An Axiomatic Approach to General Intelligence: SANC(E3) -- Self-organizing Active Network of Concepts with Energy E3
Daesuk Kwon, Won-gi Paeng
TL;DR
SANC($E_3$) presents an axiomatic, energy-based framework in which representational units (Gestalts) emerge under finite capacity by minimizing the composite energy $E_3 = \lambda_1 L_{\mathrm{rec}} + \lambda_2 C_{\mathrm{struct}} + \lambda_3 C_{\mathrm{update}}$. By distinguishing system anchors from emergent tokens and grounding learning in co-occurrence, association, and reconstruction, the approach derives token formation, compression-driven categories, and hierarchical organization as natural consequences. The framework unifies perception, imagination, prediction, planning, dialogue, and action through a single Gestalt-completion mechanism, with extensions to self, desire, thought, emotion, sleep, and social interaction. Forgetting and token evolution arise inevitably due to finite capacity, with thresholds dynamically tuned by energy optimization. If validated, SANC($E_3$) offers a principled path toward AGI that emphasizes autonomous token emergence, self-organization, and cross-level homogeneity rather than hand-designed vocabularies or supervised objectives.
Abstract
General intelligence must reorganize experience into internal structures that enable prediction and action under finite resources. Existing systems implicitly presuppose fixed primitive units -- tokens, subwords, pixels, or predefined sensor channels -- thereby bypassing the question of how representational units themselves emerge and stabilize. This paper proposes SANC(E3), an axiomatic framework in which representational units are not given a priori but instead arise as stable outcomes of competitive selection, reconstruction, and compression under finite activation capacity, governed by the explicit minimization of an energy functional E3. SANC(E3) draws a principled distinction between system tokens -- structural anchors such as {here, now, I} and sensory sources -- and tokens that emerge through self-organization during co-occurring events. Five core axioms formalize finite capacity, association from co-occurrence, similarity-based competition, confidence-based stabilization, and the reconstruction-compression-update trade-off. A key feature is a pseudo-memory-mapped I/O mechanism, through which internally replayed Gestalts are processed via the same axiomatic pathway as external sensory input. As a result, perception, imagination, prediction, planning, and action are unified within a single representational and energetic process. From the axioms, twelve propositions are derived, showing that category formation, hierarchical organization, unsupervised learning, and high-level cognitive activities can all be understood as instances of Gestalt completion under E3 minimization.