# A theory of neural emulators

Catalin C. Mitelut
Forum Basiliense, University of Basel
Foresight Institute
<EMAIL_ADDRESS>

###### Abstract

A central goal in neuroscience is to provide explanations for how animal
nervous systems can generate actions and cognitive states such as
consciousness while artificial intelligence (AI) and machine learning (ML)
seek to provide models that are increasingly better at prediction. Despite
many decades of research we have made limited progress on providing
neuroscience explanations yet there is an increased use of AI and ML methods
in neuroscience for prediction of behavior and even cognitive states. Here we
propose emulator theory (ET) and neural emulators as circuit- and scale-
independent predictive models of biological brain activity and emulator theory
(ET) as an alternative research paradigm in neuroscience. ET proposes that
predictive models trained solely on neural dynamics and behaviors can generate
functionally indistinguishable systems from their sources. That is, compared
to the biological organisms which they model, emulators may achieve
indistinguishable behavior and cognitive states - including consciousness -
without any mechanistic explanations. We posit ET via several conjectures,
discuss the nature of endogenous and exogenous activation of neural circuits,
and discuss neural causality of phenomenal states. ET provides the conceptual
and empirical framework for prediction-based models of neural dynamics and
behavior without explicit representations of idiosyncratically evolved nervous
systems.

##  1 Introduction

A central goal of neuroscience research is to provide explanatory models
marr1982vision ; churchland1992computational underlying brain function from
molecules and genetics to memory encoding, decision making and cognition
shen2022emergence . After more than a century of extensive research in anatomy
and physiology we understand anatomical connectivity better - but have made
limited progress in understanding function, especially at the whole-organism
scale, including how multi-scale dynamical interactions within the central
nervous system (CNS) give rise to our behaviors and phenomenal experiences
roland2023far . Our limited progress may be due to avoiding difficult
paradigms involving behavior krakauer2017neuroscience ;
humphries2017neuroscience , being disconnected from psychology
beste2021disconnected , or lacking large datasets and powerful models
markram2013seven . Recent controversies including possibly pursuing the wrong
approach in Alzheimer’s research for decades piller2022blots raise the
question whether seeking to provide completely mechanistic models of brain
function will ever succeed at the whole organisms level, help solve complex
diseases or explain capacities such as consciousness.

In parallel, over the past several decades deep machine learning (deep ML) and
artificial intelligence (AI) methods relying on black-box neural networks
(NNs) have created increasingly powerful predictive models that can achieve
superhuman game performance silver2016mastering , and improved language
translation popel2020transforming and language generation radford2019language
, among many other feats lecun2015deep ; alzubaidi2021review . While the value
of explanatory vs. predictive models has been debated in statistics for
decades Breiman2001 , it is also being debated in newer fields, e.g.
neuroscience bowers2023deep ; lin2023scientific and psychology
yarkoni2017choosing . Some neuroscience researchers have begun implementing
NNs for predictive modeling of neural systems richards2019deep ;
kietzmann2019deep showing they are as good or better than explanatory or
mechanistic models cichy2019deep including for decoding of spatial location
tampuu2019efficient , latent dynamics zhou2020learning or even inferring
single trial population dynamics pandarinath2018inferring .

While it is still uncertain how much predictive models will contribute to our
understanding of the brain - large-scale neural datasets are increasingly
common and AI and ML methods are likely required to understand them. In fact,
the extraordinary predictive power of Large-Language-Models (LLMs) Openai2023
in the last few years provides some evidence that prediction-only models offer
some utility for scientific and knowledge dissemination. Additionally, given
their success some have even speculated whether future LLMs could experience
conscious states butlin2023consciousness . These and other debates have
contributed to an already existing interdisciplinary research field on
"machine" or "artificial" consciousness GAMEZ2008 . Deciding on the usefulness
of modern AI in neuroscience as well as their conceptual properties is
challenging as we need to resolve conceptual, computational and experimental
problems involving questions from AI, philosophy and neuroscience.

Scope of work: emulators as a novel type and use-case for predictive models.
Here we provide a novel framework for how predictive models can contribute to
neuroscience and whether such models could generate internal states such as
consciousness. We propose the concept of neural emulators (or "emulators" for
short): predictive (joint) models of animal behavior and whole-organism neural
dynamics generated from different spatio-temporal scaled data (Fig 1). In
their simplest formulation, emulators predict behavior and neural dynamics
based on historical neural and behavioral states and can be used to study the
informational content and structure of neural activity in specific areas,
across areas and with respect to behavior. In their most complete form,
emulators learn to model the (nearly) complete causal structure of neural-
behavior interactions and can generate outputs that are indistinguishable from
the behaviors and phenomenal states of the organisms they model.

Figure 1: Circuit- and scale-agnostic neural emulators. (a). Recording from a
rodent brain (light-blue) based on parcelation (cubes) of increasing
granularity (red-hue diamonds). (b). Neural time series from parcellation in
(a) (light blue) and behavior time series (green). (c). Emulators learn joint
probability of time-series in (b). (d). Behavior output of emulators is
increasingly similar to biological behavior as parcellation granularity
increases.

Contribution of work: emulators and emulator theory. We define emulators and
propose emulator theory (ET) as a theoretical framework for measuring and
replicating the capacities of biological organisms solely via predictive
models that do not require explicit mechanisms of how neural (sub)systems
interact. ET argues that neural dynamics and causality can be simulated or
artificially generated and proposes that emulators can capture all capacities
of biological brains including possibly conscious experiences. The scope of
our work and contributions are as follows:

  1. 1.

provide a definition of neural emulators, describe the axioms and conjectures
of emulator theory (ET) and provide a description for constructing neural
emulators from neurophysiology datasets (Section 2 and Appendix C).

