Patrick-Olivier Dieu

Scientific knowledge is often discussed in terms of its relation to reality, truth, and empirical success. Less attention is given to the role played by the cognitive constraints of the systems that produce scientific knowledge in the first place. This paper examines the possibility that scientific representation is shaped not only by the structure of the world but also by the structural limitations and capacities of finite cognitive agents. Rather than treating cognitive constraints solely as obstacles to knowledge, the paper argues that they participate in the formation of scientific practices themselves. Measurement, mathematical formalization, and scientific modeling can be understood as cognitive extensions that allow finite agents to stabilize, compare, and manipulate representations beyond the limits of unaided cognition. The paper further examines a recurrent epistemological tension: the tendency to treat highly successful representational models as direct access to reality itself. While descriptive success provides strong practical and predictive justification for the use of a model, it does not automatically resolve questions concerning the ontological status of what the model represents. The central question motivating the discussion is therefore: to what extent does the descriptive success of a representational model justify treating it as access to reality itself? Rather than offering a definitive answer, the paper proposes a conceptual framework for examining how cognitive constraints, measurement practices, and representational success jointly shape the formation and interpretation of scientific knowledge.

This paper examines a simple but often overlooked consequence of a physical view of cognition. If the human brain is a finite physical system operating under universal physical constraints, and if cognitive capacities emerge from the organization of this system, then claims of principled irreproducibility of intelligence require additional justification. The argument developed here does not assume the inevitability of artificial general intelligence, artificial consciousness, or superintelligence. Instead, it focuses on a more minimal question: whether any known physical principle currently supports the view that human intelligence possesses a fundamentally non-reproducible status. By distinguishing physical implementation from functional organization, the paper argues that intelligence should be treated as a physically instantiated phenomenon whose reproducibility remains an open empirical question rather than an impossibility of principle. The objective is not to predict future technological developments, but to clarify the burden of proof surrounding claims of human cognitive exceptionalism within a physically constrained universe.

This paper proposes a minimal reformulation of representation viability in finite cognitive and computational systems. Earlier formulations within this research program relied on the notion of stabilization. However, stabilization risks introducing static, reified, or overly global interpretations that obscure the dynamic nature of representational organization. The present work replaces stabilization with the more minimal and operational notion of persistence under transformation in time. Rather than asking whether representations become globally stable, the framework investigates whether representational structures remain sufficiently persistent under transformation, perturbation, and temporal evolution. Three minimal dynamic quantities are introduced: representational accumulation, transformation-relative persistence, and accumulation–persistence coupling. The central claim is that accumulation alone does not imply persistence under transformation. This distinction allows the framework to separate systems that merely accumulate internal structure from systems whose representational organization remains dynamically viable under perturbation. The proposed framework is intentionally minimal and non-ontological. It does not posit a universal principle of stabilization, nor a theory of consciousness or ultimate physical reality. Instead, it provides a compact dynamic framework for studying representational persistence in finite systems under transformation and temporal constraints.

This paper proposes a minimal distinction between raw representational accumulation and stabilization-capable reorganization in learned systems. Contemporary learning systems can accumulate parameters, internal representations, and task-specific structures while remaining dynamically fragile under perturbation, distribution shift, or continual adaptation. This suggests that accumulation alone may not sufficiently explain the emergence of transformation-viable representational persistence. The paper introduces the distinction between: (i) raw accumulation, understood as the growth of internal representational structure without guaranteed persistence under transformation, and (ii) stabilizing accumulation, understood as forms of reorganization associated with increased persistence, coherence, and viability under perturbation. Rather than proposing a general theory of cognition or intelligence, the paper isolates this distinction as a minimal experimentally tractable problem within representation learning and adaptive systems. Particular attention is given to: representation drift, continual learning, stability/plasticity tensions, and the possibility that certain reorganization dynamics may contribute more strongly than simple representational growth to transformation-stable behavior. The paper concludes by suggesting that future work may investigate whether some forms of stabilizing reorganization correspond to lower transformation-cost trajectories compared to unstable or catastrophically reorganizing regimes.

