arXiv CSopen access

Bootstrap Theory of Representational Emergence: Explanatory Insufficiency as a Driver of Representation Learning and World Models

Bootstrap Theory of Representational Emergence: Explanatory Insufficiency as a Driver of Representation Learning and World Models Jacques Raynal1,∗ , Pierre Slangen2 , Elsa Raynal3 , Jacques Margerit4 1 Laboratory of Bioengineering and Nanosciences (LBN), University of Montpellier, Montpellier, France 2 EuroMov Digital Health in Motion, University of Montpellier, IMT Mines Alès, Alès, France 3 Certified Sophrologist, Sensorimotor Practice, Montpellier, France 4 Emeritus Professor, University of Montpellier, Montpellier, France

arXiv:2606.07303v1 [cs.LG] 5 Jun 2026

∗ Corresponding author: [email protected]

Abstract Representation learning has become a central paradigm in modern machine learning, enabling systems to move from handcrafted features to learned embeddings, latent spaces, foundation models, world models, and digital twins. However, most research focuses on how representations are optimized once a representational framework has been chosen. Less attention has been given to the question of when a new level of representation becomes necessary. We introduce the Bootstrap Theory of Representational Emergence (TBER), a framework for describing how new representations arise when existing ones become explanatorily insufficient. In this view, representational innovation is not only the result of more data, larger models, or increased computational power. It is also driven by persistent explanatory gaps revealed when a current representation can still describe observations but can no longer make their organization or transformations intelligible. TBER identifies explanatory insufficiency as a positive signal for representational transition. A representation becomes insufficient not because it is necessarily false, but because its explanatory domain has been exceeded. The proposed bootstrap dynamic follows a recursive sequence: observations reveal anomalies; anomalies expose explanatory insufficiencies; insufficiencies motivate new representations; and these new representations generate further observations and possible new insufficiencies. We formalize this process through a five-stage model: stabilized observation, anomaly detection, recognition of explanatory insufficiency, representational emergence, and provisional stabilization. We discuss how this framework applies to representation learning, latent-space construction, foundation models, world models, digital twins, adaptive biological systems, and scientific discovery. TBER suggests a possible design criterion for future artificial intelligence systems: the capacity to detect when their internal representations have reached explanatory limits. Such mechanisms could support autonomous representational evolution, self-directed model refinement, and more adaptive forms of knowledge generation.

Keywords: Representation Learning, Representational Emergence, Explanatory Insufficiency, Latent Spaces, World Models, Foundation Models, Autonomous Artificial Intelligence, Machine Learning, Meta-Representation, Adaptive Systems.

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Introduction

Representation learning is one of the central foundations of modern machine learning [14]. Its objective is not only to process observed data, but also to construct internal representations that make relevant structures, relations, and transformations more accessible to learning systems. This progression can be 1

observed historically in the transition from handcrafted features to learned embeddings, latent spaces, foundation models, world models, and digital twins [13, 14, 15, 16]. Most work in machine learning focuses on improving representations once a representational framework has already been selected. Deep learning architectures, self-supervised learning, generative modeling, foundation models, and world-model architectures provide powerful methods for learning useful internal structures from large datasets [14, 15, 16, 17]. These approaches have considerably expanded the capacity of artificial systems to classify, predict, generate, simulate, and generalize. However, a more fundamental question remains less explicitly addressed: when does a new level of representation become necessary? In many cases, the appearance of a new representation is justified retrospectively by improved performance, better compression, higher predictive accuracy, or increased transferability [13, 14, 15]. Yet these criteria do not fully explain why the previous representation became insufficient, nor why a transition toward a new representational level was required. This problem is particularly important for complex adaptive systems. In such systems, the same observable performance may be produced by different internal organizations. Conversely, important organizational transformations may remain invisible at the level of aggregate metrics [3, 8, 10, 11, 22, 23]. A representation may therefore remain descriptively useful while becoming explanatorily insufficient. It may continue to summarize observations without making the underlying organization, dynamics, or transformations intelligible. The same issue appears in contemporary artificial intelligence. Observable variables may be insufficient to capture relational structure; latent spaces may be insufficient to represent temporal transformation; predictive models may be insufficient to support simulation or planning; and world models may themselves become insufficient when systems must revise their own internal representations [14, 16, 17]. Each transition raises the same question: what makes the next representational level necessary? This article introduces the Bootstrap Theory of Representational Emergence (TBER), a general framework for describing how new representations emerge when existing ones become explanatorily insufficient. The central hypothesis is that representational innovation is driven not only by data availability, computational power, or model scaling, but also by the identification of explanatory gaps that cannot be resolved within the current representational framework. In TBER, explanatory insufficiency is interpreted as a positive signal for representational transition. A representation becomes insufficient not because it is necessarily false, but because its explanatory domain has been exceeded. When observations, relations, or transformations resist integration within the available framework, a new representation may become necessary. This perspective extends classical epistemological views in which scientific progress is driven by surprise, obstacles, ruptures, or transformations in the conditions of knowledge [1, 2, 5, 6, 7]. The theory describes this process as a recursive bootstrap dynamic. Observations reveal anomalies; anomalies expose explanatory insufficiencies; explanatory insufficiencies motivate new representations; and new representations generate new observations, which may in turn reveal further insufficiencies. This dynamic provides a general structure for understanding representational change across machine learning, scientific discovery, adaptive biological systems, and artificial intelligence [1, 2, 8, 14, 16]. The contribution of this article is theoretical rather than algorithmic. TBER does not introduce a new learning architecture or optimization method. Instead, it proposes a framework for understanding why representational transitions occur and how explanatory insufficiency can guide the emergence of new representational levels. Accordingly, this paper does not introduce a new algorithm, benchmark, empirical dataset, or optimization procedure. Its contribution is conceptual: it proposes a meta-representational framework for interpreting when and why new representational levels become necessary in machine learning, artificial intelligence, adaptive systems, and scientific discovery. 2

The remainder of the article is organized as follows. Section 2 introduces the problem of representational accumulation and the limits of performance-based justification. Section 3 defines explanatory insufficiency as an epistemic signal. Section 4 presents the bootstrap principle. Section 5 formalizes the five-stage transition model. Section 6 situates TBER in relation to existing epistemological and computational frameworks. Section 7 discusses implications for representation learning, latent spaces, foundation models, world models, and autonomous artificial intelligence. Section 8 examines adaptive biological systems as a motivating domain. Section 9 presents the founding empirical trajectory from performance to viability. Sections 10 and 11 discuss the originality, limitations, and future directions of the theory.

