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Foundations of Artificial Intelligence Frameworks: Notion and Limits of AGI

Within the limited scope of this paper, we argue that artificial general intelligence cannot emerge from current neural network paradigms regardless of scale, nor is such an approach healthy for the field at present. Drawing on various notions, discussions, present-day developments and observations, current debates and critiques, experiments, and so on in between philosophy, including the Chinese Room Argument and G…

Licence
OPEN CC-BY-4.0
Authors
Khanh Gia Bui
Published
2025-11-23 · arXiv
Language
en
Length
36705 words
Type
narrative text

Cites 147 works

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3 Future of Artificial Intelligence

The future of artificial intelligence under the current framework looks bleak. Indeed, such can be said of every ‘matured’ enough research and resource-intensive master research plan, and thus, we would have to consider an almost likely slowdown and perhaps not so dramatically, a winter age again for adoptions and maturity in other facet of technological application. During such time, however, we might as well look at what to do to try resolving such problem.

3.1 Neural architecture formalism

We would argue that the neural network idea is indeed, formal and foundational, more than it is usually attributed of. Formally, a neural architecture follows inspiration from the biological neuron in the human brain, and thus employ the philosophy of unit-based processing (Rosenblatt (1958); Minsky and Papert (1988); McCulloch and Pitts (1943)). This implies various properties. First, they are categorized conceptually into units of processing, of which all neuron $n$ admits the structure $(I,M,O)$, of the input receiver $I$, the internal processor $M$, and the output transceiver $O$. Any neuron admitting this structure then can be constructed, combined, and fully realized at will. Conceptually, this created the typed of the neuron architecture, in which all structures would have the same type for operations, such as composition of two neurons, $n_{1}\circ n_{2}=n_{2}(n_{1})$, in this case connected to each other by sequential move, for all neuron to have the sequential operation $n_{i}:I_{i}\times M_{i}\to O_{i}$. In practice, handling this might require more careful planning, but nevertheless the structure is particularly streamlined. Another property that is implied is the recursive structure that can be employed. Intrinsically, the admission of $(I,M,O)$ structure implies that any given structure can mutate $M$ for different purposes, for different processing and thereof, as long as $I$ and $O$ stays as immovable component of the neural structure. Then, Any nested sequence of neuron can be compressed to be a singular neuron, since the footprint of the operation $n_{1}\circ n_{2}$ is simply

$$ n_{1}\circ n_{2}\equiv n_{3}:(I_{1},M_{1})\to O_{1}\to(I_{2},M_{2})\to O_{2}\equiv n_{3}:(I_{1},M_{3}(M_{1},M_{2}))\to O_{2} $$

in which we clarify $M_{3}$ as the processing equivalent of both the first and the second neuron. Thus, we can nest many structures together, changing dynamics altogether, and create different type of specialized neurons, yet with only careful planning of the pair $(I,O)$ we can operate on them together at will. In fact, one can simply also connect as many input from $n_{1}$ to $n_{2}$, neglecting the rest, and the neural structure will still work. We say that $(I,O)$ represents the signature of the neural structure. A baseline, minimal neuron structure can then be defined, which fits the basic definition of a singular perceptron in theory. Let us define $\mathcal{N}_{i}$ as the $i$th arbitrary classification of neuron class. We define the criteria of minimization as

Definition 3.1 (Minimization set)**.**

Let $x$ be a neuron of arbitrary neuronal classification $\mathcal{N}$. Then, the requirement of all neuron class is to be able to distinguish its component to three parts, that is, $\min_{\mathcal{N}_{i}\in\mathcal{N}}{\mathcal{N}_{i}}\equiv\mathcal{I},\mathcal{M},\mathcal{O}$ where $\mathcal{I}$ is the input channel, $\mathcal{M}$ the internal mechanics, and the output $\mathcal{O}$. Let $i,j,k$ represents the cardinality of each part respectively, then if

$$ i=j=k=1,\quad\min_{\mathcal{N}_{q}\in\mathcal{N}}{\mathcal{N}_{q}}=\mathcal{N}_{q},\forall q\geq 0 $$

Then we call this class of neuron the minimal neuron class, and any $x\in\mathcal{N}_{i}$ of such is called the minimal neuron or standard neuron, denoted by $x_{S}$. By default, this is satisfied if $q=0$ in our construction. [^6]

Then, we defined the class of all minimal perceptron $\mathcal{N}_{0}$, or neuron unit, as followed.