  2. 2.

propose a theory of neural causality that explain how models trained solely on
prediction - such as emulators - can generate indistinguishable behavior and
first person phenomenal states of biological organisms (Section 3) and
Appendix B, and D).

Relation to previous work. Our work is related to several research paradigms
including: machine consciousness, phenomenology, philosophy and physics of
causality, and deep ML methods for modeling time-series data. We discuss our
work in relation to previous research at length in Appendix E. Briefly, in
comparison to previous work, we propose a novel interpretation for predictive
models of neural activity that is independent of architecture or mechanistic
explanations of brain function.

##  2 A framework for neural emulators

Here we define the central components of emulator theory (ET) - a proposal for
how and why artificial (i.e. computational) systems trained to predict the
behavioral and cognitive states of animals can become increasingly accurate
copies, or "emulators", of such organisms. In particular, ET proposes that
models trained on sufficiently large datasets solely to predict behavior and
phenomenal states have the capacity to generate such states - even without
access to explanatory mechanisms.111We henceforth omit the terms ”sufficiently
large” datasets and discuss further in Appendix A. ET proposes this can occur
because both behaviors and phenomenal states are causal-path independent: i.e.
the neural states supporting behavior and consciousness do not depend on a
specific neuronal pathway - only on specific neuronal dynamics.

Below we provide a framing of ET relative to computational neuroscience
approaches, describe the causal-path independence conjecture and provide a
practical approach to constructing emulators.

###  2.1 Common assumptions in explanatory models of behavior and neural
dynamics

A central goal for computational and behavior neuroscience research is to
identify explanatory mechanisms for how the nervous systems of animals can
generate behaviors and cognition. We generalize these approaches as seeking
functional descriptions of (i) behaviors and (ii) neural dynamics.222We note
that reportability of conscious states and presence of conscious states is a
topic in philosophy of mind and psychology broadly under several topics
including ”phenomenal” versus ”access consciousness” naccache2018 . Here we
focused on ”reportable” only for the purpose of having a simplified training
label for our models though this is not central to our argument and other
labels would suffice. :

$F_{t}^{b}(x_{i,t})=\mathrm{Observed\ behavior}$ (1)
$F_{t}^{c}(x_{i,t})=\mathrm{(Reportable)\ state\ of\ consciousness}$ (2)

with:

$x_{i,t}=Q(x_{i,t_{-1}},s_{t_{-1}})$ (3)

where $F_{t}^{b}$ and $F_{t}^{c}$ describe how behavior and conscious states,
respectively, are generated from $x_{i,t}$ which are measurements of neural
component $i$ (most often the spiking of a single neuron) at time $t$, and $Q$
describes the evolution of the neural components from endogenous (i.e.
$x_{i,t_{-1}}$) and exogenous inputs (or stimuli) $s_{t_{-1}}$. Thus, for
example, we want to show how neural activity in motor cortex
churchland2012neural and supporting areas SVOBODA201833 generate observable
body movements, even at the single trial level pandarinath2018inferring , by
describing how neural states (e.g. spiking of populations of neurons) generate
observables such as location of the arm or hand of an animal or the location
of a rodent in an environment.

This framework is common in computational and theoretical neuroscience (though
it is not the only one) and makes several assumptions:

  1. 1.

$Q$, $F_{t}^{b}$ and $F_{t}^{c}$ have a closed form expression that we can
eventually discover.

  2. 2.

$Q$, $F_{t}^{b}$ and $F_{t}^{c}$ will describe necessary causal mechanisms
without which neither behaviors nor cognitive states can occur.

  3. 3.

Identifying $Q$, $F_{t}^{b}$ and $F_{t}^{c}$ requires single neuron or lower
spatial scale neural data.

###  2.2 Emulators are mechanism- and spatial scale-independent predictive
models of behavior and neural dynamics

ET proposes to eliminate all three assumptions from building useful models of
the brain. In particular, ET propose that both behaviors and cognitive states
can be accurately predicted by models that do not represent or instantiate
$Q$, $F_{t}^{b}$ or $F_{t}^{c}$ and without an explicit spatio-temporal scale
of neural activity. Thus ET proposes that at a specific neural data
granularity $g$ we can build emulator $E$ to predict behaviors and conscious
states:

$E_{t}^{b}(w_{j,t,g})=\mathrm{Observed\ behavior}$ (4)
$E_{t}^{c}(w_{j,t,g})=\mathrm{(Reportable)\ state\ of\ consciousness}$ (5)
$w_{j,t,g}=R(w_{j,t_{-1},g},s_{t_{-1}})$ (6)

where $w_{j,t,g}$ is the state of parcel $j$ of a system sampled at
granularity $g$ and at time $t$ that evolves dynamically and $E_{t}^{b}$,
$E_{t}^{c}$ and $R$ are transformation learned from "big" data. Thus, for
example, emulators can be described simply by nested (black-box) neural-
network (NN) models:

$\mathrm{NN}_{2}(\mathrm{NN}_{1}(w_{j,t,g}))=\mathrm{Observed\ behavior}$ (7)
$\mathrm{NN_{3}}(\mathrm{NN_{1}}(w_{j,t,g}))=\mathrm{(Reportable)\ state\ of\
consciousness}$ (8)

where NN1, NN2 and NN3 stand for $R$, ${E_{t}^{b}}$, and ${E_{t}^{c}}$,
respectively.

