On Context-Content Uncertainty Principle

• URL: http://arxiv.org/abs/2506.20699v1
• Date: Wed, 25 Jun 2025 17:21:19 GMT
• Title: On Context-Content Uncertainty Principle
• Abstract summary: We develop a layered computational framework that derives operational principles from the Context-Content Uncertainty Principle.<n>At the base level, CCUP formalizes inference as directional entropy minimization, establishing a variational gradient that favors content-first structuring.<n>We present formal equivalence theorems, a dependency lattice among principles, and computational simulations demonstrating the efficiency gains of CCUP-aligned inference.
• Score: 5.234742752529437
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: The Context-Content Uncertainty Principle (CCUP) proposes that inference under uncertainty is governed by an entropy asymmetry between context and content: high-entropy contexts must be interpreted through alignment with low-entropy, structured content. In this paper, we develop a layered computational framework that derives operational principles from this foundational asymmetry. At the base level, CCUP formalizes inference as directional entropy minimization, establishing a variational gradient that favors content-first structuring. Building upon this, we identify four hierarchical layers of operational principles: (\textbf{L1}) \emph{Core Inference Constraints}, including structure-before-specificity, asymmetric inference flow, cycle-consistent bootstrapping, and conditional compression, all shown to be mutually reducible; (\textbf{L2}) \emph{Resource Allocation Principles}, such as precision-weighted attention, asymmetric learning rates, and attractor-based memory encoding; (\textbf{L3}) \emph{Temporal Bootstrapping Dynamics}, which organize learning over time via structure-guided curricula; and (\textbf{L4}) \emph{Spatial Hierarchical Composition}, which integrates these mechanisms into self-organizing cycles of memory, inference, and planning. We present formal equivalence theorems, a dependency lattice among principles, and computational simulations demonstrating the efficiency gains of CCUP-aligned inference. This work provides a unified theoretical foundation for understanding how brains and machines minimize uncertainty through recursive structure-specificity alignment. The brain is not just an inference machine. It is a cycle-consistent entropy gradient resolver, aligning structure and specificity via path-dependent, content-seeded simulation.

Related papers

• Information as Maximum-Caliber Deviation: A bridge between Integrated Information Theory and the Free Energy Principle [51.56484100374058]
  This work proposes that information can be defined as the deviation $$ of realized dynamics from a constrained maximum-caliber (MaxCal) path ensemble over a finite time horizon.<n>Under this definition, each of the cause/effect repertoires central to IIT 3.0 emerge directly from MaxCal variational principles.<n>Information $$ is shown to be equivalent to prediction error under accompanying predictive coding models.
  arXiv  Detail & Related papers  (2026-05-03T07:22:55Z)
• Proteo-R1: Reasoning Foundation Models for De Novo Protein Design [129.2825640976092]
  We introduce bfProteo-R1, a reasoning-guided protein design framework.<n>It decouples emphmolecular understanding from emphgeometric generation.<n>Proteo-R1 achieves stable, interpretable, and modular integration of reasoning with state-of-the-art geometric generative models.
  arXiv  Detail & Related papers  (2026-05-01T06:52:27Z)
• HIPO: Instruction Hierarchy via Constrained Reinforcement Learning [57.40686733111483]
  textscHIPO is a novel alignment framework that formulates HIF as a Constrained Markov Decision Process.<n>textscHIPO elevates system prompts from mere input context to strict algorithmic boundaries.
  arXiv  Detail & Related papers  (2026-03-17T06:12:41Z)
• A Geometrically-Grounded Drive for MDL-Based Optimization in Deep Learning [3.2452107817263003]
  This paper introduces a novel optimization framework that fundamentally integrates the Minimum Description Length (MDL) principle into the training dynamics of deep neural networks.<n>We provide a practical, computationally efficient algorithm with $O(N log N)$ per-iteration complexity (Theoremrefthm:complexity), alongside guarantees for numerical stability (Theoremrefthm:stability) and exponential convergence under convexity assumptions (Theoremrefthm:convergence_rate)<n>This work provides a principled path toward more autonomous, generalizable, and interpretable AI
  arXiv  Detail & Related papers  (2026-03-12T08:31:00Z)
• Towards A Unified PAC-Bayesian Framework for Norm-based Generalization Bounds [63.47271262149291]
  We propose a unified framework for PAC-Bayesian norm-based generalization.<n>The key to our approach is a sensitivity matrix that quantifies the network outputs with respect to structured weight perturbations.<n>We derive a family of generalization bounds that recover several existing PAC-Bayesian results as special cases.
