{"id":40429186,"url":"https://github.com/potatoinfinity/geo-llama","last_synced_at":"2026-01-20T16:01:19.653Z","repository":{"id":331600620,"uuid":"1125637766","full_name":"PotatoInfinity/Geo-Llama","owner":"PotatoInfinity","description":"Creating an AI that is 100x more efficient, has infinite memory, and exhibits mathematically certain reasoning with the utilization of Conformal Manifold by using Geometric Algebra.","archived":false,"fork":false,"pushed_at":"2026-01-18T10:28:12.000Z","size":8778,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2026-01-18T17:48:14.492Z","etag":null,"topics":["compute","conformal-geometry","efficiency","future","gapu","geometric-algebra","geometric-algorithms","large-language-models","llama4","math","mathematics","memory","modern","optimizations","paradigms","resource","rust-lang","shift","topology"],"latest_commit_sha":null,"homepage":"","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"gpl-3.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/PotatoInfinity.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2025-12-31T04:44:53.000Z","updated_at":"2026-01-18T10:28:15.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/PotatoInfinity/Geo-Llama","commit_stats":null,"previous_names":["potatoinfinity/geo-llama"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/PotatoInfinity/Geo-Llama","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PotatoInfinity%2FGeo-Llama","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PotatoInfinity%2FGeo-Llama/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PotatoInfinity%2FGeo-Llama/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PotatoInfinity%2FGeo-Llama/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/PotatoInfinity","download_url":"https://codeload.github.com/PotatoInfinity/Geo-Llama/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PotatoInfinity%2FGeo-Llama/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":28606288,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-01-20T14:45:23.139Z","status":"ssl_error","status_checked_at":"2026-01-20T14:44:16.929Z","response_time":117,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["compute","conformal-geometry","efficiency","future","gapu","geometric-algebra","geometric-algorithms","large-language-models","llama4","math","mathematics","memory","modern","optimizations","paradigms","resource","rust-lang","shift","topology"],"created_at":"2026-01-20T16:00:50.340Z","updated_at":"2026-01-20T16:01:19.637Z","avatar_url":"https://github.com/PotatoInfinity.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Geo-Llama: Foundational Theory of Structural Intelligence via Conformal Manifolds and $Cl_{4,1}$ Recursive Isometries\n\n**Date:** January 20th, 2026  \n**Authors:** Trương Minh Huy, Edward George Hirst  \n**Subject:** Geometric Deep Learning, Isotropic Spatio-Temporal Modeling, Structural Latent Manifolds\n\n![Version](https://img.shields.io/badge/version-1.1.0--theoretical-blue) ![Algebra](https://img.shields.io/badge/algebra-Cl(4,1)-red) ![Status](https://img.shields.io/badge/status-Research_In_Progress-orange)\n\n---\n\n## Abstract\n\nContemporary deep learning architectures are fundamentally constrained by their reliance on high-dimensional Euclidean embeddings and the statistical approximation of relationships. These \"Flat-AI\" models treat data points as isolated coordinates in $\\mathbb{R}^n$, necessitating massive parameter counts to emulate structural dependencies that are naturally present in complex physical and hierarchical systems. We present **Geo-Llama** (Geometric Latent Language \u0026 Manifold Architecture), a novel framework that moves beyond Euclidean translation to a native **Conformal Geometric Algebra (CGA)** representation. By encoding information into the Clifford Algebra $Cl_{4,1}$, we represent state evolution not as weight-driven shifts, but as **Isotropic Rotations** (Rotors) within a 5D Minkowski-signature manifold. This paper outlines the move from stochastic pattern matching to **structural intelligence**, detailing the advancements in **Geometric Product Attention (GPA)** and the **$O(1)$ Recursive Rotor Accumulator**. This shift enables a new class of foundation models capable of native reasoning in high-fidelity topological environments where spatial, temporal, and hierarchical constraints are primary.