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2025
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| Online Access: | https://doi.org/10.57967/hf/7197 |
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| _version_ | 1866901255831420928 |
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| author | Zixi, Li |
| author_facet | Zixi, Li |
| contents | <div> <div><span dir="ltr">This comprehensive review synthesizes twelve interconnected research papers developed during</span><br><span dir="ltr">2025, presenting a systematic critique of contemporary AI reasoning architectures. Throughout</span><br><span dir="ltr">this review, we refer to each paper by conceptual aliases emphasizing their core contributions</span><br><span dir="ltr">rather than package directory names:</span><br><span dir="ltr">Phase I (Architectural Innovations):</span> <span dir="ltr">The</span> <span dir="ltr">Pointer</span> <span dir="ltr">package is called</span> <span dir="ltr">Linear-Complexity</span><br><span dir="ltr">Modeling</span><span dir="ltr">,</span> <span dir="ltr">Tree</span> <span dir="ltr">package as</span> <span dir="ltr">Attention-Free Architecture</span><span dir="ltr">,</span> <span dir="ltr">Asterisk</span> <span dir="ltr">package as</span> <span dir="ltr">ASPP</span><br><span dir="ltr">Framework</span><span dir="ltr">, and</span> <span dir="ltr">Reason</span> <span dir="ltr">package as</span> <span dir="ltr">Categorical Failure</span><span dir="ltr">.</span><br><span dir="ltr">Phase II (Boundary Discoveries):</span> <span dir="ltr">The</span> <span dir="ltr">Computer</span> <span dir="ltr">package is called</span> <span dir="ltr">Phase Transitions</span><span dir="ltr">,</span><br><span dir="ltr">Mini</span> <span dir="ltr">package as</span> <span dir="ltr">Solution Complexity</span><span dir="ltr">,</span> <span dir="ltr">LeftRight</span> <span dir="ltr">package as</span> <span dir="ltr">Geometric Collapse</span><span dir="ltr">, and</span> <span dir="ltr">Real</span><br><span dir="ltr">package as</span> <span dir="ltr">Yonglin Formula</span><span dir="ltr">.</span><br><span dir="ltr">Phase III (Mechanistic Diagnoses):</span> <span dir="ltr">The</span> <span dir="ltr">Flood</span> <span dir="ltr">package is called</span> <span dir="ltr">Fluid Reasoning</span><span dir="ltr">,</span><br><span dir="ltr">Euler</span> <span dir="ltr">package as</span> <span dir="ltr">Euler-Stack Correspondence</span><span dir="ltr">,</span> <span dir="ltr">Prime</span> <span dir="ltr">package as</span> <span dir="ltr">Semantic Irreducibility</span><span dir="ltr">,</span><br><span dir="ltr">and</span> <span dir="ltr">Jacob</span> <span dir="ltr">package as</span> <span dir="ltr">RNN Degeneration</span><span dir="ltr">.</span><br><span dir="ltr">The chronological progression reveals a coherent narrative: from empirical observations of</span><br><span dir="ltr">architectural inefficiencies to theoretical formalizations and fundamental impossibility results,</span><br><span dir="ltr">culminating in precise mechanistic diagnoses.</span><br><span dir="ltr">The twelve papers collectively establish that current AI reasoning systems suffer from</span><br><span dir="ltr">structural inadequacies</span> <span dir="ltr">rather than merely computational or data limitations. Key findings</span><br><span dir="ltr">include:</span><br><span dir="ltr">1.</span> <span dir="ltr">Universal Collapse Phenomena</span><span dir="ltr">: Geometric collapse of backward operations (LeftRight,</span><br><span dir="ltr">A=1.000), spectral collapse of chain Jacobians to rank-1 (Jacob), linear space incapacity to</span><br><span dir="ltr">preserve topological obstructions (Flood)</span><br><span dir="ltr">2.</span> <span dir="ltr">Prior/Boundary Necessity</span><span dir="ltr">: All reasoning systems require semantic anchors (Real’s</span><br><span dir="ltr">Yonglin Formula: recursive interpretation converges to prior anchor,</span> <span dir="ltr">lim</span><span dir="ltr">n</span><span dir="ltr">→∞</span><span dir="ltr">Π</span><span dir="ltr">(</span><span dir="ltr">n</span><span dir="ltr">)</span><span dir="ltr">(</span><span dir="ltr">s</span><span dir="ltr">) =</span> <span dir="ltr">A</span><br><span dir="ltr">where</span> <span dir="ltr">Π</span><span dir="ltr">(</span><span dir="ltr">n</span><span dir="ltr">)</span><span dir="ltr">denotes</span> <span dir="ltr">n</span><span dir="ltr">-fold semantic interpretation and</span> <span dir="ltr">A</span> <span dir="ltr"><span dir="ltr">=</span> <span dir="ltr">A</span><span dir="ltr">∗</span> <span dir="ltr">reveals prior reflexive</span><br><span dir="ltr">inconsistency)</span><br><span dir="ltr">3.