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The Problem of Representational Accumulation

Contemporary science and artificial intelligence are characterized by a rapid multiplication of representational levels. In machine learning, this evolution can be seen in the progression from manually engineered features to learned embeddings, latent spaces, foundation models, world models, and digital twins [14, 15, 16]. In biomedical and digital health research, traditional clinical variables are increasingly complemented by biological markers, behavioral measurements, digital biomarkers, multimodal sensor data, and predictive models [18, 19, 20, 21]. This diversification has greatly expanded the capacity of scientific and artificial systems to describe, classify, predict, simulate, and intervene. Each new representational level may reveal aspects of a system that were inaccessible at previous levels. Latent spaces may reveal hidden relational structures; foundation models may support transfer across domains; world models may represent possible transformations; and digital twins may integrate multiple scales of observation into dynamic simulations. However, the multiplication of representations does not automatically produce greater intelligibility. A model may improve predictive accuracy without explaining the organization that generated the observed data. A latent space may separate observations without clarifying the causal or structural relations between them. A digital twin may reproduce system behavior without making explicit why a given level of representation was required. This distinction between representational performance and explanatory necessity is central to the present work. In many scientific domains, new representations are justified retrospectively by their usefulness. They are accepted because they improve classification, prediction, compression, simulation, or decision-making. This pragmatic criterion is legitimate, but incomplete. It explains why a representation is useful after it has been introduced, but not why the prior representation became insufficient, nor why the new representational level became necessary. This leads to what may be called representational accumulation. Representations are added to previous ones without an explicit account of the conditions that govern their emergence. Observable variables are supplemented by latent variables; static descriptions are supplemented by dynamic models; predictive systems are supplemented by world models; clinical measurements are supplemented by digital biomarkers. Yet the logic of transition between these levels often remains implicit. The problem is not the existence of multiple representations. Complex systems may legitimately require several complementary representational levels. The problem arises when representational multiplication is interpreted as progress in itself. More variables, larger datasets, deeper models, or more abstract latent spaces do not necessarily guarantee better explanation. They may increase descriptive power while leaving the underlying organization insufficiently understood. This issue is particularly important in complex adaptive systems. Such systems often exhibit many-to-one relationships between organization and observation: different internal organizations may generate similar

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observable outcomes. Conversely, important internal transformations may occur without producing immediate changes in aggregate performance. In this context, a representation may remain descriptively accurate while becoming explanatorily insufficient. The same difficulty appears in artificial intelligence. A learned representation may support high performance on a benchmark while remaining fragile under distribution shift. A latent space may organize training data while failing to capture the transformations required for planning. A foundation model may generalize across tasks while lacking an explicit mechanism for identifying the limits of its own representations. These cases suggest that performance alone cannot determine whether a representation is adequate. The key question is therefore not simply how to build more powerful representations, but how to recognize when a new representation is required. Before introducing a new latent space, a new model architecture, a new world model, or a new digital twin, it is necessary to identify the explanatory insufficiency that makes such a transition scientifically meaningful. TBER begins from this problem. It proposes that representational emergence should not be understood as mere accumulation, scaling, or technical refinement. Instead, new representations become scientifically necessary when existing representations encounter persistent explanatory limitations. The following section introduces this notion more precisely by defining explanatory insufficiency as an epistemic event.

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Explanatory Insufficiency as an Epistemic Event

The notion of explanatory insufficiency is central to the Bootstrap Theory of Representational Emergence. It describes the situation in which a representation remains descriptively useful but no longer provides a satisfactory account of certain observations, relations, transformations, or organizational properties of the system under study. In ordinary scientific practice, the insufficiency of a model is often interpreted as a temporary weakness. The model may be corrected, extended, calibrated, or replaced in order to restore its explanatory power. Such adjustments are legitimate and often necessary. However, they do not exhaust the meaning of insufficiency. In some cases, a persistent limitation does not merely indicate that a model requires local correction. It indicates that the current representational level has reached the boundary of its explanatory domain. TBER adopts this second interpretation. Explanatory insufficiency is not treated as an accidental failure of knowledge, but as an epistemic event. It marks the moment at which a representation reveals the limits of what it can make intelligible. A representation may remain correct within its proper domain while becoming insufficient in relation to new observations or new questions. This distinction is essential. A representation is not necessarily false because it becomes insufficient. Classical mechanics remains useful within specific domains even though it became insufficient for explaining relativistic phenomena. Observable performance metrics may remain useful for comparing systems even when they become insufficient for understanding the organizations that produce those performances. A latent space may remain useful for classification while becoming insufficient for representing temporal trajectories or counterfactual transformations. Explanatory insufficiency therefore appears in the interval between description and explanation. A representation may still describe observations, organize data, or support prediction, while failing to account for the relations that make those observations intelligible. Description concerns the ordering or summarization of phenomena. Explanation concerns the intelligibility of the relations, mechanisms, transformations, or organizational constraints that connect them.

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We define explanatory insufficiency as follows: Explanatory insufficiency occurs when a representation remains capable of describing a phenomenon, but no longer accounts satisfactorily for certain observations, relations, transformations, or organizational properties associated with that phenomenon. This definition is deliberately broader than prediction error. A prediction error may reveal an insufficiency, but explanatory insufficiency cannot be reduced to predictive failure. A model may predict accurately while remaining explanatorily poor. Conversely, a model may predict imperfectly while still revealing meaningful organizational structure. TBER therefore distinguishes predictive performance from explanatory adequacy. This distinction is particularly important in machine learning. Many systems are evaluated primarily through performance metrics such as accuracy, loss, compression, benchmark scores, or transfer performance. These measures are essential, but they do not necessarily reveal whether the learned representation captures the organization of the phenomenon. A representation can perform well while masking structural ambiguity, hidden causal heterogeneity, or unstable generalization. In complex adaptive systems, this issue becomes especially visible. A single observable pattern may be compatible with multiple internal organizations. A functional score, behavioral trajectory, or clinical biomarker may describe the system at an aggregate level while leaving its internal coordination unresolved. When the scientific objective shifts from describing performance to understanding organization, the previous representation may become insufficient. Explanatory insufficiency also plays a methodological role. It provides a criterion for deciding when a new representational level may be justified. Without such a criterion, new representations risk being introduced merely because they are technically available or computationally fashionable. In contrast, TBER proposes that a new representation becomes scientifically meaningful when it reduces an identified explanatory insufficiency. This perspective gives insufficiency a positive epistemic value. What resists explanation is not simply noise or failure. It may indicate that the phenomenon contains relational, temporal, organizational, or counterfactual structure that exceeds the current representational framework. The resistance of the phenomenon to existing representation becomes information about the limits of that representation. This interpretation connects TBER to several traditions in the philosophy of science. Peirce emphasized the role of surprising facts in triggering abductive reasoning [1]. Bachelard described scientific progress as a process of overcoming epistemological obstacles [2]. Canguilhem showed that pathological or exceptional situations may reveal dimensions of living systems that remain invisible under ordinary conditions [3, 4]. Simondon described individuation as the resolution of tensions within a system [7]. TBER extends these insights by shifting the focus from the emergence of hypotheses to the emergence of representational levels. The question is therefore not only: Which hypothesis explains this observation? but also: Which level of representation has become necessary for this observation to become intelligible? This reformulation changes the status of insufficiency. It is no longer simply an indicator that a model has failed. It becomes the mechanism through which representational systems reorganize themselves. In this 5