This paper clarifies the conceptual and methodological evolution of a research program initially developed around finite cognition, epistemic limitation, and the structural conditions of intelligibility. The early stages of the program explored whether scientific knowledge should be understood not as direct access to reality, but as the stabilization of usable structures within finite cognitive systems. Initial formulations involved broad philosophical and epistemological questions concerning mathematics, scientific explanation, model selection, and the limits of representation. Over time, the program underwent a progressive process of compression and methodological reduction. Broad ontological and cosmological claims were gradually abandoned in favor of experimentally confrontable questions centered on representation stability under transformation and perturbation. This compression led to a minimal representation-centered framework focused on: stability under transformation, representational reorganization, perturbation-dependent divergence, temporal stabilization dynamics, and architecture-dependent stability regimes in learned systems. The paper reconstructs this transition and clarifies the surviving invariant structure of the program. It argues that the final framework should not be interpreted as a general theory of cognition or scientific knowledge, but rather as a minimal experimental program for studying the dynamics of learned representations under finite constraints. Particular attention is given to the distinction between static representational similarity and transformation-dependent stability, as well as to the shift from static endpoint analysis toward temporal stabilization trajectories during learning. The paper concludes by identifying possible empirical interfaces with contemporary machine learning and neuroscience, while emphasizing that such correspondences remain heuristic and experimentally open rather than theoretically established.

Recent work on learned representations has focused primarily on static observables such as geometric similarity, invariance, robustness, and final performance. However, comparatively less attention has been devoted to the temporal organization of representation reorganization during learning itself. This paper introduces a minimal measurement framework for studying dynamic stabilization trajectories in trained systems. Rather than proposing a theory of cognition or biological learning, the framework defines operational observables intended to evaluate whether representation trajectories contain reproducible structure beyond static representation metrics. We introduce a representation reorganization observable measuring local representation change between successive optimization states during learning. The framework is explicitly methodological and falsifiable: it does not assume universal scaling laws, critical phenomena, or neurobiological equivalence. The central question investigated is whether temporal stabilization trajectories contain predictive information not captured by final accuracy or static representation similarity alone. The proposed framework therefore aims to provide a controlled experimental instrument for detecting, testing, or rejecting structured stabilization behavior in learned representations.

We introduce a measurement framework for analyzing how neural representations diverge under transformations of increasing complexity. Rather than proposing a universal theory of representation learning or invariance, we define a single observable, $\Delta(c)$, which measures inter-model variance in representation stability across heterogeneous neural architectures. The framework is designed as an empirical instrument: it specifies how to measure divergence, how to control for parameterization artifacts, and how to evaluate whether regime-like structure exists in representation sensitivity. We define a transition scale $c^*$ operationally from the behavior of $\Delta(c)$ and provide a set of robustness stress-tests intended to distinguish structural effects from smooth nonlinear or metric-induced artifacts. We do not assume the existence of universal scaling laws, critical phenomena, or phase transitions. Instead, we propose a falsifiable protocol for determining whether structured divergence regimes emerge consistently across architectures, transformation families, and representation metrics. The contribution of this work is therefore methodological rather than ontological: a minimal experimental framework for detecting, testing, or rejecting the presence of structured divergence behavior in representation stability.

Recent empirical results suggest that the relationship between representation similarity and transformation-dependent stability in neural networks is structured and non-monotonic. In particular, this relationship appears to exhibit regime-dependent behavior across transformation strengths and architectures. In this paper, we do not propose a validated theory, but a candidate structural interpretation consistent with these observations. We introduce a minimal effective functional whose projections recover similarity and stability as observables, and whose curvature structure may induce regime transitions. We emphasize that this framework is not claimed to be necessary, complete, or uniquely determined. Rather, it is proposed as a possible organizing structure that could help interpret non-monotonic coupling patterns observed in representation–transformation systems.

