textfiles/science/quantum.ani

              Evidence supporting quantum

           information processing in animals


                   James A. Donald 

                   1068 Fulton Av
                   Sunnyvale, CA 94089-1505
                   USA 


I show that quantum systems can rapidly solve some 
problems for which finite state machines require a non-
polynomially large time. This class of problems is 
closely related to the class of problems that animals 
can solve rapidly and effortlessly, but are intractable 
for computers by all known algorithms. 



1. Introduction
     Animals, including very simple animals, can 
rapidly and effortlessly perceive objects, whereas 
computers take nonpolynomial time to do this by all 
known algorithms [1, 2, 3, 4, 5, 6]. Our persistent 
inability to emulate perception gives reason to doubt 
the current paradigm and to look for an alternative 
paradigm. 
     Penrose[7] and many others [8, 9, 10] argue from 
practical considerations, Godel's theorem, and on 
philosophical grounds, that consciousness or awareness 
is non-algorithmic and so cannot be generated by a 
system that can be described by classical physics, such 
as a conventional computer, but could perhaps be 
generated by a system requiring a quantum (Hilbert 
space) description. Penrose suspects that aspects of 
quantum physics not yet understood might be needed to 
explain consciousness. In this paper we shall see that 
only known quantum physics is needed to explain 
perception.
     Bialek[11, 12] and Frolich[13] suggested on very 
different grounds that cells process information using 
quantum mechanical processes. Frolich suggested a class 
of mechanisms that might enable them to do this despite 
the high temperature and large size of biological 
membranes and macromolecules. Deutch[14] showed that 
quantum systems can solve some problems that computers 
cannot solve in polynomial time, but he did not show 
that quantum systems could solve perception problems. 
Penrose[7] conjectured that some areas where animals 
are superior to computers are of this class, but did 
not find any examples. Bialek[15] argued that 
perception is inherently non-polynomial if done 
algorithmically, and therefore neurons must be doing 
something remarkable, but he did not show that quantum 
mechanics would enable them to do this. 
     This paper will show that quantum systems can also 
rapidly solve perception problems, closing the gap 
between Bialek's argument and Deutch's result, and 
demonstrating Penrose's conjecture. This result 
supports the idea that animals perceive by processing 
sensory information quantum mechanically in hilbert 
spaces corresponding to many strongly coupled degrees 
of freedom. 

2. The Perception Problem
     Perception is the problem of inferring the 
external world from immediate sensory data by finding 
instances of known categories such that they would 
generate the immediate sensory data. Animals do this 
very well, and, for perception problems that only 
require recognizing objects as instances of innate 
categories rather than learnt categories, animals with 
very simple nervous systems sometimes perceive almost 
as well as animals with complex nervous systems such as 
ourselves, and perhaps better in some cases and some 
circumstances. Indeed animals do this so well and so 
effortlessly that people only began to recognize that 
there was a problem to be solved when we attempted to 
program computers to perceive.
     The fact that animals perceive effortlessly has 
lead to a widespread belief that some polynomial time 
algorithm must exist, yet no significant progress has 
been made in the search for an efficient perception 
algorithm. 
     A number of perception problems have been studied 
very thoroughly, in particular the target acquisition 
problem in radar and sonar, and the visual problem of 
inferring objects from two dimensional data. 
     An algorithm that could perceive in polynomial 
time is called direct perception (DP), or bottom up 
perception. Such algorithms unsuccessfully attempt to 
construct object descriptions (top level) from 
immediate data (bottom level). The algorithms that do 
work are called indirect perception (IP), or top down 
perception. Such algorithms start at the top level 
(objects) and search for a match with the immediate 
data. Such algorithms take non-polynomial time [2, 3], 
for they must try an non-polynomial number of object 
hypotheses. 
     Many top down algorithms are not strictly top down - 
they start from both top and bottom and look for a 
match in the middle, but this does not change the 
character of the algorithm. 
     Bottom up algorithms do not work. Ullman[16] gives 
examples of situations where perception must be purely 
top down because all local or explicit information is 
suppressed, scrambled or misleading, so that bottom up 
processing has nothing to start from. Gregory[17], made 
the same argument long before these acronyms were 
coined, using the example of a dalmatian against a 
background of spots. In Gregory's lucid terminology we 
perceive by forming object hypotheses that fit the 
data. 
     Kanade[5] showed that when we attempt to 
generalize the polyhedral labeling problem it no longer 
has a unique solution. (The polyhedral labeling problem 
is a special case of the problem of forming a 2 1/2 D 
image, which is the problem of identifying contours in 
an image and labeling them as silhouette, convex, 
concave, groove, or mere change in surface albedo.) His 
result means that even when there is local and explicit 
data in an image, this is not sufficient to form a 
visual perception. You also need knowledge of what 
objects are likely. This led him to perform the 
negative chair experiment: He constructed an unlikely 
unfamiliar object and had people look at it. They 
misperceived it even though it was right in front of 
them. This experiment showed that not only is light and 
shade insufficient in itself to construct 3D or 2 1/2 D 
descriptions of the image, but even with small angle 
stereoscopic and small angle apparent motion data, it 
is still insufficient. Object perception is primary. We 
do not see three dimensionally and infer objects from 
the three dimensional information. We do not see what 
we think we see - we perceive it by forming hypotheses. 
Gregory[17] made the same argument using the example of 
reversed masks, but many people argued that this was a 
special case. Kanade[5] showed the same phenomenon 
occurs with any complex object. This shows that it is 
pointless to do anything elaborate to the immediate 
data without an object hypothesis.
     The results for the target acquisition problem are 
similar to the visual perception problem: If the target 
and background signals are comparable then the only way 
to extract the target signal is to find the correct 
object hypothesis. You cannot find the correct object 
hypothesis by extracting the target signal first. This 
is a tractable problem if you are only interested in a 
single class of objects with a single orientation, for 
example a specific type of interceptor on an intercept 
course at full speed, but it is an intractable problem 
if you are interested in many different possible 
targets that can be travelling in many different 
possible directions at many different speeds, with 
several similar moving objects present at once, and 
several similar interfering radars, yet bats solve this 
problem with the effortless rapidity that animals 
always show when using their most important senses for 
normal survival purposes. 