sense, explanatory insufficiency is the epistemic event that initiates the bootstrap process described in the next section.

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The Bootstrap Principle

Having identified explanatory insufficiency as the condition that precedes representational change, the next question concerns the mechanism through which new representations emerge. TBER proposes that representational evolution follows a recursive bootstrap process in which each representational level creates the conditions for the emergence of subsequent levels. The term bootstrap is used here in a general epistemic sense. It refers to a self-generating dynamic in which a system progressively transforms its own conditions of intelligibility. Existing representations enable observation; observation reveals limitations; limitations motivate new representations; and the new representations subsequently redefine what can be observed and explained. The process therefore operates recursively rather than linearly. Within this framework, representational emergence is not understood as a simple accumulation of information. The addition of new data, variables, or computational resources does not automatically produce a new representational level. Emergence occurs when explanatory insufficiencies become sufficiently persistent that they cannot be resolved within the existing framework. At that point, the system faces a representational transition rather than a representational refinement. The bootstrap principle can be summarized as follows: Every representation creates the observational conditions that will eventually reveal its own explanatory limitations. This proposition constitutes the central claim of TBER. Representations are not only tools for understanding phenomena; they also determine the kinds of insufficiencies that can become visible. A representation allows certain questions to be asked while rendering others inaccessible. Consequently, each representational framework simultaneously expands knowledge and generates new zones of ignorance. The process can be illustrated through several examples. In classical mechanics, increasingly precise observations eventually revealed phenomena that exceeded the explanatory capacity of the classical framework. In biology, descriptive anatomy revealed organizational regularities that ultimately motivated molecular and genetic representations. In machine learning, handcrafted features revealed limitations that encouraged the development of learned embeddings and latent representations. More recently, latent representations have motivated world models and foundation models capable of representing broader domains of transformation and prediction. In each case, the transition does not arise because the previous representation becomes useless. Rather, it emerges because the previous representation encounters phenomena that it cannot fully integrate into a coherent explanatory structure. The older representation often remains valid within its original domain while becoming insufficient for a broader domain. The bootstrap principle therefore differs from purely cumulative views of knowledge. Knowledge does not progress merely by adding facts to an existing framework. Instead, periods of representational stability are punctuated by transitions in which the framework itself changes. What evolves is not only the quantity of information available, but the representational structure through which information becomes meaningful. This perspective also differs from purely revolutionary accounts of scientific change. TBER does not assume abrupt replacement of one representation by another. Multiple representational levels may coexist 6

simultaneously. Observable variables, latent spaces, predictive models, and world models can all remain useful within different explanatory domains. Representational emergence therefore produces stratification rather than simple substitution. A consequence of this view is that representational evolution has no obvious final stage. Every representational level possesses a finite explanatory domain. As observations expand and questions evolve, new insufficiencies may appear. The bootstrap process is therefore potentially open-ended. Each representational solution generates new observational possibilities, which may eventually expose further limitations. This recursive structure is particularly relevant for artificial intelligence. Contemporary systems are increasingly capable of constructing internal representations, latent spaces, and predictive models. However, most current architectures lack explicit mechanisms for identifying the explanatory limits of their own representations. They can learn representations, but they generally do not determine autonomously when an entirely new representational level becomes necessary. From the perspective of TBER, truly adaptive representational systems would require two complementary capacities. First, they must be able to construct representations that organize observations. Second, they must be able to detect explanatory insufficiencies that indicate when those representations have reached their limits. Representational intelligence would therefore involve not only learning within a representation, but also recognizing when a transition to a new representation is required. The bootstrap principle provides the conceptual foundation for this view. It transforms explanatory insufficiency from a sign of failure into a mechanism of representational evolution. In doing so, it offers a general framework for understanding how scientific knowledge, adaptive biological systems, and artificial intelligence systems may progressively generate new levels of representation. The next section formalizes this process through a five-stage model of representational transition.

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A Five-Stage Model of Representational Transition

The bootstrap principle describes the general mechanism through which representational systems evolve. To make this process operational, TBER proposes a five-stage model that characterizes the transition from one representational level to another. The model is intended as a conceptual framework rather than a deterministic law. Its purpose is to identify recurrent stages that appear across scientific discovery, adaptive biological systems, and artificial intelligence. The proposed sequence consists of five stages: 1. Stabilized Observation 2. Anomaly Detection 3. Recognition of Explanatory Insufficiency 4. Representational Emergence 5. Provisional Stabilization Together, these stages describe the recursive cycle through which representational systems evolve.

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5.1

Stage 1: Stabilized Observation

The process begins with a stabilized representational framework. At this stage, observations are organized according to an accepted set of concepts, variables, models, or representations. The framework successfully describes relevant phenomena and provides a coherent basis for interpretation. Stabilization does not imply completeness. Rather, it indicates that the representation is sufficiently effective within its current explanatory domain. Scientific communities, biological systems, and machine learning models all require periods of stability during which observations can accumulate and practical applications can develop. Examples include classical biomechanical performance metrics, latent representations used for classification tasks, established biological taxonomies, or predictive models that operate reliably within a defined domain.