Definition 3.2 (Class $\mathcal{N}_{0}$ on $\mathbb{R}$)**.**

A neuron unit $x\in\mathcal{N}$ belongs to class $\mathcal{N}_{0}(\mathbb{R})$ and is called a standard neuron on $\mathbb{R}$ if it satisfies the minimization set criteria, and can be written of the form:

$$ x=q=\sigma_{\mathcal{M}}(w\cdot p+b),\quad p\in\mathcal{I}\subset\mathbb{R},w,b\subset\mathbb{R}\subset\mathcal{M},\sigma:\mathbb{R}\to\mathbb{R}\in\mathcal{M},q\in\mathcal{O} $$

If $\sigma$ is linear unit, that is, $\sigma(wp+b)=wp+b$, then we say $x$ is a linear standard unit. [^7]

Naturally, a singular neuron is not enough, and as illustrated in Minsky and Papert (1988), they alone cannot do everything, for example, the XOR problem illustrated that particularly, there are unsolvable problems one can get with a simple perceptron. The resolution to this problem come in form of, as implied, of the streamlined nature of neural structures — what if we operate them in parallel, in larger structures called layers, and so on? This is first illustrated by Rosenblatt, and its elementary form varies a lot in the history of classical connectionism. By the form of neuron class, we classify it $\mathcal{N}_{2}$. We reserve class $\mathcal{N}_{1}$ for the class of all multiple-input neuron, of which the cardinality is $(i,1,1)$ for $i=1,\dots,n$. The motivation for $\mathcal{N}_{1}$ is that to resolve the problem of the class $\mathcal{N}_{0}$, one potential fix would be to ’fix bayonet’ and free up $i$, thus giving the construction of $(i,j,1)$. We call this multivariate neuron. If it is $(i,1,1)$, then we call it the multivariate standard neuron. All of such neurons then belong to the class $\mathcal{N}_{1}$ neuron simplex. Then, the class $\mathcal{N}_{2}$ of layer neural networks, is defined as followed.

Definition 3.3 (Class $\mathcal{N}_{2}$ structure)**.**

We fix the signature of any given structure $\mathbf{N}\in\mathcal{N}_{2}$. Let us define, for $L_{i}\in M$ the structures of layers, of which $L_{i}$ contains $n_{i,j}\in\{\mathcal{N}_{0},\mathcal{N}_{1}\}$ of subsequent lower class, and fix their cardinality of the form $(i,1,k)$. Then, a neural network $\mathbf{N}$ of the class $\mathcal{N}_{2}$ is equivalent to the following structure:

$$ \mathbf{N}\in\mathcal{N}_{2}\equiv I_{\mathbf{N}}\times M_{\mathbf{N}}(L_{1}\times L_{2}\times L_{3}\times\dots\times L_{j})\to O_{\mathbf{N}} $$

The cardinality of $\mathbf{N}$ is then $(i,j,k)$, for all $i,j,k\in\{1,\dots,n\}$. For $\mathbf{N}(i,1,k)$, we call it as the shallow neural network.

The structure of our theory on the neural formalism is influenced by the object-abstracted treatment of mathematically embedded structures, and the unit-wise principle of particular neuron. Before we meet ourselves into the notion of epistemic circularity[^8] problem, we might as well clarify a few prerequisites for such structure to exhibit.

First, we indict on the fundamental encoding environment that any object can take. The main point of any structure here is that there exists fundamentally the encoding space of two types. First is the object’s cardinality space, denoted $\Gamma=(\mathbb{N},F)$ for any given categorization $F$. Second is the encoding primitive of the field $\mathbb{R}$ for generality - in general any field is alright, and they define the analytic structure of the system itself. Any extension, for example, the $\mathbb{R}$-algebra of complex number $\mathbb{C}$ is then the primitive field’s extension. [^9]. Any type of data or system can then be decomposed to such, with additional structure on top of such primitive. Such is then called the primitive framework.