3. Quantum Solution
     All computer programs that successfully solve non-
trivial perception problems have as their hard step a 
search for the global minimum of a function. This works 
for an artificially simple microworld [4], and it also 
works when the categories consist of a short list of 
rigid objects with only two degrees of freedom in their 
position and one degree of freedom in their orientation 
[18], but if we allow irregular and elastic categories 
with many internal variables, such as occur in the real 
world, then the dimension of the space becomes much too 
large for exhaustive search (the combinatorial 
explosion, [6]). 
     In some areas of AI, such as chess, search is an 
acceptable algorithm because we merely want a good 
sequence, not the best sequence, and this can be 
achieved in polynomial time, but in perception we want 
the right object hypothesis, not merely a good object 
hypothesis. 
     Thus the problem of perceiving efficiently is 
equivalent to the problem of efficiently minimizing a 
class of many variable functions. Almost everyone who 
has confronted this problem has argued, from the fact 
that animals perceive rapidly, that it must be 
sufficient to find a good minimum, not the global 
minimum, but it all cases tried so far, algorithms that 
stop before finding the global minimum have been 
unsuccessful, as one would expect from the nature of 
the problem. 
     Any classical system performing such a 
minimization can only sample the system locally in 
phase space, thus if the function is irregular and 
general the system must find a non-polynomially large 
number of local minima before it finds the global 
minimum. This the reason why a chess playing computer 
must explicitly generate an enormous number of 
sequences and evaluate each one, and a perceiving 
computer must explicitly generate a non-polynomially 
large number of object hypotheses and evaluate each 
one, but this is not how we play chess and this is not 
how we perceive. 
     If the function to be minimized is completely 
general then the problem is non-polynomial (NP) 
complete. It is likely that animals and computers are 
both equally incapable of solving large NP complete 
problems. This leads us to expect that the class of 
functions corresponding to the class of perception 
problems is not general, but has some special property 
that enables animals to get a handle on it. 
     We shall see that the perception problem 
corresponds to the problem of finding the global 
minimum of a function of many variables, where the 
global minimum is much deeper than any other minimum. 
     One may easily show that a quantum system with a 
potential corresponding to such a function may be 
rapidly brought to the ground state by cooling where 
the ground state is not localized, followed by 
adiabatic cooling so that the ground state becomes 
substantially localized in the well containing the 
global minimum, whereas a classical system with the 
corresponding hamiltonian requires nonpolynomially 
large time to reach the corresponding ground state by 
cooling; for a classical system the ground state is 
always localized in the well so the system will rattle 
randomly from one local minimum to another, until it 
finally hits the well containing the global minimum; 
the number of local minima will be exponential in the 
number of degrees of freedom. 
     For this to work in polynomial time the momentum 
terms in the initial hamiltonian must be large enough 
relative to the potential terms to prevent substantial 
localization, which requires that the significant 
degrees of freedom of the system be initially far in 
the quantum domain. The change in state will remain 
adiabatic during the change in hamiltonian if the local 
minima are sufficiently shallow relative to the global 
minimum that the ground state is not significantly 
localized in local minima during the change. 
     We can deduce that the global minimum is much 
deeper than any local minimum from the way in which 
these functions are constructed. 
     The function to be minimized is a measure of the 
discrepancy between the perception and the immediate 
sensory data. We wish to minimize the function with 
respect to a set of variables that constitute a parse 
tree describing the external world assumed to be 
generating the immediate data (the object hypothesis). 
The grammar of the parse tree is a model of the world 
and the way in which the world interacts with the 
senses. There will be a single deep well because the 
immediate data has much higher apparent entropy than 
the parse tree data. In other words the immediate data 
is not noise, it has internal consistency in that it is 
capable of being generated from a much smaller parse 
tree. Conversely, if the immediate data was 
indistinguishable from noise, there would be no 
dominant global well. The probability that a second 
dissimilar parse tree will have a comparably good fit 
to the data varies exponentially with the difference 
between the apparent entropies of the parse tree and 
the immediate data. 
     This result is also supported by the fact that 
programs that truncate their search produce flagrant 
errors, suggesting that almost right interpretations 
are rare, and by the fact that genuinely ambiguous 
images (images with two distinct interpretations) 
seldom occur in nature but only occur when contrived by 
artists, indicating that cases where the two deepest 
wells are of comparable depth are very rare in nature. 
(We can ignore the very common case - fitting a 
stimulus of small apparent entropy, for example a 
Rorschach blot, with a complex perception.) 