In this framework, emulators are predictive models that are imperfect - i.e.
have imperfect prediction - but can improve their accuracy with increased
granularity of neural data and size of training datasets. This is similar to
many, if not most, ML approaches in data modeling. However, there are at least
two major differences. First, in the large dataset and high granularity limit
ET claims that emulators can generate phenomenal states even without an
explanation of how phenomenal states are caused. Second, and more simply, ET
claims that despite the extreme complexity of the brain, datasets generated in
practical experiments (e.g. finite-time laboratory neuroscience experiments)
are sufficient for building accurate emulators. In the remainder of this
section we address these two issues.

###  2.3 Emulators (must) model causality of phenomenal states

Emulators are more than (black-box) models that seek to predict behaviors or
conscious states - they are models that generate such outputs while modeling
the neural dynamics causing the outputs. In this sense, unlike general NNs fit
to data - emulators implicitly capture the idiosyncratically evolved neural
causal pathways by jointly modeling neural dynamics and observables.

But shouldn’t our models (predictive or mechanistic ones) first explain in
mechanistic terms the causal pathways for generating behaviors or conscious
experience before being able to generate them? In our view, this requirement
may be too conservative as it suggests a priori that (human) understanding of
neural causality must precede generation of neural causality. In our view, the
question of how we can capture the causal interactions of a neural system to
recreate its behavior and internal states - is an empirical question, and one
that ET in part seeks to address.

###  2.4 Exogenous generation of behavior and phenomenal states is already
possible

In fact, our mechanistic understanding of neural causality already lags behind
the ability to artificially generate behaviors or even conscious states in
biological organisms. In particular, we have known for almost a century how to
artificially generate conscious states via direct, i.e. exogenous, electrical
stimulation (DES). For example, in awake human neuro-surgery, activations of
neural tissue by direct (i.e. exogenous) electrical stimulation can lead to
individuals experiencing specific conscious content: emotions and novel visual
imagery lai2020acute , speech generation collee2023localization , or even
disrupting short term memory of the task itself ng2021disrupting . An even
more remarkable finding in the neuroscience of agency is that even self-
control states such as experiencing a desire or "will to act" can be elicited
by exogenous electrical stimulation fried1991functional . In mice, using light
optogenetic activation deisseroth2015optogenetics we can identify and then
artificially activate visual system neurons to generate perceptions leading to
behavior marshel2019cortical ; CARRILLOREID2019447 . We can even "tag" memory
engrams representing positive moods and reactivate them at a later time to
elicit mood-change like behaviors in mice ramirez2015activating .

Even though it is very likely that both DES and optogenetic activations engage
specific - rather than random - neural circuits and states, these are
nonetheless remarkable experimental findings. That is, there is no obvious
requirement that evolution required that organism-level behaviors or
phenomenal states can be generated simply by exogenous input \- rather, the
opposite seemed more possible given the extraordinary complexity of the brain.
Namely, that highly specific neurons and circuits must be engaged in a
particular fashion to generate behaviors and phenomenal states. In our view,
the existence of coarse-grained exogenous generation of phenomenal states (and
behavior) is a largely under-explored research approach to understanding
behavior and consciousness causality. More specific to ET, these studies
suggest that - at the very least - we may not require precise mechanistic
models of neural dynamics all the way to the synapse (or lower level) to
generate models that exhibit behavior and phenomenal states.

###  2.5 Causal path independence conjecture

More importantly, these findings suggest that neural states that support the
generation of actions or conscious states may be reacheable by multiple paths.
We formulate this into a central conjecture of ET:

  1. C1:

Path independent neural causality conjecture (PINC). Behaviors and conscious
states do not dependent on endogenous (i.e. within system) causality and they
can be generated (or reached) by completely exogenous pathways.

Here, "exogenous" means a perturbation that is external to the brain such as a
patch clamp or optogenetic excitation. In practical terms, $C1$ proposes that
sequences of neural activation $x_{i,t_{n}}$ ($n$ time steps) that are
sufficient for conscious experience or behaviors - can be generated (i.e.
caused) by exogenous sequential activation of such neural states. Thus, $C1$
implies that any mechanism required for consciousness, for example the
"ignition and broadcast within a neuronal global workspace" (GWT), "local
recurrent or re-entrant cortical processing" (recurrence), or "multiple …
representations … available to a central system" (multiple
drafts)seth2022theories \- can be activated by exogenous pathways as there is
no dependence of conscious states emerging from specific causal paths, but
only on dynamical activation.

We view PINC as central to understanding how causality can be emulated in a
artificial systems (such as computational models or emulators) which can in
turn generate behaviors and conscious states in biological and even artificial
organisms. We discuss PINC in more detail in Section 3.

Figure 2: Granularity-based neural emulators. Relationship between the
capacity (or accuracy) of a behavior (blue curve) and neural (red curve)
emulator vs the granularity of the neural data used for training with
hypothesized requirements for perfect behavior models (dashed blue line) and
conscious states (dashed red line). Proposed experiment of recording sparsely
sampled brain-wide LFP (magenta arrow) and putative emulator capacity from
such datasets (magenta dots).

###  2.6 Scalable emulators: a research paradigm

We now return to the question of whether we can collect sufficient datasets
for training mechanism-agnostic emulators. Central to this question is how to
build emulators from empirical data. We find it instrutive to start by
defining an ideal emulator as an abstract tool to help frame the practical
emulators. An ideal emulator is a model that is generated from very low (or
arbitrarily small) spatial-scale granularity parcels and very large (or
arbitrarily large) datasets. We point out that ideal emulators seek to model
the behavior of biological system but only to the level required to predict
the behaviors and phenomenal states and may not need to model synapse, or
protein-level interactions in nervous systems. In this sense, ideal emulators
model (only) the sufficient conditions for the generation of such observables.
We discuss ideal emulators in more detail in Appendix C.