5.2

Stage 2: Anomaly Detection

As observations accumulate, certain phenomena may appear that are difficult to reconcile with the existing framework. These anomalies may take many forms: unexpected observations, unexplained variability, contradictory results, instability under changing conditions, or systematic prediction errors. An anomaly does not immediately invalidate a representation. Many anomalies can be accommodated through local corrections or refinements. Nevertheless, anomalies play a crucial role because they reveal regions where explanatory coherence becomes fragile. In scientific history, anomalies have often preceded major representational transitions. In machine learning, analogous situations arise when learned representations fail under distribution shifts, when latent spaces fail to capture relevant transformations, or when predictive performance deteriorates despite increasing model complexity.

5.3

Stage 3: Recognition of Explanatory Insufficiency

The third stage constitutes the critical transition point of TBER. Here, anomalies cease to be interpreted as isolated irregularities and begin to be recognized as indicators of a deeper representational limitation. At this stage, the problem is no longer whether a particular observation is unusual, but whether the representational framework itself is capable of making the observation intelligible. The system encounters explanatory insufficiency. Importantly, the existing representation may remain useful and partially correct. The issue is not necessarily falsification. Instead, the explanatory domain of the representation has been exceeded. The framework can still describe observations but cannot satisfactorily explain the relations, transformations, or organizational structures that generate them. This recognition transforms insufficiency into an epistemic signal. The question shifts from correcting the representation to determining whether a new representational level is required.

5.4

Stage 4: Representational Emergence

Once explanatory insufficiency has been recognized, a new representational framework may emerge. This emergence is the defining event of the bootstrap process.

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The new representation introduces concepts, variables, relations, structures, or organizational principles that were unavailable within the previous framework. As a result, previously problematic observations become intelligible within a broader explanatory domain. Representational emergence may occur through theoretical innovation, experimental discovery, biological adaptation, or computational learning. Examples include the introduction of latent spaces beyond observable variables, world models beyond static prediction, genetic representations beyond descriptive morphology, or organizational analyses beyond aggregate performance measures. The essential feature of emergence is not novelty alone, but the capacity to reduce a previously identified explanatory insufficiency.

5.5

Stage 5: Provisional Stabilization

The new representation eventually enters a period of stabilization. Observations are reorganized according to the new framework, explanatory coherence is temporarily restored, and the representation becomes operational for investigation and application. This stabilization remains provisional. No representation possesses unlimited explanatory scope. Over time, new observations may reveal additional anomalies, initiating another cycle of representational transition. Representational evolution is therefore not a linear progression toward a final framework. It is an open-ended process in which successive representations continuously redefine the limits of what can be observed, explained, and understood.

5.6

Recursive Dynamics

The five stages should not be interpreted as a one-time historical sequence. They constitute a recursive dynamic that can occur at multiple scales and across multiple domains. A scientific discipline may experience several representational transitions over decades. A biological system may reorganize itself repeatedly in response to environmental constraints. An artificial intelligence system may successively construct new internal representations as it encounters increasingly complex tasks. The cycle can be summarized as follows: Stabilized observations generate anomalies; anomalies reveal explanatory insufficiencies; explanatory insufficiencies motivate representational emergence; representational emergence produces a new provisional stabilization; and the cycle begins again. The significance of this model lies in its generality. It does not depend on a specific scientific domain, learning algorithm, or biological mechanism. Instead, it describes a common structure underlying representational change itself. The following sections examine how this framework relates to existing theories of knowledge, representation learning, adaptive systems, and artificial intelligence.

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6

Relation to Existing Epistemological and Computational Frameworks

The Bootstrap Theory of Representational Emergence (TBER) does not seek to replace existing theories of knowledge, learning, or adaptation. Instead, it proposes a unifying framework for understanding the conditions under which new representational levels become necessary. In this respect, TBER intersects with several traditions in epistemology, complex systems theory, biology, and artificial intelligence while addressing a question that remains comparatively underdeveloped: the emergence of representations themselves.

6.1

Scientific Discovery and Epistemological Rupture

The role of explanatory insufficiency in TBER shares certain affinities with classical theories of scientific discovery. Peirce emphasized the importance of surprising observations in triggering abductive reasoning and hypothesis formation [1]. From this perspective, scientific progress begins when observations resist integration into existing explanatory frameworks. Bachelard similarly argued that scientific development proceeds through the overcoming of epistemological obstacles rather than through simple accumulation of facts [2]. Scientific progress therefore requires transformations in the conditions of intelligibility themselves. TBER extends this insight by focusing not on conceptual obstacles alone but on the emergence of new representational levels capable of resolving explanatory insufficiencies. Foucault’s analyses of epistemes and discursive formations likewise emphasized that knowledge is structured by historically contingent conditions of possibility [5, 6]. While TBER does not adopt a historical approach, it shares the view that observations are inseparable from the representational frameworks through which they become intelligible.

6.2

Biological Adaptation and Organizational Change

TBER also relates to biological theories that emphasize organization rather than isolated components. Varela’s theory of biological autonomy described living systems as self-producing organizations whose identity emerges through recursive processes of self-maintenance [8]. Similarly, Kauffman emphasized the role of self-organization in the emergence of biological complexity [10]. Within these frameworks, adaptation cannot be reduced to local adjustments of isolated variables. Instead, adaptive systems often undergo organizational transitions that create new modes of interaction with their environment. TBER interprets such transitions as representational events in which previously sufficient organizational frameworks become incapable of accommodating emerging constraints. The distinction between observable performance and organizational viability explored in recent studies of adaptive biological systems provides an example of this phenomenon [22, 23, 24, 25]. Observable outcomes may remain stable while significant transformations occur at deeper organizational levels. Such situations illustrate how explanatory insufficiency may emerge despite apparent descriptive adequacy.

6.3

Complex Systems and Self-Organization

The theory also shares common ground with approaches to self-organization and coordination dynamics. Kelso’s work on dynamic patterns demonstrated how collective behaviors emerge from interactions among system components without requiring centralized control [11]. Newell’s constraints-based approach similarly emphasized the role of interacting constraints in shaping behavior and organization [12]. 10

These perspectives highlight the importance of emergent organization. However, they generally focus on how organizational states arise rather than on how new representational frameworks emerge to describe and explain those states. TBER complements these approaches by examining the epistemic transitions that accompany organizational change.

6.4

Representation Learning and Machine Learning

The strongest contemporary connection of TBER lies within representation learning. Bengio and colleagues described representation learning as the process through which systems discover useful internal structures that facilitate prediction, classification, and generalization [14]. Representation learning has become one of the foundational paradigms of modern machine learning. Nevertheless, representation learning primarily addresses how representations are constructed and optimized. TBER addresses a different question: under what conditions does a new representational level become necessary? From this perspective, latent spaces, embeddings, and learned representations can be interpreted as responses to explanatory insufficiencies encountered at previous representational levels. The emergence of latent representations reflects the recognition that observable variables alone may be insufficient for capturing relevant structures within the data.

