Polished most of yesterday's work.

main.tex

@@ -191,19 +191,19 @@ degree of intensity invariance.
 % (Still can't stand some of this paragraph's structure and wording...)
 Invariance to non-informative song variations is crucial for reliable song
 recognition; however, it is not sufficient to this end. In order to recognize a
-conspecific song as such, the auditory system also needs to extract
-sufficiently informative features of the song pattern and then integrate the
-gathered information into a final categorical percept. Previous authors have
-proposed a functional model framework that describes this process --- feature
-extraction, evidence accumulation, and categorical decision making --- in both
-crickets~(\bcite{clemens2013computational}) and
+conspecific song as such, the auditory system needs to extract sufficiently
+informative features of the song pattern and then integrate the gathered
+information into a final categorical percept. Previous authors have proposed a
+functional model framework that describes this process --- feature extraction,
+evidence accumulation, and categorical decision making --- in both
+crickets~(\bcite{clemens2013computational}, \bcite{hennig2014time}) and
 grasshoppers~(\bcite{clemens2013feature}, review on
 both:~\bcite{ronacher2015computational}). Their framework provides a
 comprehensible and biologically plausible account of the computational
-mechanisms required for species-specific song recognition. As such, it has
-served as the inspiration for the development of the model pathway we propose
-here. The existing framework relies on pulse trains as input signals, which
-were designed to capture the essential structural properties of natural song
+mechanisms required for species-specific song recognition, which has served as
+the inspiration for the development of the model pathway we propose here. The
+existing framework relies on pulse trains as input signals, which were designed
+to capture the essential structural properties of natural song
 envelopes~(\bcite{clemens2013feature}). In the first step, a bank of parallel
 linear-nonlinear feature detectors is applied to the input signal. Each feature
 detector consists of a convolutional filter and a subsequent sigmoidal
@@ -215,77 +215,41 @@ animal to the presented input signal. Our model pathway adopts the general
 structure of the existing framework but modifies it in several key aspects. The
 convolutional filters, which have previously been fitted to behavioral data for
 each individual species~(\bcite{clemens2013computational}), are replaced by a
-larger, more general set of unfitted Gabor kernels in order to cover a wide
-range of possible song features for as many species as possible. Gabor kernels
-closely resemble the structure of the filters used in previous
-models~(\bcite{clemens2013computational}, \bcite{clemens2013feature},
-\bcite{hennig2014time}) as well as the measured spike-triggered averages of
-higher-order interneurons in the grasshopper auditory
-system~(\bcite{clemens2011efficient}). The fitted sigmoidal nonlinearities in
-the existing framework consistently exhibited very steep
-slopes~(\bcite{clemens2013computational}, \bcite{clemens2013feature}) and are
-therefore approximated by simpler shifted Heaviside step-functions in our
-model. Another, more substantial modification is that the outputs of the
-feature detectors are temporally averaged in a way that does not condense them
-into single feature values but retains their time-varying structure. A
-time-varying feature representation introduces a certain time constant until
-the representation stabilizes after the onset of a song. This reflects the
-continuous nature of acoustic input and auditory perception, as songs are not
-received as discrete units but processed continuously prior to the final
-categorical decision to initate a behavioral response~(SOURCE LOL). The
-most notable difference between our model pathway and the existing framework,
-however, lays in the addition of a physiologically inspired preprocessing
-portion, whose starting point corresponds to the initial reception of airborne
-sound waves. This allows the model to operate on unmodified recordings of
-natural grasshopper songs instead of condensed pulse train approximations,
-which widens its scope towards more realistic, ecologically relevant scenarios.
-For instance, we were able to investigate the contribution of different
-processing stages to the emergence of intensity-invariant song representations
-based on actual field recordings of songs at different distances from the
-sender.
-
-
-
-
-% Invariance to non-informative song variations is crucial for reliable song
-% recognition; however, it is not sufficient to this end. In order to recognize a
-% conspecific song as such, the auditory system needs to extract sufficiently