4. Objections
     Many people have vigorously argued that the brain 
is too warm and wet, macromolecules too large, heavy, 
and slow, for living things to process information 
quantum mechanically. 
     The mechanism I have described (adiabatically 
cooling the ground state) is an equilibrium mechanism 
that can only work for very small systems or at very 
low temperatures. There are however a few small 
loopholes in this argument: 
_	Although deviations from classical trajectories 
usually decline rapidly with the size of the system, in 
systems far from equilibrium deviations from the 
probabilities that one would expect from classical 
local causality decline much more slowly, for example 
the quantum scar effect [19]. (These deviations are 
what is needed to process information quantum 
mechanically in ways that have no classical equivalent, 
rather than deviations from the classical 
trajectories.)
_	Finding a short unstable closed cycle in a many 
variable chaotic system is (like finding the minimum 
energy) also an NP problem, but in phase space rather 
than coordinate space. Such trajectories are 
distinguished quantum mechanically [19], but they are 
not distinguished classically. 
_	Quantum effects tend to increase with the number 
of coupled degrees of freedom. Also systems with more 
coupled degrees of freedom tend to contradict classical 
causality in a stronger and more direct fashion. 
Frolich proposes a very large number of redundant 
degrees of freedom, moderately driven from equilibrium. 
Bialek proposes a moderate number of degrees of 
freedom, very strongly driven. 
_	Although macromolecules are too large and 
heavy, their electrons are not. In macromolecules 
containing many highly polarizable groups the groups 
will have energy eigenstates where the relative 
polarizations have substantial non-local correlations. 
The relative polarization state will effect the way in 
which such molecules cleave - one method by which cells 
process information is by cleaving and joining RNA 
chains. Another possibility is that unstable 
macromolecules with highly conjugated electron 
structures are synthesized on cell membranes by the 
oxidative polymerization of serotonin, although no such 
molecules have been found in biological systems. 

5. Predictions
     The theoretical results of this paper lead me to 
make an experimental prediction: I predict that 
perception neurons proceed in one large indivisible 
step directly from low level inputs to high level 
outputs; for example the inputs for a "face of social 
superior"[20, 21] neuron would be pixel neurons, edge 
detection neurons, and similarly low level feature 
detectors. This prediction is hard to test directly 
because neurons with high level outputs have vast 
numbers of diverse inputs and it is difficult to 
determine what most of these inputs signify. But from 
this prediction flow some predictions that are easier 
to test: 
_	Neurons that generate high level perceptions will 
be located in regions well supplied with low level 
data. The neural net model would lead us to expect some 
physical separation between low level inputs and high 
level outputs, contrary to observation [20, 21]. 
_	Plausible intermediate level outputs will be rare 
or nonexistent. For example Kendrick[20, 21] found many 
neurons that respond only to faces, but none that 
respond only to frontal or only to profile views of 
faces, and none that respond to specific distinguishing 
features of faces, neurons that respond to heads with 
horns but none that respond to horns in isolation from 
a head. 
_	Neurons that originate high level outputs will 
have star rather than tree topology because each low 
level input is only significant in the context provided 
by most of the other distinct and separate low level 
inputs 
_	The delay between low level inputs stabilizing and 
high level output starting will often be very short, 
making it implausible that there is any neural net 
generating essential intermediate level inputs. 
_	Many of the inputs will be low level. Observation 
of some low level inputs would not disprove all 
possible neural net models, since such an observation 
would not prove that intermediate level inputs were 
inessential, but it would disprove all simple standard 
neural net models which assume that a neurons output 
frequency is a simple function of its inputs, e.g. a 
weighted sum of inputs or a weighted sum of low order 
products of inputs. 

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