# Predictive coding and stochastic resonance as fundamental principles of
auditory perception

Achim Schilling Neuroscience Lab, University Hospital Erlangen, Germany
Cognitive Computational Neuroscience Group, University Erlangen-Nürnberg,
Germany  William Sedley Translational and Clinical Reseearch Institute,
Newcastle University Medical School, Newcastle upon Tyne NE2 4HH, UK  Richard
Gerum Cognitive Computational Neuroscience Group, University Erlangen-
Nürnberg, Germany  Department of Physics and Center for Vision Research, York
University, Toronto, Ontario, Canada  Claus Metzner Neuroscience Lab,
University Hospital Erlangen, Germany Biophysics Lab, University Erlangen-
Nürnberg, Germany  Konstantin Tziridis Neuroscience Lab, University Hospital
Erlangen, Germany Andreas Maier Pattern Recognition Lab, University Erlangen-
Nürnberg, Germany  Holger Schulze Neuroscience Lab, University Hospital
Erlangen, Germany Fan-Gang Zeng Center for Hearing Research, Departments of
Anatomy and Neurobiology, Biomedical Engineering, Cognitive Sciences,
Otolaryngology–Head and Neck Surgery, University of California Irvine, Irvine,
California 92697, USA  Karl J. Friston Wellcome Centre for Human Neuroimaging,
Institute of Neurology, University College London, London WC1N 3AR, UK
Patrick Krauss Neuroscience Lab, University Hospital Erlangen, Germany
Cognitive Computational Neuroscience Group, University Erlangen-Nürnberg,
Germany  Pattern Recognition Lab, University Erlangen-Nürnberg, Germany

###### Abstract

How is information processed in the brain during perception? Mechanistic
insight is achieved only when experiments are employed to test formal or
computational models. In analogy to lesion studies, phantom perception may
serve as a vehicle to understand the fundamental processing principles
underlying auditory perception. With a special focus on tinnitus – as the
prime example of auditory phantom perception – we review recent work at the
intersection of artificial intelligence, psychology, and neuroscience. In
particular, we discuss why everyone with tinnitus suffers from hearing loss,
but not everyone with hearing loss suffers from tinnitus. We argue that the
increase of sensory precision due to Bayesian inference could be caused by
intrinsic neural noise and lead to a prediction error in the cerebral cortex.
Hence, two fundamental processing principles - being ubiquitous in the brain -
provide the most explanatory power for the emergence of tinnitus: predictive
coding as a top-down, and stochastic resonance as a complementary bottom-up
mechanism. We conclude that both principles play a crucial role in healthy
auditory perception.

Keywords:
predictive coding, Bayesian brain, stochastic resonance, tinnitus,
computational modeling, neural networks, artificial intelligence, active
inference, auditory neuroscience, phantom perception

## Introduction

The ultimate goal of neuroscience is to gain a mechanistic understanding how
information is processed in the brain. Since the early beginnings of the
scientific study of the brain, lesions or more broadly anatomical damages and
their physiological effects have provided pivotal insights into brain
function. Analogously, phantom perception may serve as a vehicle to understand
the fundamental processing principles underlying perception. The prime example
of an auditory phantom perception is tinnitus, which is caused by anatomical
damages along the auditory pathway. Here we provide a mechanistic explanation
of how tinnitus emerges in the brain: namely, how the neural and mental
processes underlying perception, cognition, and behavior contribute to—and are
affected by—the development of tinnitus. These insights may not only point to
strategies, how tinnitus may be reversed or at least mitigated, but also how
auditory perception is implemented in the brain in general.
While there is broad agreement in the scientific community on these goals,
there is far less agreement on the way to achieve them. There is still a
popular belief among neuroscientific and psychological tinnitus researchers
that we are largely data driven. In other words, generating large, multi-
modal, and complex data sets—analyzed with advanced machine learning
algorithms—will lead to fundamental insights into how tinnitus emerges.
Indeed, in the last decades we have assembled a broad data base, which has
inspired models that make quantitative predictions. These predictions scaffold
new experimental paradigms that aim to unravel the mechanisms of tinnitus
perception. In the following, we summarize some of the main findings in
tinnitus research, over the last decades, and then turn to strategic questions
about how to leverage these advances, from the perspective of formal
modelling.

Some universal correlations between hearing loss, tinnitus, and neural
hyperactivity in the auditory system have been found in both animal and human
studies. These reproducible findings can be considered as the common
denominator of tinnitus research, and could offer the minimal starting point
for theoretical considerations. Tinnitus is a phenomenon arising somewhere
along the auditory pathway, but not in the inner ear [1]. Thus, it can be
shown that the spontaneous activity of neurons along the auditory pathway is
increased after hearing loss [2, 3, 4], whereas the damaged cochlea transmits
less information to the higher auditory nuclei [5, 6]. However, it has been
argued that not all alterations in neural activity in animal models, which
were caused by an acoustic trauma, are necessarily related to tinnitus [1, 7].
Although there exist some behavioral tests to check for the putative presence
of a tinnitus percept based on conditioning [8, 9] or startle responses [10,
11, 12], the reliability of these paradigms remains controversial [7, 13].
Thus, studies on human subjects complement these findings. In several recent
studies, it was shown that the tinnitus frequency lies within the range of the
hearing loss [14, 15, 16, 17]. Furthermore, Dalligna and coworkers report that
the tinnitus is directly centered at the frequency of the largest hearing loss
[16] and Keppler and coworkers report that there is no correlation between
tinnitus pitch and the edges of the impaired frequency ranges [15].
Nevertheless, there are also some studies reporting a correlation between the
edges of the hearing loss and the tinnitus pitch [18, 19, 20].

Indeed, the above neural correlates of tinnitus and hearing loss are just a
small distillation of all studies that aspire to unravel mechanisms that
underwrite tinnitus, but these findings are robust and constitute the basis of
most theoretical and computational models of tinnitus. In the 1990s the first
computational models of tinnitus emerged. These models considered decreased
lateral inhibition—due to deficient auditory input—as the main cause of
tinnitus. Gerken [21] created a feed-forward brainstem model and suggested the
inferior colliculus to be the crucial structure for tinnitus development. Kral
and Majernik [22], as well as Langner and Wallhäuser-Franke [23] pursued
computational models, based on decreased lateral inhibition. Bruce and
coworkers developed these models further and implemented lateral inhibition in
a spiking recurrent neural network [24]. In a subsequent step, the principles
were implemented in a model of the auditory cortex based on spiking neurons
[25].