\n\n---\n\n## 1. The Euclidean Crisis: Topological Entropy\n\nThe scaling laws of standard Transformers $O(N^2)$ are reaching a ceiling dictated by the entropy of flat space. This \"Euclidean Bottleneck\" manifests through:\n\n1.  **Semantic Sparsity:** In high-dimensional flat space, the **Curse of Dimensionality** ensures that tokens remain semantically distant, forcing models to rely on hyper-fine weights to capture structural nuance.\n2.  **Contextual Decay (The Memory Wall):** Euclidean memory (the KV Cache) is a non-compressed history—a growing list of points that eventually exceeds computational limits.\n3.  **Lack of Grade:** Standard vectors occupy a singular rank, preventing models from natively enforcing hierarchical or containment relationships ($A \\subset B$) without exhaustive training data.\n\n---\n\n## 2. Theoretical Framework: The $Cl_{4,1}$ Conformal Manifold\n\nGeo-Llama utilizes the **Conformal Model of Geometry**, mapping latent states into the Clifford Algebra $Cl_{4,1}$, generated by a 5D basis $\\{e_1, e_2, e_3, e_+, e_-\\}$ with the signature $(+,+,+,+,-)$.\n\n### 2.1 Latent Space Manifold Bundling\n\nRather than a single massive embedding, we treat the latent space as a **Fiber Bundle** of $H$ independent manifolds:\n\n$$ \\mathbb{R}^{d_{model}} \\xrightarrow{\\phi} \\bigoplus_{h=1}^{H} Cl_{4,1}^{(h)} $$\n\nWhere each \"Geometric Head\" operates on a 32-dimensional multivector basis. This architecture ensures that structural rotations in one manifold (e.g., spatial orientation) do not corrupt the integrity of another (e.g., logical hierarchy). By utilizing **Grades**, the model inherently encodes containment: a Token-Point can be mathematically proven to reside within a Category-Sphere via the inner product, reducing high-level reasoning to geometric intersection.\n\n---\n\n## 3. GPA: Geometric Product Attention\n\nWe redefine attention as an algebraic interaction between multivector fields. Instead of the scalar Dot-Product, we employ the full **Clifford Geometric Product**:\n\n$$ \\mathcal{A}(Q, K) = Q \\cdot K + Q \\wedge K $$\n\n*   **Symmetric Part ($Q \\cdot K$):** Captures traditional semantic similarity (proximity).\n*   **Anti-Symmetric Part ($Q \\wedge K$):** Generates a **Bivector**, representing the \"Plane of Interaction\"—the directed structural tension and rotational relationship between concepts.\n\n---\n\n## 4. The $O(1)$ Recursive Rotor Accumulator\n\nThe core innovation of Geo-Llama is the transition from \"State as Data\" to \"State as Path.\" \n\n### 4.1 From Memory Lists to Spinor States\n\nIn standard models, history is a database. In Geo-Llama, history is a **Rotor** (an element of the $Spin(4,1)$ group). Every incoming piece of structural information is transformed into a specialized rotor $R_i$, and the global context $\\Psi$ is updated through a recursive sandwich product:\n\n$$ \\Psi_{t+1} = R_{t} \\Psi_{t} \\tilde{R}_{t} $$\n\n*   **Recursive Isometry:** Because $R$ is a rotor, the geometric integrity is preserved. The system state is \"rotated\" by the meaning of new data, achieving infinite theoretical context in a fixed (32-float) memory footprint per head.\n\n---\n\n## 5. Hardware Implications: The GAPU\n\nTo realize these theoretical gains, we identify the need for specialized hardware: the **GAPU (Geometric Algebra Processing Unit)**.\n\n*   **Parallel Cayley Streams:** Unlike standard GPUs, the GAPU processes multiple manifolds in parallel through bit-masked algebraic instructions ($e_1 e_2 = e_{12}$).\n*   **Efficiency:** By loading algebraic rules into the instruction set rather than calculating them as matrices, the GAPU achieves nearly 100% compute occupancy for multivector products.