6.5

Foundation Models and World Models

Recent developments in artificial intelligence provide particularly relevant examples. Foundation models have demonstrated that large-scale representations trained across diverse domains can support remarkable transfer capabilities [15]. World models extend this idea by constructing internal representations capable of simulating possible future states and environmental dynamics [16]. These advances may be interpreted through the lens of TBER as representational transitions motivated by the limitations of earlier approaches. Feature-based systems became insufficient for capturing complex relational structures. Static predictive models became insufficient for representing transformations across time. World models emerged in response to the need for richer internal representations capable of supporting planning, simulation, and adaptation. TBER does not claim that these developments were explicitly guided by explanatory insufficiency. Rather, it proposes that explanatory insufficiency provides a coherent interpretation of why such transitions became necessary.

6.6

Autonomous Machine Intelligence

LeCun has argued that future artificial intelligence systems will require world models, predictive capabilities, and mechanisms for planning and reasoning in complex environments [17]. These developments move beyond static representation learning toward systems capable of constructing increasingly sophisticated internal models. TBER extends this trajectory one step further. If artificial systems are to become genuinely adaptive at the representational level, they may require mechanisms for detecting the explanatory limitations of their own internal representations. Such systems would not merely learn within existing representational frameworks. They would also recognize when those frameworks become insufficient and initiate representational transitions autonomously.

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This possibility constitutes one of the principal implications of TBER. The theory suggests that future advances in artificial intelligence may depend not only on better representations, but also on mechanisms capable of identifying when new representations are required.

6.7

A Distinct Contribution

The originality of TBER lies in the fact that it does not primarily explain learning, adaptation, selforganization, or scientific discovery. Instead, it focuses on the emergence of representational levels themselves. Existing frameworks explain how systems learn, organize, predict, adapt, or evolve. TBER addresses a complementary question: What makes a representational transition necessary? This question places TBER at a meta-representational level. The theory does not compete with representation learning methods, foundation-model architectures, world-model approaches, or theories of scientific discovery. Rather, it provides a framework for interpreting the transitions between representational levels when existing representations remain useful but become explanatorily insufficient. Its answer is that representational emergence is driven by explanatory insufficiency. New representations arise when existing frameworks can no longer make observations, relations, transformations, or organizational structures sufficiently intelligible. In this sense, explanatory insufficiency becomes the engine of representational evolution.

7 Implications for Representation Learning, Foundation Models, and Autonomous Artificial Intelligence The preceding sections introduced TBER as a general theory of representational transitions driven by explanatory insufficiency. This section examines its implications for contemporary machine learning and artificial intelligence. While the theory was not developed from a specific computational architecture, it offers a conceptual framework for interpreting several major trends in modern AI, including representation learning, latent-space construction, foundation models, world models, and autonomous machine intelligence.

7.1

Representation Learning as a Sequence of Representational Transitions

Representation learning is typically described as the process through which a system discovers internal structures that facilitate prediction, classification, generation, or decision-making [14]. From the perspective of TBER, representation learning can also be interpreted as a succession of responses to explanatory insufficiencies. Early machine learning systems relied heavily on handcrafted features. These representations proved effective within restricted domains but became increasingly insufficient as tasks grew in complexity. Learned embeddings emerged because manually engineered representations could not adequately capture the relational structures present in large datasets. Similarly, latent representations emerged because observable variables alone often failed to reveal the organizational regularities underlying complex phenomena. The transition toward latent spaces can 12

therefore be interpreted as a response to the explanatory insufficiency of purely observable descriptions. This perspective suggests that representational progress in machine learning is not merely the accumulation of more powerful representations. Rather, it consists of a sequence of transitions motivated by the limitations of previous representational frameworks.

7.2

Latent Spaces as Intermediate Representational Levels

Latent spaces occupy a particularly important position within TBER. They illustrate how a new representational level may emerge when observable variables become insufficient for capturing relevant structure. A latent space does not simply compress information. It reorganizes observations according to relations that are not directly visible in the original data. In many applications, latent variables provide a more coherent representation of similarity, transformation, and organization than the observable variables from which they are derived. However, latent spaces themselves possess finite explanatory domains. A latent representation may successfully organize observations while remaining insufficient for modeling temporal evolution, causal structure, counterfactual reasoning, or long-term planning. The success of latent spaces therefore does not eliminate the possibility of further representational transitions. From the perspective of TBER, latent spaces should be viewed as intermediate representational levels rather than final explanatory frameworks.

7.3

Foundation Models and Representational Generalization

The emergence of foundation models provides a particularly striking example of representational transition [15]. These models extend the concept of representation beyond task-specific learning by constructing large-scale representational structures capable of supporting transfer across multiple domains. Foundation models may be interpreted as a response to the explanatory insufficiency of narrowly specialized representations. Traditional models often achieved high performance within specific tasks while failing to generalize beyond them. Larger and more general representational frameworks emerged because existing representations could not adequately support broad transfer and adaptation. From the perspective of TBER, foundation models illustrate how explanatory insufficiencies may become visible at the level of task generalization. The transition toward increasingly general representations can be interpreted as an attempt to resolve these limitations. Nevertheless, foundation models do not eliminate representational insufficiency. They may reduce certain explanatory gaps while revealing others, including limitations related to reasoning, planning, causal inference, interpretability, and autonomous adaptation.

7.4

World Models and Internal Simulation

World models represent a further representational transition [16]. Instead of merely encoding observations, they attempt to model the dynamics that generate those observations. Their objective is not only to represent states, but also to represent possible transformations between states. Within TBER, world models emerge because static representations become insufficient for explaining temporal evolution. Prediction alone may be inadequate when a system must simulate alternative futures,

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evaluate hypothetical actions, or reason about long-term consequences. World models therefore extend representational scope from description to simulation. They provide richer explanatory structures capable of integrating observations across time. Yet they too remain provisional. A world model may represent transformations without explicitly recognizing the limits of its own representational assumptions. This observation leads naturally to the next stage of representational evolution.