Besides lateral inhibition, homeostatic plasticity [26] and central gain
changes are hypothesized to be the cause for tinnitus emergence and
manifestation. Thus, Parra and Pearlmutter developed an ”abstract” model,
where they simply defined several frequency channels with a certain input
[27]. The output was scaled with the average, which means that a decreased
input leads to a higher scaling factor. However, they did not consider a
plausible neural implementation of this mathematical model. Schaette and
Kempter further developed several computational models, investigating the
effects of central gain increase on tinnitus emergence [28, 29, 30]. Finally,
Chrostowski and coworkers developed a cortex model to investigate central gain
changes in the cortex ([31], for detailed review on computational tinnitus
models see e.g. [1]).

In 2013, Zeng introduced a model that argues that tinnitus is not caused by
increased central gain, but by increased central noise, which means an
additive neural noise, that is intrinsically generated [32]. The idea of an
additional intrinsic or extrinsic noise as an explanation for tinnitus has
gained some popularity in recent years (see e.g., Koops and Eggermont [33]).
Zeng raised the question why the brain should increase central noise levels.
This question was addressed in 2016 by Krauss and coworkers [34], who showed
that internally generated neural noise could partially restore hearing ability
after hearing loss through the effect of stochastic resonance [34, 35, 36,
37]. This hypothesis is supported by the finding that on average hearing
thresholds are better in patients suffering from hearing loss with tinnitus
compared to a control group of patients suffering from hearing loss but
without tinnitus [38]. Along the same line, the stochastic resonance and
central noise model may explain the Zwicker tone illusion [39], i.e. the
perception of a phantom sound which occurs after stimulation with notched
noise, and why auditory sensitivity for frequencies adjacent to the Zwicker
tone are improved beyond the absolute threshold of hearing during Zwicker tone
perception [40]. Furthermore, recently, a crucial prediction of the stochastic
resonance model of tinnitus development was confirmed experimentally by using
brainstem audiometry [41] and assessing behavioral signs of tinnitus [12] in
an animal model: simulated transient hearing loss improves auditory
sensitivity and leads, as a side effect, to the perception of tinnitus [42].
Both, the model from Zeng and the model from Krauss et al., are not based on a
particular or specified neural network architecture. However, in 2020,
Schilling and coworkers developed such a model based on a hybrid neural
network of spiking neurons and a deep neural network, proving that
intrinsically generated noise could indeed significantly increase speech
perception via stochastic resonance [43]. Recently, a similar hybrid neural
network model has led to further insights into the mechanisms of impaired
speech recognition caused by hearing loss [44].

In parallel to the intrinsic neural noise models from Zeng and Krauss et al.,
Sedley and coworkers developed a conceptual model, which describes tinnitus as
arising from a prediction error of the brain [45, 46]. This model is based on
the idea that the brain is a Bayesian prediction machine, trying to minimize
prediction errors or free energy [47, 48], and therefore that modifying
auditory predictions to accord with noise in the auditory pathway reduces
prediction errors, but at the expense of causing an erroneous perception (i.e.
tinnitus). More recently, a computational instantiation of this model, using a
hierarchical Gaussian filter, has been able to explain phenomenology in
individual tinnitus subjects, and their predict residual inhibition
characteristics [49]. Furthermore, Dotan and Shriki introduced a recurrent
neural network model where tinnitus-like “hallucinations” are elicited by
sensory deprivation as a result of entropy maximization [50]. Finally, Gault
and co-workers fitted audiometric data with assessed tinnitus pitches in order
to create a linear regression model of tinnitus pitch and loudness [51].
Besides these computational models that rest upon a mathematical formulation,
there exist several phenomenological models, such as the thalamo-cortical
dysrhythmia model [52, 53], the thalamic low-threshold calcium spike model
[54], the frontostriatal gating hypothesis [55, 56], and the overlapping sub-
network theory [57, 58]. Finally, there exist another Bayesian brain /
predictive coding model of tinnitus, which is kind of the polar opposite to
what Sedley and Friston have argued for. There, tinnitus is not believed to
arise from spontaneous noise increase, which higher predictions go on to
accept, but on the contrary that tinnitus arises from reduced input to the
auditory cortex, leading it to ‘make up’ or ‘fill in’ an auditory percept from
auditory memory [59]. However, this assumption contradicts the findings that
neural activity is increased after hearing loss [2, 3, 4].

As there exist various models of tinnitus development, criteria are needed to
define which models are apt to understand tinnitus development. In their
review paper Schaette and Kempter [1] define three major criteria for the
quality of a model: First, – and in line with Popper’s ideas [60] – a model
should be falsifiable, which means there should be experimental paradigms,
which could be used to test whether a model is right or wrong. Second, a model
should make quantitative predictions, as opposed to purely qualitative, often
vague, predictions (compare also [61]). Third, a model should be as simple as
possible, i.e., contain the smallest number of parameters and assumptions as
possible, a principle called Ockham’s razor [62]. Hence, when two models
explain experimental data equally well, the simpler one is considered to be
the better one.

With the huge progress of artificial intelligence (AI) during the last decade,
which is mainly due to novel hardware resources, a new discipline has been
founded, called _Cognitive Computational Neuroscience_ (CCN) as an integrative
endeavor at the intersection of AI, cognitive science and neuroscience [63,
64, kietzmann2019deep].

In this paper, we first discuss the opportunities and limitations of this new
research agenda. In particular, we present key thought experiments that
highlight the major challenges on the road towards a CCN of tinnitus. In the
light of these considerations, we subsequently review current models of
tinnitus and assess their explanatory power. Finally, we present an
integration of those models that we consider most promising, and point towards
a unified theory of tinnitus development.