In contrast to ideal emulators we propose building scalable emulators (or
simply "emulators"). Scalable emulators can be created by training predictive
models from (practical size) neural dynamics datasets of varying spatial and
temporal resolution or "granularity" (Fig 2). Emulators can thus be generated
using neural activity recorded at different granularity scales such as: single
neuron spikes, local-field-potential (LFP), or functional magnetic resonance
imaging (fMRI). Emulators will thus be trained on (simultaneously recorded)
neural dynamics and behaviors of biological organisms - to predict behavior
and neural dynamics. Does this mean that any type of data, e.g. functional
magnetic resonance imaging (fMRI) is sufficient to generate perfect or nearly
perfect emulators?

Not necessarily. We define the capacity of an emulator simply as the accuracy
of predicted behaviors and neural dynamics relative to the source (e.g. on
test or hold out data). ET proposes that - much like any other ML model -
emulator capacity or accuracy will increase with dataset size (e.g. number of
time points and number of neural areas) - and also with increased granularity
of the recordings (e.g. LFP models should do better than fMRI ones). While we
do not expect that current types of fMRI data alone is sufficient to achieve
perfect emulators, ET implies that given sufficiently large fMRI datasets
there is no theoretical prohibitions on this.

We close by providing a comparison between the dataset sizes used to train
LLMs and what is feasibly possible to generate using relatively modest
empirical paradigms in rodent neuroethology (Table 1). Considering each
individual neural parcel as a single token, and 1000Hz sampling rate, we can
in principle generate datasets of similar size used to train GPT-4 (estimated)
with just over a dozen rodents recording continuously for 24 months.

Type of model | Recording time | No. of neural parcels | No of params | No. of training tokens
---|---|---|---|---
Llama 2 | n/a | n/a | 7-70 billion | 5 trillion
GPT 4 | n/a | n/a | 1.76 trillion | O(100) trillion (est)
1 Rodent | 30 days | 32 | n/a | O(100) billion
15 Rodents | 2 years | 128 | n/a | O(100) trillion
Table 1: Comparison between training datasets for LLMs and emulators.

###  2.7 ET: Summary and Conclusion

We proposed emulators as scale-dependent predictive models of neural dynamics
and behaviors of biological organisms. We offered a conceptual theoretical
framework, i.e. ET, which suggests that sufficiently accurate models, i.e.
emulators, may generate artificial systems with the same capacities of the
biological organisms they model. We argued this occurs because accurate
emulators must instantiate models of neural dynamics that are similar to the
biological nervous systems they model - essentially emulating neural causality
of such biological nervous systems. We proposed a practical research framework
- scalable emulators that focuses on modeling of simultaneously recorded
neural and behavior data to generate increasingly accurate predictive models
as a function of the granularity or spatio-temporal scale of the recordings.

One advantage of ET framework for modeling nervous systems is that we can
balance the reductionist desire to decompose all neural states into the
smallest components with principled pragmatic-driven goals. Thus, we can
remain agnostic on both mechanisms as well as spatio-temporal scale of
recordings required to adequately model biological neural networks. In
contrast to mechanistic models sought in neuroscience, ET states we don’t need
to understand the role of all neural components across all scales if we can
identify scales that enable us to generate sufficiently accurate models.
Because there are redundancies in biological neural networks (e.g. not all
neurons or areas are required for specific capacities), we may directly pursue
model accuracy as a primary goal rather than mechanistic explanation of all
components.

In the next section we expand our discussion of the central ET conjecture -
$C1$ \- to provide a conceptual background for why neural states are causal-
path independent and why this further supports the exogenous emulation of
causality proposed by ET. We discuss additional topics on the philosophy of
causality in the context of ET in Appendix B.

##  3 A theory of path-independent neural causality

The central conjecture of ET, i.e. the path-independent-neural-causality
(PINC) proposes that we can generate behaviors and conscious states using
exogenously pathways as opposed to endogenous (or "natural") ones. We reviewed
DES and optogenetic studies in humans and mice, respectively, and argued this
provides some evidence for this. However, in our view, to fully establish
emulators as exogenous models of causality we must do more than merely argue
that some neural states can be generated exogenously. In particular, we must
show that emulators can learn to activate biological - or artificial -
circuits using models that capture and replicate causality.

In its simplest form PINC highlights limits in empirical measurement and
"measurability" of biological dynamical systems that generate phenomenal
states. For example, if we could somehow activate any neural state ("down to
the synapses") by external means - it may not be possible to measure a
difference between such neural states arising naturally and exogenously. This
is because the fundamental quantities we measure are behavioral or internal
state "readouts" - and if those are nearly identical then we cannot in
principle differentiate between their causes.

A second, related, challenge that PINC raises is about "identicality": i.e. we
may have to rethink what makes for a perfect or "ideal" model of a neural
system or biological organisms. The contribution of chaos and noise to neural
dynamics has been studied for decades in neuroscience even at the single
neuron level Mainen1995 and in drift diffusion models of decision making where
the precise timing of a decision is generally determined by noise Ratcliff2001
; Ratcliff2008 . These studies (many non-mechanistic) propose broad boundaries
on what constitutes a sufficiently accurate model of an observed neural system
- or its behavioral output. Thus, PINC raises the question of what constitutes
a perfect model - even one built from mechanistic knowledge - of a biological
organism?