7.5

Toward Autonomous Representational Systems

Most contemporary AI systems are capable of learning representations. Some are capable of constructing latent spaces, world models, and increasingly sophisticated internal structures. However, these systems generally lack explicit mechanisms for determining when their own representations have become explanatorily insufficient. Current systems learn within a representational framework. They rarely evaluate the adequacy of the framework itself. TBER suggests that a possible direction for artificial intelligence is the development of systems capable of identifying the explanatory limits of their own representations. Such systems would not merely optimize existing representations. They would also recognize when new representational levels become necessary. At a conceptual level, such a capability could involve at least three components: 1. Detection of persistent explanatory anomalies. 2. Recognition that these anomalies reflect representational rather than parametric limitations. 3. Construction of new representational frameworks capable of reducing the identified insufficiency. The transition from learning representations to generating representations constitutes one of the most significant implications of TBER.

7.6

Autonomous Scientific Discovery

The same principle applies to scientific discovery. Most scientific models operate within predefined representational frameworks. Scientific progress often occurs when observations expose limitations that cannot be resolved through parameter adjustment alone. TBER suggests that future systems for autonomous scientific discovery may require explicit mechanisms for identifying explanatory insufficiencies. Rather than merely searching for better solutions within a fixed representational space, such systems could explore the emergence of new representational levels. From this perspective, scientific creativity may be interpreted as a special case of representational emergence. The discovery of a new scientific framework corresponds to the construction of a representation capable of resolving previously persistent explanatory insufficiencies.

7.7

Representational Intelligence

These considerations lead to a broader concept that may be termed representational intelligence. Traditional machine learning focuses primarily on learning within representations. Representational intelligence would additionally involve the capacity to evaluate, transform, and replace representations when necessary. 14

Such a capability would not eliminate the need for learning, optimization, or prediction. Rather, it would operate at a higher organizational level. The system would become capable of reasoning not only about observations, but also about the adequacy of the representational structures through which those observations are interpreted. In this sense, representational intelligence may constitute a necessary component of future autonomous systems. The capacity to detect explanatory insufficiency and initiate representational transitions could become as important as the capacity to learn within an existing representational framework. The next section examines adaptive biological systems as a natural domain in which representational transitions can be observed and studied empirically.

8 Adaptive Biological Systems as a Domain of Representational Emergence While TBER is intended as a general theory of representational transitions, adaptive biological systems provide a particularly informative domain for examining its principles. Biological systems continuously face changing environmental conditions, internal perturbations, developmental transformations, and functional constraints. Their capacity to remain viable often depends on organizational adaptations that cannot be fully understood through static descriptions alone. From the perspective of TBER, biological adaptation is not merely a process of parameter adjustment. In many situations, adaptation involves transitions between organizational states that alter the relationships among components, constraints, and functions. These transitions frequently reveal the limitations of existing representational frameworks and motivate the emergence of new ones.

8.1

The Limits of Observable Performance

A central difficulty in the study of adaptive systems is that observable performance does not necessarily reflect internal organization. Similar performances may emerge from distinct organizational states, and conversely, substantial organizational transformations may occur while observable performance remains relatively stable. This problem has long been recognized in biology and physiology. Canguilhem argued that health and pathology cannot be understood solely through quantitative deviations from a norm [3, 4]. Living systems continually redefine their own norms in response to environmental and internal constraints. What appears stable at the observational level may therefore conceal important adaptive reorganizations. The same phenomenon appears in motor behavior. Identical behavioral outcomes may be produced through different coordination strategies, compensatory mechanisms, or organizational structures [11, 12]. Consequently, observable performance alone may provide an incomplete description of adaptive dynamics. Within TBER, such situations represent potential cases of explanatory insufficiency. A representation based exclusively on observable outcomes may remain descriptively accurate while becoming insufficient for understanding the organizational processes that generate those outcomes.

8.2

Adaptation as Organizational Reconfiguration

Biological adaptation often involves more than local correction of errors. Living systems may reorganize interactions among components, redistribute functional roles, modify coordination patterns, or exploit previously unused degrees of freedom.

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Varela’s concept of biological autonomy emphasizes that living systems maintain their identity through recursive organizational processes rather than through fixed structures [8]. Similarly, Kauffman’s work on self-organization suggests that biological complexity emerges through dynamic interactions among system components rather than through externally imposed designs [10]. From the perspective of TBER, such reorganizations may be interpreted as transitions between representational levels. A previously sufficient organizational description becomes incapable of accounting for emerging adaptive behaviors. New representational frameworks are then required to make these behaviors intelligible. Importantly, the new representation does not necessarily invalidate the previous one. Observable descriptions remain useful, but they become embedded within a broader framework capable of representing organizational dynamics.

8.3

Viability as an Emergent Representational Level

Recent investigations of adaptive locomotor systems provide a useful illustration of this process [22, 23, 24, 25]. Initial analyses focused primarily on observable performance metrics. These representations successfully ranked conditions according to measured outcomes and provided useful descriptive information. However, subsequent analyses revealed situations in which comparable performance scores corresponded to distinct organizational states. This observation generated an explanatory insufficiency: performance alone could not fully account for the adaptive organization of the system. The introduction of viability as an additional representational level emerged as a response to this insufficiency. Rather than describing only observed outcomes, viability incorporated organizational stability, adaptive flexibility, and the capacity of the system to maintain coherent functioning under varying constraints. From the perspective of TBER, this transition illustrates the bootstrap mechanism. Observable performance generated observations that exposed its own explanatory limitations. These limitations motivated the emergence of a broader representational framework centered on viability. The new representation subsequently generated new observations and new questions concerning internal organization. The significance of this example does not lie in the specific domain of locomotor analysis. Rather, it illustrates a general principle: representational emergence often occurs when an existing framework remains descriptively useful but becomes insufficient for explaining organizational phenomena.

8.4

Biological Systems as Natural Laboratories of Representational Transition

Adaptive biological systems provide particularly valuable environments for studying representational emergence because they continuously generate organizational novelty. Evolution, development, learning, adaptation, and compensation all create situations in which existing representations may become insufficient. These systems therefore function as natural laboratories of representational transition. Observations reveal anomalies; anomalies expose explanatory limitations; new representations emerge; and these representations reveal previously invisible dimensions of organization. From this perspective, biological adaptation and scientific discovery exhibit a common structure. Both involve recursive interactions between observation, explanatory insufficiency, and representational emergence.