  arXiv  Detail & Related papers  (2026-01-13T00:42:22Z)
• LSRIF: Logic-Structured Reinforcement Learning for Instruction Following [56.517329105764475]
  We propose a logic-structured training framework LSRIF that explicitly models instruction logic.<n> Experiments show LSRIF brings significant improvements in instruction-following and general reasoning.
  arXiv  Detail & Related papers  (2026-01-10T05:11:38Z)
• The Procrustean Bed of Time Series: The Optimization Bias of Point-wise Loss [53.542743390809356]
  This paper aims to provide a first-principles analysis of the Expectation of Optimization Bias (EOB)<n>Our analysis reveals a fundamental paradigm paradox: the more deterministic and structured the time series, the more severe the bias by point-wise loss function.<n>We present a concrete solution that simultaneously achieves both principles via DFT or DWT.
  arXiv  Detail & Related papers  (2025-12-21T06:08:22Z)
• Memory-Amortized Inference: A Topological Unification of Search, Closure, and Structure [6.0044467881527614]
  We propose textbfMemory-Amortized Inference (MAI), a formal framework that unifies learning and memory as phase transitions of a single geometric substrate.<n>We show that cognition operates by converting high-complexity search into low-complexity lookup.<n>This framework offers a rigorous explanation for the emergence of fast-thinking (intuition) from slow-thinking (reasoning)
  arXiv  Detail & Related papers  (2025-11-28T16:28:24Z)
• Step-Aware Policy Optimization for Reasoning in Diffusion Large Language Models [57.42778606399764]
  Diffusion language models (dLLMs) offer a promising, non-autoregressive paradigm for text generation.<n>Current reinforcement learning approaches often rely on sparse, outcome-based rewards.<n>We argue that this stems from a fundamental mismatch with the natural structure of reasoning.
  arXiv  Detail & Related papers  (2025-10-02T00:34:15Z)
• Information-Theoretic Bounds and Task-Centric Learning Complexity for Real-World Dynamic Nonlinear Systems [0.6875312133832079]
  Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects.<n>This paper presents a theoretical framework grounded in structured decomposition, variance analysis, and task-centric complexity bounds.
  arXiv  Detail & Related papers  (2025-09-08T12:08:02Z)
• The Recursive Coherence Principle: A Formal Constraint on Scalable Intelligence, Alignment, and Reasoning Architecture [0.0]
  Coherence is fragile unless a higher-order structure ensures semantic consistency.<n>This paper introduces the Recursive Coherence Principle (RCP)<n>We define the Functional Model of Intelligence (FMI) as the only known operator capable of satisfying the RCP at any scale.
  arXiv  Detail & Related papers  (2025-07-18T09:44:01Z)
• Information Must Flow: Recursive Bootstrapping for Information Bottleneck in Optimal Transport [5.234742752529437]
  We present a unified framework that models cognition as the directed flow of information between high-entropy context and low-entropy content.<n>Inference emerges as a cycle of bidirectional interactions, bottom-up contextual disambiguation paired with top-down content reconstruction.<n>Building on this, we propose that language emerges as a symbolic transport system, externalizing latent content to synchronize inference cycles across individuals.
  arXiv  Detail & Related papers  (2025-07-08T13:56:50Z)
• Cycle-Consistent Helmholtz Machine: Goal-Seeded Simulation via Inverted Inference [5.234742752529437]
  We introduce the emphCycle-Consistent Helmholtz Machine (C$2$HM)<n>C$2$HM reframes inference as a emphgoal-seeded, emphasymmetric process grounded in structured internal priors.<n>By offering a biologically inspired alternative to classical amortized inference, $C2$HM reconceives generative modeling as intentional simulation.
  arXiv  Detail & Related papers  (2025-07-03T17:24:27Z)
• Why Neural Network Can Discover Symbolic Structures with Gradient-based Training: An Algebraic and Geometric Foundation for Neurosymbolic Reasoning [73.18052192964349]
  We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics.<n>By lifting neural parameters to a measure space and modeling training as Wasserstein gradient flow, we show that under geometric constraints, the parameter measure $mu_t$ undergoes two concurrent phenomena.