Note—Updated and extended version of a previously published paper titled “Representation Similarity And Transformation Stability: An Empirical Study of Structural Anti-Correlation in Neural Networks.” We investigate the relationship between representation similarity and transformation-dependent stability in neural networks. While Centered Kernel Alignment (CKA) is widely used to measure representational similarity, its relationship to functional robustness under input transformations remains insufficiently understood across architectures. Across multiple experimental regimes—including architecture variation, dataset shifts, and input perturbations—we observe a statistically stable coupling between CKA and a stability metric S(M) measuring sensitivity to structured transformations. This relationship is stable under bootstrap analysis and persists across perturbation types, while exhibiting architecture-dependent sign inversion. These results suggest that representation similarity is not a sufficient predictor of transformation-dependent stability in the evaluated settings. Instead, their relationship appears structured and is consistent with a role of architectural inductive bias. We further propose a minimal structural interpretation in which this coupling depends on alignment between representation subspaces and transformation-sensitive directions.

Representation similarity metrics such as CKA are widely used to compare neural network representations across architectures and training conditions. In parallel, transformation-dependent stability measures quantify sensitivity to structured input perturbations. This work empirically investigates the relationship between these two notions. We find that representation similarity and stability exhibit a consistent positive correlation under standard evaluation conditions. However, this relationship becomes significantly weaker and more variable under structured distribution shifts. Rather than a fixed equivalence or independence, our results indicate a regime-dependent coupling between representation similarity and transformation-dependent stability. These findings suggest that representation geometry alone is insufficient to fully characterize functional stability under distributional perturbations.

Representation similarity metrics such as CKA are widely used to compare neural representations across models and layers by quantifying geometric alignment in representation space. In contrast, transformation-dependent stability functionals such as $S(M)$ characterize sensitivity to structured input perturbations. This paper provides a unified conceptual analysis of the relationship between these two notions. We first clarify their conceptual distinction and then identify the boundary conditions under which they become approximately equivalent or fundamentally decoupled. We argue that representation similarity and transformation-dependent stability capture complementary aspects of neural network behavior: one geometric, the other functional. We further clarify the status of $S(M)$ as a transformation-dependent functional and outline its basic properties. The goal of this work is not to propose a new metric, but to clarify the structural relationship between existing approaches.

We propose a minimal experimental protocol for measuring representation stability in machine learning systems under input transformations. The framework defines a stability functional $S(M)$ as the expected invariance of internal representations under stochastic perturbations. Unlike prior work that introduces theoretical or architectural modifications, this paper focuses on a reproducible evaluation procedure and includes a minimal empirical sanity check on standard vision models. The goal is not to propose a new theory of learning, but to test whether $S(M)$ behaves consistently under controlled perturbations such as noise and blur. The contribution is intentionally limited: we provide a lightweight empirical validation of the proposed functional alongside a fully reproducible evaluation protocol.

We propose a minimal empirical framework for evaluating stabilization as a measurable constraint on representations in learning systems. Building on a previously defined stabilization functional, we operationalize stabilization in terms of representational coherence under transformations induced by learning dynamics, perturbations, and re-encodings. We derive testable hypotheses in machine learning settings, including continual learning, robustness under distribution shift, and representation compression. The framework does not assume a theory of cognition or a specific architectural model, but instead investigates whether stabilization correlates systematically with robustness, compressibility, and degradation under sequential updates. The goal is to provide a falsifiable and domain-agnostic evaluation of stabilization as a structural property influencing representational viability in learning systems.

We introduce a minimal information-theoretic framework for characterizing the robustness of representations under transformations. Stabilization is defined as the expected invariance of a representation under a distribution of admissible transformations. We show that this quantity admits structural correspondences with entropy, compressibility, and mutual information, without assuming a specific model of cognition or inference. The framework isolates stabilization as a system-independent structural property of representations, intended as a general constraint applicable across different formal settings in information theory and representation learning. Rather than proposing a complete theory, the paper provides a minimal functional definition and its structural implications, while explicitly leaving empirical instantiation and domain-specific interpretation open. This allows stabilization to be treated as a candidate invariant linking robustness, compression, and information preservation across transformation processes.