-% informative features of the song pattern and then integrate the gathered
-% information into a final categorical percept. Previous authors have proposed a
-% biologically plausible functional framework that describes this process ---
-% feature extraction, evidence accumulation, and categorical decision making ---
-% in both crickets~(\bcite{clemens2013computational}) and
-% grasshoppers~(\bcite{clemens2013feature}, review on
-% both:~\bcite{ronacher2015computational}). Their framework provides a
-% comprehensive, generalizable account of the computational mechanisms required
-% for species-specific song recognition, which has served as inspiration for the development of our own model of the grasshopper auditory
-% pathway, where it now constitutes the foundation of the recognition mechanism.
-% According to the existing framework, a bank of parallel linear-nonlinear
-% feature detectors is initially applied to the input signal. Each feature
-% detector consists of a convolutional filter and a subsequent sigmoidal
-% nonlinearity. The outputs of these feature detectors are temporally averaged to
-% obtain a single feature value per detector, which is assigned a specific
-% weight. The linear combination of weighted feature values results in a single
-% preference value, which then serves as predictor for the behavioral response of
-% the animal. The model we propose here adopts this general structure but
-% modifies and several key aspects.
-
-
-
-
-\textbf{Precursor work for model construction (special thanks to authors):}
-
-Linear-nonlinear modelling of behavioral responses to artificial songs\\
-- Feature expansion as implemented in our model: Major contribution!\\
-- Bank of linear filters, nonlinearity, temporal integration, feature weighting\\
-$\rightarrow$ \cite{clemens2013computational} (crickets)\\
-$\rightarrow$ \cite{clemens2013feature} (grasshoppers)\\
-$\rightarrow$ \cite{ronacher2015computational}\\
-\textbf{Own advancements/key differences}:\\
-1) Used boxcar functions as artificial "songs" (focus on few key parameters)\\
-$\rightarrow$ Now actual, variable songs (as naturalistic as possible)\\
-2) Fitted filters to behavioral data\\
-$\rightarrow$ More general, simpler, unfitted formalized Gabor filter bank
+larger, generic set of unfitted Gabor basis functions in order to cover a wide
+range of possible song features across different species. Gabor functions
+approximate the general structure of the filters used in the existing framework
+as well as the filter functions found in various auditory
+neurons~(\bcite{rokem2006spike}, \bcite{clemens2011efficient},
+\bcite{clemens2012nonlinear}). The fitted sigmoidal nonlinearities in the
+existing framework consistently exhibited very steep slopes and are therefore
+replaced by shifted Heaviside step-functions, which results in a binarization
+of the feature detector outputs. Another, more substantial modification is that
+the feature detector outputs are temporally averaged in a way that does not
+condense them into single feature values but retains their time-varying
+structure. This is in line with the fact that songs are no discrete units but
+part of a continuous acoustic stream that the auditory system has to process in
+real time. Moreover, a time-varying feature representation only stabilizes
+after a certain delay following the onset of a song, which emphasizes the
+temporal dynamics of evidence accumulation towards a final categorical
+decision. The most notable difference between our model pathway and the
+existing framework, however, lays in the addition of a physiologically inspired
+preprocessing portion, whose starting point corresponds to the initial
+reception of airborne sound waves. This allows the model to operate on
+unmodified recordings of natural grasshopper songs instead of condensed pulse
+train approximations, which widens its scope towards more realistic,
+ecologically relevant scenarios. For instance, we were able to investigate the
+contribution of different processing stages to the emergence of
+intensity-invariant song representations based on actual field recordings of
+songs at different distances from the sender.
+% Forgive me, it's friday.
+In the following, we outline the structure of the proposed model of the
+grasshopper auditory pathway, from the initial sound reception at the tympanal
+membrane up to the generation of a high-dimensional, time-varying feature
+representation that is suitable for species-specific song recognition. We
+provide a side-by-side account of the known physiological processing steps and
+their functional approximation by basic mathematical operations. We then
+elaborate on two key mechanisms that drive the emergence of intensity-invariant
+song representations within the auditory pathway.
 
 % SCRAPPED UNTIL FURTHER NOTICE:
 % Multi-species, multi-individual communally inhabited environments\\