</span> <span dir="ltr">Logarithmic Laws</span><span dir="ltr">: Universal phase transitions in computational boundaries (Computer:</span><br><span dir="ltr">d</span><span dir="ltr">c</span><span dir="ltr">(</span><span dir="ltr">L</span><span dir="ltr">) =</span> <span dir="ltr">−</span><span dir="ltr">0</span><span dir="ltr">.</span><span dir="ltr">0809 ln(</span><span dir="ltr">L</span><span dir="ltr">) + 0</span><span dir="ltr">.</span><span dir="ltr">501</span><span dir="ltr">; Flood:</span> <span dir="ltr">κ</span><span dir="ltr">c</span><span dir="ltr">(</span><span dir="ltr">ξ</span><span dir="ltr">) =</span> <span dir="ltr">−</span><span dir="ltr">α</span><span dir="ltr">ln(</span><span dir="ltr">ξ</span><span dir="ltr">) +</span> <span dir="ltr">β</span><span dir="ltr">)</span><br><span dir="ltr">4.</span> <span dir="ltr">Discrete vs Continuous Misalignment</span><span dir="ltr">: Pseudo-Euler dynamics (</span><span dir="ltr">Φ =</span> <span dir="ltr">I</span> <span dir="ltr">+</span> <span dir="ltr">F</span><span dir="ltr">) force</span><br><span dir="ltr">irreversibility in sequential models (Euler), while stack structures admit honest discrete</span><br><span dir="ltr">dynamics</span><br><span dir="ltr">This review synthesizes these findings into a unified critique demonstrating that</span> <span dir="ltr">architec-</span><br><span dir="ltr">tural alignment</span> <span dir="ltr">with problem structures is not merely an efficiency concern but a</span> <span dir="ltr">fundamental</span><br><span dir="ltr">requirement</span> <span dir="ltr">for reasoning systems. We organize the chronological progression into three phases:</span><br><span dir="ltr">architectural innovations (Sections 1–4), boundary discoveries (Sections 5–8), and mecha-<br>nistic diagnoses (Sections 9–12), revealing how early empirical successes motivated theoretical<br>investigations that ultimately exposed deep structural limitations.</span></span></div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_57967_hf_7197 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Abstract of Structural Critique of Reasoning Zixi, Li <div> <div><span dir="ltr">This comprehensive review synthesizes twelve interconnected research papers developed during</span><br><span dir="ltr">2025, presenting a systematic critique of contemporary AI reasoning architectures. Throughout</span><br><span dir="ltr">this review, we refer to each paper by conceptual aliases emphasizing their core contributions</span><br><span dir="ltr">rather than package directory names:</span><br><span dir="ltr">Phase I (Architectural Innovations):</span> <span dir="ltr">The</span> <span dir="ltr">Pointer</span> <span dir="ltr">package is called</span> <span dir="ltr">Linear-Complexity</span><br><span dir="ltr">Modeling</span><span dir="ltr">,</span> <span dir="ltr">Tree</span> <span dir="ltr">package as</span> <span dir="ltr">Attention-Free Architecture</span><span dir="ltr">,</span> <span dir="ltr">Asterisk</span> <span dir="ltr">package as</span> <span dir="ltr">ASPP</span><br><span dir="ltr">Framework</span><span dir="ltr">, and</span> <span dir="ltr">Reason</span> <span dir="ltr">package as</span> <span dir="ltr">Categorical Failure</span><span dir="ltr">.</span><br><span dir="ltr">Phase II (Boundary Discoveries):</span> <span dir="ltr">The</span> <span dir="ltr">Computer</span> <span dir="ltr">package is called</span> <span dir="ltr">Phase Transitions</span><span dir="ltr">,</span><br><span dir="ltr">Mini</span> <span dir="ltr">package as</span> <span dir="ltr">Solution Complexity</span><span dir="ltr">,</span> <span dir="ltr">LeftRight</span> <span dir="ltr">package as</span> <span dir="ltr">Geometric Collapse</span><span dir="ltr">, and</span> <span dir="ltr">Real</span><br><span dir="ltr">package as</span> <span dir="ltr">Yonglin Formula</span><span dir="ltr">.