; (9)
so that the binary units that are turned on contribute with weight p xj( ) while the
units that are turned off contribute with weight 1- p xj( ) .
All of the information concerning the structure of the external world that is
needed to explain a given ensemble of sensory data is encoded into the
connection weights wij used in eq. 6 , and the main obstacle in utilizing a
Helmholtz machine is determining the values of these parameters.
Unfortunately when the set of input data is complex it is a computationally
intractible problem to precisely determine these parameters. However, one can
obtain approximate values for the connection weights of a Helmholtz machine
based on the observation (cf. eq’s 3 and 5) that the negative free energy -F (x,
θ, Q ) calculated using the non-equilibrium distribution Q(α) provides an lower
bound for the logarithm of the probability of generating a particular set x of
sensory inputs. In the Helmholtz machine scheme of Hinton et. al. the
parameters θ correspond to the connection weights and biases of a separate
feed forward network which is used offline to generate the “true” posterior
probability distribution Pθ α( ) . The connection strengths wij which are used in the
recognition network to explain input data are determined simultaneously with
the parameters θ by using gradient descent methods to minimize the free

energy function F(x, θ, Q ). Because the conditioning of almost any kind of
network that used to interpret observed data will be computationally tedious, it is
perhaps to be expected that artificial neural networks will increasingly be used
for the purpose of determining the parameters of belief networks; and the use of
a separate generative network for this purpose by Hinton et. al. may be a first
step in this direction.
Once the connection strengths of the Helmholtz machine have been
fixed, then the probabilities for likely explanations of given sensory data can be
rapidly determined using Eq’s 7 and 8. Thus the Helmholtz machine
architecture avoids the problem with the Boltzmann machine of having to
repetitively sample a probability distribution in order to recognize input data.
Furthermore with the use of the independence ansatz, eq. 8, this architecture
allows one to sidestep the combinatorial problem that arises when there are
exponentially many explanations. In summary, in addition to making the
learning of the structure inherent in a set of input patterns tractable, the separate
generative and recognition models used in a Helmholtz machine allow one to
arrive at definitive interpretations of instances of environmental data in real time.
Of course from the perspective of actually building sensor networks the
crucial feature of the Helmholtz machine concept is that it can apparently be
realized in a straightforward way in hardware as a distributed system of sensors
and simple data processors. In addition it would be natural in such a distributed
system to use population codes to represent both feature vectors and possible
explanations of the environmental data, thus decentralizing the cognitive
process of the machine. Once the connection strengths for each individual
hidden unit are determined they can be stored at the location of the hidden unit
and used in a simple data processor to stochastically determine the activation
level of that particular hidden unit in response to sensory inputs. It should be
emphasized that a very nice feature of this way of realizing the Helmholtz
machine architecture is that it is very robust against failures of individual
components; i.e. a significant number of individual sensors and/or hidden units
would have to fail before the system as a whole completely loses its ability to
interpret sensory data.
The actual way in which the sensors and hidden units of a Helmholtz
machine are deployed for the detection of threats or undesirable situations will
depend on the particular application. For example, in the case of a biological
warfare warning system, one might be interested in detecting expanding clouds
of small particles. For this application the particle size detectors need to be
coupled to the hidden units in such a way as to detect the motion and
expansion of a cloud of spore sized particles. Traditional methods for confirming
the presence of biological pathogens such as immunoassays would be too slow
to use in an emergency response system. However, other techniques, e.g.
spectral analysis of backscattered UV radiation, might provide sufficient hints
which together with the cloud tracking units could be used to infer whether
microbiological warfare agents have been released. This example is in fact a
good illustration of the kind of situation where a Helmholtz machine could to be
used to fuse multi-modality sensor data and compute a probability that a