## Three challenges ahead

### The challenge of developing a common formal language

In 2002, Yuri Lazebnik compared the biologists’ endeavor – of trying to
understand the building blocks and processes of living cells – with the
problems that engineers typically deal with [61]. In his opinion paper _Can a
biologist fix a radio? – Or, what I learned while studying apoptosis_ ,
Lazebnik argued that many fields of biomedical research at some point reach
_“a stage at which models, that seemed so complete, fall apart, predictions
that were considered so obvious are found to be wrong, and attempts to develop
wonder drugs largely fail. This stage is characterized by a sense of
frustration at the complexity of the process”_ [61].

Subsequently, Lazebnik discussed a number of intriguing analogies between the
physical and life sciences. In particular, he identified formal language as
the most important difference between the two. Lazebnik argues that biologists
and engineers use very different languages for describing phenomena. On the
one hand, biologists draw box-and-arrow diagrams, which are – even if a
certain diagram makes overall sense – difficult to translate into quantitative
assumptions, and hence limits its predictive or investigative value.

Indeed, these thoughts fit to the criterion for a ‘good model’ as pointed out
by Schaette and Kempter [1], ], i.e., that a model should make quantitative
predictions. However, on the other hand a model should be as simple as
possible and understandable, which means that it is important to find a
compromise between too fine-grained and too coarse-grained descriptions of the
system (see Marr’s levels of analysis [65], Fig. 1 a).

Lazebnik also remarks that scientific assumptions and conversations are often
_“vague”_ and _avoid clear, quantifiable predictions”_ [61]. A freely adapted
example drawn from Lazebnik’s paper would be a statement like _“an imbalance
of excitatory and inhibitory neural activity after hearing-loss appears to
cause an overall neural hyperactivity, which in turn seems to be correlated
with the perception of tinnitus.”_

Descriptions of electrophysiological findings are and important starting point
for hypothesis generation, but they are no more than a first step. Description
needs to be complemented with explanation and prediction (compare also the
four main goals of psychology as described e.g., in [66]).

Furthermore, Lazebnik urges a more formal common language for biological
sciences, in particular a language which has the precision and expressivity
found in engineering, physics, or computer science. Any engineer trained in
electronics for instance, is able to unambiguously understand a diagram
describing a radio or any other electronic device. Thus, engineers can discuss
a radio using terms that are common ground in the community. Furthermore, this
commonality enables engineers to identify familiar functional architectures or
motifs; even in a diagram of a completely novel device. Finally, due to the
mathematical underpinnings of the language used in engineering, it is
perfectly suited for quantitative analyses and computational modeling. For
instance, a description of a certain radio includes all key parameters of each
component like the capacity of a capacitor, but not irrelevant parameters –
that do not ‘matter’ – like its color, shape, or size.

We emphasize that this does not mean that anatomical descriptions are useless
in order to understand brain function. However, also in neurobiology there
exist both kinds of detail: those that are crucial for understanding neural
processing, and those that are not relevant variables.

Lazebnik concludes that _“the absence of such language is the flaw of
biological research that causes David’s paradox”_ , i.e., the paradoxical
phenomenon frequently observed in biology and neuroscience that _“the more
facts we learn the less we understand the process we study”_ [61].

Some conclusions for tinnitus research can be drawn from Lazebniks’ thoughts
on a more formal approach in biological sciences. The ”central gain” and
”homeostatic plasticity” theory on tinnitus emergence is a good example, how
the communication on tinnitus research can be improved. For example, Roberts
stated in 2018 that the increase of central gain is _”increase of input output
functions by forms of homeostatic plasticity”_ , which means that homeostatic
plasticity is necessarily connected to central gain adaptations [67]. In
contrast to that, Schaette and Kempter state that central gain changes can
occur within seconds and thus are not necessarily caused by homeostatic
plasticity [1]. Only on longer time-scales both effects can be regarded as
_“functionally equivalent”_ [1]. Indeed, tinnitus research would profit from a
unified terminology for the different constructs, in the best case, a
mathematical formulation.

### The challenge of developing a unified mechanistic theory

In 2014, Joshua Brown built on Lazebnik’s ideas and published the opinion
article _The tale of the neuroscientists and the computer: why mechanistic
theory matters_ [68]. In this thought experiment, a group of neuroscientists
finds an alien computer and tries to figure out its function.

First, the M/EEG researcher tried to investigate the computer. She found that
every time _“when the hard disk was assessed, the disk controller showed
higher voltages on average, and especially more power in the higher frequency
bands”_ [68].

Subsequently, the cognitive neuroscientist, i.e., the fMRI researcher argued
that M/EEG has insufficient spatial resolution to see what is going on inside
the computer. He carried out a large number of experiments, the results of
which can be summarized with the realization that during certain tasks,
certain regions seem to be more activated and that none of these components
could be understood properly in isolation. Thus, the researcher analyzed the
interactions of these components, showing that there is a vast variety of
different task-specific networks in the computer.

Finally, the electrophysiologist noted, critically, that his colleagues may
have found coarse-grained patterns of activity, but it is still unclear what
the individual circuits are doing. He starts to implant micro-electrode arrays
into the computer and probes individual circuit points by measuring voltage
fluctuations. With careful observation, the electrophysiologist identifies
units responding stochastically when certain inputs are presented, and that
nearby units seem to process similar inputs. Furthermore, each unit seems to
have characteristic tuning properties.

Brown’s tale ends with the conclusion that even though, they performed a
multitude of different empirical investigations, yielding a broad range of
interesting results, it is still highly questionable whether _“the
neuroscientists really understood how the computer works”_ [68].

This provocative thought experiment speaks to some ideas that are relevant for
tinnitus research. In 2021, four leading scientists in tinnitus research
discussed different tinnitus models at the Annual-Mid-Winter Meeting of the
Association for Otolaryngology and diagnosed a _“lack of consistency of
concepts about the neural correlate of tinnitus”_ [69]. Thus, a clearly
defined theoretical framework is needed, which helps empirical groups to
develop experimental paradigms suited to verify or falsify alternative models.
To achieve that, inter-disciplinary teams or at least an inter-disciplinary
approach is needed [70].