\n\n---\n\n## 6. Empirical Validation\n\nTo validate the theoretical advantages of the $Cl_{4,1}$ manifold, we performed a series of controlled experiments comparing Geo-Llama against standard Euclidean Transformers and domain-specific SOTA architectures.\n\n### 6.1 Recursive Spatio-Temporal Modeling (N-Body Gravity)\nIn a 5-body gravitational simulation, we measured the model's ability to learn physical laws and respect conservation principles (Energy/Momentum) without explicit enforcement over a 100-step autoregressive rollout.\n\n| Model | MSE (Motion) | Energy Drift (Physics) | Notes |\n|-------|--------------|------------------------|-------|\n| Standard Transformer | 18.63 | 214.31 | Unstable |\n| GNS (Relational) | 23.83 | 1261.01 | Suffers from coordinate drift |\n| HNN (Energy-based) | 11.12 | **61.86** | Great physics, average motion |\n| **GeoLlama (Rotor RNN)** | **5.45** | **66.13** | **Best performance on balance** |\n\n\n*   **Observation:** Geo-Llama achieved the lowest trajectory error and matched the stability of Hamiltonian NNs—which are mathematically forced to conserve energy—proving that conformal rotors naturally stay on the physical energy manifold.\n\n### 6.2 Topological Complexity (Maze Connectivity)\nWe tested the model's ability to solve connectivity tasks where simple statistical \"counting\" (e.g., magnetization) is impossible.\n\n*   **Scaling Collapse:** As grid size increased to 32x32, standard Transformers (even with 30x more parameters) collapsed to **34% MCC**, whereas Geo-Llama maintained **100% MCC**.\n*   **Curriculum Ladder:** Logic learned by the geometric \"brain\" on an 8x8 grid was successfully \"transplanted\" to 32x32 grids with near-instant convergence, whereas Euclidean models failed to generalize across spatial scales.\n\n### 6.3 Hierarchical Context Retention (Dyck-N)\nTo test the $O(1)$ Recursive Rotor Accumulator, we used the Dyck-N language task (balanced parentheses) as a proxy for structural containment.\n\n*   **Performance:** Geo-Llama achieved **99.7% accuracy** at nesting depths of 100 (sequence length 200).\n*   **Implication:** This confirms the \"Infinite Context\" capability, where the global state $\\Psi$ maintains structural integrity over deep recursive levels in a fixed memory footprint.\n\n### 6.4 Computational Efficiency\nBy engineering custom fused kernels in Triton and MLX, we reduced the materialization overhead of the Cayley table. **Geometric Linear layers now operate with only 1.2x the latency of standard PyTorch Linear layers**, making the architecture viable for large-scale deployment.\n\n---\n\n## 7. Implications and Future Directions\n\nThe transition from Euclidean vectors to Conformal multivectors marks a move toward **Topological AI**. \n\n### 7.1 Mathematical Robustness\nBy grounding AI operations in the rigorous rules of Geometric Algebra, we mitigate common failure modes such as \"Hallucination\" (which we characterize as a deviation from the structural manifold). Contradictions in data manifest as destructive interference in the Bivector plane, providing a native mechanism for logical \"red-teaming.\"\n\n### 7.2 Scaling via Geometry\nWe posit that future scaling won't come from increasing parameters, but from increasing the **Dimensionality of the Manifold**. A model that understands the geometry of its domain requires orders of magnitude less data and power to achieve structural certainty.\n\n---\n\n## 8. Conclusion\n\nThe history of AI has been a race toward \"brute-force\" statistics. Geo-Llama introduces a pivot toward **Human-Centric Geometry.** By embedding knowledge in a $Cl_{4,1}$ conformal manifold, we provide the AI with a sense of \"space,\" \"permanence,\" and \"logical hierarchy,\" enabling transformative applications in neural physics engines, robotic control, and protein folding.\n\n**Current Status:** Theory validation and kernel optimization for specialized structural benchmarks.\n\n---\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpotatoinfinity%2Fgeo-llama","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fpotatoinfinity%2Fgeo-llama","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpotatoinfinity%2Fgeo-llama/lists"}