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8.5

Toward a General Theory of Adaptive Representation

The relevance of adaptive biological systems extends beyond biology itself. Many artificial systems increasingly display adaptive properties, including learning, self-organization, planning, and environmental interaction. As these systems become more complex, they may encounter representational limitations analogous to those observed in biological systems. The study of adaptive biological organization therefore provides valuable insight into future forms of artificial intelligence. Biological systems demonstrate that successful adaptation often depends not only on optimizing existing representations but also on generating new representational frameworks when existing ones become insufficient. This observation supports the central claim of TBER: representational evolution is not an exceptional event occurring only in scientific revolutions. It is a recurrent process observable wherever complex adaptive systems encounter the limits of their current modes of intelligibility. The next section examines the empirical trajectory that motivated the development of TBER and illustrates how successive representational transitions emerged from attempts to understand adaptive locomotor organization.

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The Founding Empirical Trajectory: From Performance to Viability

The Bootstrap Theory of Representational Emergence did not originate from a purely philosophical reflection. It emerged from a sequence of empirical investigations conducted on adaptive locomotor systems, where successive explanatory insufficiencies progressively motivated the introduction of new representational levels [22, 23, 24, 25]. The initial objective of these studies was straightforward: to compare experimental locomotor conditions using aggregated biomechanical performance metrics. Observable variables derived from gait measurements were combined into global performance scores capable of ranking different experimental conditions according to their apparent effectiveness. At this first stage, the representational framework appeared satisfactory. Performance scores provided a coherent descriptive summary of the observed data and allowed comparisons across experimental conditions. The representation corresponded to what TBER identifies as a stabilized observational framework. However, further analyses progressively revealed a first explanatory insufficiency. Different experimental conditions occasionally produced similar global performance scores while exhibiting distinct biomechanical organizations. The observable ranking remained informative, but it no longer appeared sufficient for understanding the internal structure of locomotor adaptation [22]. This observation motivated the introduction of a second representational level focused on organization rather than performance alone. The resulting analyses demonstrated that comparable observable outcomes could emerge from different organizational states. The explanatory target therefore shifted from performance measurement to organizational characterization [22]. The introduction of organizational descriptors resolved part of the insufficiency, but generated new questions. Some organizational states appeared more stable than others despite producing similar observable outcomes. The distinction between organization and organizational persistence could not be fully represented within the existing framework. A second explanatory insufficiency therefore emerged. This limitation motivated the introduction of a

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third representational level centered on viability. Rather than describing only performance or organization, viability sought to characterize the capacity of a locomotor system to maintain coherent functioning under varying constraints [23]. The viability framework improved explanatory coherence but revealed an additional limitation. Systems exhibiting similar viability profiles could still differ in their internal structure. This observation suggested the existence of hidden organizational variables that were not directly accessible through observable measurements. To address this problem, subsequent analyses introduced latent-space representations [24]. Latent variables provided a means of approximating internal organizational structure from observable locomotor data. This transition represented another representational emergence motivated by explanatory insufficiency. The latent-space analyses revealed yet another limitation. Although latent representations captured previously inaccessible organizational information, they remained primarily descriptive. They provided an approximation of internal organization but did not explicitly explain why successive representational transitions had become necessary. This final insufficiency motivated the development of the bootstrap framework itself [25]. The question shifted from identifying latent organizational states to understanding the mechanism through which new representational levels emerge. The resulting theoretical formulation became the Bootstrap Theory of Representational Emergence. From the perspective of TBER, this empirical trajectory illustrates a complete representational cycle. Observable performance generated organizational questions. Organizational analyses generated viability questions. Viability analyses generated latent-space representations. Latent-space analyses generated questions concerning representational emergence itself. The significance of this trajectory extends beyond the specific domain of locomotor analysis. Its value lies in demonstrating that representational emergence can be observed empirically as a sequence of responses to explanatory insufficiencies. The successive representational levels were not introduced because they were technically available, but because previous levels became incapable of providing satisfactory explanations for newly observed phenomena. In this sense, the empirical trajectory provides a concrete illustration of the central claim of TBER: representational evolution is driven by explanatory insufficiency. New representational levels emerge when existing frameworks remain descriptively useful but become insufficient for understanding the organization, dynamics, or viability of the systems they describe.

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Discussion: Originality, Scope, and Limitations of TBER

The Bootstrap Theory of Representational Emergence proposes a framework for understanding representational transitions across scientific inquiry, adaptive biological systems, and artificial intelligence. Its central claim is that new representational levels emerge when existing representations become explanatorily insufficient. This perspective shifts attention from the optimization of representations to the conditions that make representational change necessary.

10.1

From Representation Learning to Representational Emergence

A first contribution of TBER is the distinction between representation learning and representational emergence.

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Most contemporary machine learning research focuses on learning increasingly effective representations from data [14]. The objective is to improve predictive performance, generalization, compression, transferability, or simulation. These approaches successfully explain how representations can be optimized. TBER addresses a different problem. Rather than asking how a representation is learned, it asks why a new representational level becomes necessary. The theory therefore operates at a higher epistemic level than conventional representation learning. It concerns transitions between representational frameworks rather than learning within a fixed framework. This distinction may become increasingly relevant as artificial intelligence systems evolve toward greater autonomy. Learning within a representation and generating a new representation may ultimately constitute distinct forms of intelligence.

10.2

Explanatory Insufficiency as a Positive Signal

A second contribution concerns the interpretation of insufficiency itself. In many scientific and engineering contexts, insufficiency is viewed primarily as a failure. Prediction errors, anomalies, and inconsistencies are often treated as problems to be minimized or eliminated. TBER proposes a different interpretation. Explanatory insufficiency is viewed as a positive epistemic signal indicating that a representational framework has reached the limits of its explanatory domain. The significance of insufficiency lies not in the failure itself, but in the information it provides concerning the boundaries of the current representation. This perspective transforms explanatory limits into drivers of representational innovation. What cannot be explained becomes an indicator of where new representational possibilities may emerge.

10.3

A General Framework Across Domains

A third contribution is the generality of the framework. The bootstrap process described by TBER does not depend on a specific scientific discipline, computational architecture, or biological mechanism. Similar representational transitions can be identified in scientific revolutions, adaptive biological systems, machine learning, digital health, and complex systems research. The theory therefore proposes a common interpretative structure linking phenomena that are usually studied independently. Scientific discovery, biological adaptation, and representational learning may differ in their mechanisms, but they appear to share a common logic of transition driven by explanatory insufficiency. This generality represents both a strength and a challenge. A broad framework may reveal common structures across domains, but it also requires careful empirical validation within each domain.