Below we build our intuition for PINC using various levels of abstract thought
experiments attached to hypotheses. We start with the input source
indistinguishability (ISI) hypothesis which states that from a first person
perspective it is impossible to distinguish whether the behavior output or
conscious state of an organism was generated by endogenous or exogenous
pathways. Second, the path-independent causality (PIC) hypothesis restates
$C1$ (see Section 2) in the framework of causal models and highlights the lack
of causal-path requirements for neural system dynamics. Lastly, the model
system divergence (MSD) hypothesis proposes that because of noise and chaotic
dynamics - there can be no a priori thresholds for distinguishing between the
output of a dynamical system driven by a (sufficiently accurate) emulator and
a system driven by ground-truth mechanistic model.

###  3.1 ISI: all neuronal states can be reached exogenously

We begin with a model of a 2-neuron circuit receiving input from sensory and
internal state systems (i.e. "native" input) and generating downstream output
(Fig 3a). From an external perspective (i.e. the general perspective of an
experimental neuroscientist) this system can be completely described by the
spike trains of all the nodes (Fig 3b). Having access to such spike trains -
we can imagine removing (or ablating) the native connections to this circuit
and directly or "artificially" simulating inputs (e.g. using patch clamps)
(Fig 3c). Such an artificially driven system would have identical333We assume
determinism here, without loss of generality. spike rasters with the original
system (Fig 3d). More importantly, as our artificially driven system is
functionally identical to our native one - from a first person perspective
there is no experiment that we can do to determine whether the neural states
are generated by native or artificial inputs.

Figure 3: Input source indistinguishability (ISI). (a) A two neuron local
network receiving "native" sensory and internal state input and generating
downstream output. (b) Spike rasters for network in (a). (c) Same as (a) but
inputs to network are simulated by an external system. (d) Same as (a) but for
simulated system as in (c) results in identical spike rasters. (e) Left:
single neuron receiving axonal inputs (red) from various sources and
outputting a spike pattern (green); Right: proposed spike rasters for (e). (f)
Left: same as (e) but axonal inputs are simulated by external system; Right:
identical raster to (e) achieved by simulated system in (f). (g) Left: a self-
driving recurrent neural network; Right: proposed spike rasters for (g). (h)
Left: same as (g) but with recurrent inputs removed and simulated inputs;
Right: identical spike raster as in (g) achieved by simulated system in (h).

This thought experiment can be modified ad infinitum. For example, we can
consider smaller size scales by modeling synapse activations (Fig 3e,f) and we
can consider complex recurrent neural networks by increasing the complexity of
the connectivity (Fig 3g,h). In all cases, if we can adequately model the
neural dynamics and artificially generate them - from a first person behavior
it is not possible to determine how causality was achieved.

Does this argument extend to arbitrary scales, e.g. the whole brain - and what
are the implications for cognition or consciousness? With respect to
viability, single neuron activations is increasingly achievable tong2023single
. At the phenomenal level, ISI hypothesizes that all neural states including
those underpinning conscious states can can be achieved by artificial
activation of neurons even in complex recurrent networks. More specifically,
ISI proposes that irrespective of the necessary neural states for
consciousness - such states can be artificially generated with a sufficiently
powerful model of neural activity and precise activation (see discussion above
on DES).

###  3.2 PIC: all neural states are causal path agnostic

Conscious states are thought to unfold on the scale of hundreds of
milliseconds to seconds northoff2020neural ; kent2019duration and most
neuroscience theories of consciousness require complex interactions across
many neural systems where temporal dynamics matter seth2022theories . Given
that we may not be able to distinguish the source of neural inputs - does this
mean that dynamics (e.g. order of activation or recurrence) do not matter for
complex states such as cognition or consciousness?

The path-independent causality conjecture (PIC) builds on ISI and proposes
that while neural dynamics may matter for the generation of conscious states,
the causal paths do not. That is, from a first person perspective - it is
impossible to distinguish the causal pathway by which the necessary and
sufficient neuronal states for consciousness are achieved. Thus, at best, only
temporal dynamics matter and that causal pathways can be simulated with
sufficient manipulation. How is this possible?

To show this we study a causal model of conscious state generation (Fig 4). In
particular, we study the causal generation of sufficient neural states S1 and
S2 for the generation of conscious state C. In this framework the direct
causes (i.e. parents) of C are S1 and S2 which are in turn caused by their own
parents (P1 and P2; Fig 4a). Thus, given S1 and S2, C is independent of the
parents:

$C\perp\\!\\!\\!\perp(P_{1},P_{2})\mid(S_{1},S_{2})$ (9)

In this causal framework, because C is caused solely by S1 and S2, the causes
of by S1 and S2 can be arbitrarily set or determined (Fig 4b).444For clarity,
objections that ”conscious” states require many other interacting parts,
including states such as P1 and P2 to be activated, we simply add more
exogenous causal paths to represent their activations as well. Thus, if we
replace endogenous input (i.e. parents P1 and P2) with exogenous input -
conscious state $C$ is still achieved. 555We note this description generalizes
to all possible neural states from simple two neuron systems to large
recursively activated networks. For example, in HOT S1 can represent lower
order representations and S2 higher order, or in GWT S1 can represent
globalization of information and S2 attention being brought to the states.

Figure 4: Path-independent causality conjecture (PIC). (a) Causal graph of two
necessary and sufficient biophysical neural states, S1 and S2, required for
phenomenal conscious state C. In the native state, neural states S1 and S2 are
caused by endogenous prior states P1 and P2 (e.g. sensory and internal state
processing). (b) Same as (a) but neural states S1 and S2 are generated via
exogenous (e.g. artificially generated) inputs resulting in the same
phenomenal cognitive state C irrespective of the causal path of activation of
necessary and sufficient biophysical neural states.

