From ArrowSpace to Graph Wiring

ArrowSpace: Spectral Indexing of Embeddings using taumode (λτ)

Paper:

• Introduces ArrowSpace as a spectral vector search library that blends semantic similarity with graph Laplacian energies via the synthetic λτ (taumode) index.
• Establishes the core idea that a single bounded λτ score can act as a computationally cheap proxy for "how much an item deviates from learned structure," operationally useful for active learning, RAG tails, and OOD detection.
• Provides the initial Laplacian-based data model and pipelines that later get abstracted into more general graph wiring over feature manifolds, and sets the invariant that the manifold is built in feature space rather than item space.

Code: arrowspace (Rust library) · CVE benchmark & tails analysis · Testable code

Graph Wiring: Eigenstructures for Vector Datasets and LLM Operations

Paper:

• Generalises the ArrowSpace intuition into a graph wiring framework that builds discrete graphs from arbitrary vector spaces by transposing data into feature space and wiring features via nearest‑neighbour pairing.
• Shows that the resulting feature‑space Laplacian behaves as a discrete Laplace–Beltrami operator; minimising its Rayleigh quotient corresponds to minimising Dirichlet energy, which under conformal constraints is equivalent to constructing a discrete minimal surface (worldsheet) in feature space.
• Provides the theoretical foundation that ties together λ‑style indices, epiplexity interpretations, and topology‑aware metrics like MRR‑Top0 into a unified manifold‑based view of vector datasets and LLM operations.

Code: arrowspace · surfface

MRR-Top0: A Topology-Aware Extension of Mean Reciprocal Rank

Paper:

• Extends classical MRR with a topology-aware score (MRR‑Top0) that evaluates the full top‑k list using graph signals such as personalized PageRank, conductance, and modularity, rather than only the first relevant hit.
• Provides a quantitative lens on "tails quality" of retrieval results, critical for long‑term multi‑query stability in RAG systems and for comparing spectral/topological search methods like ArrowSpace's λτ against cosine baselines.
• Establishes Topological PageRank (MRR‑Top0) as a central metric for assessing spectral manifolds and measuring whether λ‑aware search truly improves semantic coherence and tail stability in practice.

Code: topological-pagerank / MRR‑Top0

Epiplexity And Graph Wiring: An Empirical Study for the Design of a Generic Algorithm

Paper:

• Connects ArrowSpace's λ scores and the emerging graph wiring perspective to epiplexity, treating λ as a cheap proxy for how much an item deviates from the learned manifold structure.
• Uses MRR‑Top0 and tails‑sensitive scores (developed on the CVE benchmarks) to study how epiplexity‑weighted retrieval behaves, with a focus on tail behavior, OOD items, and active learning candidates.
• Empirically tests how a generic algorithm can use Laplacian‑derived λ, epiplexity, and topological quality metrics together to design spectral/topological search strategies better aligned with RAG workloads.

Code: epiplexity and Graph Wiring · test_2_CVE_db.txt and related CVE pipelines in arrowspace experiments

arrowspace: Vector Spaces and Graph Wiring

Interview/Podcast: MLOps Community Podcast

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