This paper proposes a functional decomposition of stabilization in finite cognitive systems. Stabilization is treated as a composite property of representations involving persistence over time, predictive coherence, robustness under transformation, and compression efficiency. The framework remains conceptual and non-reductive: it does not assume a single underlying mechanism, but interprets stabilization as a multi-realized property emerging from interacting constraints on representation and cognition. By introducing operational proxies for each component, the paper outlines potential connections to cognitive science, neuroscience, and computational modeling without committing to a fully empirical model. The aim is to clarify how representational viability can be structurally characterized under cognitive constraints, providing a bridge between epistemic structure and measurable proxies.

This paper provides a higher-level consolidation of a previously developed framework on finite cognition and representational stabilization. Whereas earlier work focused on structural organization and formal decompositions of stabilization processes, the present contribution operates at a more abstract level, clarifying the general conditions under which the framework itself is intelligible and applicable. It identifies three minimal constraints—cognitive finitude, stabilization of representations, and replication across systems—as necessary conditions for the formation and persistence of scientific knowledge. Within this perspective, intelligibility is characterized by regime-dependent stability, with distinct transitions between coherent, critical, and unstable regimes under increasing informational load. The aim is not to extend the formal structure of the framework, but to clarify its global epistemic interpretation and its limits of applicability as a cognitive system-relative model of scientific knowledge.

This paper consolidates a series of works on finite cognition and stabilization into a single structured framework. It does not propose a new physical theory or a predictive model, but clarifies the conceptual organization underlying previous formulations. The central claim is that scientific representations are produced and used by finite cognitive systems subject to constraints on memory, processing capacity, and representational precision. In addition to standard criteria such as predictive accuracy and simplicity, model viability is also affected by how representations behave under transformation during use (e.g., recombination, compression, and reinterpretation). This work refers to this constraint as stabilization: the capacity of a representation to remain internally coherent and operationally usable under such transformation processes. Stabilization is not introduced as a measurable physical quantity, but as a structural constraint describing conditions under which representations remain cognitively functional. The framework distinguishes three levels of description: conceptual assumptions about finite cognition, structural relations between representational variables, and domain-dependent operational proxies. These levels are not assumed to reduce to a single formal system, but are intended to prevent conflation between conceptual structure and empirical measurement. The aim is purely integrative: to provide a consistent interpretative map of previously introduced elements and to make explicit the assumptions governing their use.

Standard approaches to model evaluation assume that representations remain stable once selected. In practice, scientific models are continuously transformed through use, reinterpretation, and integration into new contexts. This paper introduces representational stabilization as a structural constraint on model viability under finite cognitive conditions. Stabilization is defined as the capacity of a representation to maintain coherence under iterated cognitive transformations, including reformulation, compression, and contextual adaptation. A minimal dynamic perspective is proposed in which representations are treated as trajectories subject to transformation and perturbation. Stability is then interpreted as resistance to representational drift over time rather than as a static property. The framework is intentionally under-specified and heuristic. Its purpose is to clarify structural dependencies between cognitive constraints, transformation dynamics, and model usability, rather than to provide a complete formal theory.

This paper extends Finite Cognition and Model Selection: An Operational Framework for Stabilization by explicitly incorporating cognitive fragility and biological processing lag (T_bio) into a generalized stabilization framework. Stabilization is formalized as a balance between Negentropy (structural coherence, redundancy, knowledge integration) and Entropy (information load, cognitive strain, perturbations, information flux), with operational proxies provided for simulation and minimal testing. While the formulation is abstract and partly symbolic, all limitations—including linearity assumptions, weight calibration, and simplifications—are explicitly acknowledged, providing a transparent, reproducible, and conceptually rigorous foundation for studying finite cognition across domains such as AI, scientific modeling, and cognitive systems. This framework allows the reader to evaluate representational viability under bounded cognition, even in the absence of full empirical calibration.