###  3.3 MSD: emulator outputs may be indistinguishable from mechanistic
models and biological organism outputs

Our last hypothesis - MSD - states that there are no a priori methods for
distinguishing between sufficiently accurate predictive models (i.e.
emulators) and models built from a complete mechanistic theory of neurvous
system function. Fundamentally, this hypothesis suggests that we must define
empirical tests and thresholds for what constitutes a sufficiently accurate
model of a biological neural system. We discuss this in more detail in
Appendix D.

##  4 Limitations

Our proposal has some limitations. In particular, ET does not describe the
content of conscious states or the necessary and sufficient conditions for
generating them. ET primarily states that such states can be achieved via
artificial activations - or ultimately within completely artificial systems
that model biological neural networks in sufficient detail. Additionally, ET
proposes that experimentally viable emulators are possible but it is an
empirical question that needs to be investigated. Similarly, we did not
discuss the size of the datasets required but also the neural-area specificity
of our datasets. We envision that neural data from some areas such as frontal
and sensory systems (known to be involved in conscious state and behavior
generation) may provide more information for our models. In this sense,
building emulators in the near-term (i.e. before technologies to record from
the whole brain are available) should benefit from neuroanatomical targeting.

Lastly, we did not discuss neural architectures required for generation of
conscious states. ET is agnostic to the role of architectures (or even
anatomical modularity) in generating behavior and conscious states. In
particular, ET does not make any commitments to the requirement of specific
neural circuits - but only indirectly supports whatever artificial NN
architectures are required to model of causality. However, given the universal
approximation theorem, given sufficiently expressive NNs and large enough
datasets - ET suggests architectures do not matter. In this context, ET may be
interpreted to suggest that biological organisms developed specific neural
architectures due to biophysical and energy constraints not potentially
required for artificial or synthetic NNs.

##  5 Concluding remarks

Here we proposed emulators as predictive models of organism behavior and
cognitive states trained solely on historical neural dynamics and behavioral
states. We offered ET as a framework for understanding how emulators can be
built, what they can achieve and suggested benefits and limitations. ET also
points to the need for developing increasingly nuanced empirical tests to
determine whether models of complex systems exhibit the capacities of the
originals including internal phenomenal experiences. In our view, once models
of biological neural networks achieve high precision - it is not only possible
that they experience conscious states - but likely that they do so.

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## Appendix / supplemental material

##  Appendix A Terminology

Below we provide descriptions and working definitions of some of the terms in
our work.

Sufficient accurate emulator or model. Sufficiently accurate is an empirically
derivable term. It refers to whether a model behaves (or generates output)
that is so close to our biological system that we cannot distinguish the
differences. As we point out in our main text, a central implication of ET is
that we will need increasingly nuanced tests for behavior and conscious states
and, more critically, we may need to set these thresholds empirically - i.e.
without a clear theory.

Perfect models. Similar to "sufficiently accurate", we reserve this term to
mean a synthetic or computational model that is indistinguishable from the
organism or neural system it is seeking to model.

Sufficiently large or big datasets. This term refers to the dataset size
required to generate a sufficiently accurate emulator. As explained in the
main text, ET proposes that even fMRI data might be good enough to generate
accurate emulators, but it is likely that significantly more data (and perhaps
lower noise fMRI datasets) will be required. This would be in contrast to
using data from single neuronal activations for emulators which in principle
contain more information and less noise and could be smaller in size.

Phenomenal or conscious states. We use this term to refer to the internal,
first-person, observation that is generally not accessible from the third
person perspective. We note that did not distinguish between phenomenal and
access consciousness and that we referred to phenomenal states as a type of
"reportable" state. While some have argued that such states may be in
principle experienced - but not reportable, it is central to our work which
only requires some way to measure conscious states - usually from a third
person perspective.

Coarse grained or exogenous activation. These terms refer to the lack of
precision in direct-electrical-stimulation or optogenetic activation. Such
exogenous neural activations generally target many neurons and neural
circuits. Even in cases where a single neuron is activated, such inputs are
still artificial - relative to an endogenous activation of the neuron which
generally involves likely dozens but possibly hundreds of inputs form
anterograde neurons and increasingly more from those cells’ parental inputs.

Neural state. This term refers usually to the simultaneous activity of the
entire neural system we study. In systems neuroscience, a neural state is also
called a population vector or state and can represent the activity of each
neuron recorded (e.g. being active or not) within a 1millisecond or larger
time windows (depending on analysis carried out).

Behaviors or actions. We used this term to refer to the behavior of an
animals, such as a mouse moving its body, or its limbs in space.

Emulator. Predictive (joint) models of animal behavior and whole-organism
neural dynamics generated from different spatio-temporal scaled data. We
generally intend the term emulator to refer to the model and its physical
instantiation (i.e. operation) on a physical computer system.

Emulator theory. A theoretical framework for measuring and replicating the
capacities of biological organisms solely via predictive models that do not
require explicit mechanisms of how neural (sub)systems interact.

##  Appendix B The physics of neural causality

While ET may not be required to explain how to generate consciousness - it may
require to describe how neural causality works in biophysical organisms (e.g.
mammals) and whether such causality can be present in artificial ones.
Neuroscience does not directly adress the philosophy or physics of neural
state causality - and only provides high-level candidate theories of causality
(nearly all correlation-based) (e.g. seth2022theories ). Arguably, there is an
implicit reductionist assumption to all these theories - that consciousness is
caused by specific pathways and it emerges from the activity of lower-level or
more fundamental systems.

Here we seek to address the question of what causality may look like in
"carbon-based" organisms and whether our best physics or philosophical
theories of causality preclude artificial organisms from similar causal
phenomena. We begin by briefly commenting on the science and physics of
causality - a field without a specific consensus especially with respect to
complex physical systems. We then discuss causality in emulations and the
sufficient conditions for recreation of all source capacities in an emulated
system.