### The challenge of developing appropriate analysis methods

In 2017 Jonas and Kording implemented the thought experiment of Brown in an
experimental study. In their study _“Could a neuroscientist understand a
microprocessor?”_ [71] the authors address this question by emulating a
classical microprocessor, the _MOS 6502_ , which was implemented as the
central processing unit (CPU) in the Apple I, the Commodore 64, and the Atari
Video Game System, in the 1970s and 1980s. In contrast to contemporary CPUs,
like Intel’s _i9-9900K_ , that consist of more than 3 billion transistors, the
_MOS 6502_ only consisted of 3,510 transistors, served as a “model organism”
in the mentioned study, and performed three different “behaviors”, i.e. three
classical video games (Donkey Kong, Space Invaders and Pitfall).

The idea behind this approach is that the microprocessor, as an artificial
information processing system, has three decisive advantages over natural
nervous systems. Firstly, it is fully understood at all levels of description
and complexity, from its gross architecture and the overall data flow, through
logical gate primitives, to the dynamics of single transistors. Secondly, its
internal state is fully accessible without any restrictions to temporal or
spatial resolution. And thirdly, it offers the ability to perform invasive
experiments on it. Using this framework, the authors applied a wide range of
popular data analysis methods from neuroscience to investigate the structural
and dynamical properties of the microprocessor. The methods used included –
but were not restricted to – Granger causality for analyzing task specific
functional connectivity, time-frequency analysis as a hallmark of M/EEG
research, spike pattern statistics, dimensionality reduction, lesions, and
tuning curve analysis.

The authors concluded that although each of the applied methods yielded
results strikingly similar to what is known from neuroscientific or
psychological studies, none of them could actually elucidate how the
microprocessor works, or more broadly speaking, was appropriate to gain a
mechanistic understanding of the investigated system.

There are potential criticisms of this study; for example, the brain is no
computer and thus the drawn parallels are insufficient. Nevertheless, the idea
to use a known model system to check for the validity of the evaluation
procedures and common methods is a seminal principle. In 2009 Bennett and
coworkers performed an even stranger experiment, when they used standard fMRI
and statistics techniques to analyze the brain activity of a dead salmon, and
indeed found a BOLD signal due to stimulation [72]. At first glance this
experiment seemed to be at least useless if not even funny, but it was a wake-
up call and indeed changed the way fMRI data is evaluated. Nowadays there
exist strict rules how to correct for multiple testing in fMRI research, to
prevent pseudo-effects being a result of wrong statistical testing [72, 73].
In computational neuroscience and AI research, newly developed methods are
always applied to standard data sets such as MNIST [74, 75] or artificially
generated data sets with known properties (e.g. [76, 77, 41]). The principle
of using fully known – even trivial systems – to test the validity of tools,
methods or even theories could be an important device in tinnitus research.
Even in computational modeling, simply implementing a system in all details
without a theory, which serves as a solid base, will not lead to a real
understanding. Indeed, theory needs computational modeling, but the statement
is also true the other way around [78]. Thus, computational models have to be
checked in a sense that they should fulfill the minimum requirement – that
they can explain well understood and simple phenomena, as a back-check for
further conclusions.

## Towards a cognitive computational neuroscience of tinnitus

### What does it mean to understand a system?

If popular analysis methods fail to deliver mechanistic understanding, what
are the alternative approaches? Most obviously, narrative hypotheses about the
structure and function of the system under investigation will help. Instead of
simply describing data features with correlations, coherence, Granger
causality et cetera – in the hope of learning something about the functioning
of the system under investigation – it would be much more effective to have a
concrete hypothesis about the structure or function architecture of the system
and then search for empirical evidence for that and alternative hypotheses.

Note that, this does not exclude explorative analysis of existing data, in
order to generate new hypotheses. However, as we pointed out in a previous
publication [79], in order to avoid statistical errors due to _“HARKing”_
111HARKING (Hypothesizing after results are known) is defined as generating
scientific statements exclusively based on the analysis of huge data sets
without previous hypotheses. [80, 81] and to guarantee consistency of the
results, it is necessary to apply e.g. re-sampling techniques such as sub-
sampling [41], or alternatively, the well-established machine learning
practice of cross-validation: i.e. splitting the data set into multiple parts
before the beginning of the evaluation. One part is used for generating new
hypotheses, and another part for subsequently statistically testing these
hypotheses. Accumulation of such data-driven knowledge may finally even lead
to a new theory.

Ideally, the verbally defined (narrative) hypotheses to be experimentally
tested would be derived from such an underlying theory. As Kurt Lewin, the
father of modern experimental psychology, pointed out: _“There is nothing so
practical as a good theory”_ [82]. If we had theorized that the microprocessor
from the thought experiment above performs arithmetic calculations, we could
have derived the hypothesis, for example, that there must be something like
1-bit adders, and could have searched for them specifically.

Conversely, Allan Newell, one of the fathers of artificial intelligence,
stated that _“You can‘t play 20 questions with nature and win”_ [83]. This
suggests that testing one narrative hypothesis after another will never lead
to a mechanistic understanding. So, this raises the fundamental question of
what it actually means to ‘understand’ a system.

Yuri Lazebnik argued that understanding of a system is achieved when one could
fix a broken implementation: _“Understanding of a particular region or part of
a system would occur when one could describe so accurately the inputs, the
transformation, and the outputs that one brain region could be replaced with
an entirely synthetic component”_ [61]. In engineering terms, this
understanding can be simply described as $y=f(x)$, where $x$ is the input, $y$
is the output, and $f$ is the transformation. Fourier, Hilbert, rectifier,
transformers etc. are all details; we can examine the input and output
functions in frequency or time domains, in real or complex domains – these are
all tools.