10.4

Relationship to Existing Theories

TBER should not be interpreted as a replacement for existing theories of learning, adaptation, selforganization, or scientific change. The theory complements rather than competes with these frameworks. Representation learning explains how representations are acquired. Self-organization explains how collective structures emerge. Viability theory explains how systems maintain acceptable trajectories under constraints. Scientific epistemology explains how knowledge evolves. 19

TBER addresses a distinct question: how and why new representational levels emerge when existing ones become insufficient. The theory is therefore best understood as a meta-representational framework that operates above individual explanatory models.

10.5

Limitations

Several limitations should be acknowledged. First, TBER is currently a conceptual theory rather than a formal mathematical model. Consequently, the present article should not be read as proposing an implementable machine-learning method. It defines a theoretical criterion for interpreting representational transitions, not an operational pipeline for detecting or generating them automatically. Although the five-stage transition framework provides a structured description of representational emergence, the theory does not yet specify quantitative criteria for detecting explanatory insufficiency. Second, the empirical trajectory that motivated the theory originates from a specific domain involving adaptive locomotor systems [22, 23, 24, 25]. While the proposed framework appears applicable beyond this domain, broader empirical validation remains necessary. Third, explanatory insufficiency may be difficult to operationalize. In practice, the distinction between a correctable anomaly and a genuine representational limitation may not always be clear. Future work will need to develop criteria capable of distinguishing these situations more rigorously. Fourth, the theory does not claim that all representational transitions follow exactly the same pathway. Real systems may exhibit overlapping transitions, partial reorganizations, or hybrid representational structures that do not fit neatly into the five-stage model.

10.6

Toward a Science of Representational Transitions

Despite these limitations, TBER suggests that representational emergence itself may constitute a legitimate object of scientific investigation. Scientific inquiry has traditionally focused on observations, hypotheses, models, mechanisms, and predictions. TBER proposes that transitions between representational levels deserve comparable attention. If explanatory insufficiency can be identified, characterized, and eventually formalized, representational emergence may become accessible to systematic investigation. Such a development would have implications not only for epistemology and complex systems research, but also for the design of future artificial intelligence systems capable of autonomous representational evolution. From this perspective, TBER should be viewed as an initial step toward a broader science of representational transitions.

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Future Directions and Conclusion

TBER opens several directions for future research in machine learning, artificial intelligence, adaptive systems, and the philosophy of scientific modeling. Its central proposition is that representational systems evolve when explanatory insufficiencies reveal the limits of existing frameworks. If this proposition is valid, then future work should not only design better representations, but also develop methods for detecting when a representation has become insufficient. 20

11.1

Operationalizing Explanatory Insufficiency

A first direction concerns the operational definition of explanatory insufficiency. In its current form, the concept is theoretical. Future work should investigate whether explanatory insufficiency can be associated with measurable indicators such as persistent prediction failure, instability under distribution shift, loss of transferability, mismatch between latent organization and observed behavior, or inability to represent temporal transformations. Such indicators would make it possible to distinguish ordinary model error from genuine representational limitation. This distinction is essential if TBER is to become useful for computational systems capable of monitoring the adequacy of their own representations.

11.2

Toward Autonomous Representational Evolution

A second direction concerns artificial intelligence systems capable of autonomous representational evolution. Current machine learning systems can learn powerful representations, but they usually do so within predefined architectural and representational constraints. They rarely determine for themselves when a new representational level is required. TBER suggests that future systems may need explicit mechanisms for detecting explanatory insufficiencies and generating new representational frameworks in response. Such systems would move beyond representation learning toward representational self-transformation. This capacity could play an important role in autonomous scientific discovery, continual learning, open-ended learning, and adaptive world-model construction.

11.3

Applications to Scientific Discovery

A third direction concerns scientific discovery. Many scientific breakthroughs can be interpreted as representational transitions triggered by explanatory insufficiencies. Future work could apply TBER retrospectively to historical cases in physics, biology, neuroscience, and medicine in order to determine whether the five-stage transition model captures recurring patterns of representational change. Such analyses could clarify whether explanatory insufficiency is merely a useful metaphor or a more general mechanism underlying scientific progress.

11.4

Applications to Adaptive Biological Systems

A fourth direction concerns adaptive biological systems. Biological systems provide a rich empirical domain because they continuously reorganize under internal and external constraints. Locomotion, posture, development, neuroplasticity, pathology, and rehabilitation all involve situations in which observable performance may fail to reveal underlying organization. Further studies could investigate whether transitions from performance metrics to organizational descriptors, latent representations, viability analysis, and predictive approximation follow the bootstrap sequence proposed in this article.

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11.5

Conclusion

This article introduced the Bootstrap Theory of Representational Emergence as a framework for understanding how new levels of representation become necessary. The theory proposes that representational transitions are driven by explanatory insufficiency: the situation in which an existing representation remains descriptively useful but can no longer make certain observations, relations, transformations, or organizational structures intelligible. TBER describes this process as a recursive bootstrap dynamic. Stabilized representations generate observations; observations reveal anomalies; anomalies expose explanatory insufficiencies; insufficiencies motivate representational emergence; and new representations create provisional stabilizations that may later reveal further limitations. The framework provides a common interpretation of representation learning, latent spaces, foundation models, world models, digital twins, adaptive biological systems, and scientific discovery. Its contribution is theoretical rather than algorithmic: it does not propose a new model architecture, but a way to understand why new representational levels emerge. The central implication is that future intelligent systems may benefit from more than the ability to learn within existing representations. They may also benefit from the ability to recognize the limits of their own representations and generate new ones when those limits become explanatory obstacles. In this sense, explanatory insufficiency should not be regarded merely as a failure of representation. It may be the very mechanism through which representation evolves. This trajectory also provides the conceptual basis for later representation-aware reasoning frameworks, in which the central task is not to produce a direct conclusion, but to determine whether the current representational level is sufficient for the problem under consideration.

Author Contributions Jacques Raynal conceived the Bootstrap Theory of Representational Emergence (TBER), developed the theoretical framework, synthesized the empirical trajectory underlying the theory, and wrote the original manuscript. Pierre Slangen contributed to the conceptual development of the framework, participated in the interpretation of the representational transitions described in the manuscript, and critically revised the text. Elsa Raynal contributed to the conceptual discussion of adaptive systems and representational emergence and revised the manuscript. Jacques Margerit contributed to the scientific supervision of the project, theoretical validation of the framework, and critical revision of the manuscript. All authors approved the final manuscript.

Funding No external funding was received for this work.

Conflicts of Interest The authors declare no conflict of interest. 22

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