Channel-independent and sensor-independent stimulus representations
David N. Levin
a͒
Department of Radiology, University of Chicago, Chicago, Illinois 60637
͑Received 28 October 2004; accepted 3 October 2005; published online 23 November 2005͒
This paper shows how a machine, which observes stimuli through an uncharacterized, uncalibrated
channel and sensor, can glean machine-independent information ͑i.e., channel- and
sensor-independent information͒ about the stimuli. This is possible if the following two conditions
are satisfied by the observed stimulus and by the observing device, respectively: ͑1͒ the stimulus’
trajectory in the space of all possible configurations has a well-defined local velocity covariance
matrix; ͑2͒ the observing device’s sensor state is invertibly related to the stimulus state. The first
condition guarantees that the statistical properties of the stimulus time series endow the stimulus
configuration space with a differential geometric structure ͑a metric and parallel transfer procedure͒,
which can then be used to represent relative stimulus configurations in a
coordinate-system-independent manner. This requirement is satisfied by a large variety of physical
systems, and, in general, it is expected to be satisfied by stimulus trajecteries that densely cover
stimulus state space and that have velocity distributions varying smoothly across that space. The
second condition implies that the machine defines a specific coordinate system on the stimulus state
space, with the nature of that coordinate system depending on the machine’s channels and detectors.
Thus, machines with different channels and sensors “see” the same stimulus trajectory through state
space, but in different machine-specific coordinate systems. It is shown that this requirement is
almost certainly satisfied by any device that measures more than 2d independent properties of the
stimulus, where d is the number of stimulus degrees of freedom. Taken together, the two conditions
guarantee that the observing device can record the stimulus time series in its machine-specific
coordinate system and then derive coordinate-system-independent ͑and, therefore,
machine-independent͒ representations of relative stimulus configurations. The resulting description
is an “inner” property of the stimulus time series in the sense that it does not depend on extrinsic
factors such as the observer’s choice of a coordinate system in which the stimulus is viewed ͑i.e.,
the observer’s choice of channels and sensors͒. In other words, the resulting description is an
intrinsic property of the evolution of the “real” stimulus that is “out there” broadcasting energy to
the observer. This methodology is illustrated with analytic examples and with a numerically
simulated experiment. In an intelligent sensory device, this kind of representation “engine” could
function as a “front end” that passes channel- and sensor-independent stimulus representations to a
pattern recognition module. After a pattern recognizer has been trained in one of these devices, it
could be used without a change in other devices having different channels and sensors. © 2005
American Institute of Physics. ͓DOI: 10.1063/1.2128687͔
I. INTRODUCTION
Conventional sensory devices typically detect energy
from an evolving physical stimulus and then use the resulting
signal time series to reconstruct the temporal evolution of the
stimulus state. If that state is numerically represented by the
stimulus’ configuration in a specific coordinate system, it can
only be recovered if the sensory device’s response has been
calibrated with respect to that coordinate system. For ex-
ample, if a camera is observing a moving particle, the parti-
cle’s position in the laboratory coordinate system can only be
recovered if the camera has a known response to the particle
at known positions in that coordinate system. This calibra-
tion is typically done by exposing the system to a “test pat-
tern” of known stimulus states and by recording the relation-
ship between those states and the device’s sensor states. Such
calibration “tables” make it possible for two machines to
compensate for differences in their channels and sensors and
thereby create identical representations of identical stimulus
states.
Remarkably, different humans seem to create similar
representations of the world without using such explicit cali-
bration procedures. Specifically, two individuals with similar
life experiences tend to represent the world in the same way
despite apparently uncompensated differences in the chan-
nels and sensors through which they observe the world. For
instance, two observers tend to produce similar representa-
tions of auditory stimuli despite unknown differences in their
external and middle ears, their cochleae, and the neural ar-
chitectures of their primary auditory cortices. The results of
this biological “experiment” suggest the possibility of build-
ing machines that observe stimuli through different channels
and sensors and that independently create identical stimulus
representations without using any physical knowledge of
those channels or sensors.
a͒
Electronic mail: d-levin@uchicago.edu
JOURNAL OF APPLIED PHYSICS 98, 104701 ͑2005͒
0021-8979/2005/98͑10͒/104701/12/$22.50 © 2005 American Institute of Physics98, 104701-1