According to David Marr, one can seek to understand a system at complementary
levels of analysis [65]. He distinguished the computational, the algorithmic
and the implementational level of analysis (see Fig. 1 a). The _computational
level_ is the most coarse-grained level of analysis. It asks what is the
problem or task the system is seeking to solve via computation, that results
in the observed phenomena; in our context, phantom perceptions like tinnitus.
This level of analysis is addressed by the fields of psychology and cognitive
neuroscience. In contrast, the _implementational level_ represents the most
fine-grained description of a system. Here, the system’s concrete, physical
layout is analyzed. In computer science and engineering, this corresponds to
the exact hardware architecture and the individual software realization, with
a particular programming language. In the brain, where there exists no clear
distinction between software and hardware (or wetware), this level of
description corresponds to the structural design of ion channels, synapses,
neurons, local circuits and larger systems, and the physiological processes
these components are subject to. This level of analysis can be considered as
the hallmark of physiology and neurobiology. Finally, the _algorithmic level_
takes an intermediate position between the previously described levels. It is
about which algorithms—that are physically realized at the implementational
level—the system employs to manipulate its internal representations, in order
to solve the tasks and problems identified at the computational level. In
computer science, the algorithmic level would be described independently of a
specific programming language by abstract pseudo code.

We argue that analysis at the algorithmic level is most crucial to understand
auditory phantom perceptions like tinnitus or Zwicker tone. Only by knowing
the algorithms that underlie normal auditory perception, we will gain a
detailed understanding of what exactly happens under certain pathological
conditions such as hearing loss. And which processes eventually cause the
development of tinnitus, so that we can mitigate or reverse these processes.

Which discipline addresses this level of analysis in tinnitus research?
Computational neuroscience comes to mind immediately. However, in “good old-
fashioned” computational neuroscience, great efforts have been made to model
the physiological processes at the level of single neurons, dendrites, axons,
synapses, or even ion channels, leading to increasingly complex computational
models. These models, mostly based on systems of coupled differential
equations, can mimic experimental data in great detail. Perhaps the most
popular among these models is the famous Hodgkin-Huxley model [84], which
reproduces the temporal course of the membrane potential of a single neuron
with impressive accuracy. These types of models are of great importance to
deepen our understanding of fundamental physiological processes. However, in
our opinion, they must also be considered as belonging to the implementational
level of analysis, since they merely describe the physical realization of the
algorithms, rather than the algorithms themselves.

In the following section, we will discuss emerging research directions that
speak to the algorithmic level of analysis in the context of tinnitus
research.

Figure 1: Marr’s Levels of Analysis: a: The scheme illustrates how measurement
methods (such as MEG, EEG, etc.), neuroscientific disciplines, as well as
theoretical models can be structured in three different levels of analysis
(according to Marr [65]). b: Tinnitus models in the light of the three levels
of analysis; The gray bars illustrate how the different models cover the
different levels of analysis (implementational, algorithmic, computational).
The central noise model and the stochastic resonance model can be unified
(b1). The homeostatic plasticity model is a specification of the central gain
model (b2).

### The integration of artificial intelligence in tinnitus research

As we argued above, hypothesis testing alone does not lead to a mechanistic
understanding. Instead, it needs to be complemented by the construction of
task-pointing computational models, since only synthesis in a computer
simulation can reveal the interaction of proposed components entailed by a
mechanistic explanation, i.e., which algorithms are realized, and whether they
can account for the perceptual, cognitive or behavioral function in question.
As Nobel laureate and theoretical physicist Richard Feynman pointed out:
_“What I cannot create, I do not understand.”_

Along these lines, one may consider extending the four goals of psychology,
i.e., to describe, explain, predict, and change cognition and behavior [66],
by adding a fifth one: to build synthetic cognition and behavior.

As pointed out in previous publications [85, 86, 87, 88, 63], these
computational models can be based on constructs from artificial intelligence,
for example deep learning [89, 90]. A related development in artificial
intelligence rests upon the explicit use of generative models, leading to
formulations of action and perception, in terms of predictive coding and
active inference. Examples of their application to auditory processing and
hallucinations range from examining the role of certain oscillatory
frequencies in message passing, through to simulations of active listening and
speech perception. Please see [91, 92, 93, 94, 95, 96, 97] for details. Both
deep learning and predictive processing accounts rest upon message passing on
neural networks.

Artificial deep neural networks are designed to solve problems clearly defined
at the computational level of analysis, in our case auditory perception tasks
like, e.g., speech recognition. These models are precisely defined at an
algorithmic level, which is completely independent from any individual
programming language or specific software library, i.e., the implementational
level of analysis. Hence, these algorithms could, at least in principle, also
be realized in the brain as biological neural networks. Once we have built
such models and algorithms in computer simulations, we can subsequently
compare their dynamics and internal representations with brain—and behavioral
data—in order to reject or adjust putative models, thereby successively
increasing biological fidelity [63]. Vice versa, the ensuing models may also
serve to generate new testable hypotheses about cognitive and neural
processing in auditory neuroscience.

This research approach – of combining artificial intelligence, cognitive
science, and neuroscience – has been coined as _Cognitive Computational
Neuroscience_ (CCN) [63]. Furthermore, besides the advantages discussed above,
this approach furnishes the opportunity for in silico testing of new, putative
treatment interventions for conditions like tinnitus, prior to in vivo
experiments. In this way, CCN may even serve to reduce the number of animal
experiments.

However, we note that Cognitive Computational Neuroscience of auditory
perception is not only beneficial for neuroscience. As noted in [98],
understanding biological brains could play a vital role in building
intelligent machines, and that current advances in artificial intelligence
have been inspired by the study of neural computation in humans and animals.
Thus, Cognitive Computational Neuroscience of auditory perception, may
contribute to the development of neuroscience-inspired artificial intelligence
systems in the domain of natural language processing [99]. Finally,
neuroscience may even serve to investigate _machine behavior_ [100], i.e.,
illuminate the black box of deep learning [101, 102]. However, so far, most AI
research these days does not even attempt to mimic or understand brain or
biology in general.