Model selection frameworks such as Bayesian inference and Minimum Description Length (MDL) assume that candidate models can be stably represented and manipulated. Real cognitive and computational systems, however, are finite, constrained in memory, computation, and representational fidelity. This paper operationalizes stabilization, the principle that a model must persist, transform, and integrate reliably to remain viable. We formalize stabilization as a dynamic, multi-objective function, define measurable proxies for each component, propose simulation protocols to evaluate model viability under realistic constraints, and examine cross-domain manifestations of stabilization. This framework bridges conceptual insights from finite cognition with practical model assessment, moving beyond classical error- or complexity-based selection toward a system-constrained notion of model survival and practical usability.

This paper develops a structural account of scientific knowledge grounded in the constraints of finite cognition. It argues that what is commonly taken as “knowledge of reality” is better understood as the stabilization of representations under resource limitations. Stabilization is interpreted as a form of operational negentropy: a constrained reduction of uncertainty relative to a cognitive system. The framework challenges naive realism without collapsing into relativism, and proposes that scientific models are selected and maintained based on their stability under perturbation rather than their access to an unconstrained underlying reality.

This paper proposes an empirical framework to test the hypothesis that model selection is constrained not only by empirical adequacy and formal complexity, but also by the cognitive limitations of agents. We formalize a selection functional incorporating empirical error, cognitive cost, and error severity, and derive experimentally testable predictions that diverge from standard Bayesian and Minimum Description Length (MDL) approaches. A controlled experimental protocol is outlined to evaluate whether human agents systematically deviate from purely formal optimization due to finite cognitive constraints.

Scientific knowledge depends on cognitive systems that are finite in memory, processing capacity, and representational resources. This paper proposes that the stabilization of information is a necessary structural condition for cognition and, consequently, for the emergence of scientific knowledge. Rather than treating knowledge as a direct representation of reality “as it is,” the framework characterizes it as arising from the interaction between bounded cognitive systems and structured regularities in the environment. Mathematics is interpreted as an extension of cognitive representational capabilities, while scientific models correspond to stabilized structures that can be maintained, manipulated, and communicated under constraints. The framework further analyzes the role of replication in preserving representations across time and systems, and the emergence of thresholds of intelligibility when informational complexity exceeds cognitive capacity. It is argued that amplification—through conceptual tools, instrumentation, and artificial systems—extends the range of accessible structures without removing underlying constraints. These constraints give rise to regimes in which intelligibility degrades even when formal manipulation remains possible. The paper develops a conceptual framework supported by a minimal formal model inspired by dynamical systems and information-theoretic considerations, and situates the proposal in relation to existing approaches in philosophy of science, cognitive science, and learning theory. The result is a structural account of the conditions under which scientific knowledge becomes possible, persists, and breaks down.

Scientific knowledge depends on cognitive systems that are finite in memory, attention, and representational capacity. This paper proposes that stabilization of information is a necessary condition for cognition, and therefore for the production of scientific knowledge. Mathematics is interpreted as a formal extension of cognitive capabilities, while scientific models emerge from the interaction between cognitive structures and environmental regularities. Rather than describing reality “as it is in itself,” science reflects the space of what can be stabilized, represented, and manipulated within bounded cognitive systems. The framework further analyzes thresholds of intelligibility, the role of replication in maintaining knowledge, and the effects of amplification through tools and artificial systems. While these mechanisms extend cognitive reach, they do not eliminate structural constraints. The result is a unified epistemological framework describing the conditions under which knowledge becomes possible, its limits, and the regimes in which intelligibility degrades.