Definition 3.4 (Primitive framework)**.**

Let us define the primitive framework $\mathcal{P}_{0}$ of the dual $(\Gamma,\mathbb{R})$ where $\Gamma=(\mathbb{N},F)$ is the cardinality encoding space, and $\mathbb{R}$ is the base field primitive of the analytical encoding. An object $X\in\mathcal{P}_{0}$ admits a dual representation,

$$ X\mapsto(\gamma(X),\rho(X)) $$

for $\gamma:\mathrm{Obj}\to\Gamma$ of cardinality encoding, and $\rho:\mathrm{Obj}\to\mathcal{E}(\mathbb{R})$ for the field extension of $\mathbb{R}$ category, or the category of all $\mathbb{R}$-algebras. For $\mathcal{E}(\mathbb{R})$ without extension, then $\mathcal{E}(\mathbb{R})\cong\{\mathbb{R}\}$ of all $\mathbb{R}$-algebra.

For a structure that is supposed to be unit-wise constructed like neural network and the like, one of the main principle is the principle of abstraction. With this, come the idea of layer. Specifically, a layer separates abstraction in terms of subspace. Let us take an example of such kind for clarification. Let us define the primitive framework $\mathcal{P}_{0}$ as now the layer $L_{0}$ of this layering scheme. Then, we define the layer $\mathcal{L}_{1}$ of all unit-wised neuron-like units taking over the representation scheme on $\mathcal{L}_{0}$. We then define the structure of the neuron class $\mathcal{N}_{1}$ upon such as followed.

Definition 3.5 (Base neuron class)**.**

We define the base neuron class $\mathcal{N}_{1}\equiv L_{1}$ as followed. For any $\mathcal{U}\in L_{1}$ for $\mathcal{U}$ as unit-wise construction over $L_{0}$, then every $\mathcal{U}$ satisfies the input signature $\mathcal{I}_{sig}:\mathcal{E}^{\prime}(\mathbb{R})\to L_{0}$, output signature $\mathcal{O}_{sig}:L_{0}\to\mathcal{E}^{\prime}(\mathbb{R})$, and $\mathcal{C}_{ext}$ as extensible construction over $L_{0}$, for $\mathcal{E}^{\prime}(\mathbb{R})$ particular extension on analytical encoding of $L_{0}$. The type template of a neural unit $\mathcal{U}\in L_{0}\equiv\mathcal{N}_{1}$ is then defined as $\mathcal{U}=\langle\mathcal{I}_{sig},\mathcal{C}_{ext},\mathcal{O}_{sig}\rangle$ where $\mathcal{I}_{sig}$ and $\mathcal{O}_{sig}$ are invariant as type.

Those definitions directly link it to type theory, while such development is perhaps more complex. In general, this specifies the type, of a particular unit using the invariant analytical typing in the general environment linking to it. This is the outer typing of a given model construct, of which defers the type of which interaction between the environment, or the global space state happens and what is received of such. While the ambiance space can be forgiving, such cannot be said for the typing of given structure, since it must have the correct typing for identification. The extension is then is fairly simple, but the more important notion is the equivalence of the variant $C_{ext}$ extensible unit of the inner structure itself.

Another type of extension can also happen in the sense of $\gamma(X)$. In certain sense, $\gamma(\cdot)$ can always be richer than the cardinality encoding, but with the use of extensible precursor-usage representation. Suppose a grid-like ordering can be made of the spatial ordering type using information of the precursor $\gamma(X)$. Then, such object then is extended to be a dual-extended representation:

$$ X\mapsto(\gamma(X),\rho(X))\times F_{\gamma}(X) $$

where $F_{\gamma}(X)$ organizes the different constituent part in cardinality argument, of positional placement, or else. Such freedom can be made and thus, categorize different extensions into various packages. This can then be extended further and further of such, thus making it more sophisticated and will reach, fundamentally, to the current neural network, its specialization and variations, and so on. Indeed, we have implicitly obtained the hierarchical construction