In other neuroscientific strands, such as research on spatial navigation, the
fusion of classical neuroscience and AI has already led to major
breakthroughs, and still promises further advances in the future [103]. For
example, on the one hand Stachenfeld and colleagues developed a mathematical
framework for the function of place and grid cells in the entorhinal-
hippocampal system based on predictive coding [104, 105], on the other hand,
researchers from Google DeepMind developed artificial agents based on Long-
short-Term-Memory (LSTM, [106, 107]) neurons, in which place and grid cells
emerged automatically [108]. In another AI model, Gerum and coworkers showed
that spatial navigation in a maze could be achieved by very small neural
networks, which are trained with an evolutionary algorithm and are
evolutionary pruned [109].

## Towards a unified model of tinnitus development

### The hierarchy of the different tinnitus models

In the following section, we describe a path towards a CCN of tinnitus
research. Thus, in a first step we have to go back to Labzebnik [61] and find
a way to communicate efficiently and formally about various tinnitus models.
Extant tinnitus models can be sorted by the different levels of analysis
according to Marr [65], which means that each model can be assigned to one or
more of the three categories (see Fig. 1 b): implementational level (molecular
mechanisms, synapses etc.), algorithmic level (how neural signals are
translated to information processing), and computational level (what are the
basic mathematical imperatives for processing, see also paragraph: What does
it mean to understand a system?).

The three levels of analysis can be easily illustrated with the _Lateral
Inhibition Model_ of tinnitus, which describes tinnitus as a result of
decreased lateral inhibition (e.g. [110, 22]) due to decreased cochlear input;
e.g., caused by a noised-induced cochlear synaptopathy [6]. Thus, the lateral
inhibition model explains tinnitus on all different levels of description. The
implementational level (see Marrs level of analysis Fig. 1 a), which
corresponds to the molecular mechanisms of lateral inhibition, is nearly fully
understood. For example, in the dorsal cochlear nucleus cartwheel cells
release glycine to inhibit fusiform cells, which are excitatory [111, 112,
113]. The computational role of inhibition is to narrow the input range of the
fusiform cells [111]. To provide contrast enhancement via lateral inhibition,
neurons surrounding a certain excitatory neuron, which receives auditory
input, are inhibited. This wiring scheme ‘sharpens’ the tuning curves of
neurons along the auditory pathway. The wiring scheme corresponds to the
algorithmic level of analysis. The computational level of description is the
mathematical description of decreased lateral inhibition. Thus, hearing loss
leads to decreased input from the cochlea, which causes a decreased firing
rate of the inhibitory neurons and thus to disinhibition of subsequent
excitatory neurons. These properties can be easily written down in simple
mathematical formulas. This means that the underlying mechanisms of the
lateral inhibition model of tinnitus are fully understood from specific
neurotransmitter processes to an abstract mathematical formulation. This is
the goal of cognitive computational neuroscience. However, the fact that the
model explains tinnitus manifestation on all scales does not say anything
about the correctness of the model’s predictions. Indeed, a good model should
be understood on all scales (implementational to computational), but it must
also fit experimental observations, which is not the case in the _Lateral
Inhibition Model_. Other models trying to explain tinnitus do not provide the
full explanatory power.

The thalamic bursting theory – which proposes that bursting neurons in the
thalamus cause tinnitus – has a valid explanation for the origin of the spike
bursts (low threshold calcium spikes, for details see [54]). However, it
remains elusive, in terms of how these bursts cause tinnitus. Other top-down
models – such as the predictive coding model [45], based on the Bayesian Brain
theory – provide a valid mathematical description of the proposed mechanisms,
but largely lack an explanation of how the Bayesian statistics can be
implemented in a neural network and thus in the brain [114]. However, there
exist some first approaches toward neural networks for Bayesian inference
which will ultimately prove possible, but are still not fully developed [115].
Other tinnitus models describe macro-phenomena such as the thalamo-cortical
dysrhythmia [52], or describe tinnitus as a result of overlapping neural
circuits [57]. Those models are phenomenological, but do not provide a
mathematical description and thus are difficult to falsify or test in silico.

### A critical role of stochastic resonance

In the following paragraph we provide an in-depth discussion of central noise
and central gain, as possible causes for tinnitus, and consider how to
adjudicate between—or combine—these two theories. To discuss these two models
and their relationship, it is necessary to introduce a proper nomenclature.
Thus, in the following we refer to the mathematical description of Zeng, who
describes central gain as a linear amplification factor $g$, which increases
the input signal $I$. Central noise $N$ is a further additive term (see eq. 1)
[32, 116].

$\displaystyle s=\mathrm{\textbf{{g}}}\cdot I+\mathrm{\textbf{{N}}}$ (1)

Thus, also in most other studies central gain increase refers to an
amplification of the input signal and is always associated with stimulus-
evoked activity (for an extensive review see [117]). In contrast to that,
central noise is related to an increase of spontaneous activity in the absence
of any external stimulation. Additionally, it is necessary to distinguish
between the observable effect, i.e., increased central gain and central noise,
and the underlying principles and mechanisms, e.g., homeostatic plasticity
[26], feedback loops [118] or stochastic resonance (SR) [119, 120, 121]. In
reality, the increased gain and noise cannot be fully decoupled, for example,
an increased excitability of neurons along the auditory pathway caused by
homeostatic plasticity automatically leads to an amplification of neural
noise. Thus, the formula of the neural signal could be altered so that the
amplification factor also has an effect on the central noise (mixing term:
$g\cdot n$ in equation 2).

$\displaystyle s=g\cdot(I+N)$ (2)

Several neural mechanisms are considered here. First, homeostatic plasticity
has been implicated for tinnitus generation (e.g. [122]), however this
mechanism is simply too slow to explain acute tinnitus phenomena after a noise
trauma caused by a sudden loud stimulus [123].