</span><br><span dir="ltr">Phase III (Mechanistic Diagnoses):</span> <span dir="ltr">The</span> <span dir="ltr">Flood</span> <span dir="ltr">package is called</span> <span dir="ltr">Fluid Reasoning</span><span dir="ltr">,</span><br><span dir="ltr">Euler</span> <span dir="ltr">package as</span> <span dir="ltr">Euler-Stack Correspondence</span><span dir="ltr">,</span> <span dir="ltr">Prime</span> <span dir="ltr">package as</span> <span dir="ltr">Semantic Irreducibility</span><span dir="ltr">,</span><br><span dir="ltr">and</span> <span dir="ltr">Jacob</span> <span dir="ltr">package as</span> <span dir="ltr">RNN Degeneration</span><span dir="ltr">.</span><br><span dir="ltr">The chronological progression reveals a coherent narrative: from empirical observations of</span><br><span dir="ltr">architectural inefficiencies to theoretical formalizations and fundamental impossibility results,</span><br><span dir="ltr">culminating in precise mechanistic diagnoses.</span><br><span dir="ltr">The twelve papers collectively establish that current AI reasoning systems suffer from</span><br><span dir="ltr">structural inadequacies</span> <span dir="ltr">rather than merely computational or data limitations. Key findings</span><br><span dir="ltr">include:</span><br><span dir="ltr">1.</span> <span dir="ltr">Universal Collapse Phenomena</span><span dir="ltr">: Geometric collapse of backward operations (LeftRight,</span><br><span dir="ltr">A=1.000), spectral collapse of chain Jacobians to rank-1 (Jacob), linear space incapacity to</span><br><span dir="ltr">preserve topological obstructions (Flood)</span><br><span dir="ltr">2.</span> <span dir="ltr">Prior/Boundary Necessity</span><span dir="ltr">: All reasoning systems require semantic anchors (Real’s</span><br><span dir="ltr">Yonglin Formula: recursive interpretation converges to prior anchor,</span> <span dir="ltr">lim</span><span dir="ltr">n</span><span dir="ltr">→∞</span><span dir="ltr">Π</span><span dir="ltr">(</span><span dir="ltr">n</span><span dir="ltr">)</span><span dir="ltr">(</span><span dir="ltr">s</span><span dir="ltr">) =</span> <span dir="ltr">A</span><br><span dir="ltr">where</span> <span dir="ltr">Π</span><span dir="ltr">(</span><span dir="ltr">n</span><span dir="ltr">)</span><span dir="ltr">denotes</span> <span dir="ltr">n</span><span dir="ltr">-fold semantic interpretation and</span> <span dir="ltr">A</span> <span dir="ltr"><span dir="ltr">=</span> <span dir="ltr">A</span><span dir="ltr">∗</span> <span dir="ltr">reveals prior reflexive</span><br><span dir="ltr">inconsistency)</span><br><span dir="ltr">3.</span> <span dir="ltr">Logarithmic Laws</span><span dir="ltr">: Universal phase transitions in computational boundaries (Computer:</span><br><span dir="ltr">d</span><span dir="ltr">c</span><span dir="ltr">(</span><span dir="ltr">L</span><span dir="ltr">) =</span> <span dir="ltr">−</span><span dir="ltr">0</span><span dir="ltr">.</span><span dir="ltr">0809 ln(</span><span dir="ltr">L</span><span dir="ltr">) + 0</span><span dir="ltr">.</span><span dir="ltr">501</span><span dir="ltr">; Flood:</span> <span dir="ltr">κ</span><span dir="ltr">c</span><span dir="ltr">(</span><span dir="ltr">ξ</span><span dir="ltr">) =</span> <span dir="ltr">−</span><span dir="ltr">α</span><span dir="ltr">ln(</span><span dir="ltr">ξ</span><span dir="ltr">) +</span> <span dir="ltr">β</span><span dir="ltr">)</span><br><span dir="ltr">4.</span> <span dir="ltr">Discrete vs Continuous Misalignment</span><span dir="ltr">: Pseudo-Euler dynamics (</span><span dir="ltr">Φ =</span> <span dir="ltr">I</span> <span dir="ltr">+</span> <span dir="ltr">F</span><span dir="ltr">) force</span><br><span dir="ltr">irreversibility in sequential models (Euler), while stack structures admit honest discrete</span><br><span dir="ltr">dynamics</span><br><span dir="ltr">This review synthesizes these findings into a unified critique demonstrating that</span> <span dir="ltr">architec-</span><br><span dir="ltr">tural alignment</span> <span dir="ltr">with problem structures is not merely an efficiency concern but a</span> <span dir="ltr">fundamental</span><br><span dir="ltr">requirement</span> <span dir="ltr">for reasoning systems. We organize the chronological progression into three phases:</span><br><span dir="ltr">architectural innovations (Sections 1–4), boundary discoveries (Sections 5–8), and mecha-<br>nistic diagnoses (Sections 9–12), revealing how early empirical successes motivated theoretical<br>investigations that ultimately exposed deep structural limitations.</span></span></div> </div> |
| title | Abstract of Structural Critique of Reasoning |
| url | https://doi.org/10.57967/hf/7197 |