###  B.1 How are effects "caused" in complex dynamical (nervous) systems?

The philosophy and physics of causality is still a developing field with the
most common proposals for what "causality" means focusing on the transference
or transmission of physical properties from one part to another or
conservation of quantities across interactions Fair1979-FAICAT ;
Salmon1984-SALSEA ; Dowe2000-DOWPC-2 . In these frameworks, we can
conceptualize of a neuron as causing another neuron to spike by passing on
some physical properties (e.g. sufficient volume of glutamate molecules, or
sufficiently large membrane current). However, many higher-order capacities
(e.g. perception or cognition) simply cannot be reduced to cause-effect
explanations between single neurons due to the infeasibility of tracking all
the physics - but also the fact that cumulative effects of many neurons lead
to an emergent property (i.e. cognition) that is dynamical and almost always
independent of any individual single neuron. Some conceptual proposals for
"causality by dynamics" have been put forward fazekas2021dynamical . In these
dynamical systems explanations, "[c]ause and effect states are … regions of
the state space, and the causal claim asserts a connection between these two
regions". More specifically, "what makes a causal claim true is how the
physical states it picks out are related by time evolution…". In simpler
terms, in a complex dynamical system an effect is caused if the time evolution
of the causal state is likely or "sufficiently" likely to lead to the effect
state. Importantly, this definition is permissive enough to bridge the
biophysical-cognitive divide.

Computational neuroscientists have already identified how the dynamics of
populations of neurons are at least supportive of, if not central to, brain
function pouget2003inference ; averbeck2006neural ; vyas2020computation . In
this "computation by population" paradigm “a neural population constitutes a
dynamical system that, through its temporal evolution, performs a computation
to, for example, generate and control movement". There have been several
successful models using population level dynamical trajectories (e.g.
mazor2005transient ; churchland2012neural ; gardner2022toroidal ).666For
example mazor2005transient , when presented with different odors, the
individual principal neurons (PNs) of the locust’s olfactory system exhibit a
brief transient ON signal that is quite similar across all neurons and odors.
However, when pooling the neurons together into a “population vector”,
principal-component-analysis (PCA) visualizations show that odor processing
has a substantially different dynamical trajectory at the population level for
the different odors including fixed points and within-odor trial variance well
below the inter-odor variance.. And while population dynamics are usually
visualized using dimensionality reduction tools such as PCA, there are
suggestions that such tools are more than interpretation aids and “show us how
neural circuits actually operate and compute” humphries2020strong . This
implies that in some sense computation is achieved by populations - not just
individual neurons.

Given this we draw two conclusions. First, we lack a complete theory of
physical causality especially when it comes to complex dynamical systems.
Second, and more central to our question, in a complex dynamical system such
as the brain, the (i) physical states and (ii) their dynamical evolution are
the only things we can measure and they must account for the emergence of
macro-states such as consciousness from micro-states.

###  B.2 Can software systems (emulators or simulators) cause or experience
cognition?

The above discussion suggests that if we can recreate both neural states and
their dynamical changes in a model or a "simulation" - we are essentially
recreating all the components of the original systems and there is nothing
else to explain about such systems. While such simulations could solve the
same tasks of the source systems - would such simulations "experience"
cognitive states?

In our view, there is nothing in physics prohibiting complete emulation or
simulation including internal states of consciousness of self-organizing-
systems. We can formulate this claim around David Marr’s well known
computational theory of vision marr1982vision containing three levels:
computational, algorithmic and implementational (Fig 5). The distinctions are
that "[t]he Computational theory tells us what function is being computed, for
example, the square root function; the algorithmic level provides a means of
carrying out the computation, for example, Newton’s method of approximating
square roots" whereas at "the implementation level… the same algorithm can be
implemented in different hardware" Kitcher1988 . In this space, an emulator is
a computational system that captures both the input-output functions of a
source-system and possibly its algorithmic, circuit-mechanistic and
biophysical-substrate implementations (Fig 4). Thus emulators seek a -
potentially - biophysical copy of an original source system, while simulators
are largely interested in matching the computation level only (i.e. input-
output function) of the system studied.

We propose this as a working definition, amenable to change, of how to
distinguish between software vs. hardware-software models of biophysical
systems. Our central claim, however, is that in the infinite - or
"sufficiently granular" - limit emulators will contain all the components of
the biophysical systems they are seeking to model and must necessarily also
have all their capacities including internal conscious states. More specific
to this section, emulators of dynamical systems cannot be distinguished from
the dynamical systems themselves. The central weakness or unknown, however,
that we do not know at what level of brain emulation we get consciousness.

Figure 5: Different depths of models. Relative to David Marr’s marr1982vision
three levels of modeling (green rectangle), emulators model all levels of a
biophysical system, while simulators model only behavior.

###  B.3 Conclusion: rethinking the need for infinite reductionism in the
causality of non-physical states

In this section we highlighted the limited conceptual agreement on the physics
of causality and the implications on limitations for emulating complex
biophysical organisms. Our framework suggests that a biophysical emulator
could generate indistinguishable neural but also behavioral dynamics from a
source, e.g. optimal motor responses and planning.