In contrast, neural circuits operating on faster time scales can explain acute
tinnitus: namely, tinnitus is caused by a sub-cortical feedback loop adapting
neural noise input into the auditory system [35]. Here we suggest that
stochastic resonance plays a critical role in not only generating tinnitus but
also restoring hearing [34, 35, 37]. To illustrate this role, we rewrite
equation 2 in a classical signal detection task, in which the neural signal
has to reach a threshold So for the input signal $I$ to be detected:

$\displaystyle s=g\uparrow\cdot(I\downarrow+N\uparrow)$ (3)

In cases of hearing loss, the input $I$ is effectively reduced. Therefore, to
reach the same neural threshold, one could either increase the central noise
$N$, or the central gain $G$, or both. Because increasing gain results in a
squared increase in variance [116], which increases the difficulty of signal
detection, it is not the most economical means of compensating for hearing
loss in cognitive neural computation (e.g., Occam’s razor). Instead, it makes
sense to add internal neural noise to lift weak input signals above the
sensory threshold, a mechanism known as stochastic resonance (SR) [119, 120,
121]. In traditional SR, a nonlinear device such as hard thresholding, and
periodic signals are needed [120]. Recently, it has been shown that auto-
correlation can serve as an estimator for the information content of the
signal, even if it is non-periodic [35].

The critical role of stochastic resonance is supported by broad empirical
evidence:

First, additional intrinsic neural noise [34, 38] as well as external acoustic
noise [124] can improve pure-tone hearing thresholds by approximately 5 dB.
However, this 5 dB threshold decrease (i.e., improvement) does not explain why
this mechanism is evolutionary advantageous, as the cost of a potentially
annoying and morbid tinnitus perception may be high. In a computational model,
it has been showed that frequency-specific intrinsic neural noise has the
potential to significantly improve speech recognition by a far larger amount
(up to a factor of 2) [43]. This improvement in speech comprehension and the
perception of complex sounds – which could be also important for orienting
animals as warning sounds – could be an explanation for the emergence of this
mechanism in our auditory system during evolution. In recent studies, the fact
that different modalities use SR to improve the signal has been proven [125,
126]. It seems that SR and especially cross-modal SR is a universal principle
of sensory processing [36].

Second, central noise is needed to stabilize a biological system. Zeng showed
that _“mathematically, the loudness at threshold is infinite when the internal
noise is zero (c = 0), and vice versa. This is a fundamental argument for why
the brain has or needs internal noise because infinite loudness is clearly
biologically unacceptable”_ [127].

Third, the central noise model based on the SR mechanism provides a
mechanistic explanation for the purpose of the somatosensory projections to
auditory nuclei such as the DCN [128, 129, 130]. Actually, very recently,
Koops and Eggermont argued that _“increased and uncorrelated noise,
potentially the result from a noise source outside of the auditory pathway”_
[33] might play a major role in tinnitus development. Potentially, this
somatosensory input is nothing else than intrinsically generated neural noise,
which is modulated in the DCN to leverage SR in the auditory system. This
theory accords with the finding that tinnitus can be modulated by
somatosensory input like, e.g., jaw movement [131, 132, 133]. Furthermore,
tinnitus development can be prevented [134] or suppressed [135, 136, 137] by
the presentation of external acoustic noise, which works best when the noise
spectrum covers the impaired frequencies and the tinnitus pitch [135, 136,
137]. In a recent study, a novel approach has been developed combining
somatosensory stimulation with auditory stimulation, in order to modulate the
tinnitus loudness [138]. Finally, it has been demonstrated that electro-
tactile stimulation of the finger tips enhances cochlear implant speech
recognition in noise [139], Mandarin tone recognition [140], and melody
recognition [141]. While the authors did not make any mention of stochastic
resonance or internal noise, it is a reasonable assertion that the observed
effect might have acted via cross-modal stochastic resonance [36].

Figure 2: Stochastic resonance model of tinnitus induction: In the healthy
auditory system, the input signal (a) can pass the detection threshold
resulting in a supra-threshold signal as output (b). In case of hearing loss,
the input signal remains below the threshold (c), resulting in zero output.
However, if the optimum amount neural noise (d) is added to the weak signal,
then signal plus noise can pass the threshold again (e), making a previously
undetectable signal, detectable again (f). The optimum amount of noise depends
on the momentary statistics of the input signal, and is continuously adjusted
via a feed-back loop. This processing principle is called adaptive stochastic
resonance.

### Tinnitus and the Bayesian brain

The central gain and the central noise model provide a sophisticated and
mathematically well-developed explanation for the tinnitus-related neural
hyperactivity in the brainstem. However, these theories do not explain why
this hyperactivity is transmitted through the thalamus and induces a conscious
experience. Furthermore, the models do not make predictions on tinnitus
heterogeneity. In particular, tinnitus is probably always caused by hearing
loss, but hearing loss does not necessarily lead to tinnitus [142]. The only
model with a solid mathematical background dealing with this issue is the
sensory precision model from Sedley et al. [45] which is based on the
algorithmic formulation of predictive coding within the computational
“Bayesian brain” hypothesis [143, 47, 114, 144, 145, 59]. Bayesian
formulations of predictive processing are based on the Bayes theorem (eq. 4,
[146, 147]) that describes, mathematically, how to update beliefs in the light
of new incoming information.

$\displaystyle p(x|o)\sim p(o|x)\,p(x)$ (4)

In our context, the brain is continuously updating its posterior belief
distribution $p(x|o)$ ) about the actual sound intensity $x$, given auditory
afferents or observations $o$. This posterior belief is presumably correlated
with the auditory perception and subjective loudness. This update is achieved
by combining the prior expectations $p(x)$, descending from the higher regions
of the processing hierarchy, with precision weighted prediction errors
ascending from below, which mathematically report the likelihood $p(o|x)$ (cf.
Fig. 3). ‘Likelihood’ refers to the probability that the pattern of sensory
input indicates a particular underlying sensory event (such as a specific word
being spoken). In predictive coding, Bayesian belief updating—from prior to
posterior beliefs (cf. Equation 4) – are driven by prediction errors; namely,
sensory information that is newsworthy, in the sense that it has not been
predicted. The precision weighting reflects the precision of the likelihood;
that is, a precise likelihood mapping means that sensory prediction errors are
more informative and therefore produce more belief updating higher in the
auditory hierarchy. Physiologically, this is usually associated with an
increase in the postsynaptic gain or excitability of neuronal populations
reporting prediction errors (usually superficial pyramidal cells in the
cortex): see [91, 148, 149, 150, 151, 152, 144] for a predictive coding
account of neuronal message passing and their role in hallucinatory phenomena.