  arXiv  Detail & Related papers  (2025-06-26T22:40:30Z)
• Simplicial methods in the resource theory of contextuality [0.0]
  Building on the theory of simplicial distributions, we introduce event scenarios as a functorial generalization of presheaf-theoretic measurement scenarios.<n>We define symmetric monoidal structures on these categories and extend the distribution functor to a setting, yielding a resource theory that generalizes the presheaf-theoretic notion of simulations.
  arXiv  Detail & Related papers  (2025-05-29T21:14:55Z)
• Learning Identifiable Structures Helps Avoid Bias in DNN-based Supervised Causal Learning [56.22841701016295]
  Supervised Causal Learning (SCL) is an emerging paradigm in this field.<n>Existing Deep Neural Network (DNN)-based methods commonly adopt the "Node-Edge approach"
  arXiv  Detail & Related papers  (2025-02-15T19:10:35Z)
• Structural Entropy Guided Probabilistic Coding [52.01765333755793]
  We propose a novel structural entropy-guided probabilistic coding model, named SEPC.<n>We incorporate the relationship between latent variables into the optimization by proposing a structural entropy regularization loss.<n> Experimental results across 12 natural language understanding tasks, including both classification and regression tasks, demonstrate the superior performance of SEPC.
  arXiv  Detail & Related papers  (2024-12-12T00:37:53Z)
• Sequential Representation Learning via Static-Dynamic Conditional Disentanglement [58.19137637859017]
  This paper explores self-supervised disentangled representation learning within sequential data, focusing on separating time-independent and time-varying factors in videos. We propose a new model that breaks the usual independence assumption between those factors by explicitly accounting for the causal relationship between the static/dynamic variables. Experiments show that the proposed approach outperforms previous complex state-of-the-art techniques in scenarios where the dynamics of a scene are influenced by its content.
  arXiv  Detail & Related papers  (2024-08-10T17:04:39Z)
• A Canonicalization Perspective on Invariant and Equivariant Learning [54.44572887716977]
  We introduce a canonicalization perspective that provides an essential and complete view of the design of frames. We show that there exists an inherent connection between frames and canonical forms. We design novel frames for eigenvectors that are strictly superior to existing methods.
  arXiv  Detail & Related papers  (2024-05-28T17:22:15Z)
• Semantic Loss Functions for Neuro-Symbolic Structured Prediction [74.18322585177832]
  We discuss the semantic loss, which injects knowledge about such structure, defined symbolically, into training. It is agnostic to the arrangement of the symbols, and depends only on the semantics expressed thereby. It can be combined with both discriminative and generative neural models.
  arXiv  Detail & Related papers  (2024-05-12T22:18:25Z)
• PAC-Chernoff Bounds: Understanding Generalization in the Interpolation Regime [6.645111950779666]
  This paper introduces a distribution-dependent PAC-Chernoff bound that exhibits perfect tightness for interpolators.<n>We present a unified theoretical framework revealing why certain interpolators show an exceptional generalization, while others falter.
  arXiv  Detail & Related papers  (2023-06-19T14:07:10Z)
• On Broken Symmetry in Cognition [5.234742752529437]
  This paper argues that both cognitive evolution and development unfold via symmetry-breaking transitions.<n>First, spatial symmetry is broken through bilateral body plans and neural codes like grid and place cells.<n>Third, goal-directed simulation breaks symmetry between internal self-models and the external world.
  arXiv  Detail & Related papers  (2023-03-07T19:48:13Z)
• Formal context reduction in deriving concept hierarchies from corpora using adaptive evolutionary clustering algorithm star [15.154538450706474]
  The process of deriving concept hierarchies from corpora is typically a time-consuming and resource-intensive process. The resulting lattice of formal context is evaluated to the standard one using concept lattice-invariants. The results show that adaptive ECA* performs concept lattice faster than other mentioned competitive techniques in different fill ratios.
  arXiv  Detail & Related papers  (2021-07-10T07:18:03Z)
• On dissipative symplectic integration with applications to gradient-based optimization [77.34726150561087]
  We propose a geometric framework in which discretizations can be realized systematically. We show that a generalization of symplectic to nonconservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error.
  arXiv  Detail & Related papers  (2020-04-15T00:36:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.