$$ \mathcal{P}_{0}\subset\mathcal{P}_{1}\subset\dots\mathcal{P}_{n} $$

with increased specific direction of increment. This framework a notion of which in general, can be called the specific constraint chain, in which a specific toolchain of increment recursive construction is created, from a transformation $\Phi_{i}:\mathcal{P}_{i}\to\mathcal{P}_{i+1}$, thus create a tower of hierarchy of framework. With any self-component extension, for example, at the layer $\mathcal{P}_{L}$ (of which in certain construction as $\mathcal{P}_{2}$), we can define the add-on $\Lambda_{i,X}:\mathcal{P}_{i}\to\mathcal{P}_{i}^{\prime}$, that modifies the internal structure with added mass or added cardinality, but retain the core principle construct.

While this is a prototype, it certainly focuses on the main axis of development that would be detrimental to the topic of interpretability, capacity, analysis and so on. We can indeed, extend this particular base template of a neuron class to much greater strength, of which address partially concerns in both implementation, and analysis. Type and neuron specification classifies neuron into different class of components instead of the mundane functional structure that we currently have, but also individualized and structuralized the connection, information and signature aspect of a processing unit. This allows for more grounded expression and composition rule, for example, the complexity metric of individual components of a larger construction of neural network, of which then can be expressed by individual neurons, and such neuron’s individual’s components. Dynamics works the same, however, it will shift - instead of learning as a back-tracking process, we can express backpropagation as a kind of internal mechanism on addition to the working framework, and the components such measures. In all, the framework is not category per se, but a layered analytic machinery of which naturally (or at least intended of) to construct and describe how architecture can emerge from iterated constraints extension of primitive computational units. In essence, we can also treat the framework as to say each $\mathcal{P}_{i}$ to correspond to a functional space of realizable computation (as seen in the abstraction to $\mathbb{R}$-algebra at least), and different structural addition. Furthermore, one can also use such framework to either construct from scratch, and also enables of the process for structural optimization, basically, turning the system considered in such framework, into a basis, resource-optimization or construction game, where analytics and structural design are grouped and unified, and also taken into consideration more sophisticatedly as a resource. Such submodules’ implication can then also contain the learning mechanism module, of which now is intrinsic of the system, and not simply external of a process itself.

Furthermore, the primitive framework itself serves of a detrimental role in expressing system-wide, modelling-style and global specification of the working space. While we speak of hypothesis class $\mathcal{H}$ or $\mathcal{C}$ for example, such class can only infer, usually of specific function class, definitions, requirements, and so on. With this, we can express them both in a set-theoretical way of cardinality and field-extension similar to embedded vector space, and also encoding such as the numerical encoding typically seen in computing system, and structural addition and expression explicitly considered so. The goal is then also to provide a concrete groundwork on conceptually model the system dynamics and its constituent parts, in the face of increasing developmental pace and new architectures floating around from heuristic choices. In similar sense, using only category theory is an ill-advised method to formalize such, and hence we would like to not agree on such stance. Indeed, there are problems and pitfalls, as well as the immaturity of the functional structure itself, but per a prototype, the general conceptual idea of this particular framework is fairly sound, and would be able to provide deeper insight and more sophisticated interpretation, rather than just simple neural network functions before.

Again, such theory and treatment does not claim to solve the problem directly, as even now it is not elucidated yet if such model can be even feasible of holding certain conceptual works. Instead, what it might do is to extend and allow for the backward construction - by formalize in the sense of restructure the current messy architecture, and enable the incremental construction in both depth and breath of the neural unit concept. If such can be enabled, emergence, percolation, and so on, could be reached in due time. It is then the task to develop such theory toward maturity, while still retain backward compatibility toward the simpler and present system.