According to Sedley and coworkers [45], even in a silent environment, lower
levels of the auditory hierarchy report only low amplitude auditory signals,
which are relatively compatible with the default hypothesis of ‘silence’
(i.e., large posterior probabilities for low sound intensities). In normal
hearing, these ‘tinnitus precursors’ are ignored by attenuating their
precision – a process sometimes associated with sensory attenuation. However,
if the brain recognizes sensory de-afferentation due to hearing loss, it may
assign more precision to ascending auditory prediction errors (e.g. through
increased central gain), thereby falsely interpreting tinnitus precursors as
an auditory percept. In short, a failure of sensory attenuation means that
‘silence’ is misinterpreted as ‘sound’ – and tinnitus ensues [45].

However, this Bayesian account makes no specific claims about the neural
mechanisms that mediate changes in precision or the tinnitus precursor. To
furnish a complete mechanistic explanation, a process theory, such as the
central noise model, is needed. For example, the predictive coding model
suggests that aberrant precision (i.e., synaptic gain control) leads to a
misinterpretation of auditory afferents such that ‘silence’ is misinterpreted
as a phantom ‘sound’. This computational account can now be supplemented with
the process theory afforded by central noise gain. In brief, central noise
augments postsynaptic gain—via stochastic resonance—to adaptively respond to
the loss of precise sensory afferents. At the same time, the requisite central
noise augments – or supplants – the ‘tinnitus precursor’. On this view, the
central noise model equips a computational (Bayesian inference) account with
an implementational (stochastic neuronal resonance) mechanism that is
consistent with an algorithmic (predictive coding) formulation of auditory
processing and tinnitus.

Figure 3: Predictive coding model of tinnitus induction: a: Prior: the
probability of a certain percept ($x$: loudness); b: Likelihood: The
probability that an auditory observations o leads to a certain auditory
percept $x$; c: The posterior corresponds to the perceived loudness. A hearing
loss (dark gray: after hearing loss, light gray: healthy condition) leads to
an increased precision and mean of the likelihood, which leads to an increased
mean of the posterior and thus to a tinnitus percept.

## Conclusion and Outlook

In conclusion, the combination of the process theory of central noise increase
and adaptive stochastic resonance – as a bottom-up mechanism – together with
the computational model of predictive coding – as a complementary top-down
mechanism – provides an integrated explanation of tinnitus induction as well
as its heterogeneity (cf. Figure 4). Furthermore, the models provide a
mathematical framework, which can be used to make quantitative predictions
that can be tested through novel experimental paradigms. Since both SR and
predictive coding as universal processing mechanisms are ubiquitous in the
brain, we speculate that the presented integrative framework may extend to the
perception of other sensory modalities and even beyond to certain aspects of
cognition and behavior in general.

A current challenge is a network theory of predictive coding, which explains
how these computations are implemented in the brain [114]. See [148, 150, 144,
153, 154, 155] for attempts to place predictive coding in the larger context
of Bayesian belief updating in the brain.

Our integrated model of auditory (phantom) perception demonstrates that the
fusion of computational neuroscience, AI, and experimental neuroscience leads
to innovative ideas and paves the way for further advances in neuroscience and
AI research. For instance, novel evaluation techniques for neurophysiological
data based on AI and Bayesian statistics were recently established [156, 157,
158, 159], the role of noise in neural networks and other biological
information processing systems was considered in [160, 161, 162, 163], and the
benefit and application of noise and randomness in Machine Learning approaches
was further investigated in [43, 164, 165]. On the one hand, the fusion of
these complementary fields may evince the neural mechanisms of tinnitus (CCN,
[63]) and information processing principles that underwrite functional brain
architectures. On the other hand (neuroscience-inspired AI, [98]) may
accelerate research in machine learning. We hope that the four major steps
towards a CCN of tinnitus, i.e. (i) _finding an exact language_ , (ii)
_developing a mechanistic theory_ , (iii) _testing the methods in fully
specified test systems_ , and (iv) _merging AI with computational and
experimental neuroscience_ , will afford novel opportunities in tinnitus
research.

Figure 4: Unified theory of tinnitus development: The unified model can be
divided into two main parts: the bottom-up model (central noise and SR) and
the top-down model (predictive coding). Implementation Model: Decreased input
from the cochlea due to a hearing loss is compensated by the addition of
intrinsically generated neural noise (central noise) from the somatosensory
system, which is used to restore hearing through the exploitation of the
stochastic resonance phenomenon and accompanying increase in postsynaptic gain
or sensitivity in the auditory hierarchy. The optimal neural noise level is
constantly tuned via a feedback loop, which maximizes information
transmission, quantifiable as auto-correlation of the input signal. This
feedback loop increases the average noise amplitude and decreases the variance
of the noise distribution (increased sensory precision). The noisy signal is
further propagated upwards and, after cochlear damage, additionally amplified
along the auditory pathway by homeostatic plasticity. The amplified noisy
signal is the input to a second feedback loop in higher brain areas such as
the auditory cortex. Algorithmic model: The descending part of this second
loop predicts the auditory input (prior), whereas the ascending part contains
the prediction error (likelihood). The persistent mis-prediction of the
auditory input prevents the thalamus from suppressing the signal, hence it
becomes conscious and is finally perceived as tinnitus.

## Acknowledgments

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation): grant KR5148/2-1 (project number 436456810) to PK, and
grant SCHI 1482/3-1 (project number 451810794) to AS. Additionally, PK was
supported by the Emerging Talents Initiative (ETI) of the University Erlangen-
Nuremberg (grant 2019/2-Phil-01), and KF is supported by funding for the
Wellcome Centre for Human Neuroimaging (Ref: 205103/Z/16/Z) and a Canada-UK
Artificial Intelligence Initiative (Ref: ES/T01279X/1). Furthermore, the
research leading to these results has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (ERC Grant No. 810316 to AM). Finally, we wish to thank
Arnaud Norena for useful discussion.

## Author contributions

All authors discussed the cited studies and their interpretation, developed
the presented unified model, and wrote the manuscript.

## Competing interests

The authors declare no competing financial interests.

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