##  Appendix C Ideal emulators

In the main text we proposed ideal emulators as systems that - in the infinite
granularity and infinite data-size limit - can perfectly model all the
necessary and sufficient components of a biological organism that generate
behavior and conscious states.777We note that we generally mean ideal neural
emulators - but drop the term ”neural” for simplicity. As an example, an ideal
emulator can be thought of as a complete biophysical copy of an animal’s
nervous system, from atoms to synapses to neuron connections - that can be
reconstructed based on access to "big" data. However, as we are interested in
predicting behavior and conscious states of biological organisms - not
synaptic, molecular or atomic interactions - an ideal emulator will focus on
learning to model these two types of output primarily. The existence of ideal
emulators is essentially a restatement of the universal approximation
theoremHORNIK1989359 ; csaji2001approximation but linking neural states to
behavioral and phenomenal states. Within such a framework, the central axiom
of ET is:

  1. A1:

Ideal emulator are equivalent to their sources. There is no empirical test
that can distinguish between the behavior output or conscious states
experienced by a biological organism and those generated by an ideal emulator
of such an organism.

We first note that $A1$ is a statement about how we measure conscious states -
in an emulator or a biological organism - rather than how conscious states
emerge in a biological organism. That is, $A1$ states that consciousness must
be present (by definition) in an ideal emulator which is trained to predict
the behavior and conscious states of a biological organism - even if those are
never explicitly represented or even known by a human model designer.

Within the "levels of analysis" framework provided by David Marr
marr1982vision an ideal emulator is a system that can model all components of
an organisms including the subsystem (e.g. vision) level computations, their
algorithms, and circuit-level and even biophysical implementations (such as
intracellular mechanisms and dynamics)(Fig 5).

In contrast, we define a simulator as a system that models the behavioral
outputs of a biological system without any specific "lower-level"
constraints.888We provide a discussion on zombie consciousness in the appendix

##  Appendix D MSD: model system divergence hypothesis

Figure 6: Emulators learn joint distributions and activate neuronal
populations. (a). Six-node recurrent neural network. (b). Proposed spike
trains for network in (a). (c). Emulators learn the joint probability
distribution from empirical observations. (d). Emulators can now drive the
neural activity in a similar neural network that has no endogenous
connections. e. Proposed spike trains obtained from (d) are similar to those
in the endogenous case in (b). f. The evolution of two identical dynamical
systems driven ground-truth mechanistic-based models (NN1 and NN2 is as
divergent (or different) as the evolution of an emulator based dynamical
system (ENN) from the two models (inset: putative distributions of path
differences over time).

The model system divergence hypothesis (MSD) is essentially a statement about
the inherent noise and chaotic dynamics of the neural systems we seek to
model.

Given a neural network (e.g. an RNN) (Fig 6a) that generates spiking time
series (Fig 6b) - a neural emulator is a model that learns the joint
probability of the neural time series (i.e. spike rasters here) and
additionally behavior outputs999We note that organism-level behavior outputs
is in principle encoded in the neural states of the organism, and this
secondary requirement is somewhat redundant. (Fig 6c). As argued in the main
text, such a model can artificially drive the origial biological network (Fig
6d) to generate similar (or identical) spiking time series (Fig 6e). Thus,
given these inherent components of biological neural networks, two systems
driven by NNs with identical connectivity weights and starting states that
evolve on a constrained manifold - can nonetheless diverge substantially (Fig
6f - green and red curves). MSD states that the it is not possible to
statistically distinguish (by empirical measurements alone) between a
dynamical system built on ground-truth mechanistic models of biological system
and a (sufficiently accurate) emulator-driven NNs (Fig 6f; inset histograms).

MSD thus specifically highlights that relying on "precise" or accurate
dynamics of neural systems models may not be enough to distinguish ground-
truth mechanistic models of nervous systems and increasingly accurate
emulators (or any other class of models). In particular, as emulators become
increasingly precise in capturing the dynamics of a biological organism -
there may be no clear or discrete moment when complex capacities such as
"conscious" states are being generated.

##  Appendix E Relation to previous work

Given the various interdisciplinary notions discussed in our work, we selected
to focus mostly (and only at a high level) on the literature dealing with the
philosophy and phenomenology of conscious states and topics related to machine
consciousness.

A central theme in artificial intelligence that is linked to understanding
brain function is whether we can copy, emulate, or upload brains or minds to
digital systems. In this field there increase discussions around humans minds
being copied to machines Chalmers2010-CHATSA or "mind-uploading" GOERTZEL2007
; Goertzel2012 . Even setting aside the limited scientific progress on this
front - there are significant and unresolved conceptual challenges Makin2019
including lack of frameworks Bamford2012-BAMAFF , the lack of clarity around
whether digital copies will experience consciousness or have a personal
identity Haggstrom2017 ; Pigliucci2014 . In parallel,while we still don’t know
the necessary or sufficient conditions for conscious states in biological
organisms, there are suggestions of a scattershot approach
butlin2023consciousness to increase the probability of this.

Progress in machine consciousness has also been framed around core principles
GAMEZ2008 including creating machines whose behavior and cognitive
characteristics are associated with consciousness, have similar architectures
to conscious systems (i.e. humans) or actually experience phenomenal conscious
states. For the later, the believe is that the "hard" problem of consciousness
needs to be solved first Chalmers2010-CHATSA . Others like Moor1988 and
Prinz2003 suggest that it is not possible to know whether artificial systems
can be conscious because we can not isolate or separate the factors for
consciousness. In contrast, ET proposes that we do not have to solve hard
problem to create conscious machines nor have similar architectures as long
the the machines outward behavior matches that of the source organisms - and
we achieve such behaviors via modeling neural dynamics.

Lastly, Searle1980 in the famous "Chinese room" experiment suggests that an
artificial system that does "mindless" translation by rules (or lookup tables)
does not amount to understand a language, for example, and therefore cannot
have phenomenal states. ET propose that if the artificial system produces the
"mindless" translation by modeling the causal components of a real - e.g.
biological organism that can translate - then there is an equivalence between
the biological and the artificial system and it is difficult to distinguish
between the two systems - aside from some molecular components of their
makeup.

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