3.2 The learning theoretic

The most important theory or rather, functionality of mutation that enables certain model to facilitate dynamic changes, are indeed the theoretical notion of the learning procedure. Toward such end, generalization of the theory itself, and what is meant of the notion that was typically seen, for example, generalization, and so on, is in the question for clarification, and both development of such. This section will only outline the basic philosophical thought of the implication of a learning action in the machine-theoretic lens, for further expansion of the topic to be reserved in future works and separated developments. The main goal, however, would be to realize the entire picture of how the learning process is expressed, usually, and what can be gained from such framing.

What we attempted as learning would be inherently built upon the perspective of a system dynamic. Specifically, we see that we can utilize existing idea, for example, the simple agent system in Stanford Encyclopedia of Philosophy (2018) as the critique system. The implication is then simple - we posit that within this observation or insight, we can reveal more about the dynamics of which our models are taking, and what to construct next of requirements. For now, let us denote the agent of interest as $A$. This agent has the internal mechanism $M$, the sensory $S$ and the action $F$, of which it uses of the operating environment $E$ surrounding of which $S$ can sense, marginally of its intended features. We posit the following definition, of which applies for all constructs, lest of only the singular artificial intelligence subject.

Definition 3.6 (Construct)**.**

A construct is a conceptual encapsulation of two components: The machine in broad term which houses the operational facility, and optionally, the existential facility of the construct, and the process, or rather, its state(s) of being. These two makes up a functional construct of interest.

The existence of such model can be realized in certain ‘situation’ by the resource it occupies of the existence of such. Under the computationalism approach, such includes time complexity, memory allocation, and structural interpretation via the native encoding language (such is numerical). The observation system of interest includes the resource as the observations itself - usually expressed also via the native encoding language itself, attaining the structure choice of the environment - for example, continuous observations or discrete observations that can be isolated of a concrete state. Such observation itself, is governed by the selective rule of the system’s environment, of which draw out such result we see of the environment. Those natural information are inherently hidden, from the perspective of the agent sensory system itself, or rather of the inherent way of receiving information from the sensory unit configured of choice. Moving on from such, we emphasize the need to clearing out the problem of existential facility, and operational facility of any given agent system of interest, and thus, also the environment at will. While it can be said that the environment would be less susceptible to such framing, from the perspective of an objective constructivism approach, the environment itself being used on said agent, is within the limit in which the designer (human, etc, intelligent agency), can argue and consider of such. Thereby, there exists existential facilities - those that support such construction and regard of the environment (for example, a physical environment consideration requires the basis of laws of physics for potential framing of such laws) that is procured to the model itself, and thus form the basis of the existential facility thereof. Operational facility comes in hand as the actual functional, observables that exist as object of interest within said environment $E$. The model itself attains such level of existential-operational facilities on itself, however, the existential facilities here form the basis of its construction, while the operational facilities form the basis of its actual process and operations thereof itself. Simply speak, such notion of more naturally applied for an actionable, constructible system of interest. For the agent itself, computationalism induces on the property of being constructed on the basis of the computable system, i.e. computers. Thus, it bears constraints, encoding specification, structural mechanism of the computable system that it is based on upon. For example, this can be as we have already mentioned, the need for numerical encoding in modern computing system, the memory and time-constraint of which makes certain operation or specific operation of interest infeasible of the resource sensitive to such computational object ($NP$-hard problems, etc), or the complication in constructing certain architecture or expression of the model agent of interest (for example, a system of language, abstracted to either procedural or OOP, presents architectural abstraction in which can make constructions difficult even within a singular basis of computation). Such makes up how and what can the paradigm, for even the biological neuron abstraction can take within the respect of such computational system, reduced to an input-and-activation unit, or later on where the more computably-optimized schema is the layering scheme. Such is then can be linked to the operational facilities, of which contains two separate entities of consideration - the mass, or rather, facilities, and the process, of which considers the operational itself of the agent.