dangerous siuation had arisen even though the data provided by each sensor
modality is highly ambiguous. It should be noted that nothing about the physics
of how clouds of microbiological agents spread or the physics of remote
sensing needs to be understood a priori by the Helmholtz machine. A Helmholtz
machine is capable of self-learning, and all that is required to recognize that a
biological warfare attack is underway is that the Helmholtz machine be trained
to recognize the regularities and structure of the sensory inputs expected for
such an attack.
5. Intelligent agents for sentient networks
In a Helmholtz machine network both the processed data and
computational processes are distributed throughout the network. If the sensor
and data processor nodes are physically separated then some means must be
provided for these nodes to communicate with each other. This communication
support must be capable of relaying the activation levels of the binary units in
one level of the network to the units in the next level of the network within a
relevancy time interval. Since each node of the network maintains a list of the
other nodes it must communicate with, it may be convenient to make use of
Ethernet networking technology to implement the Helmholtz machine
architecture. Indeed one advantage of configuring the Helmholtz machine as an
Ethernet is that one could take advantage of the IEEE standards (1451.1 and
1451.2) for connecting sensors to microprocessors and the sensor plus
microprocessor to a network [18]. A significant caveat here though is that in
practice it may only be possible to configure the Helmholtz machine as an
Ethernet if the nodes can be connected by wires or cables.
In cases where the nodes of the network are geographically separated it
may be necessary to use wireless communications; and in these cases it may
be more desirable to use some other interface between the sensor plus
microprocessor and the network than the TCP/IP agent used in Ethernets. In
general though one will want to use time division multiplexing for the
communications in order to minimize the total energy expended in network
communications. In particular if one uses an internal clock for the network as a
whole in which each node is assigned a talk and listen time slot, then all
communication devices can be powered down except during those few time
slots in which they participate.
The total bandwidth required for the network communications will be
determined by the response time desired and the number of nodes that must
communicate with each other during a clock cycle. Generally, each hidden
processor unit needs to communicate with every binary unit in the previous
layer of the network. However, only a small number of bits needs to be
transmitted between any two nodes at any given time, and this will reduce local
bandwidth requirements. Furtherrmore in many practical cases the connection
strengths between distant units may be negligible so that communication need
be carried out only between nearby neighbors. Thus it appears that for the
network as a whole an Internet-like model for the communications where local
networks feed data to hubs which can communicate with each other using much

higher bandwidth transmission channels might be appropriate. In any case
because of the practical requirement to conserve energy resources
asynchronous sampling techniques like those used by pager receivers would
probably not be acceptable for the nodes of a distributed Helmholtz machine
network. In the next section we suggest that this practical requirement may have
some profound consequences for our understanding of the cerebral cortex.
6. Artificial consciousness?
If a network of sensors and simple processors configured as a Helmholtz
machine might be considered to be sentient , an obvious question is under what
conditions would such networks become “conscious”? The neurophysiological
meaning of consciousness is still a matter of considerable controversy.
Nevertheless following the suggestion by Crick and Koch [19 ] that
consciousness is intimately related to the presence in the cerebral cortex of 40
Hz oscillations, there is increasing evidence [20] that coordination of the
activities within the cerebral cortex by an internal clock is somehow responsible
for the unique awareness of the external world associated with consciousness.
In addition an intriguing mathematical interpretation for a correlation between
the use of an internal clock in a neural network and conscious awareness has
recently emerged [21]; namely construction of a continuous 3-dimensional
manifold from a foliation of 2-dimensional representations of feature vectors will
not be topologically possible without using an internal clock if the 2-dimensional
representations lie on a topologically non-trivial surface.
As noted previously layering in a belief network is essential for
accomodating hierarchical explanations of the input data. Furthermore in the
case of a Helmholtz machine it is natural to represent these hierarchical
features or “interpretations” using 2-dimensional population codes. An
interesting question is under what circumstances can a foliation of 2-
dimensional population code representations be fused together to form a 3-
dimensional manifold? There is compelling evidence that the human brain
makes use of continuous 3-dimensional representations of the external world
[22], and indeed construction of such representations may be a very nice way of
fusing different data modalities in artificial threat detection systems. The
interesting topological fact is that this will only be possible if there is an internal
clock and each node is assigned a time slot. In fact 2-dimensional data
representations will necessarily lie on a topologically non-trivial surface if they
are part of a Hopfield-like network. Further this circumstance will occur naturally
if the feature vectors are self-organized [21], and in addition Hopfield-like
networks could serve the purpose of error correction for feature vectors [23]. An
additional benefit [21] of fusing topologically non-trivial representations of
feature vectors is that the only stable excited states for the network are those
that correspond to excitations on the boundary; i.e. variations in input data. This
of course is very reminescent of the phenomenology of the conscious cerebral
cortex. Thus perhaps our most exciting observation is that with some slight
modifications the Helmholtz machine architecture might provide a framework for
creating artificially consciousness in a network of sensors and data processors.

Acknowledgements
I am very grateful to John Woodworth and Alan Spero for encouraging me to
think about the collective properties of sensor networks. I would also like to
thank Jim Barbieri, Bill Buchanan and Dave Fuess for helpful discusssions. This
work was supported under DOE contract W-7405-ENG-48.
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