This paper consolidates a conceptual framework in which cognition is understood as a finite, interaction-dependent process constrained by the stabilization and replication of information. Within this perspective, intelligibility is not a primitive property but an emergent consequence of the capacity of a system to maintain coherent internal representations under perturbations. The framework further proposes that stabilization is not purely continuous but may exhibit system-dependent threshold behaviors, marking transitions between regimes of coherent and degraded representation. While partially operationalizable, the framework remains underdetermined without formal mathematical grounding, domain-specific integration, and systematic empirical validation. The objective of this work is to present a conceptually robust formulation that delineates its own limits and defines the precise conditions under which it can be formalized, tested, and potentially integrated into existing scientific domains.

This text consolidates and unifies the author’s previously published works, providing a single, coherent framework while preserving all original contributions. This framework rigorously formalizes the conditions of finite cognition, the structural basis of knowledge, and the boundaries of scientific understanding. It situates human and artificial cognition within a shared architecture defined by stabilization, replication, and symbolic manipulation of informational patterns. By introducing the Titan Lock, which identifies the minimal conditions of intelligibility, the framework delineates the space of meaningful discourse, distinguishes formal structure from full comprehension, and highlights the structural fragility introduced by amplification of cognition. The document provides a foundation for both theoretical and empirical investigation while remaining defensible against classical critiques of dogmatism or naïve realism.

This text extends the author’s conceptual framework on finite cognition and the structural limits of knowledge by proposing concrete experimental approaches for empirical investigation. It situates human and artificial cognition within shared constraints of stabilization, replication, and symbolic manipulation of patterns. By operationalizing the Titan Lock and other core principles, the document outlines behavioral, neuroimaging, and computational experiments designed to test the boundaries of intelligibility, amplification, and saturation. These proposals provide a bridge between theory and empirical science, offering a methodologically sound way to validate or falsify key aspects of the framework without compromising its foundational rigor.

This text consolidates and unifies the author’s previously published works, providing a single, coherent framework that preserves all original contributions. The framework formalizes the structural conditions of finite cognition, the foundations of knowledge, and the boundaries of scientific understanding. It situates both human and artificial intelligence within a shared cognitive architecture defined by information stabilization, symbolic replication, and pattern manipulation. Introducing the Titan Lock, the framework delineates the minimal conditions of intelligibility, separates formal structure from full comprehension, and highlights structural fragility arising from amplification of cognition. This comprehensive approach provides a rigorous foundation for theoretical analysis, empirical investigation, cognitive science, and artificial intelligence research, remaining defensible against classical critiques of dogmatism or naïve realism.

This note strengthens a conceptual framework previously introduced, emphasizing the structural limits of cognition, the necessity of information stabilization, and the emergent properties of knowledge. By addressing potential critiques—triviality, epistemology-ontology confusion, lack of discriminative power, and non-falsifiability—it clarifies the robustness of the framework. The “Titan Lock” principle is articulated explicitly, providing a diagnostic tool for assessing the boundaries of what any finite cognitive system can stabilize, replicate, and symbolically manipulate. The framework is applicable to biological, artificial, or hypothetical cognitive agents, offering predictive and explanatory power concerning the limits of scientific and formal inquiry.

This work proposes a universal framework in which cognition itself defines the boundaries of all possible knowledge. Knowledge emerges only insofar as information can be stabilized, replicated, and symbolically manipulated within finite cognitive networks—biological, artificial, or otherwise. Scientific laws, mathematical formalisms, and theoretical models do not reveal reality as it is in itself; they formalize the traces that cognition can access. Quantum mechanics, cosmology, and extreme physics explore regimes where stabilization becomes fragile, and amplification of cognition—through technology, instruments, or artificial systems—can extend reach but also increases structural fragility and saturation of intelligibility. The framework introduces the “Titan Lock,” defining the space of all intelligibility constrained by finite cognition, stabilization, and replication. Layers of reality inaccessible to cognition remain forever outside direct comprehension, emphasizing the structural limits of understanding. By situating science and mathematics as products of cognition rather than direct mirrors of reality, this work provides a coherent, cross-disciplinary perspective on epistemic limits, reproducibility, and the formal conditions of knowledge itself.