Inherently, we see there exists two internal mechanisms of interest. One, belongs to the model itself, now we denote $M_{A}$, and one is the mechanism, or the law of which observations in $E$ is observed, denoted $M_{E}$. Such internal mechanisms are often more considerately important than the sensory actions itself, and of which generally comes in two main categorization. The internal mechanism classified via exposure, contains the internal interface of which is more closely linked to the specificity of the sensory system and external action potential (i.e. the action unit), and the follow-up fully internal system of which can be theorized to control and operate in unification of such sense. In a sense, what we define is the delegation of interface, in which the existential and operating facilities are handled via separated specialized interface, and so on. While it is said so as to in one way or another, partially support the theory of fragmented intelligence, such is also needed to be reminded of that in terms of internal structure, such interface bears heavy deviation toward the sensory experience itself. Or rather, the action handling is inherent of the dynamic observed by and acted upon by the sensor, and usually do not reflect such of the internal structure, aside from the internal structure’s interface strength, and the effectiveness of the interface-to-sensor structure. When speaking such system, $M_{E}$ is delegated observations in which $M_{E}\to M_{E,S}$, or $M_{E}^{\prime}$ for short, taking into account the sensory perception itself. The information received from $M_{E}$ by $A$ is inherently shallow, and can only be interpreted inside $S$’s capability itself. However, such information is extended in a different case.

Next, we further the position that there exists the process of the operational facilities, of which handles the operation itself. This concept requires us to handle the concept of state, as per natural it is of to classify and quantize the ‘condition’ and ‘resource’, or ‘structure’ of a given subject, model, theory, and so on, at any given situation, without mutation[^10]. Such discrete state is handled and intrinsic of any operating structure, hence $M_{E}$ and $M_{A}$. While we do not go into many details of the philosophical inquiry about state transition, one thing can be sure is that they hold more information than the simple static observation. Thus comes the notion of a static system observation, or dynamic system observation. The singular $M_{E}\to M_{E,S}$ represents the static case, in which observations are frozen in time or any arbitrary notion $t$ as a ‘snapshot’, while the copula $\{M_{E}\to M_{E,S}\}_{t}$ represents the dynamic case, in which such arbitrary ‘state snapshot’ now contains the relative previous or future states of the system. Hence, it allows for multi-facet information, with respect to the static case of such. The system can have these properties in many ways, for example, if the system itself is a mask, then it contains the notion for the static-dynamic mask only, while the lower-level under that mask can still be dynamic - thus those concepts are system-dependent.

What we have said are to set up the system by itself, the model in which operations are there to work, and the system observation in which $A$ itself are tasked of, given its capability thereof that can be quantified. Now, come to the question: what is the learning dynamics, and how should it be important of?

Naively observing such, we can understand that the sensor itself is not good of forming, acting purely as the information receiver themselves. Without the interface, it can do nothing, but we also encounter such fact that without any knowledge or interpretation, the interface only serves as an increased per length tool - just like a bridge from $Q\to P$, it does not do anything beside lengthens the signal travel time. Thereby, it requires interpretation to be built upon, in which development of the interface on sensors must be indicted of. It is also here that we see the limitation of the sensory information received from $M_{E}$, and the limitation coming from $S$ itself. $S$, even in dynamic of static case, cannot see everything there is of the measure provided on the landscape of the system. For example, if the system expresses itself majorly in $(x,y,z,t_{1},\theta)$, but the sensor can only connect to, or know of, $\theta$, this leaves an extreme gap in information. Assuming such snapshot copula for $\theta$ alone to be influenced by a network in which the other quantities interact, with its own underlying constructs and interactions, then abnormality, sudden changes, outliers, roughness of $\theta$ cannot be explained any further but to set it as noise. The snapshot itself might also leave questionable gaps between observation itself. For example, there might only exist the state in which energies are there in discrete intervals, and there are regions in which no observation are made, mainly out of structural constraints on the system of its value on itself. The snapshot itself also does not hold any information, without interpreter, even in dynamic case — as for in such case can only be no more than a bunch of discrete and individual observables without structural adherence, i.e. we see it as function, but the system itself experience it in a non-function sense, would not be able to triangulate such. This is fairly mitigated when the data itself is rich enough in information, and thus allows for what is usually called single-shot operation, however, such case is typically rare, and within the current framework, the operation that led to such development is more likely to be categorized as inconsistent. Thus, we can then consider it a disorganized bunch of observation, and not inherently obtains the notion of relation, let alone function. Such pushes for the internal mechanism, or any supporting substrate, that can ‘interpret’, using our analogy, and construct certain system inside the modelled agent itself, both in restricted case of singular subject, or in dynamic cases of data, and within poor or rich data quality and observation density.

