Skip to content
← Back to explorer

A Gauge Theory of Superposition: Toward a Sheaf-Theoretic Atlas of Neural Representations

Hossein Javidnia · Feb 28, 2026 · Citations: 0

Open arXiv Find Implementation RSS feed Shortlist (0)

Data freshness

Extraction: Fresh

Check recency before relying on this page for active eval decisions. Use stale pages as context and verify against current hub results.

Metadata refreshed

Feb 28, 2026, 10:05 PM

Recent

Extraction refreshed

Mar 7, 2026, 10:43 AM

Fresh

Extraction source

Runtime deterministic fallback

Confidence 0.15

Abstract

We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts. Contexts are clustered into a stratified context complex; each chart carries a local feature space and a local information-geometric metric (Fisher/Gauss--Newton) identifying predictively consequential feature interactions. This yields a Fisher-weighted interference energy and three measurable obstructions to global interpretability: (O1) local jamming (active load exceeds Fisher bandwidth), (O2) proxy shearing (mismatch between geometric transport and a fixed correspondence proxy), and (O3) nontrivial holonomy (path-dependent transport around loops). We prove and instantiate four results on a frozen open LLM (Llama~3.2~3B Instruct) using WikiText-103, a C4-derived English web-text subset, and \texttt{the-stack-smol}. (A) After constructive gauge fixing on a spanning tree, each chord residual equals the holonomy of its fundamental cycle, making holonomy computable and gauge-invariant. (B) Shearing lower-bounds a data-dependent transfer mismatch energy, turning $D_{\mathrm{shear}}$ into an unavoidable failure bound. (C) We obtain non-vacuous certified jamming/interference bounds with high coverage and zero violations across seeds/hyperparameters. (D) Bootstrap and sample-size experiments show stable estimation of $D_{\mathrm{shear}}$ and $D_{\mathrm{hol}}$, with improved concentration on well-conditioned subsystems.

Low-signal caution for protocol decisions

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.15 (below strong-reference threshold).
  • No explicit evaluation mode was extracted from available metadata.
  • No benchmark/dataset or metric anchors were extracted.
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Runtime deterministic fallback missing

No explicit feedback protocol extracted.

Evidence snippet: We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts.

Evaluation Modes

missing

None explicit

Confidence: Low Source: Runtime deterministic fallback missing

Validate eval design from full paper text.

Evidence snippet: We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts.

Quality Controls

missing

Not reported

Confidence: Low Source: Runtime deterministic fallback missing

No explicit QC controls found.

Evidence snippet: We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Runtime deterministic fallback missing

No benchmark anchors detected.

Evidence snippet: We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts.

Reported Metrics

missing

Not extracted

Confidence: Low Source: Runtime deterministic fallback missing

No metric anchors detected.

Evidence snippet: We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts.

Rater Population

missing

Unknown

Confidence: Low Source: Runtime deterministic fallback missing

Rater source not explicitly reported.

Evidence snippet: We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math
  • Extraction source: Runtime deterministic fallback

Evaluation Lens

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.15
  • Flags: low_signal, possible_false_positive, runtime_fallback_extraction

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Deterministic synthesis

We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts. HFEPX protocol signal is limited in abstract-level metadata, so treat it as adjacent context. Updated from current HFEPX corpus.

Generated Mar 7, 2026, 10:43 AM · Grounded in abstract + metadata only

Key Takeaways

  • We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas…
  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Verify metric definitions before comparing against your eval pipeline.

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts.

Why It Matters For Eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

Category-Adjacent Papers (Broader Context)

These papers are nearby in arXiv category and useful for broader context, but not necessarily protocol-matched to this paper.

Need human evaluators for your AI research? Scale annotation with expert AI Trainers.

Post a Job Get a Quote