This, naturally expresses the notion of learning as an integral part of the system dynamic, however much more sophisticated in the sense of arbitrary ’adaptation’ of a system instead. From such, we can clearly distinguish two types of learning - one of which is structural learning, where the adaptation availability is for the structure of the model itself, while the other is of operational learning, where the process itself is modified of said adaptation. They allow for different mode of mutation, and also different mode of modification with specified behaviours. The learning sequence then can be copulated into different parts, of which we essentially posit that structural learning is of higher priority than operational learning, though in certain sense, operational can be utilized much better. What that said, we need to take on the priori on which learning is necessary. While we have been speaking of the necessity of it as a functional construct to interpret, create interface of which we can apply on, and so on. But we are skipping the natural justification of learning mechanics, which is very hard and is not relevant in our creation (though might be so in a difference sense[^11]), we need to resolve, then, the objective of learning. This is a very hard question, and indeed, have no satisfactory answer. Indeed, the only way that we can typically see, is the scheme in which we introduce logical impulse in which is interpreted of a sense, as favourable. That is, clarify an objective $\ell$ to reach, then of certainty, introduce the reward/punishment in which either get you closer to the objective, or further out. This hits the wall of replication and mimicking, but no actual constraints, as we have argued in previous sections. Typically, what we do in both supervised learning or semi-supervised learning scheme, or even unsupervised scheme, we often resort to either ’specialized designing’ - in the case of unsupervised learning and all, or external modification as of supervised or semi-supervised case, in which as said, remove the learning functional, outside the working model itself. Inductive bias - or so is what it is called of, as the bias from the designer perspective, coming to the model, and so on so forth. External modification relieves the model from the burden of determining the meaning in its own space, of the action of learning and the generation of such, but in turn makes the model inflexible, less sophisticated, inherently shallow, static, and overall poorly designed on its own merit. Those solutions are temperamental, not permanent, nor it is in the long-run effective, though there is no doubt of its success in contemporary machine learning structures. As to push further, it is then to be believed that it is insufficient for such task. It is just similar as the replica problem of the imposed observations that we see. It feels like we are seeing patterns or uncovering something in data, or nature, usually can be agreed as such, but certain cases overvalued of such observations, while living in the world of which rules we create ourselves.

The issues can be relieved, in certain sense, of certain solution, for example, to build the model within the newfound theory of modelling, of which the philosophy of constructing such ‘AI’ model as to be from first component - i.e. ground zero, and of which the operating environment of said given model is rich enough as to interpret different types of rewards or similar-purpose responses. Or, in certain sense, couple uniform randomization, and replicate the genetic evolutional pattern, as seen in perhaps many researches on such algorithms of such, for example, Stanley and Miikkulainen (2002b); Stanley and Miikkulainen (2004); Stanley and Miikkulainen (2002a); O’Neill and Ryan (2001); Ryan et al. (1998); Zhang et al. (2020); Khamesian and Malek (2021); Volná (2005); Sher (2013), and as to allow the observation in which the learning adaptation itself generates the ‘purpose’, within reason and within probable causation chain (though, we must be careful of the overstretched implications). Or, perhaps there exists certain other structural construct that allows such, of philosophy and mechanism that embed such on its own. Structural and operational learning notion can be applied into many current frameworks of learning requirements, though most of the time we are entangled within fixed operational, dynamic structural (for example, SVM), or fixed structural, dynamic operational (any reasonable learning framework of existence with many-phase inference) learning. If we can resolve the natural occurrence, not necessarily as to not encode the notion of learning itself, since we are allowed up to certain point, to encode them to the model as of a shortcut and heuristic baseline, then the structural-operational learning sequence would be much obliged of help, and certainly would provide a larger and richer theoretical grounding toward the generality of the learning concept.